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GitHub

API

Main analysis functions

TransitionsInTimeseries.estimate_changes — Function
estimate_changes(config::ChangesConfig, x [,t]) → result

Estimate possible transitions for input timeseries x using the approach specified in the configuration type config, see ChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).

Return the output as subtype of ChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

source

Sliding window

TransitionsInTimeseries.SlidingWindowConfig — Type
SlidingWindowConfig <: ChangesConfig
+SlidingWindowConfig(indicators, change_metrics; kwargs...)

A configuration that can be given to estimate_changes. It estimates transitions by a sliding window approach:

  1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
  2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.

indicators can be a single function or a tuple of indicators. Similarly, change_metrics can be a tuple or a single function. If tuples, the length of indicators and change_metrics must match. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

The results output corresponding to SlidingWindowConfig is SlidingWindowResults.

Step 1. is skipped if nothing is provided as indicators, in which case the change metrics are estimated directly from input data.

Keyword arguments

  • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.
  • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.
  • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_changes using the keyword whichtime. Options include:
    • last: use the last timepoint of each window
    • midpoint: use the mid timepoint of each time window
    • first: use first timepoint of each window
    In fact, the indicators time vector is computed simply via
    t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)
    so any other function of the time window may be given to extract the time point itself, such as mean or median.
  • T = Float64: Element type of input timeseries to initialize some computations.
source
TransitionsInTimeseries.SlidingWindowResults — Type
SlidingWindowResults <: ChangesResults

A struct containing the output of estimate_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

It has the following fields that the user may access

  • x: the input timeseries.

  • t: the time vector of the input timeseries.

  • x_indicator, the indicator timeseries (matrix with each column one indicator).

  • t_indicator, the time vector of the indicator timeseries.

  • x_change, the change metric timeseries (matrix with each column one change metric).

  • t_change, the time vector of the change metric timeseries.

  • config::SlidingWindowConfig, what was used for the analysis.

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Segmented window

TransitionsInTimeseries.SegmentedWindowConfig — Type
SegmentedWindowConfig <: IndicatorsChangeConfig
+SegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)

A configuration that can be given to estimate_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:

  1. For each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).
  2. For each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d

tseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.

The results output corresponding to SlidingWindowConfig is SegmentedWindowResults.

Keyword arguments

  • width_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.
  • min_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.
source
TransitionsInTimeseries.SegmentedWindowResults — Type
SegmentedWindowResults <: ChangesResults

A struct containing the output of estimate_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

It has the following fields that the user may access

  • x: the input timeseries.

  • t: the time vector of the input timeseries.

  • x_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.

  • t_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.

  • x_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.

  • t_change, the time vector of the change metric.

  • config::SegmentedWindowConfig, what was used for the analysis.

  • i1::Vector{Int} indices corresponding to start time of each segment.

  • i2::Vector{Int} indices corresponding to end time of each segment.

  • precomp_change_metrics vector containing the precomputed change metrics of each segment.

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Slope change

TransitionsInTimeseries.SlopeChangeConfig — Type
SlopeChangeConfig <: ChangesConfig
+SlopeChangeConfig(; indicator = nothing, kw...)

A configuration that can be given to estimate_changes. It estimates a change of slope in the timeseries by fitting two connected linear segments to the timeseries, returning the results (i.e., the two-linear fits) as SlopeChangeResults.

Keyword arguments

  • indicator = nothing: if not nothing. Otherwise it should be a function f(x) -> Real. The slope fitting is then done over an indicator of the timeseries, which itself is estimated via a sliding window exactly as in SlidingWindowConfig.
  • width_ind, stride_ind, whichtime: exactly as in SlidingWindowConfig if indicator is not nothing.
source
TransitionsInTimeseries.SlopeChangeResults — Type
SlopeChangeResults <: ChangesResults

A struct containing the output of estimate_changes used with SlopeChangeConfig. It can be used for further analysis, visualization, or given to significant_transitions. The only significance type that you can use this with significant_transitions is SlopeChangeSignificance.

It has the following fields that the user may access:

  • x: the input timeseries.
  • t: the time vector of the input timeseries.
  • x_indicator, the indicator timeseries.
  • t_indicator, the time vector of the indicator timeseries.
  • t_change, the time the slope changes.
  • fitparams = a, b, c, d, the fitted linear coefficients, a + b*t before. t_change and c + d*t after t_change.
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Significance testing

TransitionsInTimeseries.significant_transitions — Function
significant_transitions(res::ChangesResults, signif::Significance)

Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as the changes stored in res (which typically is stored in the field res.x_change). flags is true wherever a change metric of res is deemed significant.

source
TransitionsInTimeseries.SurrogatesSignificance — Type
SurrogatesSignificance <: Significance
+SurrogatesSignificance(; kwargs...)

A configuration struct for significance testing significant_transitions using timeseries surrogates.

Keyword arguments

  • surromethod = RandomFourier(): method to generate surrogates
  • n = 1000: how many surrogates to generate
  • rng = Random.default_rng(): random number generator for the surrogates
  • p = 0.05: threshold for significance of the p-value
  • tail = :both: tail type used, see below

Description

When used with ChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in ChangesResults.

Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

source
TransitionsInTimeseries.ThresholdSignificance — Type
ThresholdSignificance(threshold::Real; tail = :right) <: Significance

A configuration struct for significance testing in significant_transitions. Significance is estimated by comparing the value of each change metric with the given threshold. Values that exceed the threshold (if tail = :right) or subseed the threshold (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

source
TransitionsInTimeseries.SigmaSignificance — Type
SigmaSignificance(; factor = 3.0, tail = :both) <: Significance

A configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing how many standard deviations (σ) the value exceeds the mean value (μ). Values that exceed (if tail = :right) μ + factor*σ, or subseed (if tail = :left) μ - factor*σ are deemed significant. If tail = :both then either condition is checked.

factor can also be a vector of values, in which case a different value is used for each change metric.

See also QuantileSignificance.

source
TransitionsInTimeseries.QuantileSignificance — Type
QuantileSignificance(; p = 0.95, tail = :both) <: Significance

A configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

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TransitionsInTimeseries.SlopeChangeSignificance — Type
SlopeChangeSignificance(; moe_slope, moe_offset, slope_diff = moe_slope, pvalue = 0.05)

Test whether the result of SlopeChangeResults is statistically significant.

Two tests are done:

  1. Check whether the margin of error of the fitted parameters a, b, c, d of the two linear segments a + b*t, c + d*t is less than the specified margins of error, for a chosen pvalue.
  2. Test that the two slopes b, d have difference greater than slope_diff.

The Boolean & of the above two is the final test.

The margin of error is simply half the size of the confidence interval, also known as radius of the confidence interval.

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Indicators

Note that any Julia function can be an indicator or change metric, so the list here is only just a couple of indicators directly implemented in this package.

Value distribution

Statistics.mean — Function
mean(A::AbstractArray, w::AbstractWeights[, dims::Int])

Compute the weighted mean of array A with weight vector w (of type AbstractWeights). If dim is provided, compute the weighted mean along dimension dims.

Examples

n = 20
+x = rand(n)
+w = rand(n)
+mean(x, weights(w))
source
StatsBase.skewness — Function
skewness(v, [wv::AbstractWeights], m=mean(v))

Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

source
StatsBase.kurtosis — Function
kurtosis(v, [wv::AbstractWeights], m=mean(v))

Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

source

Critical Slowing Down

Statistics.var — Function
var(x::AbstractArray, w::AbstractWeights, [dim]; mean=nothing, corrected=false)

Compute the variance of a real-valued array x, optionally over a dimension dim. Observations in x are weighted using weight vector w. The uncorrected (when corrected=false) sample variance is defined as:

\[\frac{1}{\sum{w}} \sum_{i=1}^n {w_i\left({x_i - μ}\right)^2 }\]

where $n$ is the length of the input and $μ$ is the mean. The unbiased estimate (when corrected=true) of the population variance is computed by replacing $\frac{1}{\sum{w}}$ with a factor dependent on the type of weights used:

  • AnalyticWeights: $\frac{1}{\sum w - \sum {w^2} / \sum w}$
  • FrequencyWeights: $\frac{1}{\sum{w} - 1}$
  • ProbabilityWeights: $\frac{n}{(n - 1) \sum w}$ where $n$ equals count(!iszero, w)
  • Weights: ArgumentError (bias correction not supported)
source
var(ce::CovarianceEstimator, x::AbstractVector; mean=nothing)

Compute the variance of the vector x using the estimator ce.

source
TransitionsInTimeseries.ar1_whitenoise — Function
ar1_whitenoise(x::AbstractVector)

Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

\[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

source

Spectrum

TransitionsInTimeseries.LowfreqPowerSpectrum — Type
LowfreqPowerSpectrum(; q_lofreq = 0.1)

Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

lfps = precompute( LowfreqPowerSpectrum() )

Keyword arguments:

  • q_lofreq: a number between 0 and 1 that characterises which portion of the

frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

source
TransitionsInTimeseries.PrecomputedLowfreqPowerSpectrum — Type
PrecomputedLowfreqPowerSpectrum

A struct containing all the precomputed fields to efficiently perform repetitive computation of the low-frequency power spectrum (LFPS), a number between 0 and 1 that characterizes the amount of power contained in the low frequencies of the power density spectrum of x. Once lfps::PrecomputedLowfreqPowerSpectrum is initialized, it can be used as a function to obtain the LFPS of x::AbstractVector by:

lfps(x)
source

Nonlinear dynamics

Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.

For example, using the permutation entropy as an indicator is as simple as doing

using ComplexityMeasures
+est = OrdinalPatterns(; m = 3) # order 3
+# create a function that given timeseries returns permutation entropy
+indicator = x -> entropy_normalized(est, x)

and giving the created indicator to e.g., SlidingWindowConfig.

Change metrics

Slope

TransitionsInTimeseries.kendalltau — Function
kendalltau(x::AbstractVector)

Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

source
TransitionsInTimeseries.spearman — Function
spearman(x::AbstractVector)

Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

source

Value distribution differences

TransitionsInTimeseries.difference_of_means — Function
difference_of_means(x::AbstractArray)

Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

# assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

source

Make your own indicator/metric!

The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:

Surrogates

For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

Sliding windows

TransitionsInTimeseries.WindowViewer — Type
WindowViewer(x; width, stride)

Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

If not given, the keywords width, stride are respectively taken as default_window_width(x) and 1.

source
TransitionsInTimeseries.windowmap — Function
windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

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Load data

Visualization

TransitionsInTimeseries.plot_indicator_changes — Function
plot_indicator_changes(res) → (fig, axs)

Return fig::Figure and axs::Matrix{Axis}, on which res::ChangesResults has been visualised.

Keyword arguments:

  • colors = default_colors sets the colors of the line plots that are to

be cycled through. The default correspond to the color scheme of Julia Dynamics.

  • `indicatornames = defaultindicatorlabel(res), chametricnames =

defaultchametriclabel(res)sets the labels for the indicators and the change metrics, with the default inferring them from the names ofres.config.indicatorsandres.config.change_metrics`.

  • accent_linewidth = 3 sets the line width for the original signals (the

surrogates have linewidth = 1)

source
TransitionsInTimeseries.plot_significance! — Function
plot_significance!(axs, res, signif)

Update the axs::Matrix{Axis} of a figure obtained with plot_indicator_changes(res) with the signif::SurrogatesSignificance.

Keyword arguments:

  • flags = nothing provides the significance flags, for instance obtained by

thresholding the pvalues.

  • nsurro = 20 sets the number of surrogates to plot.
source

Utils

default_window_width
diff --git a/dev/assets/documenter.js b/dev/assets/documenter.js new file mode 100644 index 00000000..c6562b55 --- /dev/null +++ b/dev/assets/documenter.js @@ -0,0 +1,1050 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 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+$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`${querystring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(querystring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` + + `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/dev/assets/themes/documenter-dark.css b/dev/assets/themes/documenter-dark.css new file mode 100644 index 00000000..777353c9 --- /dev/null +++ b/dev/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ 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.pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--documenter-dark .is-focused.button,html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active,html.theme--documenter-dark .pagination-ellipsis:active,html.theme--documenter-dark .file-cta:active,html.theme--documenter-dark .file-name:active,html.theme--documenter-dark .select select:active,html.theme--documenter-dark .textarea:active,html.theme--documenter-dark .input:active,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:active,html.theme--documenter-dark .button:active,html.theme--documenter-dark .is-active.pagination-previous,html.theme--documenter-dark .is-active.pagination-next,html.theme--documenter-dark .is-active.pagination-link,html.theme--documenter-dark .is-active.pagination-ellipsis,html.theme--documenter-dark .is-active.file-cta,html.theme--documenter-dark .is-active.file-name,html.theme--documenter-dark .select select.is-active,html.theme--documenter-dark .is-active.textarea,html.theme--documenter-dark .is-active.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-active,html.theme--documenter-dark .is-active.button{outline:none}html.theme--documenter-dark .pagination-previous[disabled],html.theme--documenter-dark .pagination-next[disabled],html.theme--documenter-dark .pagination-link[disabled],html.theme--documenter-dark .pagination-ellipsis[disabled],html.theme--documenter-dark .file-cta[disabled],html.theme--documenter-dark .file-name[disabled],html.theme--documenter-dark .select select[disabled],html.theme--documenter-dark .textarea[disabled],html.theme--documenter-dark .input[disabled],html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input[disabled],html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark fieldset[disabled] .pagination-previous,fieldset[disabled] html.theme--documenter-dark .pagination-next,html.theme--documenter-dark fieldset[disabled] .pagination-next,fieldset[disabled] html.theme--documenter-dark .pagination-link,html.theme--documenter-dark fieldset[disabled] .pagination-link,fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis,fieldset[disabled] html.theme--documenter-dark .file-cta,html.theme--documenter-dark fieldset[disabled] .file-cta,fieldset[disabled] html.theme--documenter-dark .file-name,html.theme--documenter-dark fieldset[disabled] .file-name,fieldset[disabled] html.theme--documenter-dark .select select,fieldset[disabled] html.theme--documenter-dark .textarea,fieldset[disabled] html.theme--documenter-dark .input,fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar 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html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark 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html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark 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.button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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kbd.button{background-color:#363636;border-color:#363636;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark 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.button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#f4c72f;box-shadow:none;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fefaec;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fdf7e0;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fdf3d3;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#c13930;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(203,60,51,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#b7362e;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:#cb3c33;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-outlined.is-focused{background-color:#cb3c33;border-color:#cb3c33;color:#fff}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:2px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#fff;border-color:#dbdbdb;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#f5f5f5;border-color:#dbdbdb;color:#7a7a7a;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:2px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#cdc3e3;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#f5f5f5;border-left:5px solid #dbdbdb;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #dbdbdb;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#cdc3e3}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#cdc3e3}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#cdc3e3}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 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Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/dev/devdocs/index.html b/dev/devdocs/index.html new file mode 100644 index 00000000..690b1dc9 --- /dev/null +++ b/dev/devdocs/index.html @@ -0,0 +1,2 @@ + +Developer's documentation · TransitionsInTimeseries.jl
GitHub

Developer's documentation

This documentation addresses users that would like to contribute to the software by either solving bugs, improving documentation, or adding new methods. All contributions come in the form of Pull Requests, for which we strongly advise to follow good practices in scientific code, which means that they are properly formatted, documented, tested, etc.

New indicators or change metrics

As explained already in e.g., SlidingWindowConfig, new indicators or change metrics are standard Julia functions, so you only need to define such a function (and document it, test it, etc.).

New pipeline for estimating changes

This means to contribute a fundamentally new "pipeline" for estimating/detecting transitions in timeseries. This new pipeline defines what a "transition" means. To add a new pipeline follow these steps:

  1. Define a new subtype of ChangesConfig
  2. Define a new subtype of ChangesResults
  3. Add a method for estimate_changes which accepts the new ChangesConfig subtype you defined and returns the ChangesResults subtype you defined.

And that's it!

Optionally you can further extend:

  • TransitionsInTimeseries.plot_indicator_changes with the new ChangesResults type you defined. Note the plotting functions are in the ext folder of the repository.
  • significant_transitions(res::ChangesResults, signif::Significance) with your new ChangesResults type and as many Significance subtypes you have the capacity to extend for.

New pipeline for estimating significance

Statistically significant changes are "transitions". However, what "significant" means is not universal. There are different ways to test for significance and TransitionsInTimeseries.jl allows various methods.

To add a new pipeline for estimating significance follow these steps:

  1. Define a new subtype of Significance
  2. Extend significant_transitions(res::ChangesResults, signif::Significance) with your new type and as many ChangesResults subtypes as you have capacity for.

And that's it! Unfortunately so far we have found no way to make the significant_transitions code agnostic of the changes result, so you would need to add a method manually for every ChangesResults.

Optionally you can further extend TransitionsInTimeseries.plot_significance! (which you can find in the ext folder) for visualizing the significance results.

diff --git a/dev/examples/do-events.jl b/dev/examples/do-events.jl new file mode 100644 index 00000000..f40cd308 --- /dev/null +++ b/dev/examples/do-events.jl @@ -0,0 +1,329 @@ +#= +# Dansgaard-Oescher events and Critical Slowing Down + +The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project +([NGRIP](https://en.wikipedia.org/wiki/North_Greenland_Ice_Core_Project)) are, +to this date, the best proxy record for the Dansgaard-Oeschger events +([DO-events](https://en.wikipedia.org/wiki/Dansgaard%E2%80%93Oeschger_event)). +DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees +of regional warming within 100 years. They happened quasi-periodically over the +last glacial cycle due to transitions between strong and weak states of the Atlantic +Meridional Overturning Circulation and might be therefore be the most prominent +examples of abrupt transitions in the field of climate science. We here propose +to hindcast these events by applying the theory of Critical Slowing Down (CSD) +on the NGRIP data, which can be found [here](https://www.iceandclimate.nbi.ku.dk/data/) +in its raw format. This analysis has already been done in [boers-early-warning-2018](@cite) +and we here try to reproduce Figure 2.d-f. + +## Preprocessing NGRIP + +Data pre-processing is not part of TransitionsInTimeseries.jl, +but a step the user has to do before using the package. +To present an example with a complete scientific workflow, +we will showcase typical data pre-processing here, that consist of the following steps: +1. Load the data, reverse and offset it to have time vector = time before 2000 AD. +2. Filter non-unique points in time and sort the data. +3. Regrid the data from uneven to even sampling. + +The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are +respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual +$r$, i.e. the fluctuations of the system around the attractor, which, within the CSD +theory, is assumed to be tracked. Over this example, it will appear that the +convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written +for plotting and preprocessing. + +### Step 1: +=# + +using DelimitedFiles, Downloads + +function load_ngrip() + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP.csv") + data, labels = readdlm(tmp, header = true) + return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors +end + +t1, x1 = load_ngrip() + +#= +### Step 2 +=# + +uniqueidx(v) = unique(i -> v[i], eachindex(v)) +function keep_unique(t, x) + unique_idx = uniqueidx(t) + return t[unique_idx], x[unique_idx] +end + +function sort_timeseries!(t, x) + p = sortperm(t) + permute!(t, p) + permute!(x, p) + return nothing +end + +t2, x2 = keep_unique(t1, x1) +sort_timeseries!(t2, x2) + +#= +### Step 3 +=# + +using BSplineKit + +function regrid2evensampling(t, x, dt) + itp = BSplineKit.interpolate(t, x, BSplineOrder(4)) + tspan = (ceil(minimum(t)), floor(maximum(t))) + t_even = collect(tspan[1]:dt:tspan[2]) + x_even = itp.(t_even) + return t_even, x_even +end + +dt = 5.0 # dt = 5 yr as in (Boers 2018) +t3, x3 = regrid2evensampling(t2, x2, dt) + +#= +### Step 4 + +For the final step we drop the indices: +=# + +using DSP + +function chebyshev_filter(t, x, fcutoff) + ii = 10 # Chebyshev filtering requires to prune first points of timeseries. + responsetype = Highpass(fcutoff, fs = 1/dt) + designmethod = Chebyshev1(8, 0.05) + r = filt(digitalfilter(responsetype, designmethod), x) + xtrend = x - r + return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end] +end + +fcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018) +t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff) + +#= +Let's now visualize our data in what will become our main figure. +For the segmentation of the DO-events, we rely on the tabulated +data from [rasmussen-stratigraphic-2014](@cite) (which will soon be available as downloadable): +=# + +using CairoMakie, Loess + +function loess_filter(t, x; span = 0.005) + loessmodel = loess(t, x, span = span) + xtrend = Loess.predict(loessmodel, t) + r = x - xtrend + return t, x, xtrend, r +end + +function kyr_xticks(tticks_yr) + tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)] + return (tticks_yr, tticks_kyr) +end + +function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks) + fig = Figure(size = (1600, 1200), fontsize = 24) + + ## Original timeseries with transition marked by vertical lines + ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)", + xaxisposition = :top, xticks = xticks) + lines!(ax1, traw, xraw, color = (:gray70, 0.5)) + lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3) + vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3) + + ## Residual timeseries + ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + lines!(ax2, t, r, color = :gray50, linewidth = 1) + + ## Axes for variance and AC1 timeseries + ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$", + xticks = xticks) + + axs = [ax1, ax2, ax3, ax4] + [xlims!(ax, xlims) for ax in axs] + ylims!(axs[1], (-48, -34)) + rowgap!(fig.layout, 10) + return fig, axs +end + +xlims = (-60e3, -10e3) +xticks = kyr_xticks(-60e3:5e3:5e3) +t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160, + 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703] +tloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +fig + +#= +## Hindcast on NGRIP data + +As one can see... there is not much to see so far. +Residuals are impossible to simply eye-ball and we therefore use +TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression +slope of the residual's variance and lag-1 autocorrelation (AC1) over time. +In many examples of the literature, including [boers-early-warning-2018](@cite), +the CSD analysis is performed over segments (sometimes only one) of the timeseries, +such that a significance value is obtained for each segment. By using +`SegmentedWindowConfig`, dealing with segments can be easily done in +TransitionsInTimeseries.jl and is demonstrated here: +=# + +using TransitionsInTimeseries, StatsBase +using Random: Xoshiro + +ac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase +indicators = (var, ac1) +change_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope()) +tseg_start = t_rasmussen[1:end-1] .+ 200 +tseg_end = t_rasmussen[2:end] .- 200 +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) # require >=100 data points to estimate change metric +results = estimate_changes(config, r, t) +signif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) + +#= +That's it! We can now visualise our results with a generic function that we will re-use later: +=# + +function plot_segment_analysis!(axs, results, signif) + (; t_indicator, x_indicator) = results + for k in eachindex(t_indicator) # loop over the segments + for i in axes(signif.pvalues, 2) # loop over the indicators + if !isnan(signif.pvalues[k, i]) # plot if segment long enough + ## Plot indicator timeseries and its linear regression + ti, xi = t_indicator[k], x_indicator[k][:, i] + lines!(axs[i+2], ti, xi, color = Cycled(1)) + m, p = ridgematrix(ti, 0.0) * xi + if signif.pvalues[k, i] < 0.05 + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3) + else + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3) + end + end + end + end +end +plot_segment_analysis!(axs, results, signif) +fig + +#= +In [boers-early-warning-2018](@cite), 13/16 and 7/16 true positives are respectively +found for the variance and AC1, with 16 referring to the total number of transitions. +The timeseries actually includes 18 transition but, in +[boers-early-warning-2018](@cite), some segments are considered too small to be analysed. +In contrast, we here respectively find 9/16 true positives +for the variance and 3/16 for AC1. We can track down the discrepancies to be in the +surrogate testing, since the indicator timeseries computed here are almost exactly +similar to those of [boers-early-warning-2018](@cite). This mismatch points +out that packages like TransitionsInTimeseries.jl are desirable for research to be +reproducible, especially since CSD is gaining attention - not only within the +scientific community but also in popular media. + +## CSD: only a necessary condition, only in some cases + +For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies +a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the +SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore +a **necessary condition** for crossing one of these bifurcations - although it is not +always assessable by analysing the timeseries due to practical limitations (e.g. sparse +data subject to large measurement noise). It is nonetheless not given that DO-events, +as many other real-life applications, can be seen as a codimension-1 fold, Hopf or +transcritical bifurcations. Besides this, we emphasise that CSD is **not a sufficient +condition** for assessing a transition being ahead in near future, since a resilience +loss can happen without actually crossing any bifurcation. This can be illustrated on +the present example by performing the same analysis only until few hundred years before +the transition: +=# + +tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) +results = estimate_changes(config, r, t) +signif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +plot_segment_analysis!(axs, results, signif) +fig + +#= +For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. +This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. +We therefore believe, as already suggested in some studies, +that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD. + +We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. +Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. +The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. +To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC). + +!!! warning "Degrees of freedom" + These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). + This leads to a large number of degrees of freedom (DoF). + Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice. + +!!! info "Future improvement" + Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. + This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias. + +## Hindcasting simulated DO-events + +In CLIMBER-X, the EMIC described in [willeit-earth-2022](@cite), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. +Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. +We run this analysis over two exemplary simulation outputs: +=# + +t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050], + [1, 3500, 4370, 5790, 7200, 8140]] +t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]] +tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]] +tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50] + +figvec = Figure[] + +for j in 1:2 + ## Download the data and perform loess filtering on it + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" * + "master/timeseries/climberx-do$(j)-omaxa.csv") + data = readdlm(tmp) + tcx, xcx = data[1, 1000:end], data[2, 1000:end] + t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02) + + ## Initialize figure + xlims = (0, last(tcx)) + xticks = kyr_xticks(xlims[1]:1e3:xlims[2]) + fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks) + ylims!(axs[1], (5, 40)) + axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$" + + ## Run sliding analysis and update figure with results + dt = mean(diff(tcx)) + config = SegmentedWindowConfig( + indicators, change_metrics, tseg_start[j], tseg_end[j], + whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100) + results = estimate_changes(config, r, t) + signif = SurrogatesSignificance(n = 1_000, tail = [:right, :right], rng = Xoshiro(1995)) + flags = significant_transitions(results, signif) + + plot_segment_analysis!(axs, results, signif) + vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3) + push!(figvec, fig) +end +figvec[1] + +#= +It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case: +=# + +figvec[2] + +#= +Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience. +=# \ No newline at end of file diff --git a/dev/examples/do-events/3835a9d2.png b/dev/examples/do-events/3835a9d2.png new file mode 100644 index 00000000..e1cfc2bd Binary files /dev/null and b/dev/examples/do-events/3835a9d2.png differ diff --git a/dev/examples/do-events/3f28f250.png b/dev/examples/do-events/3f28f250.png new file mode 100644 index 00000000..75e2c4b9 Binary files /dev/null and b/dev/examples/do-events/3f28f250.png differ diff --git a/dev/examples/do-events/7494cf2f.png b/dev/examples/do-events/7494cf2f.png new file mode 100644 index 00000000..43103ed8 Binary files /dev/null and b/dev/examples/do-events/7494cf2f.png differ diff --git a/dev/examples/do-events/ba06f092.png b/dev/examples/do-events/ba06f092.png new file mode 100644 index 00000000..f90d89c3 Binary files /dev/null and b/dev/examples/do-events/ba06f092.png differ diff --git a/dev/examples/do-events/ecdc7c2d.png b/dev/examples/do-events/ecdc7c2d.png new file mode 100644 index 00000000..a2964079 Binary files /dev/null and b/dev/examples/do-events/ecdc7c2d.png differ diff --git a/dev/examples/do-events/index.html b/dev/examples/do-events/index.html new file mode 100644 index 00000000..aa95eef3 --- /dev/null +++ b/dev/examples/do-events/index.html @@ -0,0 +1,191 @@ + +Dansgaard-Oescher events and Critical Slowing Down · TransitionsInTimeseries.jl
GitHub

Dansgaard-Oescher events and Critical Slowing Down

The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.

Preprocessing NGRIP

Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:

  1. Load the data, reverse and offset it to have time vector = time before 2000 AD.
  2. Filter non-unique points in time and sort the data.
  3. Regrid the data from uneven to even sampling.

The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.

Step 1:

using DelimitedFiles, Downloads
+
+function load_ngrip()
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+        "master/timeseries/NGRIP.csv")
+    data, labels = readdlm(tmp, header = true)
+    return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors
+end
+
+t1, x1 = load_ngrip()
([-59944.5, -59939.6, -59935.9, -59930.5, -59925.0, -59919.0, -59914.3, -59909.4, -59904.5, -59899.7  …  -27.40000000000009, -27.40000000000009, -27.299999999999955, -27.299999999999955, -27.200000000000045, -27.09999999999991, -27.09999999999991, -27.0, -26.90000000000009, -26.799999999999955], [-43.52, -42.94, -42.13, -40.04, -41.09, -43.57, -42.28, -41.2, -44.07, -44.53  …  -35.29, -35.18, -35.51, -36.03, -36.52, -37.12, -37.41, -37.21, -36.62, -35.52])

Step 2

uniqueidx(v) = unique(i -> v[i], eachindex(v))
+function keep_unique(t, x)
+    unique_idx = uniqueidx(t)
+    return t[unique_idx], x[unique_idx]
+end
+
+function sort_timeseries!(t, x)
+    p = sortperm(t)
+    permute!(t, p)
+    permute!(x, p)
+    return nothing
+end
+
+t2, x2 = keep_unique(t1, x1)
+sort_timeseries!(t2, x2)

Step 3

using BSplineKit
+
+function regrid2evensampling(t, x, dt)
+    itp = BSplineKit.interpolate(t, x, BSplineOrder(4))
+    tspan = (ceil(minimum(t)), floor(maximum(t)))
+    t_even = collect(tspan[1]:dt:tspan[2])
+    x_even = itp.(t_even)
+    return t_even, x_even
+end
+
+dt = 5.0        # dt = 5 yr as in (Boers 2018)
+t3, x3 = regrid2evensampling(t2, x2, dt)
([-59944.0, -59939.0, -59934.0, -59929.0, -59924.0, -59919.0, -59914.0, -59909.0, -59904.0, -59899.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-43.445268010797946, -42.85408835164853, -41.357360665158936, -39.9365468206892, -41.60554051352076, -43.57000000000001, -42.145558689100454, -41.33160823883399, -44.273597725729985, -44.4622612304012  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46])

Step 4

For the final step we drop the indices:

using DSP
+
+function chebyshev_filter(t, x, fcutoff)
+    ii = 10             # Chebyshev filtering requires to prune first points of timeseries.
+    responsetype = Highpass(fcutoff, fs = 1/dt)
+    designmethod = Chebyshev1(8, 0.05)
+    r = filt(digitalfilter(responsetype, designmethod), x)
+    xtrend = x - r
+    return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]
+end
+
+fcutoff = 0.95 * 0.01   # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)
+t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)
([-59899.0, -59894.0, -59889.0, -59884.0, -59879.0, -59874.0, -59869.0, -59864.0, -59859.0, -59854.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-44.4622612304012, -44.264401428210874, -44.02956767939856, -42.29334237357212, -42.594341674200344, -41.09704877854712, -40.39837540966913, -44.369155046413255, -42.74492506508012, -43.737014520530145  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46], [-43.89287787976461, -48.663435112414156, -51.31169981050155, -51.269094666491796, -49.90310432724566, -47.721430022512344, -44.36050569418247, -43.87556827410048, -43.57802291229893, -41.36870967826094  …  -34.81349114528442, -36.01634453179986, -36.150446802907226, -36.37595639697143, -35.96843653265903, -33.899634243732976, -32.49784036951535, -33.06575312724142, -34.07956188682297, -34.4079080530096], [-0.5693833506365866, 4.399033684203284, 7.282132131102991, 8.975752292919669, 7.308762653045311, 6.624381243965224, 3.9621302845133433, -0.493586772312777, 0.8330978472188112, -2.368304842269206  …  -0.30650885471557926, -0.17365546820014846, 1.0104468029072273, -0.684043603028572, 1.0384365326590237, -0.3303657562670192, -1.0321596304846505, -2.0242468727585807, 0.07956188682296689, -0.05209194699039831])

Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):

using CairoMakie, Loess
+
+function loess_filter(t, x; span = 0.005)
+    loessmodel = loess(t, x, span = span)
+    xtrend = Loess.predict(loessmodel, t)
+    r = x - xtrend
+    return t, x, xtrend, r
+end
+
+function kyr_xticks(tticks_yr)
+    tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)]
+    return (tticks_yr, tticks_kyr)
+end
+
+function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)
+    fig = Figure(size = (1600, 1200), fontsize = 24)
+
+    # Original timeseries with transition marked by vertical lines
+    ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)",
+        xaxisposition = :top, xticks = xticks)
+    lines!(ax1, traw, xraw, color = (:gray70, 0.5))
+    lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)
+    vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)
+
+    # Residual timeseries
+    ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    lines!(ax2, t, r, color = :gray50, linewidth = 1)
+
+    # Axes for variance and AC1 timeseries
+    ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$",
+        xticks = xticks)
+
+    axs = [ax1, ax2, ax3, ax4]
+    [xlims!(ax, xlims) for ax in axs]
+    ylims!(axs[1], (-48, -34))
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+
+xlims = (-60e3, -10e3)
+xticks = kyr_xticks(-60e3:5e3:5e3)
+t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,
+                38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]
+tloess, _, xloess, rloess = loess_filter(t3, x3)    # loess-filtered signal for visualization
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+fig
Example block output

Hindcast on NGRIP data

As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:

using TransitionsInTimeseries, StatsBase
+using Random: Xoshiro
+
+ac1(x) = sum(autocor(x, [1]))   # AC1 from StatsBase
+indicators = (var, ac1)
+change_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope())
+tseg_start = t_rasmussen[1:end-1] .+ 200
+tseg_end = t_rasmussen[2:end] .- 200
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)        # require >=100 data points to estimate change metric
+results = estimate_changes(config, r, t)
+signif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
18×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 1  0
+ 1  1
+ 1  1
+ 1  1
+ 0  0
+ 1  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 1  0

That's it! We can now visualise our results with a generic function that we will re-use later:

function plot_segment_analysis!(axs, results, signif)
+    (; t_indicator, x_indicator) = results
+    for k in eachindex(t_indicator)             # loop over the segments
+        for i in axes(signif.pvalues, 2)        # loop over the indicators
+            if !isnan(signif.pvalues[k, i])     # plot if segment long enough
+                # Plot indicator timeseries and its linear regression
+                ti, xi = t_indicator[k], x_indicator[k][:, i]
+                lines!(axs[i+2], ti, xi, color = Cycled(1))
+                m, p = ridgematrix(ti, 0.0) * xi
+                if signif.pvalues[k, i] < 0.05
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)
+                else
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)
+                end
+            end
+        end
+    end
+end
+plot_segment_analysis!(axs, results, signif)
+fig
Example block output

In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are desirable for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.

CSD: only a necessary condition, only in some cases

For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:

tseg_end = t_rasmussen[2:end] .- 700    # stop analysis 500 years earlier than before
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)
+results = estimate_changes(config, r, t)
+signif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+plot_segment_analysis!(axs, results, signif)
+fig
Example block output

For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD.

We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).

Degrees of freedom

These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.

Future improvement

Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.

Hindcasting simulated DO-events

In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:

t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],
+                 [1, 3500, 4370, 5790, 7200, 8140]]
+t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]
+tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]
+tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]
+
+figvec = Figure[]
+
+for j in 1:2
+    # Download the data and perform loess filtering on it
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" *
+        "master/timeseries/climberx-do$(j)-omaxa.csv")
+    data = readdlm(tmp)
+    tcx, xcx = data[1, 1000:end], data[2, 1000:end]
+    t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)
+
+    # Initialize figure
+    xlims = (0, last(tcx))
+    xticks = kyr_xticks(xlims[1]:1e3:xlims[2])
+    fig, axs = plot_do(tcx, xcx,  t, xtrend, t, r, t_transitions[j], extrema(t), xticks)
+    ylims!(axs[1], (5, 40))
+    axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$"
+
+    # Run sliding analysis and update figure with results
+    dt = mean(diff(tcx))
+    config = SegmentedWindowConfig(
+        indicators, change_metrics, tseg_start[j], tseg_end[j],
+        whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)
+    results = estimate_changes(config, r, t)
+    signif = SurrogatesSignificance(n = 1_000, tail = [:right, :right], rng = Xoshiro(1995))
+    flags = significant_transitions(results, signif)
+
+    plot_segment_analysis!(axs, results, signif)
+    vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)
+    push!(figvec, fig)
+end
+figvec[1]
Example block output

It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:

figvec[2]
Example block output

Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.

diff --git a/dev/examples/ks_paleojump.jl b/dev/examples/ks_paleojump.jl new file mode 100644 index 00000000..012e0254 --- /dev/null +++ b/dev/examples/ks_paleojump.jl @@ -0,0 +1,168 @@ +# # Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries + +# The goal of this example is to show how simple it is to re-create an analysis _similar_ +# to what was done in the paper +# "Automatic detection of abrupt transitions in paleoclimate records", +# [Bagniewski2021](@cite). The same analysis was then used to create a database +# of transitions in paleoclimate records in [Bagniewski2023](@cite) +# Using TransitionsInTimeseries.jl and HypothesisTests.jl, +# the analysis becomes a 10-lines-of-code script (for a given timeseries). + +# ## Scientific background + +# The approach of [Bagniewski2021](@cite) is based on the [two-sample +# Kolmogorov Smirnov test](https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test#Two-sample_Kolmogorov%E2%80%93Smirnov_test). +# It tests whether the samples from two datasets or timeseries +# are distributed according to the same cumulative density function or not. +# This can be estimated by comparing the value of the _KS-statistic_ +# versus some threshold that depends on the required confidence. + +# The application of this test for identifying transitions in timeseries is simple: + +# 1. A sliding window analysis is performed in the timesries +# 1. In each window, the KS statistic is estimated between the first half and the second +# half of the timeseries within this window. +# 1. Transitions are defined by when the KS statistic exceeds a particular value +# based on some confidence. The transition occurs in the middle of the window. + +# We should point out that in [Bagniewski2021](@cite) the authors did a +# more detailed analysis: analyzed many different window widths, added a +# conditional clause to exclude transitions that do not exceed a predefined minimum +# "jump" in the data, and also added another conditional clause that +# filtered out transitions that are grouped in time (which is a natural consequence +# of using the Kolmogorov-Smirov test for detecting transitions). +# +# Here we won't do that post processing, mainly because it is rather simple +# to include these additional conditional clauses to filter transitions after they are found. + +# ## Steps for TransitionsInTimeseries.jl + +# Doing this kind of work with TransitionsInTimeseries.jl is so easy you won't even trip! +# This analysis follows the same sliding window approach showcased in our [Tutorial](@ref), +# and it even excludes the "indicator" aspect: the change metric is estimated directly +# from the input data! + +# As such, we really only need to define/do these things before we have finished the analysis: + +# 1. Load the input data (we will use the same example as the NGRIP data of +# [Dansgaard-Oescher events and Critical Slowing Down](@ref) example) +# and set the appropriate time window. +# 3. Define the function that estimates the change metric (i.e., the KS-statistic) +# 3. Perform the sliding window analysis as in the [Tutorial](@ref) with [`estimate_changes`](@ref) +# 4. Estimate the "confident" transitions in the data by comparing the estimated +# KS-statistic with a predefined threshold. + +# ## Load timeseries and window length +# Following the Dansgaard-Oescher events example, we load +# the data after all the processing steps done in that example: + +using DelimitedFiles, CairoMakie + +tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP_processed.csv") +data = readdlm(tmp) +t, xtrend, xresid, xloess = collect.(eachcol(data)) + +fig, ax = lines(t, xtrend; axis = (ylabel = "NGRIP (processed)", xlabel = "time")) +lines!(ax, t, xloess; linewidth = 2) +fig + +# For the window, since we are using a sliding window here, we will be using a +# window of length 500 (which is approximately 1/2 to 1/4 the span between typical +# transitions found by [rasmussen-stratigraphic-2014](@cite)). + +window = 500 + +# ## Defining the change metric function + +# HypothesisTest.jl implements the Kolmogorov-Smirnov test, however here we are interested +# in the value of the test iself (the so-called KS-statistic), rather than a p-value. +# To this end, we define the following function to compute the statistic, +# which also normalizes it as in [Bagniewski2021](@cite). + +using HypothesisTests + +function normalized_KS_statistic(timeseries) + N = length(timeseries) + i = N÷2 + x = view(timeseries, 1:i) + y = view(timeseries, (i+1):N) + kstest = ApproximateTwoSampleKSTest(x, y) + nx = ny = i # length of each timeseries half of total + n = nx*ny/(nx + ny) # written fully for concreteness + D_KS = kstest.δ # can be compared directly with sqrt(-log(α/2)/2) + ## Rescale according to eq. (5) of the paper + rescaled = 1 - ((1 - D_KS)/(1 - sqrt(1/n))) + return rescaled +end + +N = 1000 # the statistic is independent of `N` for large enough `N`! +x = randn(N) +y = 1.8randn(N) .+ 1.0 +z = randn(N) +w = 0.6randn(N) .- 2.0 + +fig, ax = density(x; color = ("black", 0.5), strokewidth = 4.0, label = "reference distribution") +ax.title = "showcase of normalized KS-statistic" +for q in (y, z, w) + D_KS = normalized_KS_statistic(vcat(x, q)) + density!(ax, q; label = "D_KS = $(D_KS)") +end +axislegend(ax) +fig + +# ## Perform the sliding window analysis + +# This is just a straightforward call to [`estimate_changes`](@ref). +# In fact, it is even simpler than the tutorial. Here we skip completely +# the "indicator" estimation step, and we evaluate the change metric directly +# on input data. We do this by simply passing `nothing` as the indicators. + +using TransitionsInTimeseries + +config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 500) + +results = estimate_changes(config, xtrend, t) + +# Which we can visualize +function visualize_results(results) + fig, ax1 = lines(t, xtrend; axis = (ylabel = "NGRIP (processed)",)) + ax2, = lines(fig[2, 1], results.t_change, vec(results.x_change), axis = (ylabel = "D_KS (normalized)", xlabel = "time")) + linkxaxes!(ax1, ax2) + hidexdecorations!(ax1; grid = false) + xloess_normed = (xloess .- minimum(xloess))./(maximum(xloess) - minimum(xloess)) + lines!(ax2, t, xloess_normed; color = ("gray", 0.5)) + fig +end + +visualize_results(results) + +# By overplotting the (smoothened) NGRIP timeseries and the +# normalized KS-statistic, it already becomes pretty clear +# that the statistic peaks when transitions occur. + +# The same thing happens if we alter the window duration + +config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 200) +results = estimate_changes(config, xtrend, t) +visualize_results(results) + +# So one can easily obtain extra confidence by varying window +# size as in [Bagniewski2021](@cite). + +# ## Identifying "confident" transitions + +# As this identification here is done via a simple threshold, +# identifying the transitions is a nearly trivial call +# to [`significant_transitions`](@ref) with [`ThresholdSignificance`](@ref) + +signif = ThresholdSignificance(0.5) # or any other threshold +flags = significant_transitions(results, signif) + +fig = visualize_results(results) +axDKS = content(fig[2,1]) +vlines!(axDKS, results.t_change[vec(flags)], color = ("red", 0.25)) +fig + +# We could proceed with a lot of preprocessing as in [Bagniewski2021](@cite) +# but we skip this here for the sake of simplicity. \ No newline at end of file diff --git a/dev/examples/ks_paleojump/217f75ed.png b/dev/examples/ks_paleojump/217f75ed.png new file mode 100644 index 00000000..d2eb077c Binary files /dev/null and b/dev/examples/ks_paleojump/217f75ed.png differ diff --git a/dev/examples/ks_paleojump/414a766b.png b/dev/examples/ks_paleojump/414a766b.png new file mode 100644 index 00000000..dd97c251 Binary files /dev/null and b/dev/examples/ks_paleojump/414a766b.png differ diff --git a/dev/examples/ks_paleojump/709306e6.png b/dev/examples/ks_paleojump/709306e6.png new file mode 100644 index 00000000..7ee0264b Binary files /dev/null and b/dev/examples/ks_paleojump/709306e6.png differ diff --git a/dev/examples/ks_paleojump/b1e01a66.png b/dev/examples/ks_paleojump/b1e01a66.png new file mode 100644 index 00000000..2d01c522 Binary files /dev/null and b/dev/examples/ks_paleojump/b1e01a66.png differ diff --git a/dev/examples/ks_paleojump/ed8344ce.png b/dev/examples/ks_paleojump/ed8344ce.png new file mode 100644 index 00000000..7fdfa08c Binary files /dev/null and b/dev/examples/ks_paleojump/ed8344ce.png differ diff --git a/dev/examples/ks_paleojump/index.html b/dev/examples/ks_paleojump/index.html new file mode 100644 index 00000000..7578e1be --- /dev/null +++ b/dev/examples/ks_paleojump/index.html @@ -0,0 +1,68 @@ + +Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries · TransitionsInTimeseries.jl
GitHub

Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries

The goal of this example is to show how simple it is to re-create an analysis similar to what was done in the paper "Automatic detection of abrupt transitions in paleoclimate records", (Bagniewski et al., 2021). The same analysis was then used to create a database of transitions in paleoclimate records in (Bagniewski et al., 2023) Using TransitionsInTimeseries.jl and HypothesisTests.jl, the analysis becomes a 10-lines-of-code script (for a given timeseries).

Scientific background

The approach of (Bagniewski et al., 2021) is based on the two-sample Kolmogorov Smirnov test. It tests whether the samples from two datasets or timeseries are distributed according to the same cumulative density function or not. This can be estimated by comparing the value of the KS-statistic versus some threshold that depends on the required confidence.

The application of this test for identifying transitions in timeseries is simple:

  1. A sliding window analysis is performed in the timesries
  2. In each window, the KS statistic is estimated between the first half and the second half of the timeseries within this window.
  3. Transitions are defined by when the KS statistic exceeds a particular value based on some confidence. The transition occurs in the middle of the window.

We should point out that in (Bagniewski et al., 2021) the authors did a more detailed analysis: analyzed many different window widths, added a conditional clause to exclude transitions that do not exceed a predefined minimum "jump" in the data, and also added another conditional clause that filtered out transitions that are grouped in time (which is a natural consequence of using the Kolmogorov-Smirov test for detecting transitions).

Here we won't do that post processing, mainly because it is rather simple to include these additional conditional clauses to filter transitions after they are found.

Steps for TransitionsInTimeseries.jl

Doing this kind of work with TransitionsInTimeseries.jl is so easy you won't even trip! This analysis follows the same sliding window approach showcased in our Tutorial, and it even excludes the "indicator" aspect: the change metric is estimated directly from the input data!

As such, we really only need to define/do these things before we have finished the analysis:

  1. Load the input data (we will use the same example as the NGRIP data of Dansgaard-Oescher events and Critical Slowing Down example) and set the appropriate time window.
  2. Define the function that estimates the change metric (i.e., the KS-statistic)
  3. Perform the sliding window analysis as in the Tutorial with estimate_changes
  4. Estimate the "confident" transitions in the data by comparing the estimated KS-statistic with a predefined threshold.

Load timeseries and window length

Following the Dansgaard-Oescher events example, we load the data after all the processing steps done in that example:

using DelimitedFiles, CairoMakie
+
+tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+    "master/timeseries/NGRIP_processed.csv")
+data = readdlm(tmp)
+t, xtrend, xresid, xloess = collect.(eachcol(data))
+
+fig, ax = lines(t, xtrend; axis = (ylabel = "NGRIP (processed)", xlabel = "time"))
+lines!(ax, t, xloess; linewidth = 2)
+fig
Example block output

For the window, since we are using a sliding window here, we will be using a window of length 500 (which is approximately 1/2 to 1/4 the span between typical transitions found by (Rasmussen et al., 2014)).

window = 500
500

Defining the change metric function

HypothesisTest.jl implements the Kolmogorov-Smirnov test, however here we are interested in the value of the test iself (the so-called KS-statistic), rather than a p-value. To this end, we define the following function to compute the statistic, which also normalizes it as in (Bagniewski et al., 2021).

using HypothesisTests
+
+function normalized_KS_statistic(timeseries)
+    N = length(timeseries)
+    i = N÷2
+    x = view(timeseries, 1:i)
+    y = view(timeseries, (i+1):N)
+    kstest = ApproximateTwoSampleKSTest(x, y)
+    nx = ny = i # length of each timeseries half of total
+    n = nx*ny/(nx + ny) # written fully for concreteness
+    D_KS = kstest.δ # can be compared directly with sqrt(-log(α/2)/2)
+    # Rescale according to eq. (5) of the paper
+    rescaled = 1 - ((1 - D_KS)/(1 - sqrt(1/n)))
+    return rescaled
+end
+
+N = 1000 # the statistic is independent of `N` for large enough `N`!
+x = randn(N)
+y = 1.8randn(N) .+ 1.0
+z = randn(N)
+w = 0.6randn(N) .- 2.0
+
+fig, ax = density(x; color = ("black", 0.5), strokewidth = 4.0, label = "reference distribution")
+ax.title = "showcase of normalized KS-statistic"
+for q in (y, z, w)
+    D_KS = normalized_KS_statistic(vcat(x, q))
+    density!(ax, q; label = "D_KS = $(D_KS)")
+end
+axislegend(ax)
+fig
Example block output

Perform the sliding window analysis

This is just a straightforward call to estimate_changes. In fact, it is even simpler than the tutorial. Here we skip completely the "indicator" estimation step, and we evaluate the change metric directly on input data. We do this by simply passing nothing as the indicators.

using TransitionsInTimeseries
+
+config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 500)
+
+results = estimate_changes(config, xtrend, t)
SlidingWindowResults
+ input timeseries:              6975-element Vector{Float64}
+ indicators:                    nothing
+ indicator (window, stride):    (100, 1)
+ change metrics:                [:normalized_KS_statistic]
+ change metric (window, stride): (500, 1)
+

Which we can visualize

function visualize_results(results)
+    fig, ax1 = lines(t, xtrend; axis = (ylabel = "NGRIP (processed)",))
+    ax2, = lines(fig[2, 1], results.t_change, vec(results.x_change), axis = (ylabel = "D_KS (normalized)", xlabel = "time"))
+    linkxaxes!(ax1, ax2)
+    hidexdecorations!(ax1; grid = false)
+    xloess_normed = (xloess .- minimum(xloess))./(maximum(xloess) - minimum(xloess))
+    lines!(ax2, t, xloess_normed; color = ("gray", 0.5))
+    fig
+end
+
+visualize_results(results)
Example block output

By overplotting the (smoothened) NGRIP timeseries and the normalized KS-statistic, it already becomes pretty clear that the statistic peaks when transitions occur.

The same thing happens if we alter the window duration

config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 200)
+results = estimate_changes(config, xtrend, t)
+visualize_results(results)
Example block output

So one can easily obtain extra confidence by varying window size as in (Bagniewski et al., 2021).

Identifying "confident" transitions

As this identification here is done via a simple threshold, identifying the transitions is a nearly trivial call to significant_transitions with ThresholdSignificance

signif = ThresholdSignificance(0.5) # or any other threshold
+flags = significant_transitions(results, signif)
+
+fig = visualize_results(results)
+axDKS = content(fig[2,1])
+vlines!(axDKS, results.t_change[vec(flags)], color = ("red", 0.25))
+fig
Example block output

We could proceed with a lot of preprocessing as in (Bagniewski et al., 2021) but we skip this here for the sake of simplicity.

diff --git a/dev/examples/logistic.jl b/dev/examples/logistic.jl new file mode 100644 index 00000000..b9163cdf --- /dev/null +++ b/dev/examples/logistic.jl @@ -0,0 +1,203 @@ +# # Permutation entropy for dynamic regime changes + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ## Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +## time-dependent logistic map, so that the `r` parameter increases with time +r1 = 3.83 +r2 = 3.86 +N = 2000 +rs = range(r1, r2; length = N) + +function logistic_drifting_rule(u, rs, n) + r = rs[n+1] # time is `n`, starting from 0 + return SVector(r*u[1]*(1 - u[1])) +end + +ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs) +x = trajectory(ds, N-1)[1][:, 1] + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ## Using a simpler change metric + +# Now, let's compute various indicators and their changes, +# focusing on the permutation entropy as an indicator. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries, ComplexityMeasures + +function permutation_entropy(m) + est = SymbolicPermutation(; m) # order 3 + indicator = x -> entropy_normalized(est, x) + return indicator +end + +indicators = (var, ar1_whitenoise, permutation_entropy(4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as stride half the window width +metric = (difference_of_means, difference_of_means, difference_of_means) + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = SlidingWindowConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = estimate_changes(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (size = (600, 600),)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + if i < 3 + hidexdecorations!(ax; grid = false) + else + ax.xlabel = "r (time)" + end + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ## Significance via random Fourier surrogates + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +using Random: Xoshiro +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 1000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42), + ) + flags = significant_transitions(results, signif) + + ## and also plot the flags with same color + for (i, indicator) in enumerate(indicators) + ## To make things visually clear, we will also plot some example surrogate + ## timeseries for each indicator and change metric pair + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surromethod) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric[i], p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1) + end + ## Plot the flags as vertical dashed lines + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = color, linestyle = :dash, linewidth = 3 + ) + end + ## add a title to the figure with how we estimate significance + content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod))) +end + +surromethod = RandomFourier() +overplot_surrogate_significance!(fig, surromethod) + +fig + +# ## Different surrogates +# %% #src +# Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# highlighting the _local_ dynamics or information that preserves the local +# changes of dynamical behavior. + +# A surrogate type that does a better job in preserving local sharp +# changes in the timeseries (and hence provides **stricter** +# surrogate-based significance) is for example `RelativePartialRandomization`. + +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = RelativePartialRandomization(0.25) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "gray") +fig + +# Our results have improved. In the permutation entropy, we see only two +# transitions detected as significant, which is correct: only two +# real dynamical transitions exist in the data. +# In the other two indicators we also see fewer transitions, but as we +# have already discussed, no results with the other indicators should +# be taken into meaningful consideration, as these indicators +# are simply inappropriate for what we are looking for here. + +# ## Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be less strict and more simple with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`SigmaSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation. + +fig = plot_change_metrics() +flags = significant_transitions(results, SigmaSignificance(factor = 5.0)) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = Cycled(3), linestyle = :dash, linewidth = 3 + ) +end +content(fig[1, 1]).title = "significance from std" +fig diff --git a/dev/examples/logistic/1446887f.png b/dev/examples/logistic/1446887f.png new file mode 100644 index 00000000..e6de9658 Binary files /dev/null and b/dev/examples/logistic/1446887f.png differ diff --git a/dev/examples/logistic/32bfb484.png b/dev/examples/logistic/32bfb484.png new file mode 100644 index 00000000..245f2707 Binary files /dev/null and b/dev/examples/logistic/32bfb484.png differ diff --git a/dev/examples/logistic/79a77bed.png b/dev/examples/logistic/79a77bed.png new file mode 100644 index 00000000..89500998 Binary files /dev/null and b/dev/examples/logistic/79a77bed.png differ diff --git a/dev/examples/logistic/7dd3de76.png b/dev/examples/logistic/7dd3de76.png new file mode 100644 index 00000000..9c645e50 Binary files /dev/null and b/dev/examples/logistic/7dd3de76.png differ diff --git a/dev/examples/logistic/d61a7118.png b/dev/examples/logistic/d61a7118.png new file mode 100644 index 00000000..19742c79 Binary files /dev/null and b/dev/examples/logistic/d61a7118.png differ diff --git a/dev/examples/logistic/index.html b/dev/examples/logistic/index.html new file mode 100644 index 00000000..879cdfa9 --- /dev/null +++ b/dev/examples/logistic/index.html @@ -0,0 +1,128 @@ + +Permutation entropy for dynamic regime changes · TransitionsInTimeseries.jl
GitHub

Permutation entropy for dynamic regime changes

Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.

This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.

Logistic map timeseries

A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map

using DynamicalSystemsBase
+using CairoMakie
+
+# time-dependent logistic map, so that the `r` parameter increases with time
+r1 = 3.83
+r2 = 3.86
+N = 2000
+rs = range(r1, r2; length = N)
+
+function logistic_drifting_rule(u, rs, n)
+    r = rs[n+1] # time is `n`, starting from 0
+    return SVector(r*u[1]*(1 - u[1]))
+end
+
+ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)
+x = trajectory(ds, N-1)[1][:, 1]
2000-element Vector{Float64}:
+ 0.5
+ 0.9575
+ 0.15585767321160574
+ 0.5039019545917718
+ 0.9574529422362281
+ 0.15602441103002537
+ 0.5043473227583317
+ 0.9574501255597653
+ 0.1560361152301728
+ 0.5043840906474082
+ ⋮
+ 0.4253904015445437
+ 0.9434836074964187
+ 0.20581843730311683
+ 0.6309301050251992
+ 0.8988117342940414
+ 0.3510584545931264
+ 0.8793611090928393
+ 0.40948549063776396
+ 0.9333718681550522

Plot it, using as time the parameter value (they coincide)

fig, ax = lines(rs, x; linewidth = 0.5)
+ax.xlabel = "r (time)"
+ax.ylabel = "x"
+fig
Example block output

In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.

Using a simpler change metric

Now, let's compute various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.

using TransitionsInTimeseries, ComplexityMeasures
+
+function permutation_entropy(m)
+    est = SymbolicPermutation(; m) # order 3
+    indicator = x -> entropy_normalized(est, x)
+    return indicator
+end
+
+indicators = (var, ar1_whitenoise, permutation_entropy(4))
+indistrings = ("var", "ar1", "pe")
("var", "ar1", "pe")

In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width

metric = (difference_of_means, difference_of_means, difference_of_means)
+
+width_ind = N÷100
+width_cha = 20
+stride_cha = 10
+
+config = SlidingWindowConfig(indicators, metric;
+    width_ind, width_cha, stride_cha,
+)
+
+results = estimate_changes(config, x, rs)
SlidingWindowResults
+ input timeseries:              2000-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise, Symbol("#1")]
+ indicator (window, stride):    (20, 1)
+ change metrics:                [:difference_of_means, :difference_of_means, :difference_of_means]
+ change metric (window, stride): (20, 10)
+

Let's now plot the change metrics of the indicators

function plot_change_metrics()
+    fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (size = (600, 600),))
+    hidexdecorations!(ax; grid = false)
+    # plot all change metrics
+    for (i, c) in enumerate(eachcol(results.x_change))
+        ax, = scatterlines(fig[i+1, 1], results.t_change, c;
+            axis = (ylabel = indistrings[i],), label = "input"
+        )
+        if i < 3
+            hidexdecorations!(ax; grid = false)
+        else
+            ax.xlabel = "r (time)"
+        end
+    end
+    return fig
+end
+
+fig = plot_change_metrics()
Example block output

We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)

Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.

Significance via random Fourier surrogates

One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.

Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!

surromethod = RandomFourier()
+
+# Define a function because we will re-use later
+using Random: Xoshiro
+function overplot_surrogate_significance!(fig, surromethod, color = "black")
+
+    signif = SurrogatesSignificance(;
+        n = 1000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),
+    )
+    flags = significant_transitions(results, signif)
+
+    # and also plot the flags with same color
+    for (i, indicator) in enumerate(indicators)
+        # To make things visually clear, we will also plot some example surrogate
+        # timeseries for each indicator and change metric pair
+        for _ in 1:10
+            s = TimeseriesSurrogates.surrogate(x, surromethod)
+            p = windowmap(indicator, s; width = width_ind)
+            q = windowmap(metric[i], p; width = width_cha, stride = stride_cha)
+            lines!(fig[i+1, 1], results.t_change, q;  color = (color, 0.2), linewidth = 1)
+        end
+        # Plot the flags as vertical dashed lines
+        vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+            color = color, linestyle = :dash, linewidth = 3
+        )
+    end
+    # add a title to the figure with how we estimate significance
+    content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod)))
+end
+
+surromethod = RandomFourier()
+overplot_surrogate_significance!(fig, surromethod)
+
+fig
Example block output

Different surrogates

Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

surromethod = RelativePartialRandomization(0.25)
+fig = plot_change_metrics()
+overplot_surrogate_significance!(fig, surromethod, "gray")
+fig
Example block output

Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

Simpler Significance

Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

fig = plot_change_metrics()
+flags = significant_transitions(results, SigmaSignificance(factor = 5.0))
+
+# Plot the flags
+for (i, indicator) in enumerate(indicators)
+    vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+        color = Cycled(3), linestyle = :dash, linewidth = 3
+    )
+end
+content(fig[1, 1]).title = "significance from std"
+fig
Example block output
diff --git a/dev/index.html b/dev/index.html new file mode 100644 index 00000000..106d6ccf --- /dev/null +++ b/dev/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
GitHub

TransitionsInTimeseries.jl

TransitionsInTimeseries.jl

TransitionsInTimeseries — Module

TransitionsInTimeseries.jl

CI codecov Package Downloads

TransitionsInTimeseries.jl is a free and open-source software to easily analyse transitions within timeseries in a reproducible, performant, extensible and reliable way. In contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:

  1. Provide the analysis pipelines with new indicators, which can be either self-written or imported from other packages. In particular, the latter offers thousands of metrics that can indicate transitions right out of the box.
  2. Add new analysis pipelines for finding transitions.
  3. Add new ways for significance testing.

TransitionsInTimeseries is a registered Julia package and can be installed by running:

] add TransitionsInTimeseries

All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

source
Star us on GitHub!

If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

Content

Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

  • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
  • Makes the surrogate analysis to test for significance under the hub.
  • Can be easily extended by any user without touching the source code.
  • Reduces the programming overhead for any researcher willing to benchmark new methods.
  • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
  • Increases trustworthiness thanks to a large test suite.
Similar projects

An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

Approaches

Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

diff --git a/dev/objects.inv b/dev/objects.inv new file mode 100644 index 00000000..cb12258f Binary files /dev/null and b/dev/objects.inv differ diff --git a/dev/refs.bib b/dev/refs.bib new file mode 100644 index 00000000..8cc9690b --- /dev/null +++ b/dev/refs.bib @@ -0,0 +1,87 @@ + +@article{willeit-earth-2022, + title = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1: {Climate} model description and validation​​​​​​​​​​​​​​}, + volume = {15}, + issn = {1991-9603}, + shorttitle = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1}, + url = {https://gmd.copernicus.org/articles/15/5905/2022/}, + doi = {10.5194/gmd-15-5905-2022}, + abstract = {The newly developed fast Earth system model CLIMBER-X is presented. The climate component of CLIMBER-X consists of a 2.5-D semi-empirical statistical–dynamical atmosphere model, a 3-D frictional–geostrophic ocean model, a dynamic–thermodynamic sea ice model and a land surface model. All the model components are discretized on a regular lat–long grid with a horizontal resolution of 5 ◦ × 5 ◦. The model has a throughput of ∼ 10 000 simulation years per day on a single node with 16 CPUs on a high-performance computer and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to {\textgreater} 100 000 years. A comprehensive evaluation of the model performance for the present day and the historical period shows that CLIMBER-X is capable of realistically reproducing many observed climate characteristics, with results that generally lie within the range of state-of-theart general circulation models. The analysis of model performance is complemented by a thorough assessment of climate feedbacks and model sensitivities to changes in external forcings and boundary conditions. Limitations and applicability of the model are critically discussed. CLIMBER-X also includes a detailed representation of the global carbon cycle and is coupled to an ice sheet model, which will be described in separate papers. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.}, + language = {en}, + number = {14}, + urldate = {2022-08-11}, + journal = {Geoscientific Model Development}, + author = {Willeit, Matteo and Ganopolski, Andrey and Robinson, Alexander and Edwards, Neil R.}, + month = jul, + year = {2022}, + pages = {5905--5948}, + file = {Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:/home/jan/Zotero/storage/75NKS975/Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:application/pdf}, +} + +@article{boers-early-warning-2018, + title = {Early-warning signals for {Dansgaard}-{Oeschger} events in a high-resolution ice core record}, + volume = {9}, + issn = {2041-1723}, + url = {http://www.nature.com/articles/s41467-018-04881-7}, + doi = {10.1038/s41467-018-04881-7}, + language = {en}, + number = {1}, + urldate = {2022-10-28}, + journal = {Nature Communications}, + author = {Boers, Niklas}, + month = dec, + year = {2018}, + pages = {2556}, + file = {Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:/home/jan/Zotero/storage/DS97Z9UC/Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:application/pdf}, +} + +@article{rasmussen-stratigraphic-2014, + title = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records: refining and extending the {INTIMATE} event stratigraphy}, + volume = {106}, + issn = {02773791}, + shorttitle = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0277379114003485}, + doi = {10.1016/j.quascirev.2014.09.007}, + abstract = {Due to their outstanding resolution and well-constrained chronologies, Greenland ice-core records provide a master record of past climatic changes throughout the Last InterglacialeGlacial cycle in the North Atlantic region. As part of the INTIMATE (INTegration of Ice-core, MArine and TErrestrial records) project, protocols have been proposed to ensure consistent and robust correlation between different records of past climate. A key element of these protocols has been the formal definition and ordinal numbering of the sequence of Greenland Stadials (GS) and Greenland Interstadials (GI) within the most recent glacial period. The GS and GI periods are the Greenland expressions of the characteristic DansgaardeOeschger events that represent cold and warm phases of the North Atlantic region, respectively. We present here a more detailed and extended GS/GI template for the whole of the Last Glacial period. It is based on a synchronization of the NGRIP, GRIP, and GISP2 ice-core records that allows the parallel analysis of all three records on a common time scale. The boundaries of the GS and GI periods are defined based on a combination of stable-oxygen isotope ratios of the ice (d18O, reflecting mainly local temperature) and calcium ion concentrations (reflecting mainly atmospheric dust loading) measured in the ice. The data not only resolve the well-known sequence of DansgaardeOeschger events that were first defined and numbered in the ice-core records more than two decades ago, but also better resolve a number of short-lived climatic oscillations, some defined here for the first time. Using this revised scheme, we propose a consistent approach for discriminating and naming all the significant abrupt climatic events of the Last Glacial period that are represented in the Greenland ice records. The final product constitutes an extended and better resolved Greenland stratotype sequence, against which other proxy records can be compared and correlated. It also provides a more secure basis for investigating the dynamics and fundamental causes of these climatic perturbations.}, + language = {en}, + urldate = {2023-10-04}, + journal = {Quaternary Science Reviews}, + author = {Rasmussen, Sune O. and Bigler, Matthias and Blockley, Simon P. and Blunier, Thomas and Buchardt, Susanne L. and Clausen, Henrik B. and Cvijanovic, Ivana and Dahl-Jensen, Dorthe and Johnsen, Sigfus J. and Fischer, Hubertus and Gkinis, Vasileios and Guillevic, Myriam and Hoek, Wim Z. and Lowe, J. John and Pedro, Joel B. and Popp, Trevor and Seierstad, Inger K. and Steffensen, Jørgen Peder and Svensson, Anders M. and Vallelonga, Paul and Vinther, Bo M. and Walker, Mike J.C. and Wheatley, Joe J. and Winstrup, Mai}, + month = dec, + year = {2014}, + pages = {14--28}, + file = {Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:/home/jan/Zotero/storage/VSUTVWPN/Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:application/pdf}, +} + +@article{Bagniewski2023, +abstract = {Tipping points (TPs) in Earth's climate system have been the subject of increasing interest and concern in recent years, given the risk that anthropogenic forcing could cause abrupt, potentially irreversible, climate transitions. Paleoclimate records are essential for identifying past TPs and for gaining a thorough understanding of the underlying nonlinearities and bifurcation mechanisms. However, the quality, resolution, and reliability of these records can vary, making it important to carefully select the ones that provide the most accurate representation of past climates. Moreover, as paleoclimate time series vary in their origin, time spans, and periodicities, an objective, automated methodology is crucial for identifying and comparing TPs. To address these challenges, we introduce the open-source PaleoJump database, which contains a collection of carefully selected, high-resolution records originating in ice cores, marine sediments, speleothems, terrestrial records, and lake sediments. These records describe climate variability on centennial, millennial and longer time scales and cover all the continents and ocean basins. We provide an overview of their spatial distribution and discuss the gaps in coverage. Our statistical methodology includes an augmented Kolmogorov–Smirnov test and Recurrence Quantification Analysis; it is applied here, for illustration purposes, to selected records in which abrupt transitions are automatically detected and the presence of potential tipping elements is investigated. These transitions are shown in the PaleoJump database along with other essential information about the records, including location, temporal scale and resolution, as well as temporal plots. This open-source database represents, therefore, a valuable resource for researchers investigating TPs in past climates.}, +archivePrefix = {arXiv}, +arxivId = {2206.06832}, +author = {Bagniewski, Witold and Rousseau, Denis Didier and Ghil, Michael}, +doi = {10.1038/s41598-023-30592-1}, +eprint = {2206.06832}, +isbn = {0123456789}, +issn = {20452322}, +journal = {Scientific Reports}, +number = {1}, +pages = {1--18}, +pmid = {36934110}, +publisher = {Nature Publishing Group UK}, +title = {{The PaleoJump database for abrupt transitions in past climates}}, +url = {https://doi.org/10.1038/s41598-023-30592-1}, +volume = {13}, +year = {2023} +} +@article{Bagniewski2021, +abstract = {Bifurcations and tipping points (TPs) are an important part of the Earth system's behavior. These critical points represent thresholds at which small changes in the system's parameters or in the forcing abruptly switch it from one state or type of behavior to another. Current concern with TPs is largely due to the potential of slow anthropogenic forcing to bring about abrupt, and possibly irreversible, change to the physical climate system and impacted ecosystems. Paleoclimate proxy records have been shown to contain abrupt transitions, or "jumps,"which may represent former instances of such dramatic climate change events. These transitions can provide valuable information for identifying critical TPs in current and future climate evolution. Here, we present a robust methodology for detecting abrupt transitions in proxy records that is applied to ice core and speleothem records of the last climate cycle. This methodology is based on the nonparametric Kolmogorov-Smirnov (KS) test for the equality, or not, of the probability distributions associated with two samples drawn from a time series, before and after any potential jump. To improve the detection of abrupt transitions in proxy records, the KS test is augmented by several other criteria and it is compared with recurrence analysis. The augmented KS test results show substantial skill when compared with more subjective criteria for jump detection. This test can also usefully complement recurrence analysis and improve upon certain aspects of its results.}, +author = {Bagniewski, W. and Ghil, M. and Rousseau, D. D.}, +doi = {10.1063/5.0062543}, +issn = {10897682}, +journal = {Chaos}, +number = {11}, +pmid = {34881579}, +publisher = {AIP Publishing LLC}, +title = {{Automatic detection of abrupt transitions in paleoclimate records}}, +volume = {31}, +year = {2021} +} diff --git a/dev/refs/index.html b/dev/refs/index.html new file mode 100644 index 00000000..07e23643 --- /dev/null +++ b/dev/refs/index.html @@ -0,0 +1,2 @@ + +References · TransitionsInTimeseries.jl
GitHub

References

diff --git a/dev/search_index.js b/dev/search_index.js new file mode 100644 index 00000000..f9c39080 --- /dev/null +++ b/dev/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"EditURL = \"tutorial.jl\"","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any preprocessing of raw data first, such as detrending. This not part of TransitionsInTimeseries.jl and yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries. Alternatively, the change metric can be estimated over the whole segment, as examplified in the section Segmented windows.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector,\n# we obtain the last time step of each window.\n# This therefore only uses information from `k-width+1` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\n\nfunction gridfig(nrows, ncols)\n fig = Figure()\n axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)\n for j in 1:ncols, i in 1:nrows]\n rowgap!(fig.layout, 10)\n return fig, axs\nend\nfig, axs = gridfig(2, 1)\nlines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))\nlines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))\naxs[1].title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nlines!(axs[2], t_change, change_nl, label = \"nonlin\", color = Cycled(2))\nlines!(axs[2], t_change, change_s, label = \"surrogate\", color = Cycled(3))\naxislegend()\naxs[2].title = \"change metric\"\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig, axs = gridfig(2, 2)\naxs[1].title = \"linear\"\naxs[2].title = \"nonlinear\"\n\nfor (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change) # ; color = Cycled(j)\n lines!(axsig, t_change, pval) # ; color = Cycled(j+2)\nend\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a ChangesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"tutorial/#Sliding-windows","page":"Tutorial","title":"Sliding windows","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using estimate_changes.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope())\n\n# choices go into a configuration struct\nconfig = SlidingWindowConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last)\n\n# choices are processed\nresults = estimate_changes(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can conveniently plot the information contained in results by using plot_indicator_changes:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig = plot_indicator_changes(results)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesSignificance and the function significant_transitions. Finally, we can conveniently plot the results obtained by updating the figure obtained above with plot_significance!:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = [:right, :right])\nflags = significant_transitions(results, signif)\nplot_significance!(fig, results, signif, flags = flags)\nfig","category":"page"},{"location":"tutorial/#segmented_windows","page":"Tutorial","title":"Segmented windows","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The analysis shown so far relies on sliding windows of the change metric. This is particularly convenient for transition detection tasks. Segmented windows for the change metric computation are however preferable when it comes to prediction tasks. By only slightly modifying the syntax used so far, one can perform the same computations on segmented windows, as well as visualise the results conveniently:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"config = SegmentedWindowConfig(indicators, change_metrics,\n t[1:1], t[1200:1200]; whichtime = last, width_ind = 200,\n min_width_cha = 100)\nresults = estimate_changes(config, input, t)\nsignif = SurrogatesSignificance(n = 1000, tail = [:right, :right])\nflags = significant_transitions(results, signif)\nfig = plot_changes_significance(results, signif)","category":"page"},{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"estimate_changes\nChangesConfig\nChangesResults","category":"page"},{"location":"api/#TransitionsInTimeseries.estimate_changes","page":"API","title":"TransitionsInTimeseries.estimate_changes","text":"estimate_changes(config::ChangesConfig, x [,t]) → result\n\nEstimate possible transitions for input timeseries x using the approach specified in the configuration type config, see ChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).\n\nReturn the output as subtype of ChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.ChangesConfig","page":"API","title":"TransitionsInTimeseries.ChangesConfig","text":"ChangesConfig\n\nSupertype for how \"changes\" in a timeseries are estimated in estimate_changes. \"Changes\" deemed statistically significant in significant_transitions are \"transitions\" in the timeseries.\n\nExisting subtypes of ChangesConfig are:\n\nSlidingWindowConfig.\nSegmentedWindowConfig.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.ChangesResults","page":"API","title":"TransitionsInTimeseries.ChangesResults","text":"ChangesResults\n\nSupertype used to gather results of estimate_changes. The concrete subtype instances are described in the docstrings of configuration types.\n\n\n\n\n\n","category":"type"},{"location":"api/#Sliding-window","page":"API","title":"Sliding window","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"SlidingWindowConfig\nSlidingWindowResults","category":"page"},{"location":"api/#TransitionsInTimeseries.SlidingWindowConfig","page":"API","title":"TransitionsInTimeseries.SlidingWindowConfig","text":"SlidingWindowConfig <: ChangesConfig\nSlidingWindowConfig(indicators, change_metrics; kwargs...)\n\nA configuration that can be given to estimate_changes. It estimates transitions by a sliding window approach:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.\n\nindicators can be a single function or a tuple of indicators. Similarly, change_metrics can be a tuple or a single function. If tuples, the length of indicators and change_metrics must match. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nThe results output corresponding to SlidingWindowConfig is SlidingWindowResults.\n\nStep 1. is skipped if nothing is provided as indicators, in which case the change metrics are estimated directly from input data.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowResults","page":"API","title":"TransitionsInTimeseries.SlidingWindowResults","text":"SlidingWindowResults <: ChangesResults\n\nA struct containing the output of estimate_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nconfig::SlidingWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Segmented-window","page":"API","title":"Segmented window","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"SegmentedWindowConfig\nSegmentedWindowResults","category":"page"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowConfig","page":"API","title":"TransitionsInTimeseries.SegmentedWindowConfig","text":"SegmentedWindowConfig <: IndicatorsChangeConfig\nSegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)\n\nA configuration that can be given to estimate_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:\n\nFor each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).\nFor each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d\n\ntseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.\n\nThe results output corresponding to SlidingWindowConfig is SegmentedWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.\nmin_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowResults","page":"API","title":"TransitionsInTimeseries.SegmentedWindowResults","text":"SegmentedWindowResults <: ChangesResults\n\nA struct containing the output of estimate_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.\nt_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.\nx_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.\nt_change, the time vector of the change metric.\nconfig::SegmentedWindowConfig, what was used for the analysis.\ni1::Vector{Int} indices corresponding to start time of each segment.\ni2::Vector{Int} indices corresponding to end time of each segment.\nprecomp_change_metrics vector containing the precomputed change metrics of each segment.\n\n\n\n\n\n","category":"type"},{"location":"api/#Slope-change","page":"API","title":"Slope change","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"SlopeChangeConfig\nSlopeChangeResults","category":"page"},{"location":"api/#TransitionsInTimeseries.SlopeChangeConfig","page":"API","title":"TransitionsInTimeseries.SlopeChangeConfig","text":"SlopeChangeConfig <: ChangesConfig\nSlopeChangeConfig(; indicator = nothing, kw...)\n\nA configuration that can be given to estimate_changes. It estimates a change of slope in the timeseries by fitting two connected linear segments to the timeseries, returning the results (i.e., the two-linear fits) as SlopeChangeResults.\n\nKeyword arguments\n\nindicator = nothing: if not nothing. Otherwise it should be a function f(x) -> Real. The slope fitting is then done over an indicator of the timeseries, which itself is estimated via a sliding window exactly as in SlidingWindowConfig.\nwidth_ind, stride_ind, whichtime: exactly as in SlidingWindowConfig if indicator is not nothing.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlopeChangeResults","page":"API","title":"TransitionsInTimeseries.SlopeChangeResults","text":"SlopeChangeResults <: ChangesResults\n\nA struct containing the output of estimate_changes used with SlopeChangeConfig. It can be used for further analysis, visualization, or given to significant_transitions. The only significance type that you can use this with significant_transitions is SlopeChangeSignificance.\n\nIt has the following fields that the user may access:\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries.\nt_indicator, the time vector of the indicator timeseries.\nt_change, the time the slope changes.\nfitparams = a, b, c, d, the fitted linear coefficients, a + b*t before. t_change and c + d*t after t_change.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"significant_transitions\nSignificance\nSurrogatesSignificance\nThresholdSignificance\nSigmaSignificance\nQuantileSignificance\nSlopeChangeSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::ChangesResults, signif::Significance)\n\nEstimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as the changes stored in res (which typically is stored in the field res.x_change). flags is true wherever a change metric of res is deemed significant.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.Significance","page":"API","title":"TransitionsInTimeseries.Significance","text":"Significance\n\nSupertype used to test for significance in significant_transitions. Changes that are statistically significant are \"transitions\".\n\nValid subtypes are:\n\nSurrogatesSignificance.\nSigmaSignificance.\nQuantileSignificance.\nThresholdSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: Significance\nSurrogatesSignificance(; kwargs...)\n\nA configuration struct for significance testing significant_transitions using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\n\nDescription\n\nWhen used with ChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in ChangesResults.\n\nNote that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.ThresholdSignificance","page":"API","title":"TransitionsInTimeseries.ThresholdSignificance","text":"ThresholdSignificance(threshold::Real; tail = :right) <: Significance\n\nA configuration struct for significance testing in significant_transitions. Significance is estimated by comparing the value of each change metric with the given threshold. Values that exceed the threshold (if tail = :right) or subseed the threshold (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SigmaSignificance","page":"API","title":"TransitionsInTimeseries.SigmaSignificance","text":"SigmaSignificance(; factor = 3.0, tail = :both) <: Significance\n\nA configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing how many standard deviations (σ) the value exceeds the mean value (μ). Values that exceed (if tail = :right) μ + factor*σ, or subseed (if tail = :left) μ - factor*σ are deemed significant. If tail = :both then either condition is checked.\n\nfactor can also be a vector of values, in which case a different value is used for each change metric.\n\nSee also QuantileSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :both) <: Significance\n\nA configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\nQuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlopeChangeSignificance","page":"API","title":"TransitionsInTimeseries.SlopeChangeSignificance","text":"SlopeChangeSignificance(; moe_slope, moe_offset, slope_diff = moe_slope, pvalue = 0.05)\n\nTest whether the result of SlopeChangeResults is statistically significant.\n\nTwo tests are done:\n\nCheck whether the margin of error of the fitted parameters a, b, c, d of the two linear segments a + b*t, c + d*t is less than the specified margins of error, for a chosen pvalue.\nTest that the two slopes b, d have difference greater than slope_diff.\n\nThe Boolean & of the above two is the final test.\n\nThe margin of error is simply half the size of the confidence interval, also known as radius of the confidence interval.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Note that any Julia function can be an indicator or change metric, so the list here is only just a couple of indicators directly implemented in this package.","category":"page"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"StatsBase.mean\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean","page":"API","title":"Statistics.mean","text":"mean(A::AbstractArray, w::AbstractWeights[, dims::Int])\n\nCompute the weighted mean of array A with weight vector w (of type AbstractWeights). If dim is provided, compute the weighted mean along dimension dims.\n\nExamples\n\nn = 20\nx = rand(n)\nw = rand(n)\nmean(x, weights(w))\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"StatsBase.var\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var","page":"API","title":"Statistics.var","text":"var(x::AbstractArray, w::AbstractWeights, [dim]; mean=nothing, corrected=false)\n\nCompute the variance of a real-valued array x, optionally over a dimension dim. Observations in x are weighted using weight vector w. The uncorrected (when corrected=false) sample variance is defined as:\n\nfrac1sumw sum_i=1^n w_ileft(x_i - μright)^2 \n\nwhere n is the length of the input and μ is the mean. The unbiased estimate (when corrected=true) of the population variance is computed by replacing frac1sumw with a factor dependent on the type of weights used:\n\nAnalyticWeights: frac1sum w - sum w^2 sum w\nFrequencyWeights: frac1sumw - 1\nProbabilityWeights: fracn(n - 1) sum w where n equals count(!iszero, w)\nWeights: ArgumentError (bias correction not supported)\n\n\n\n\n\nvar(ce::CovarianceEstimator, x::AbstractVector; mean=nothing)\n\nCompute the variance of the vector x using the estimator ce.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum\nPrecomputedLowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.PrecomputedLowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.PrecomputedLowfreqPowerSpectrum","text":"PrecomputedLowfreqPowerSpectrum\n\nA struct containing all the precomputed fields to efficiently perform repetitive computation of the low-frequency power spectrum (LFPS), a number between 0 and 1 that characterizes the amount of power contained in the low frequencies of the power density spectrum of x. Once lfps::PrecomputedLowfreqPowerSpectrum is initialized, it can be used as a function to obtain the LFPS of x::AbstractVector by:\n\nlfps(x)\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.","category":"page"},{"location":"api/","page":"API","title":"API","text":"For example, using the permutation entropy as an indicator is as simple as doing","category":"page"},{"location":"api/","page":"API","title":"API","text":"using ComplexityMeasures\nest = OrdinalPatterns(; m = 3) # order 3\n# create a function that given timeseries returns permutation entropy\nindicator = x -> entropy_normalized(est, x)","category":"page"},{"location":"api/","page":"API","title":"API","text":"and giving the created indicator to e.g., SlidingWindowConfig.","category":"page"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope\nPrecomputedRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.PrecomputedRidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.PrecomputedRidgeRegressionSlope","text":"PrecomputedRidgeRegressionSlope\n\nA struct containing the precomputed ridge regression matrix. Once rrslope::PrecomputedRidgeRegressionSlope is initialized, it can be used as a function to obtain the ridge regression slope of x::AbstractVector by applying:\n\nrrslope(x)\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.precompute","page":"API","title":"TransitionsInTimeseries.precompute","text":"precompute(f, t)\n\nPrecompute the function f given a time vector t.\n\n\n\n\n\n","category":"function"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are respectively taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"api/#Visualization","page":"API","title":"Visualization","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"plot_indicator_changes\nplot_significance!\nplot_changes_significance","category":"page"},{"location":"api/#TransitionsInTimeseries.plot_indicator_changes","page":"API","title":"TransitionsInTimeseries.plot_indicator_changes","text":"plot_indicator_changes(res) → (fig, axs)\n\nReturn fig::Figure and axs::Matrix{Axis}, on which res::ChangesResults has been visualised.\n\nKeyword arguments:\n\ncolors = default_colors sets the colors of the line plots that are to\n\nbe cycled through. The default correspond to the color scheme of Julia Dynamics.\n\n`indicatornames = defaultindicatorlabel(res), chametricnames =\n\ndefaultchametriclabel(res)sets the labels for the indicators and the change metrics, with the default inferring them from the names ofres.config.indicatorsandres.config.change_metrics`.\n\naccent_linewidth = 3 sets the line width for the original signals (the\n\nsurrogates have linewidth = 1)\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.plot_significance!","page":"API","title":"TransitionsInTimeseries.plot_significance!","text":"plot_significance!(axs, res, signif)\n\nUpdate the axs::Matrix{Axis} of a figure obtained with plot_indicator_changes(res) with the signif::SurrogatesSignificance.\n\nKeyword arguments:\n\nflags = nothing provides the significance flags, for instance obtained by\n\nthresholding the pvalues.\n\nnsurro = 20 sets the number of surrogates to plot.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.plot_changes_significance","page":"API","title":"TransitionsInTimeseries.plot_changes_significance","text":"plot_changes_significance(res, signif) → (fig, axs)\n\nReturn fig::Figure and axs::Matrix{Axis}, on which res::ChangesResults and signif::SurrogatesSignificance have been visualised. The source code is as simple as:\n\nfig, axs = plot_indicator_changes(res; kwargs...)\nplot_significance!(axs, res, signif; kwargs...)\n\nFor more information, refer to plot_indicator_changes and plot_significance!.\n\n\n\n\n\n","category":"function"},{"location":"api/#Utils","page":"API","title":"Utils","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"default_window_width","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"EditURL = \"do-events.jl\"","category":"page"},{"location":"examples/do-events/#Dansgaard-Oescher-events-and-Critical-Slowing-Down","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The delta^18O timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.","category":"page"},{"location":"examples/do-events/#Preprocessing-NGRIP","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Preprocessing NGRIP","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Load the data, reverse and offset it to have time vector = time before 2000 AD.\nFilter non-unique points in time and sort the data.\nRegrid the data from uneven to even sampling.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The time and delta^18O vectors resulting from the i-th preprocessing step are respectively called t_i and x_i. The final step consists in obtaining a residual r, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.","category":"page"},{"location":"examples/do-events/#Step-1:","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 1:","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DelimitedFiles, Downloads\n\nfunction load_ngrip()\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP.csv\")\n data, labels = readdlm(tmp, header = true)\n return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors\nend\n\nt1, x1 = load_ngrip()","category":"page"},{"location":"examples/do-events/#Step-2","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 2","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"uniqueidx(v) = unique(i -> v[i], eachindex(v))\nfunction keep_unique(t, x)\n unique_idx = uniqueidx(t)\n return t[unique_idx], x[unique_idx]\nend\n\nfunction sort_timeseries!(t, x)\n p = sortperm(t)\n permute!(t, p)\n permute!(x, p)\n return nothing\nend\n\nt2, x2 = keep_unique(t1, x1)\nsort_timeseries!(t2, x2)","category":"page"},{"location":"examples/do-events/#Step-3","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 3","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using BSplineKit\n\nfunction regrid2evensampling(t, x, dt)\n itp = BSplineKit.interpolate(t, x, BSplineOrder(4))\n tspan = (ceil(minimum(t)), floor(maximum(t)))\n t_even = collect(tspan[1]:dt:tspan[2])\n x_even = itp.(t_even)\n return t_even, x_even\nend\n\ndt = 5.0 # dt = 5 yr as in (Boers 2018)\nt3, x3 = regrid2evensampling(t2, x2, dt)","category":"page"},{"location":"examples/do-events/#Step-4","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 4","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the final step we drop the indices:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DSP\n\nfunction chebyshev_filter(t, x, fcutoff)\n ii = 10 # Chebyshev filtering requires to prune first points of timeseries.\n responsetype = Highpass(fcutoff, fs = 1/dt)\n designmethod = Chebyshev1(8, 0.05)\n r = filt(digitalfilter(responsetype, designmethod), x)\n xtrend = x - r\n return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]\nend\n\nfcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)\nt, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using CairoMakie, Loess\n\nfunction loess_filter(t, x; span = 0.005)\n loessmodel = loess(t, x, span = span)\n xtrend = Loess.predict(loessmodel, t)\n r = x - xtrend\n return t, x, xtrend, r\nend\n\nfunction kyr_xticks(tticks_yr)\n tticks_kyr = [\"$t\" for t in Int.(tticks_yr ./ 1e3)]\n return (tticks_yr, tticks_kyr)\nend\n\nfunction plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)\n fig = Figure(size = (1600, 1200), fontsize = 24)\n\n # Original timeseries with transition marked by vertical lines\n ax1 = Axis(fig[1, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"$\\delta^{18}$O (permil)\",\n xaxisposition = :top, xticks = xticks)\n lines!(ax1, traw, xraw, color = (:gray70, 0.5))\n lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)\n vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)\n\n # Residual timeseries\n ax2 = Axis(fig[2, 1], ylabel = L\"Residual $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n lines!(ax2, t, r, color = :gray50, linewidth = 1)\n\n # Axes for variance and AC1 timeseries\n ax3 = Axis(fig[3, 1], ylabel = L\"Variance $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n ax4 = Axis(fig[4, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"Lag-1 autocor. $\\,$\",\n xticks = xticks)\n\n axs = [ax1, ax2, ax3, ax4]\n [xlims!(ax, xlims) for ax in axs]\n ylims!(axs[1], (-48, -34))\n rowgap!(fig.layout, 10)\n return fig, axs\nend\n\nxlims = (-60e3, -10e3)\nxticks = kyr_xticks(-60e3:5e3:5e3)\nt_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,\n 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]\ntloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nfig","category":"page"},{"location":"examples/do-events/#Hindcast-on-NGRIP-data","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcast on NGRIP data","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using TransitionsInTimeseries, StatsBase\nusing Random: Xoshiro\n\nac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase\nindicators = (var, ac1)\nchange_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope())\ntseg_start = t_rasmussen[1:end-1] .+ 200\ntseg_end = t_rasmussen[2:end] .- 200\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100) # require >=100 data points to estimate change metric\nresults = estimate_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"That's it! We can now visualise our results with a generic function that we will re-use later:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"function plot_segment_analysis!(axs, results, signif)\n (; t_indicator, x_indicator) = results\n for k in eachindex(t_indicator) # loop over the segments\n for i in axes(signif.pvalues, 2) # loop over the indicators\n if !isnan(signif.pvalues[k, i]) # plot if segment long enough\n # Plot indicator timeseries and its linear regression\n ti, xi = t_indicator[k], x_indicator[k][:, i]\n lines!(axs[i+2], ti, xi, color = Cycled(1))\n m, p = ridgematrix(ti, 0.0) * xi\n if signif.pvalues[k, i] < 0.05\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)\n else\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)\n end\n end\n end\n end\nend\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are desirable for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.","category":"page"},{"location":"examples/do-events/#CSD:-only-a-necessary-condition,-only-in-some-cases","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"CSD: only a necessary condition, only in some cases","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential U, which defines the deterministic term f = -U of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100)\nresults = estimate_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that \"resilience-loss indicators\" is a more accurate name than \"early-warning signals\" when using CSD.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"We draw attention upon the fact that the delta^18O timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"warning: Degrees of freedom\nThese sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"info: Future improvement\nSupporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.","category":"page"},{"location":"examples/do-events/#Hindcasting-simulated-DO-events","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcasting simulated DO-events","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],\n [1, 3500, 4370, 5790, 7200, 8140]]\nt_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]\ntseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]\ntseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]\n\nfigvec = Figure[]\n\nfor j in 1:2\n # Download the data and perform loess filtering on it\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\" *\n \"master/timeseries/climberx-do$(j)-omaxa.csv\")\n data = readdlm(tmp)\n tcx, xcx = data[1, 1000:end], data[2, 1000:end]\n t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)\n\n # Initialize figure\n xlims = (0, last(tcx))\n xticks = kyr_xticks(xlims[1]:1e3:xlims[2])\n fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks)\n ylims!(axs[1], (5, 40))\n axs[1].ylabel = L\"Max. Atlantic overturning (Sv) $\\,$\"\n\n # Run sliding analysis and update figure with results\n dt = mean(diff(tcx))\n config = SegmentedWindowConfig(\n indicators, change_metrics, tseg_start[j], tseg_end[j],\n whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)\n results = estimate_changes(config, r, t)\n signif = SurrogatesSignificance(n = 1_000, tail = [:right, :right], rng = Xoshiro(1995))\n flags = significant_transitions(results, signif)\n\n plot_segment_analysis!(axs, results, signif)\n vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)\n push!(figvec, fig)\nend\nfigvec[1]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"figvec[2]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"EditURL = \"ks_paleojump.jl\"","category":"page"},{"location":"examples/ks_paleojump/#Kolmogorov-Smirnov-test-for-detecting-transitions-in-paleoclimate-timeseries","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"The goal of this example is to show how simple it is to re-create an analysis similar to what was done in the paper \"Automatic detection of abrupt transitions in paleoclimate records\", (Bagniewski et al., 2021). The same analysis was then used to create a database of transitions in paleoclimate records in (Bagniewski et al., 2023) Using TransitionsInTimeseries.jl and HypothesisTests.jl, the analysis becomes a 10-lines-of-code script (for a given timeseries).","category":"page"},{"location":"examples/ks_paleojump/#Scientific-background","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Scientific background","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"The approach of (Bagniewski et al., 2021) is based on the two-sample Kolmogorov Smirnov test. It tests whether the samples from two datasets or timeseries are distributed according to the same cumulative density function or not. This can be estimated by comparing the value of the KS-statistic versus some threshold that depends on the required confidence.","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"The application of this test for identifying transitions in timeseries is simple:","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"A sliding window analysis is performed in the timesries\nIn each window, the KS statistic is estimated between the first half and the second half of the timeseries within this window.\nTransitions are defined by when the KS statistic exceeds a particular value based on some confidence. The transition occurs in the middle of the window.","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"We should point out that in (Bagniewski et al., 2021) the authors did a more detailed analysis: analyzed many different window widths, added a conditional clause to exclude transitions that do not exceed a predefined minimum \"jump\" in the data, and also added another conditional clause that filtered out transitions that are grouped in time (which is a natural consequence of using the Kolmogorov-Smirov test for detecting transitions).","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"Here we won't do that post processing, mainly because it is rather simple to include these additional conditional clauses to filter transitions after they are found.","category":"page"},{"location":"examples/ks_paleojump/#Steps-for-TransitionsInTimeseries.jl","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Steps for TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"Doing this kind of work with TransitionsInTimeseries.jl is so easy you won't even trip! This analysis follows the same sliding window approach showcased in our Tutorial, and it even excludes the \"indicator\" aspect: the change metric is estimated directly from the input data!","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"As such, we really only need to define/do these things before we have finished the analysis:","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"Load the input data (we will use the same example as the NGRIP data of Dansgaard-Oescher events and Critical Slowing Down example) and set the appropriate time window.\nDefine the function that estimates the change metric (i.e., the KS-statistic)\nPerform the sliding window analysis as in the Tutorial with estimate_changes\nEstimate the \"confident\" transitions in the data by comparing the estimated KS-statistic with a predefined threshold.","category":"page"},{"location":"examples/ks_paleojump/#Load-timeseries-and-window-length","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Load timeseries and window length","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"Following the Dansgaard-Oescher events example, we load the data after all the processing steps done in that example:","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"using DelimitedFiles, CairoMakie\n\ntmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP_processed.csv\")\ndata = readdlm(tmp)\nt, xtrend, xresid, xloess = collect.(eachcol(data))\n\nfig, ax = lines(t, xtrend; axis = (ylabel = \"NGRIP (processed)\", xlabel = \"time\"))\nlines!(ax, t, xloess; linewidth = 2)\nfig","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"For the window, since we are using a sliding window here, we will be using a window of length 500 (which is approximately 1/2 to 1/4 the span between typical transitions found by (Rasmussen et al., 2014)).","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"window = 500","category":"page"},{"location":"examples/ks_paleojump/#Defining-the-change-metric-function","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Defining the change metric function","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"HypothesisTest.jl implements the Kolmogorov-Smirnov test, however here we are interested in the value of the test iself (the so-called KS-statistic), rather than a p-value. To this end, we define the following function to compute the statistic, which also normalizes it as in (Bagniewski et al., 2021).","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"using HypothesisTests\n\nfunction normalized_KS_statistic(timeseries)\n N = length(timeseries)\n i = N÷2\n x = view(timeseries, 1:i)\n y = view(timeseries, (i+1):N)\n kstest = ApproximateTwoSampleKSTest(x, y)\n nx = ny = i # length of each timeseries half of total\n n = nx*ny/(nx + ny) # written fully for concreteness\n D_KS = kstest.δ # can be compared directly with sqrt(-log(α/2)/2)\n # Rescale according to eq. (5) of the paper\n rescaled = 1 - ((1 - D_KS)/(1 - sqrt(1/n)))\n return rescaled\nend\n\nN = 1000 # the statistic is independent of `N` for large enough `N`!\nx = randn(N)\ny = 1.8randn(N) .+ 1.0\nz = randn(N)\nw = 0.6randn(N) .- 2.0\n\nfig, ax = density(x; color = (\"black\", 0.5), strokewidth = 4.0, label = \"reference distribution\")\nax.title = \"showcase of normalized KS-statistic\"\nfor q in (y, z, w)\n D_KS = normalized_KS_statistic(vcat(x, q))\n density!(ax, q; label = \"D_KS = $(D_KS)\")\nend\naxislegend(ax)\nfig","category":"page"},{"location":"examples/ks_paleojump/#Perform-the-sliding-window-analysis","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Perform the sliding window analysis","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"This is just a straightforward call to estimate_changes. In fact, it is even simpler than the tutorial. Here we skip completely the \"indicator\" estimation step, and we evaluate the change metric directly on input data. We do this by simply passing nothing as the indicators.","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"using TransitionsInTimeseries\n\nconfig = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 500)\n\nresults = estimate_changes(config, xtrend, t)","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"Which we can visualize","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"function visualize_results(results)\n fig, ax1 = lines(t, xtrend; axis = (ylabel = \"NGRIP (processed)\",))\n ax2, = lines(fig[2, 1], results.t_change, vec(results.x_change), axis = (ylabel = \"D_KS (normalized)\", xlabel = \"time\"))\n linkxaxes!(ax1, ax2)\n hidexdecorations!(ax1; grid = false)\n xloess_normed = (xloess .- minimum(xloess))./(maximum(xloess) - minimum(xloess))\n lines!(ax2, t, xloess_normed; color = (\"gray\", 0.5))\n fig\nend\n\nvisualize_results(results)","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"By overplotting the (smoothened) NGRIP timeseries and the normalized KS-statistic, it already becomes pretty clear that the statistic peaks when transitions occur.","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"The same thing happens if we alter the window duration","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 200)\nresults = estimate_changes(config, xtrend, t)\nvisualize_results(results)","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"So one can easily obtain extra confidence by varying window size as in (Bagniewski et al., 2021).","category":"page"},{"location":"examples/ks_paleojump/#Identifying-\"confident\"-transitions","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Identifying \"confident\" transitions","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"As this identification here is done via a simple threshold, identifying the transitions is a nearly trivial call to significant_transitions with ThresholdSignificance","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"signif = ThresholdSignificance(0.5) # or any other threshold\nflags = significant_transitions(results, signif)\n\nfig = visualize_results(results)\naxDKS = content(fig[2,1])\nvlines!(axDKS, results.t_change[vec(flags)], color = (\"red\", 0.25))\nfig","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"We could proceed with a lot of preprocessing as in (Bagniewski et al., 2021) but we skip this here for the sake of simplicity.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"EditURL = \"logistic.jl\"","category":"page"},{"location":"examples/logistic/#Permutation-entropy-for-dynamic-regime-changes","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.","category":"page"},{"location":"examples/logistic/#Logistic-map-timeseries","page":"Permutation entropy for dynamic regime changes","title":"Logistic map timeseries","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using DynamicalSystemsBase\nusing CairoMakie\n\n# time-dependent logistic map, so that the `r` parameter increases with time\nr1 = 3.83\nr2 = 3.86\nN = 2000\nrs = range(r1, r2; length = N)\n\nfunction logistic_drifting_rule(u, rs, n)\n r = rs[n+1] # time is `n`, starting from 0\n return SVector(r*u[1]*(1 - u[1]))\nend\n\nds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)\nx = trajectory(ds, N-1)[1][:, 1]","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Plot it, using as time the parameter value (they coincide)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig, ax = lines(rs, x; linewidth = 0.5)\nax.xlabel = \"r (time)\"\nax.ylabel = \"x\"\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.","category":"page"},{"location":"examples/logistic/#Using-a-simpler-change-metric","page":"Permutation entropy for dynamic regime changes","title":"Using a simpler change metric","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Now, let's compute various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using TransitionsInTimeseries, ComplexityMeasures\n\nfunction permutation_entropy(m)\n est = SymbolicPermutation(; m) # order 3\n indicator = x -> entropy_normalized(est, x)\n return indicator\nend\n\nindicators = (var, ar1_whitenoise, permutation_entropy(4))\nindistrings = (\"var\", \"ar1\", \"pe\")","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"metric = (difference_of_means, difference_of_means, difference_of_means)\n\nwidth_ind = N÷100\nwidth_cha = 20\nstride_cha = 10\n\nconfig = SlidingWindowConfig(indicators, metric;\n width_ind, width_cha, stride_cha,\n)\n\nresults = estimate_changes(config, x, rs)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's now plot the change metrics of the indicators","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"function plot_change_metrics()\n fig, ax = lines(rs, x; axis = (ylabel = \"input\",), figure = (size = (600, 600),))\n hidexdecorations!(ax; grid = false)\n # plot all change metrics\n for (i, c) in enumerate(eachcol(results.x_change))\n ax, = scatterlines(fig[i+1, 1], results.t_change, c;\n axis = (ylabel = indistrings[i],), label = \"input\"\n )\n if i < 3\n hidexdecorations!(ax; grid = false)\n else\n ax.xlabel = \"r (time)\"\n end\n end\n return fig\nend\n\nfig = plot_change_metrics()","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.","category":"page"},{"location":"examples/logistic/#Significance-via-random-Fourier-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Significance via random Fourier surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RandomFourier()\n\n# Define a function because we will re-use later\nusing Random: Xoshiro\nfunction overplot_surrogate_significance!(fig, surromethod, color = \"black\")\n\n signif = SurrogatesSignificance(;\n n = 1000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),\n )\n flags = significant_transitions(results, signif)\n\n # and also plot the flags with same color\n for (i, indicator) in enumerate(indicators)\n # To make things visually clear, we will also plot some example surrogate\n # timeseries for each indicator and change metric pair\n for _ in 1:10\n s = TimeseriesSurrogates.surrogate(x, surromethod)\n p = windowmap(indicator, s; width = width_ind)\n q = windowmap(metric[i], p; width = width_cha, stride = stride_cha)\n lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1)\n end\n # Plot the flags as vertical dashed lines\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = color, linestyle = :dash, linewidth = 3\n )\n end\n # add a title to the figure with how we estimate significance\n content(fig[1, 1]).title = \"surrogates: \"*string(nameof(typeof(surromethod)))\nend\n\nsurromethod = RandomFourier()\noverplot_surrogate_significance!(fig, surromethod)\n\nfig","category":"page"},{"location":"examples/logistic/#Different-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Different surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RelativePartialRandomization(0.25)\nfig = plot_change_metrics()\noverplot_surrogate_significance!(fig, surromethod, \"gray\")\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.","category":"page"},{"location":"examples/logistic/#Simpler-Significance","page":"Permutation entropy for dynamic regime changes","title":"Simpler Significance","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig = plot_change_metrics()\nflags = significant_transitions(results, SigmaSignificance(factor = 5.0))\n\n# Plot the flags\nfor (i, indicator) in enumerate(indicators)\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = Cycled(3), linestyle = :dash, linewidth = 3\n )\nend\ncontent(fig[1, 1]).title = \"significance from std\"\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nTransitionsInTimeseries.jl is a free and open-source software to easily analyse transitions within timeseries in a reproducible, performant, extensible and reliable way. In contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:\n\nProvide the analysis pipelines with new indicators, which can be either self-written or imported from other packages. In particular, the latter offers thousands of metrics that can indicate transitions right out of the box.\nAdd new analysis pipelines for finding transitions.\nAdd new ways for significance testing.\n\nTransitionsInTimeseries is a registered Julia package and can be installed by running:\n\n] add TransitionsInTimeseries\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\nAlternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"devdocs/#Developer's-documentation","page":"Developer's documentation","title":"Developer's documentation","text":"","category":"section"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"This documentation addresses users that would like to contribute to the software by either solving bugs, improving documentation, or adding new methods. All contributions come in the form of Pull Requests, for which we strongly advise to follow good practices in scientific code, which means that they are properly formatted, documented, tested, etc.","category":"page"},{"location":"devdocs/#New-indicators-or-change-metrics","page":"Developer's documentation","title":"New indicators or change metrics","text":"","category":"section"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"As explained already in e.g., SlidingWindowConfig, new indicators or change metrics are standard Julia functions, so you only need to define such a function (and document it, test it, etc.).","category":"page"},{"location":"devdocs/#New-pipeline-for-estimating-changes","page":"Developer's documentation","title":"New pipeline for estimating changes","text":"","category":"section"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"This means to contribute a fundamentally new \"pipeline\" for estimating/detecting transitions in timeseries. This new pipeline defines what a \"transition\" means. To add a new pipeline follow these steps:","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"Define a new subtype of ChangesConfig\nDefine a new subtype of ChangesResults\nAdd a method for estimate_changes which accepts the new ChangesConfig subtype you defined and returns the ChangesResults subtype you defined.","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"And that's it!","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"Optionally you can further extend:","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"TransitionsInTimeseries.plot_indicator_changes with the new ChangesResults type you defined. Note the plotting functions are in the ext folder of the repository.\nsignificant_transitions(res::ChangesResults, signif::Significance) with your new ChangesResults type and as many Significance subtypes you have the capacity to extend for.","category":"page"},{"location":"devdocs/#New-pipeline-for-estimating-significance","page":"Developer's documentation","title":"New pipeline for estimating significance","text":"","category":"section"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"Statistically significant changes are \"transitions\". However, what \"significant\" means is not universal. There are different ways to test for significance and TransitionsInTimeseries.jl allows various methods.","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"To add a new pipeline for estimating significance follow these steps:","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"Define a new subtype of Significance\nExtend significant_transitions(res::ChangesResults, signif::Significance) with your new type and as many ChangesResults subtypes as you have capacity for.","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"And that's it! Unfortunately so far we have found no way to make the significant_transitions code agnostic of the changes result, so you would need to add a method manually for every ChangesResults.","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"Optionally you can further extend TransitionsInTimeseries.plot_significance! (which you can find in the ext folder) for visualizing the significance results.","category":"page"},{"location":"refs/#References","page":"References","title":"References","text":"","category":"section"},{"location":"refs/","page":"References","title":"References","text":"Bagniewski, W.; Ghil, M. and Rousseau, D. D. (2021). Automatic detection of abrupt transitions in paleoclimate records. Chaos 31.\n\n\n\nBagniewski, W.; Rousseau, D. D. and Ghil, M. (2023). The PaleoJump database for abrupt transitions in past climates. Scientific Reports 13, 1–18, arXiv:2206.06832.\n\n\n\nBoers, N. (2018). Early-warning signals for Dansgaard-Oeschger events in a high-resolution ice core record. Nature Communications 9, 2556. Accessed on Oct 28, 2022.\n\n\n\nRasmussen, S. O.; Bigler, M.; Blockley, S. P.; Blunier, T.; Buchardt, S. L.; Clausen, H. B.; Cvijanovic, I.; Dahl-Jensen, D.; Johnsen, S. J.; Fischer, H.; Gkinis, V.; Guillevic, M.; Hoek, W. Z.; Lowe, J. J.; Pedro, J. B.; Popp, T.; Seierstad, I. K.; Steffensen, J. P.; Svensson, A. M.; Vallelonga, P.; Vinther, B. M.; Walker, M. J.; Wheatley, J. J. and Winstrup, M. (2014). A stratigraphic framework for abrupt climatic changes during the Last Glacial period based on three synchronized Greenland ice-core records: refining and extending the INTIMATE event stratigraphy. Quaternary Science Reviews 106, 14–28. Accessed on Oct 4, 2023.\n\n\n\nWilleit, M.; Ganopolski, A.; Robinson, A. and Edwards, N. R. (2022). The Earth system model CLIMBER-X v1.0 – Part 1: Climate model description and validation​​​​​​​​​​​​​​. Geoscientific Model Development 15, 5905–5948. Accessed on Aug 11, 2022.\n\n\n\n","category":"page"}] +} diff --git a/dev/siteinfo.js b/dev/siteinfo.js new file mode 100644 index 00000000..33434919 --- /dev/null +++ b/dev/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "dev"; diff --git a/dev/tutorial.jl b/dev/tutorial.jl new file mode 100644 index 00000000..25a60a91 --- /dev/null +++ b/dev/tutorial.jl @@ -0,0 +1,263 @@ +#= + +# Tutorial + +## [Workflow] (@id workflow) + +Computing transition indicators consists of the following steps: + +1. Doing any preprocessing of raw data first, such as detrending. _This not part of TransitionsInTimeseries.jl_ and yields the **input timeseries**. +2. Estimating the timeseries of an indicator by sliding a window over the input timeseries. +3. Computing the changes of the indicator by sliding a window over its timeseries. Alternatively, the change metric can be estimated over the whole segment, as examplified in the section [Segmented windows](@ref segmented_windows). +4. Generating many surrogates that preserve important statistical properties of the original timeseries. +5. Performing step 2 and 3 for the surrogate timeseries. +6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data. + +These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports. + +## [Tutorial -- Educational] (@id example_stepbystep) + +### Raw input data + +Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by: + +```math +\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t) +``` + +with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with [Makie](https://docs.makie.org/stable/)) such prototypical data to test some indicators can be done by simply running: +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_linear) +lines!(ax, t, x_nlinear) +ax.title = "raw data" +fig + +#= +### Preprocessing + +!!! note "Not part of TransitionsInTimeseries.jl" + Any timeseries preprocessing, such as the de-trending step we do here, + is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher. + + +The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1. +=# + +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +#= +At this point, `x_l_fluct` and `x_nl_fluct` are considered the **input timeseries**. + +!!! info "Detrending in Julia" + Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as [Loess.jl](https://github.com/JuliaStats/Loess.jl) or [DSP.jl](https://docs.juliadsp.org/latest/contents/). There the detrending step consists of subtracting the smoothed signal from the original one. + +### Indicator timeseries + +We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the **input timeseries**, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as [`ar1_whitenoise`](@ref): +=# + +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +## By mapping `last::Function` over a windowviewer of the time vector, +## we obtain the last time step of each window. +## This therefore only uses information from `k-width+1` to `k` at time step `k`. +## Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +#= +The lines plotted above are the **indicator timeseries**. + +### Change metric timeseries + +From here, we process the **indicator timeseries** to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the **change metric timeseries**. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a [`RidgeRegressionSlope`](@ref): +=# + +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + +#= +### Timeseries surrogates + +As expected from [Critical Slowing Down](@ref approaches), an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance. + +In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the [TimeseriesSurrogates.jl](https://github.com/JuliaDynamics/TimeseriesSurrogates.jl) Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that `TimeseriesSurrogates` is re-exported by `TransitionsInTimeseries`, so that you don't have to `using` both of them. + +To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries. +=# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) + +function gridfig(nrows, ncols) + fig = Figure() + axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false) + for j in 1:ncols, i in 1:nrows] + rowgap!(fig.layout, 10) + return fig, axs +end +fig, axs = gridfig(2, 1) +lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2)) +lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3)) +axs[1].title = "real signal vs. surrogate(s)" + +## compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2)) +lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3)) +axislegend() +axs[2].title = "change metric" + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +### Quantifying significance + +To quantify the significance of the values of the **change metric timeseries** we perform a standard surrogate test by computing the [p-value](https://en.wikipedia.org/wiki/P-value) w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically `p<0.05`) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time: +=# + +n_surrogates = 1_000 +fig, axs = gridfig(2, 2) +axs[1].title = "linear" +axs[2].title = "nonlinear" + +for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + ## Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change) # ; color = Cycled(j) + lines!(axsig, t_change, pval) # ; color = Cycled(j+2) +end + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar. + +Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section. + +## [Tutorial -- TransitionsInTimeseries.jl] (@id example_fastforward) + +TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go. + +The interface is simple, and directly parallelizes the [Workflow](@ref workflow). It is based on the creation of a [`ChangesConfig`](@ref), which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate. + +### Sliding windows + +The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +## input timeseries and time +input = x_nl_fluct = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(t, input) +ax.title = "input timeseries" +fig + +#= +To perform all of the above analysis we follow a 2-step process. + +Step 1, we decide what indicators and change metrics to use in [`SlidingWindowConfig`](@ref) and apply those via +a sliding window to the input timeseries using [`estimate_changes`](@ref). +=# + +## These indicators are suitable for Critical Slowing Down +indicators = (var, ar1_whitenoise) + +## use the ridge regression slope for both indicators +change_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope()) + +## choices go into a configuration struct +config = SlidingWindowConfig(indicators, change_metrics; + width_ind = 400, width_cha = 30, whichtime = last) + +## choices are processed +results = estimate_changes(config, input, t) + +#= +We can conveniently plot the information contained in `results` by using +`plot_indicator_changes`: +=# + +fig = plot_indicator_changes(results) + +#= +Step 2 is to estimate significance using [`SurrogatesSignificance`](@ref) +and the function [`significant_transitions`](@ref). Finally, we can +conveniently plot the results obtained by updating the figure obtained +above with `plot_significance!`: +=# + +signif = SurrogatesSignificance(n = 1000, tail = [:right, :right]) +flags = significant_transitions(results, signif) +plot_significance!(fig, results, signif, flags = flags) +fig + +#= +### [Segmented windows] (@id segmented_windows) + +The analysis shown so far relies on sliding windows of the change metric. +This is particularly convenient for transition detection tasks. Segmented +windows for the change metric computation are however preferable when it +comes to prediction tasks. By only slightly modifying the syntax used so far, +one can perform the same computations on segmented windows, as well as +visualise the results conveniently: +=# + +config = SegmentedWindowConfig(indicators, change_metrics, + t[1:1], t[1200:1200]; whichtime = last, width_ind = 200, + min_width_cha = 100) +results = estimate_changes(config, input, t) +signif = SurrogatesSignificance(n = 1000, tail = [:right, :right]) +flags = significant_transitions(results, signif) +fig = plot_changes_significance(results, signif) diff --git a/dev/tutorial/03a9efaf.png b/dev/tutorial/03a9efaf.png new file mode 100644 index 00000000..71684476 Binary files /dev/null and b/dev/tutorial/03a9efaf.png differ diff --git a/dev/tutorial/1b3f597e.png b/dev/tutorial/1b3f597e.png new file mode 100644 index 00000000..3afb8f3b Binary files /dev/null and b/dev/tutorial/1b3f597e.png differ diff --git a/dev/tutorial/278caa53.png b/dev/tutorial/278caa53.png new file mode 100644 index 00000000..16fb7f4e Binary files /dev/null and b/dev/tutorial/278caa53.png differ diff --git a/dev/tutorial/4cd2f6a3.png b/dev/tutorial/4cd2f6a3.png new file mode 100644 index 00000000..3ad9ffae Binary files /dev/null and b/dev/tutorial/4cd2f6a3.png differ diff --git a/dev/tutorial/6ccd1579.png b/dev/tutorial/6ccd1579.png new file mode 100644 index 00000000..b74c7ca8 Binary files /dev/null and b/dev/tutorial/6ccd1579.png differ diff --git a/dev/tutorial/8621b213.png b/dev/tutorial/8621b213.png new file mode 100644 index 00000000..d2e0a919 Binary files /dev/null and b/dev/tutorial/8621b213.png differ diff --git a/dev/tutorial/a534bebb.png b/dev/tutorial/a534bebb.png new file mode 100644 index 00000000..fc614c3d Binary files /dev/null and b/dev/tutorial/a534bebb.png differ diff --git a/dev/tutorial/adbb8d4a.png b/dev/tutorial/adbb8d4a.png new file mode 100644 index 00000000..af02a8ae Binary files /dev/null and b/dev/tutorial/adbb8d4a.png differ diff --git a/dev/tutorial/f28a0721.png b/dev/tutorial/f28a0721.png new file mode 100644 index 00000000..f2f422f9 Binary files /dev/null and b/dev/tutorial/f28a0721.png differ diff --git a/dev/tutorial/fe1b9ec9.png b/dev/tutorial/fe1b9ec9.png new file mode 100644 index 00000000..98f8942d Binary files /dev/null and b/dev/tutorial/fe1b9ec9.png differ diff --git a/dev/tutorial/index.html b/dev/tutorial/index.html new file mode 100644 index 00000000..3ef0d835 --- /dev/null +++ b/dev/tutorial/index.html @@ -0,0 +1,128 @@ + +Tutorial · TransitionsInTimeseries.jl
GitHub

Tutorial

Workflow

Computing transition indicators consists of the following steps:

  1. Doing any preprocessing of raw data first, such as detrending. This not part of TransitionsInTimeseries.jl and yields the input timeseries.
  2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
  3. Computing the changes of the indicator by sliding a window over its timeseries. Alternatively, the change metric can be estimated over the whole segment, as examplified in the section Segmented windows.
  4. Generating many surrogates that preserve important statistical properties of the original timeseries.
  5. Performing step 2 and 3 for the surrogate timeseries.
  6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

Tutorial – Educational

Raw input data

Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

\[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig
Example block output

Preprocessing

Not part of TransitionsInTimeseries.jl

Any timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig
Example block output

At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

Detrending in Julia

Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

Indicator timeseries

We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector,
+# we obtain the last time step of each window.
+# This therefore only uses information from `k-width+1` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig
Example block output

The lines plotted above are the indicator timeseries.

Change metric timeseries

From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig
Example block output

Timeseries surrogates

As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

# Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+
+function gridfig(nrows, ncols)
+    fig = Figure()
+    axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)
+        for j in 1:ncols, i in 1:nrows]
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+fig, axs = gridfig(2, 1)
+lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))
+lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))
+axs[1].title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2))
+lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3))
+axislegend()
+axs[2].title = "change metric"
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig
Example block output

Quantifying significance

To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

n_surrogates = 1_000
+fig, axs = gridfig(2, 2)
+axs[1].title = "linear"
+axs[2].title = "nonlinear"
+
+for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change)   # ; color = Cycled(j)
+    lines!(axsig, t_change, pval)       # ; color = Cycled(j+2)
+end
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig
Example block output

As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

Tutorial – TransitionsInTimeseries.jl

TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a ChangesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

Sliding windows

The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig
Example block output

To perform all of the above analysis we follow a 2-step process.

Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using estimate_changes.

# These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope())
+
+# choices go into a configuration struct
+config = SlidingWindowConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last)
+
+# choices are processed
+results = estimate_changes(config, input, t)
SlidingWindowResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope, :PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

We can conveniently plot the information contained in results by using plot_indicator_changes:

fig = plot_indicator_changes(results)
Example block output

Step 2 is to estimate significance using SurrogatesSignificance and the function significant_transitions. Finally, we can conveniently plot the results obtained by updating the figure obtained above with plot_significance!:

signif = SurrogatesSignificance(n = 1000, tail = [:right, :right])
+flags = significant_transitions(results, signif)
+plot_significance!(fig, results, signif, flags = flags)
+fig
Example block output

Segmented windows

The analysis shown so far relies on sliding windows of the change metric. This is particularly convenient for transition detection tasks. Segmented windows for the change metric computation are however preferable when it comes to prediction tasks. By only slightly modifying the syntax used so far, one can perform the same computations on segmented windows, as well as visualise the results conveniently:

config = SegmentedWindowConfig(indicators, change_metrics,
+    t[1:1], t[1200:1200]; whichtime = last, width_ind = 200,
+    min_width_cha = 100)
+results = estimate_changes(config, input, t)
+signif = SurrogatesSignificance(n = 1000, tail = [:right, :right])
+flags = significant_transitions(results, signif)
+fig = plot_changes_significance(results, signif)
Example block output
diff --git a/index.html b/index.html new file mode 100644 index 00000000..6a5afc30 --- /dev/null +++ b/index.html @@ -0,0 +1,2 @@ + + diff --git a/previews/PR17/assets/documenter.js b/previews/PR17/assets/documenter.js new file mode 100644 index 00000000..6adfbbbf --- /dev/null +++ b/previews/PR17/assets/documenter.js @@ -0,0 +1,331 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fas", "fa-copy"); + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-times"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-times"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); + }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR17/assets/search.js b/previews/PR17/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR17/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
  • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR17/assets/themes/documenter-dark.css b/previews/PR17/assets/themes/documenter-dark.css new file mode 100644 index 00000000..aedf20e6 --- /dev/null +++ b/previews/PR17/assets/themes/documenter-dark.css @@ -0,0 +1,7396 @@ +@charset "UTF-8"; +/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */ +@keyframes spinAround { + from { + transform: rotate(0deg); } + to { + transform: rotate(359deg); } } + +html.theme--documenter-dark .tabs, html.theme--documenter-dark .pagination-previous, +html.theme--documenter-dark .pagination-next, +html.theme--documenter-dark .pagination-link, +html.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .breadcrumb, html.theme--documenter-dark .file, html.theme--documenter-dark .button, .is-unselectable, html.theme--documenter-dark .modal-close, html.theme--documenter-dark .delete { + -webkit-touch-callout: none; + -webkit-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; } + +html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after, html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after { + border: 3px solid transparent; + border-radius: 2px; + border-right: 0; + border-top: 0; + content: " "; + display: block; + height: 0.625em; + margin-top: -0.4375em; + pointer-events: none; + position: absolute; + top: 50%; + transform: rotate(-45deg); + transform-origin: center; + width: 0.625em; } + +html.theme--documenter-dark .admonition:not(:last-child), html.theme--documenter-dark .tabs:not(:last-child), html.theme--documenter-dark .message:not(:last-child), html.theme--documenter-dark .list:not(:last-child), html.theme--documenter-dark .level:not(:last-child), html.theme--documenter-dark .breadcrumb:not(:last-child), html.theme--documenter-dark .highlight:not(:last-child), html.theme--documenter-dark .block:not(:last-child), html.theme--documenter-dark .title:not(:last-child), +html.theme--documenter-dark .subtitle:not(:last-child), html.theme--documenter-dark .table-container:not(:last-child), html.theme--documenter-dark .table:not(:last-child), html.theme--documenter-dark .progress:not(:last-child), html.theme--documenter-dark .notification:not(:last-child), html.theme--documenter-dark .content:not(:last-child), html.theme--documenter-dark .box:not(:last-child) { + margin-bottom: 1.5rem; } + +html.theme--documenter-dark .modal-close, html.theme--documenter-dark .delete { + -moz-appearance: none; + -webkit-appearance: none; + background-color: rgba(10, 10, 10, 0.2); + border: none; + border-radius: 290486px; + cursor: pointer; + pointer-events: auto; + display: inline-block; + flex-grow: 0; + flex-shrink: 0; + font-size: 0; + height: 20px; + max-height: 20px; + max-width: 20px; + min-height: 20px; + min-width: 20px; + outline: none; + position: relative; + vertical-align: top; + width: 20px; } + html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::before, html.theme--documenter-dark .modal-close::after, html.theme--documenter-dark .delete::after { + background-color: white; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::before { + height: 2px; + width: 50%; } + html.theme--documenter-dark .modal-close::after, html.theme--documenter-dark .delete::after { + height: 50%; + width: 2px; } + html.theme--documenter-dark .modal-close:hover, html.theme--documenter-dark .delete:hover, html.theme--documenter-dark .modal-close:focus, html.theme--documenter-dark .delete:focus { + background-color: rgba(10, 10, 10, 0.3); } + html.theme--documenter-dark .modal-close:active, html.theme--documenter-dark .delete:active { + background-color: rgba(10, 10, 10, 0.4); } + html.theme--documenter-dark .is-small.modal-close, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.modal-close, html.theme--documenter-dark .is-small.delete, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.delete { + height: 16px; + max-height: 16px; + max-width: 16px; + min-height: 16px; + min-width: 16px; + width: 16px; } + html.theme--documenter-dark .is-medium.modal-close, html.theme--documenter-dark .is-medium.delete { + height: 24px; + max-height: 24px; + max-width: 24px; + min-height: 24px; + min-width: 24px; + width: 24px; } + html.theme--documenter-dark .is-large.modal-close, html.theme--documenter-dark .is-large.delete { + height: 32px; + max-height: 32px; + max-width: 32px; + min-height: 32px; + min-width: 32px; + width: 32px; } + +html.theme--documenter-dark .control.is-loading::after, html.theme--documenter-dark .select.is-loading::after, html.theme--documenter-dark .loader, html.theme--documenter-dark .button.is-loading::after { + animation: spinAround 500ms infinite linear; + border: 2px solid #dbdbdb; + border-radius: 290486px; + border-right-color: transparent; + border-top-color: transparent; + content: ""; + display: block; + height: 1em; + position: relative; + width: 1em; } + +html.theme--documenter-dark .hero-video, html.theme--documenter-dark .modal-background, html.theme--documenter-dark .modal, html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img, +html.theme--documenter-dark .image.is-square .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img, +html.theme--documenter-dark .image.is-1by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img, +html.theme--documenter-dark .image.is-5by4 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img, +html.theme--documenter-dark .image.is-4by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img, +html.theme--documenter-dark .image.is-3by2 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img, +html.theme--documenter-dark .image.is-5by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img, +html.theme--documenter-dark .image.is-16by9 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img, +html.theme--documenter-dark .image.is-2by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img, +html.theme--documenter-dark .image.is-3by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img, +html.theme--documenter-dark .image.is-4by5 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img, +html.theme--documenter-dark .image.is-3by4 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img, +html.theme--documenter-dark .image.is-2by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img, +html.theme--documenter-dark .image.is-3by5 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img, +html.theme--documenter-dark .image.is-9by16 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img, +html.theme--documenter-dark .image.is-1by2 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img, +html.theme--documenter-dark .image.is-1by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, .is-overlay { + bottom: 0; + left: 0; + position: absolute; + right: 0; + top: 0; } + +html.theme--documenter-dark .pagination-previous, +html.theme--documenter-dark .pagination-next, +html.theme--documenter-dark .pagination-link, +html.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .file-cta, +html.theme--documenter-dark .file-name, html.theme--documenter-dark .select select, html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .button { + -moz-appearance: none; + -webkit-appearance: none; + align-items: center; + border: 1px solid transparent; + border-radius: 4px; + box-shadow: none; + display: inline-flex; + font-size: 1rem; + height: 2.25em; + justify-content: flex-start; + line-height: 1.5; + padding-bottom: calc(0.375em - 1px); + padding-left: calc(0.625em - 1px); + padding-right: calc(0.625em - 1px); + padding-top: calc(0.375em - 1px); + position: relative; + vertical-align: top; } + html.theme--documenter-dark .pagination-previous:focus, + html.theme--documenter-dark .pagination-next:focus, + html.theme--documenter-dark .pagination-link:focus, + html.theme--documenter-dark .pagination-ellipsis:focus, html.theme--documenter-dark .file-cta:focus, + html.theme--documenter-dark .file-name:focus, html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .button:focus, html.theme--documenter-dark .is-focused.pagination-previous, + html.theme--documenter-dark .is-focused.pagination-next, + html.theme--documenter-dark .is-focused.pagination-link, + html.theme--documenter-dark .is-focused.pagination-ellipsis, html.theme--documenter-dark .is-focused.file-cta, + html.theme--documenter-dark .is-focused.file-name, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-focused.button, html.theme--documenter-dark .pagination-previous:active, + html.theme--documenter-dark .pagination-next:active, + html.theme--documenter-dark .pagination-link:active, + html.theme--documenter-dark .pagination-ellipsis:active, html.theme--documenter-dark .file-cta:active, + html.theme--documenter-dark .file-name:active, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .button:active, html.theme--documenter-dark .is-active.pagination-previous, + html.theme--documenter-dark .is-active.pagination-next, + html.theme--documenter-dark .is-active.pagination-link, + html.theme--documenter-dark .is-active.pagination-ellipsis, html.theme--documenter-dark .is-active.file-cta, + html.theme--documenter-dark .is-active.file-name, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .is-active.button { + outline: none; } + html.theme--documenter-dark .pagination-previous[disabled], + html.theme--documenter-dark .pagination-next[disabled], + html.theme--documenter-dark .pagination-link[disabled], + html.theme--documenter-dark .pagination-ellipsis[disabled], html.theme--documenter-dark .file-cta[disabled], + html.theme--documenter-dark .file-name[disabled], html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], html.theme--documenter-dark .button[disabled], fieldset[disabled] html.theme--documenter-dark .pagination-previous, html.theme--documenter-dark fieldset[disabled] .pagination-previous, + fieldset[disabled] html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark fieldset[disabled] .pagination-next, + fieldset[disabled] html.theme--documenter-dark .pagination-link, + html.theme--documenter-dark fieldset[disabled] .pagination-link, + fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis, + html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis, fieldset[disabled] html.theme--documenter-dark .file-cta, html.theme--documenter-dark fieldset[disabled] .file-cta, + fieldset[disabled] html.theme--documenter-dark .file-name, + html.theme--documenter-dark fieldset[disabled] .file-name, fieldset[disabled] html.theme--documenter-dark .select select, fieldset[disabled] html.theme--documenter-dark .textarea, fieldset[disabled] html.theme--documenter-dark .input, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark fieldset[disabled] .select select, html.theme--documenter-dark .select fieldset[disabled] select, html.theme--documenter-dark fieldset[disabled] .textarea, html.theme--documenter-dark fieldset[disabled] .input, html.theme--documenter-dark fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search > input, fieldset[disabled] html.theme--documenter-dark .button, html.theme--documenter-dark fieldset[disabled] .button { + cursor: not-allowed; } + +/*! minireset.css v0.0.4 | MIT License | github.com/jgthms/minireset.css */ +html, +body, +p, +ol, +ul, +li, +dl, +dt, +dd, +blockquote, +figure, +fieldset, +legend, +textarea, +pre, +iframe, +hr, +h1, +h2, +h3, +h4, +h5, +h6 { + margin: 0; + padding: 0; } + +h1, +h2, +h3, +h4, +h5, +h6 { + font-size: 100%; + font-weight: normal; } + +ul { + list-style: none; } + +button, +input, +select, +textarea { + margin: 0; } + +html { + box-sizing: border-box; } + +*, *::before, *::after { + box-sizing: inherit; } + +img, +embed, +iframe, +object, +video { + height: auto; + max-width: 100%; } + +audio { + max-width: 100%; } + +iframe { + border: 0; } + +table { + border-collapse: collapse; + border-spacing: 0; } + +td, +th { + padding: 0; } + td:not([align]), + th:not([align]) { + text-align: left; } + +.is-clearfix::after { + clear: both; + content: " "; + display: table; } + +.is-pulled-left { + float: left !important; } + +.is-pulled-right { + float: right !important; } + +.is-clipped { + overflow: hidden !important; } + +.is-size-1 { + font-size: 3rem !important; } + +.is-size-2 { + font-size: 2.5rem !important; } + +.is-size-3 { + font-size: 2rem !important; } + +.is-size-4 { + font-size: 1.5rem !important; } + +.is-size-5 { + font-size: 1.25rem !important; } + +.is-size-6 { + font-size: 1rem !important; } + +.is-size-7, html.theme--documenter-dark .docstring > section > a.docs-sourcelink { + font-size: 0.75rem !important; } + +@media screen and (max-width: 768px) { + .is-size-1-mobile { + font-size: 3rem !important; } + .is-size-2-mobile { + font-size: 2.5rem !important; } + .is-size-3-mobile { + font-size: 2rem !important; } + .is-size-4-mobile { + font-size: 1.5rem !important; } + .is-size-5-mobile { + font-size: 1.25rem !important; } + .is-size-6-mobile { + font-size: 1rem !important; } + .is-size-7-mobile { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 769px), print { + .is-size-1-tablet { + font-size: 3rem !important; } + .is-size-2-tablet { + font-size: 2.5rem !important; } + .is-size-3-tablet { + font-size: 2rem !important; } + .is-size-4-tablet { + font-size: 1.5rem !important; } + .is-size-5-tablet { + font-size: 1.25rem !important; } + .is-size-6-tablet { + font-size: 1rem !important; } + .is-size-7-tablet { + font-size: 0.75rem !important; } } + +@media screen and (max-width: 1055px) { + .is-size-1-touch { + font-size: 3rem !important; } + .is-size-2-touch { + font-size: 2.5rem !important; } + .is-size-3-touch { + font-size: 2rem !important; } + .is-size-4-touch { + font-size: 1.5rem !important; } + .is-size-5-touch { + font-size: 1.25rem !important; } + .is-size-6-touch { + font-size: 1rem !important; } + .is-size-7-touch { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1056px) { + .is-size-1-desktop { + font-size: 3rem !important; } + .is-size-2-desktop { + font-size: 2.5rem !important; } + .is-size-3-desktop { + font-size: 2rem !important; } + .is-size-4-desktop { + font-size: 1.5rem !important; } + .is-size-5-desktop { + font-size: 1.25rem !important; } + .is-size-6-desktop { + font-size: 1rem !important; } + .is-size-7-desktop { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1216px) { + .is-size-1-widescreen { + font-size: 3rem !important; } + .is-size-2-widescreen { + font-size: 2.5rem !important; } + .is-size-3-widescreen { + font-size: 2rem !important; } + .is-size-4-widescreen { + font-size: 1.5rem !important; } + .is-size-5-widescreen { + font-size: 1.25rem !important; } + .is-size-6-widescreen { + font-size: 1rem !important; } + .is-size-7-widescreen { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1408px) { + .is-size-1-fullhd { + font-size: 3rem !important; } + .is-size-2-fullhd { + font-size: 2.5rem !important; } + .is-size-3-fullhd { + font-size: 2rem !important; } + .is-size-4-fullhd { + font-size: 1.5rem !important; } + .is-size-5-fullhd { + font-size: 1.25rem !important; } + .is-size-6-fullhd { + font-size: 1rem !important; } + .is-size-7-fullhd { + font-size: 0.75rem !important; } } + +.has-text-centered { + text-align: center !important; } + +.has-text-justified { + text-align: justify !important; } + +.has-text-left { + text-align: left !important; } + +.has-text-right { + text-align: right !important; } + +@media screen and (max-width: 768px) { + .has-text-centered-mobile { + text-align: center !important; } } + +@media screen and (min-width: 769px), print { + .has-text-centered-tablet { + text-align: center !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-centered-tablet-only { + text-align: center !important; } } + +@media screen and (max-width: 1055px) { + .has-text-centered-touch { + text-align: center !important; } } + +@media screen and (min-width: 1056px) { + .has-text-centered-desktop { + text-align: center !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-centered-desktop-only { + text-align: center !important; } } + +@media screen and (min-width: 1216px) { + .has-text-centered-widescreen { + text-align: center !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-centered-widescreen-only { + text-align: center !important; } } + +@media screen and (min-width: 1408px) { + .has-text-centered-fullhd { + text-align: center !important; } } + +@media screen and (max-width: 768px) { + .has-text-justified-mobile { + text-align: justify !important; } } + +@media screen and (min-width: 769px), print { + .has-text-justified-tablet { + text-align: justify !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-justified-tablet-only { + text-align: justify !important; } } + +@media screen and (max-width: 1055px) { + .has-text-justified-touch { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) { + .has-text-justified-desktop { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-justified-desktop-only { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) { + .has-text-justified-widescreen { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-justified-widescreen-only { + text-align: justify !important; } } + +@media screen and (min-width: 1408px) { + .has-text-justified-fullhd { + text-align: justify !important; } } + +@media screen and (max-width: 768px) { + .has-text-left-mobile { + text-align: left !important; } } + +@media screen and (min-width: 769px), print { + .has-text-left-tablet { + text-align: left !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-left-tablet-only { + text-align: left !important; } } + +@media screen and (max-width: 1055px) { + .has-text-left-touch { + text-align: left !important; } } + +@media screen and (min-width: 1056px) { + .has-text-left-desktop { + text-align: left !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-left-desktop-only { + text-align: left !important; } } + +@media screen and (min-width: 1216px) { + .has-text-left-widescreen { + text-align: left !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-left-widescreen-only { + text-align: left !important; } } + +@media screen and (min-width: 1408px) { + .has-text-left-fullhd { + text-align: left !important; } } + +@media screen and (max-width: 768px) { + .has-text-right-mobile { + text-align: right !important; } } + +@media screen and (min-width: 769px), print { + .has-text-right-tablet { + text-align: right !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-right-tablet-only { + text-align: right !important; } } + +@media screen and (max-width: 1055px) { + .has-text-right-touch { + text-align: right !important; } } + +@media screen and (min-width: 1056px) { + .has-text-right-desktop { + text-align: right !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-right-desktop-only { + text-align: right !important; } } + +@media screen and (min-width: 1216px) { + .has-text-right-widescreen { + text-align: right !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-right-widescreen-only { + text-align: right !important; } } + +@media screen and (min-width: 1408px) { + .has-text-right-fullhd { + text-align: right !important; } } + +.is-capitalized { + text-transform: capitalize !important; } + +.is-lowercase { + text-transform: lowercase !important; } + +.is-uppercase { + text-transform: uppercase !important; } + +.is-italic { + font-style: italic !important; } + +.has-text-white { + color: white !important; } + +a.has-text-white:hover, a.has-text-white:focus { + color: #e6e6e6 !important; } + +.has-background-white { + background-color: white !important; } + +.has-text-black { + color: #0a0a0a !important; } + +a.has-text-black:hover, a.has-text-black:focus { + color: black !important; } + +.has-background-black { + background-color: #0a0a0a !important; } + +.has-text-light { + color: whitesmoke !important; } + +a.has-text-light:hover, a.has-text-light:focus { + color: #dbdbdb !important; } + +.has-background-light { + background-color: whitesmoke !important; } + +.has-text-dark { + color: #363636 !important; } + +a.has-text-dark:hover, a.has-text-dark:focus { + color: #1c1c1c !important; } + +.has-background-dark { + background-color: #363636 !important; } + +.has-text-primary { + color: #4eb5de !important; } + +a.has-text-primary:hover, a.has-text-primary:focus { + color: #27a1d2 !important; } + +.has-background-primary { + background-color: #4eb5de !important; } + +.has-text-link { + color: #2ad7e6 !important; } + +a.has-text-link:hover, a.has-text-link:focus { + color: #17b7c5 !important; } + +.has-background-link { + background-color: #2ad7e6 !important; } + +.has-text-info { + color: #3489da !important; } + +a.has-text-info:hover, a.has-text-info:focus { + color: #226fb9 !important; } + +.has-background-info { + background-color: #3489da !important; } + +.has-text-success { + color: #259a12 !important; } + +a.has-text-success:hover, a.has-text-success:focus { + color: #1a6c0d !important; } + +.has-background-success { + background-color: #259a12 !important; } + +.has-text-warning { + color: #f4c72f !important; } + +a.has-text-warning:hover, a.has-text-warning:focus { + color: #e4b30c !important; } + +.has-background-warning { + background-color: #f4c72f !important; } + +.has-text-danger { + color: #cb3c33 !important; } + +a.has-text-danger:hover, a.has-text-danger:focus { + color: #a23029 !important; } + +.has-background-danger { + background-color: #cb3c33 !important; } + +.has-text-black-bis { + color: #121212 !important; } + +.has-background-black-bis { + background-color: #121212 !important; } + +.has-text-black-ter { + color: #242424 !important; } + +.has-background-black-ter { + background-color: #242424 !important; } + +.has-text-grey-darker { + color: #363636 !important; } + +.has-background-grey-darker { + background-color: #363636 !important; } + +.has-text-grey-dark { + color: #4a4a4a !important; } + +.has-background-grey-dark { + background-color: #4a4a4a !important; } + +.has-text-grey { + color: #7a7a7a !important; } + +.has-background-grey { + background-color: #7a7a7a !important; } + +.has-text-grey-light { + color: #b5b5b5 !important; } + +.has-background-grey-light { + background-color: #b5b5b5 !important; } + +.has-text-grey-lighter { + color: #dbdbdb !important; } + +.has-background-grey-lighter { + background-color: #dbdbdb !important; } + +.has-text-white-ter { + color: whitesmoke !important; } + +.has-background-white-ter { + background-color: whitesmoke !important; } + +.has-text-white-bis { + color: #fafafa !important; } + +.has-background-white-bis { + background-color: #fafafa !important; } + +.has-text-weight-light { + font-weight: 300 !important; } + +.has-text-weight-normal { + font-weight: 400 !important; } + +.has-text-weight-medium { + font-weight: 500 !important; } + +.has-text-weight-semibold { + font-weight: 600 !important; } + +.has-text-weight-bold { + font-weight: 700 !important; } + +.is-family-primary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-secondary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-sans-serif { + font-family: "Montserrat", sans-serif !important; } + +.is-family-monospace { + font-family: "Source Code Pro", monospace !important; } + +.is-family-code { + font-family: "Source Code Pro", monospace !important; } + +.is-block { + display: block !important; } + +@media screen and (max-width: 768px) { + .is-block-mobile { + display: block !important; } } + +@media screen and (min-width: 769px), print { + .is-block-tablet { + display: block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-block-tablet-only { + display: block !important; } } + +@media screen and (max-width: 1055px) { + .is-block-touch { + display: block !important; } } + +@media screen and (min-width: 1056px) { + .is-block-desktop { + display: block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-block-desktop-only { + display: block !important; } } + +@media screen and (min-width: 1216px) { + .is-block-widescreen { + display: block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-block-widescreen-only { + display: block !important; } } + +@media screen and (min-width: 1408px) { + .is-block-fullhd { + display: block !important; } } + +.is-flex { + display: flex !important; } + +@media screen and (max-width: 768px) { + .is-flex-mobile { + display: flex !important; } } + +@media screen and (min-width: 769px), print { + .is-flex-tablet { + display: flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-flex-tablet-only { + display: flex !important; } } + +@media screen and (max-width: 1055px) { + .is-flex-touch { + display: flex !important; } } + +@media screen and (min-width: 1056px) { + .is-flex-desktop { + display: flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-flex-desktop-only { + display: flex !important; } } + +@media screen and (min-width: 1216px) { + .is-flex-widescreen { + display: flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-flex-widescreen-only { + display: flex !important; } } + +@media screen and (min-width: 1408px) { + .is-flex-fullhd { + display: flex !important; } } + +.is-inline { + display: inline !important; } + +@media screen and (max-width: 768px) { + .is-inline-mobile { + display: inline !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-tablet { + display: inline !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-tablet-only { + display: inline !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-touch { + display: inline !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-desktop { + display: inline !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-desktop-only { + display: inline !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-widescreen { + display: inline !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-widescreen-only { + display: inline !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-fullhd { + display: inline !important; } } + +.is-inline-block { + display: inline-block !important; } + +@media screen and (max-width: 768px) { + .is-inline-block-mobile { + display: inline-block !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-block-tablet { + display: inline-block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-block-tablet-only { + display: inline-block !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-block-touch { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-block-desktop { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-block-desktop-only { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-block-widescreen { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-block-widescreen-only { + display: inline-block !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-block-fullhd { + display: inline-block !important; } } + +.is-inline-flex { + display: inline-flex !important; } + +@media screen and (max-width: 768px) { + .is-inline-flex-mobile { + display: inline-flex !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-flex-tablet { + display: inline-flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-flex-tablet-only { + display: inline-flex !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-flex-touch { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-flex-desktop { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-flex-desktop-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-flex-widescreen { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-flex-widescreen-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-flex-fullhd { + display: inline-flex !important; } } + +.is-hidden { + display: none !important; } + +.is-sr-only { + border: none !important; + clip: rect(0, 0, 0, 0) !important; + height: 0.01em !important; + overflow: hidden !important; + padding: 0 !important; + position: absolute !important; + white-space: nowrap !important; + width: 0.01em !important; } + +@media screen and (max-width: 768px) { + .is-hidden-mobile { + display: none !important; } } + +@media screen and (min-width: 769px), print { + .is-hidden-tablet { + display: none !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-hidden-tablet-only { + display: none !important; } } + +@media screen and (max-width: 1055px) { + .is-hidden-touch { + display: none !important; } } + +@media screen and (min-width: 1056px) { + .is-hidden-desktop { + display: none !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-hidden-desktop-only { + display: none !important; } } + +@media screen and (min-width: 1216px) { + .is-hidden-widescreen { + display: none !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-hidden-widescreen-only { + display: none !important; } } + +@media screen and (min-width: 1408px) { + .is-hidden-fullhd { + display: none !important; } } + +.is-invisible { + visibility: hidden !important; } + +@media screen and (max-width: 768px) { + .is-invisible-mobile { + visibility: hidden !important; } } + +@media screen and (min-width: 769px), print { + .is-invisible-tablet { + visibility: hidden !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-invisible-tablet-only { + visibility: hidden !important; } } + +@media screen and (max-width: 1055px) { + .is-invisible-touch { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) { + .is-invisible-desktop { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-invisible-desktop-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) { + .is-invisible-widescreen { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-invisible-widescreen-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1408px) { + .is-invisible-fullhd { + visibility: hidden !important; } } + +.is-marginless { + margin: 0 !important; } + +.is-paddingless { + padding: 0 !important; } + +.is-radiusless { + border-radius: 0 !important; } + +.is-shadowless { + box-shadow: none !important; } + +.is-relative { + position: relative !important; } + +html.theme--documenter-dark { + /* This file contain the overall layout. + * + * The main container is
    that is identified by id #documenter. + */ + /*! + Theme: a11y-dark + Author: @ericwbailey + Maintainer: @ericwbailey + + Based on the Tomorrow Night Eighties theme: https://github.com/isagalaev/highlight.js/blob/master/src/styles/tomorrow-night-eighties.css +*/ + /* Comment */ + /* Red */ + /* Orange */ + /* Yellow */ + /* Green */ + /* Blue */ + /* Purple */ } + html.theme--documenter-dark html { + background-color: #1e1e20; + font-size: 16px; + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + html.theme--documenter-dark article, + html.theme--documenter-dark aside, + html.theme--documenter-dark figure, + html.theme--documenter-dark footer, + html.theme--documenter-dark header, + html.theme--documenter-dark hgroup, + html.theme--documenter-dark section { + display: block; } + html.theme--documenter-dark body, + html.theme--documenter-dark button, + html.theme--documenter-dark input, + html.theme--documenter-dark select, + html.theme--documenter-dark textarea { + font-family: "Montserrat", sans-serif; } + html.theme--documenter-dark code, + html.theme--documenter-dark pre { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; + font-family: "Source Code Pro", monospace; } + html.theme--documenter-dark body { + color: #fbfbfb; + font-size: 1em; + font-weight: 400; + line-height: 1.5; } + html.theme--documenter-dark a { + color: #2ad7e6; + cursor: pointer; + text-decoration: none; } + html.theme--documenter-dark a strong { + color: currentColor; } + html.theme--documenter-dark a:hover { + color: #97ebf3; } + html.theme--documenter-dark code { + background-color: #312550; + color: #fff; + font-size: 0.875em; + font-weight: normal; + padding: 0.1em; } + html.theme--documenter-dark hr { + background-color: whitesmoke; + border: none; + display: block; + height: 2px; + margin: 1.5rem 0; } + html.theme--documenter-dark img { + height: auto; + max-width: 100%; } + html.theme--documenter-dark input[type="checkbox"], + html.theme--documenter-dark input[type="radio"] { + vertical-align: baseline; } + html.theme--documenter-dark small { + font-size: 0.875em; } + html.theme--documenter-dark span { + font-style: inherit; + font-weight: inherit; } + html.theme--documenter-dark strong { + color: #cdc3e3; + font-weight: 700; } + html.theme--documenter-dark fieldset { + border: none; } + html.theme--documenter-dark pre { + -webkit-overflow-scrolling: touch; + background-color: #312550; + color: #fbfbfb; + font-size: 0.875em; + overflow-x: auto; + padding: 1.25rem 1.5rem; + white-space: pre; + word-wrap: normal; } + html.theme--documenter-dark pre code { + background-color: transparent; + color: currentColor; + font-size: 1em; + padding: 0; } + html.theme--documenter-dark table td, + html.theme--documenter-dark table th { + vertical-align: top; } + html.theme--documenter-dark table td:not([align]), + html.theme--documenter-dark table th:not([align]) { + text-align: left; } + html.theme--documenter-dark table th { + color: #cdc3e3; } + html.theme--documenter-dark .box { + background-color: white; + border-radius: 6px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #fbfbfb; + display: block; + padding: 1.25rem; } + html.theme--documenter-dark a.box:hover, html.theme--documenter-dark a.box:focus { + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #2ad7e6; } + html.theme--documenter-dark a.box:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #2ad7e6; } + html.theme--documenter-dark .button { + background-color: white; + border-color: #dbdbdb; + border-width: 1px; + color: #363636; + cursor: pointer; + justify-content: center; + padding-bottom: calc(0.375em - 1px); + padding-left: 0.75em; + padding-right: 0.75em; + padding-top: calc(0.375em - 1px); + text-align: center; + white-space: nowrap; } + html.theme--documenter-dark .button strong { + color: inherit; } + html.theme--documenter-dark .button .icon, html.theme--documenter-dark .button .icon.is-small, html.theme--documenter-dark .button #documenter .docs-sidebar form.docs-search > input.icon, html.theme--documenter-dark #documenter .docs-sidebar .button form.docs-search > input.icon, html.theme--documenter-dark .button .icon.is-medium, html.theme--documenter-dark .button .icon.is-large { + height: 1.5em; + width: 1.5em; } + html.theme--documenter-dark .button .icon:first-child:not(:last-child) { + margin-left: calc(-0.375em - 1px); + margin-right: 0.1875em; } + html.theme--documenter-dark .button .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: calc(-0.375em - 1px); } + html.theme--documenter-dark .button .icon:first-child:last-child { + margin-left: calc(-0.375em - 1px); + margin-right: calc(-0.375em - 1px); } + html.theme--documenter-dark .button:hover, html.theme--documenter-dark .button.is-hovered { + border-color: #b5b5b5; + color: #97ebf3; } + html.theme--documenter-dark .button:focus, html.theme--documenter-dark .button.is-focused { + border-color: #3c5dcd; + color: #363636; } + html.theme--documenter-dark .button:focus:not(:active), html.theme--documenter-dark .button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .button:active, html.theme--documenter-dark .button.is-active { + border-color: #4a4a4a; + color: #363636; } + html.theme--documenter-dark .button.is-text { + background-color: transparent; + border-color: transparent; + color: #fbfbfb; + text-decoration: underline; } + html.theme--documenter-dark .button.is-text:hover, html.theme--documenter-dark .button.is-text.is-hovered, html.theme--documenter-dark .button.is-text:focus, html.theme--documenter-dark .button.is-text.is-focused { + background-color: whitesmoke; + color: #cdc3e3; } + html.theme--documenter-dark .button.is-text:active, html.theme--documenter-dark .button.is-text.is-active { + background-color: #e8e8e8; + color: #cdc3e3; } + html.theme--documenter-dark .button.is-text[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-text { + background-color: transparent; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-white { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:hover, html.theme--documenter-dark .button.is-white.is-hovered { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:focus, html.theme--documenter-dark .button.is-white.is-focused { + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:focus:not(:active), html.theme--documenter-dark .button.is-white.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .button.is-white:active, html.theme--documenter-dark .button.is-white.is-active { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white { + background-color: white; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-white.is-inverted { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-hovered { + background-color: black; } + html.theme--documenter-dark .button.is-white.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-white.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + html.theme--documenter-dark .button.is-white.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-outlined.is-focused { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-white.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:hover, html.theme--documenter-dark .button.is-black.is-hovered { + background-color: #040404; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:focus, html.theme--documenter-dark .button.is-black.is-focused { + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:focus:not(:active), html.theme--documenter-dark .button.is-black.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .button.is-black:active, html.theme--documenter-dark .button.is-black.is-active { + background-color: black; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-black.is-inverted { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-black.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted { + background-color: white; + border-color: transparent; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-loading::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-outlined.is-focused { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-black.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-light { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:hover, html.theme--documenter-dark .button.is-light.is-hovered { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:focus, html.theme--documenter-dark .button.is-light.is-focused { + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:focus:not(:active), html.theme--documenter-dark .button.is-light.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .button.is-light:active, html.theme--documenter-dark .button.is-light.is-active { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-light.is-inverted { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-hovered { + background-color: #292929; } + html.theme--documenter-dark .button.is-light.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted { + background-color: #363636; + border-color: transparent; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-outlined.is-focused { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-light.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark, html.theme--documenter-dark .content kbd.button { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:hover, html.theme--documenter-dark .content kbd.button:hover, html.theme--documenter-dark .button.is-dark.is-hovered, html.theme--documenter-dark .content kbd.button.is-hovered { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:focus, html.theme--documenter-dark .content kbd.button:focus, html.theme--documenter-dark .button.is-dark.is-focused, html.theme--documenter-dark .content kbd.button.is-focused { + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:focus:not(:active), html.theme--documenter-dark .content kbd.button:focus:not(:active), html.theme--documenter-dark .button.is-dark.is-focused:not(:active), html.theme--documenter-dark .content kbd.button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .button.is-dark:active, html.theme--documenter-dark .content kbd.button:active, html.theme--documenter-dark .button.is-dark.is-active, html.theme--documenter-dark .content kbd.button.is-active { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark[disabled], html.theme--documenter-dark .content kbd.button[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark, fieldset[disabled] html.theme--documenter-dark .content kbd.button { + background-color: #363636; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-dark.is-inverted, html.theme--documenter-dark .content kbd.button.is-inverted { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted:hover, html.theme--documenter-dark .content kbd.button.is-inverted:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered { + background-color: #e8e8e8; } + html.theme--documenter-dark .button.is-dark.is-inverted[disabled], html.theme--documenter-dark .content kbd.button.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-loading::after, html.theme--documenter-dark .content kbd.button.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-dark.is-outlined, html.theme--documenter-dark .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-outlined.is-focused { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-dark.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-primary, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:hover, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-hovered.docs-sourcelink { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:focus, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:focus:not(:active), html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus:not(:active), html.theme--documenter-dark .button.is-primary.is-focused:not(:active), html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .button.is-primary:active, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:active, html.theme--documenter-dark .button.is-primary.is-active, html.theme--documenter-dark .docstring > section > a.button.is-active.docs-sourcelink { + background-color: #39acda; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary[disabled], html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-primary.is-inverted, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-primary.is-inverted[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-loading.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-primary.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-primary.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + box-shadow: none; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-link { + background-color: #2ad7e6; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:hover, html.theme--documenter-dark .button.is-link.is-hovered { + background-color: #1ed5e5; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:focus, html.theme--documenter-dark .button.is-link.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:focus:not(:active), html.theme--documenter-dark .button.is-link.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .button.is-link:active, html.theme--documenter-dark .button.is-link.is-active { + background-color: #1acddc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link { + background-color: #2ad7e6; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-link.is-inverted { + background-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-link.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-link.is-outlined { + background-color: transparent; + border-color: #2ad7e6; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-outlined.is-focused { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after { + border-color: transparent transparent #2ad7e6 #2ad7e6 !important; } + html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-link.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined { + background-color: transparent; + border-color: #2ad7e6; + box-shadow: none; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #2ad7e6 #2ad7e6 !important; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-info { + background-color: #3489da; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:hover, html.theme--documenter-dark .button.is-info.is-hovered { + background-color: #2983d8; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:focus, html.theme--documenter-dark .button.is-info.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:focus:not(:active), html.theme--documenter-dark .button.is-info.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .button.is-info:active, html.theme--documenter-dark .button.is-info.is-active { + background-color: #267ccf; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info { + background-color: #3489da; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-info.is-inverted { + background-color: #fff; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-info.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-info.is-outlined { + background-color: transparent; + border-color: #3489da; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-outlined.is-focused { + background-color: #3489da; + border-color: #3489da; + color: #fff; } + html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after { + border-color: transparent transparent #3489da #3489da !important; } + html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-info.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined { + background-color: transparent; + border-color: #3489da; + box-shadow: none; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #3489da #3489da !important; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-success { + background-color: #259a12; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:hover, html.theme--documenter-dark .button.is-success.is-hovered { + background-color: #228f11; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:focus, html.theme--documenter-dark .button.is-success.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:focus:not(:active), html.theme--documenter-dark .button.is-success.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .button.is-success:active, html.theme--documenter-dark .button.is-success.is-active { + background-color: #20830f; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success { + background-color: #259a12; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-success.is-inverted { + background-color: #fff; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-success.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-success.is-outlined { + background-color: transparent; + border-color: #259a12; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-outlined.is-focused { + background-color: #259a12; + border-color: #259a12; + color: #fff; } + html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after { + border-color: transparent transparent #259a12 #259a12 !important; } + html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-success.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined { + background-color: transparent; + border-color: #259a12; + box-shadow: none; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #259a12 #259a12 !important; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-warning { + background-color: #f4c72f; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:hover, html.theme--documenter-dark .button.is-warning.is-hovered { + background-color: #f3c423; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:focus, html.theme--documenter-dark .button.is-warning.is-focused { + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:focus:not(:active), html.theme--documenter-dark .button.is-warning.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .button.is-warning:active, html.theme--documenter-dark .button.is-warning.is-active { + background-color: #f3c017; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning { + background-color: #f4c72f; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered { + background-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + border-color: transparent; + box-shadow: none; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-loading::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + html.theme--documenter-dark .button.is-warning.is-outlined { + background-color: transparent; + border-color: #f4c72f; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-outlined.is-focused { + background-color: #f4c72f; + border-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after { + border-color: transparent transparent #f4c72f #f4c72f !important; } + html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + html.theme--documenter-dark .button.is-warning.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined { + background-color: transparent; + border-color: #f4c72f; + box-shadow: none; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused { + background-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #f4c72f #f4c72f !important; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + box-shadow: none; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-danger { + background-color: #cb3c33; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:hover, html.theme--documenter-dark .button.is-danger.is-hovered { + background-color: #c13930; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:focus, html.theme--documenter-dark .button.is-danger.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:focus:not(:active), html.theme--documenter-dark .button.is-danger.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .button.is-danger:active, html.theme--documenter-dark .button.is-danger.is-active { + background-color: #b7362e; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger { + background-color: #cb3c33; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-danger.is-inverted { + background-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-danger.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-danger.is-outlined { + background-color: transparent; + border-color: #cb3c33; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-outlined.is-focused { + background-color: #cb3c33; + border-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after { + border-color: transparent transparent #cb3c33 #cb3c33 !important; } + html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-danger.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined { + background-color: transparent; + border-color: #cb3c33; + box-shadow: none; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #cb3c33 #cb3c33 !important; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .button.is-normal { + font-size: 1rem; } + html.theme--documenter-dark .button.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .button.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .button[disabled], fieldset[disabled] html.theme--documenter-dark .button { + background-color: white; + border-color: #dbdbdb; + box-shadow: none; + opacity: 0.5; } + html.theme--documenter-dark .button.is-fullwidth { + display: flex; + width: 100%; } + html.theme--documenter-dark .button.is-loading { + color: transparent !important; + pointer-events: none; } + html.theme--documenter-dark .button.is-loading::after { + position: absolute; + left: calc(50% - (1em / 2)); + top: calc(50% - (1em / 2)); + position: absolute !important; } + html.theme--documenter-dark .button.is-static { + background-color: whitesmoke; + border-color: #dbdbdb; + color: #7a7a7a; + box-shadow: none; + pointer-events: none; } + html.theme--documenter-dark .button.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + html.theme--documenter-dark .buttons { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .buttons .button { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth) { + margin-right: 0.5rem; } + html.theme--documenter-dark .buttons:last-child { + margin-bottom: -0.5rem; } + html.theme--documenter-dark .buttons:not(:last-child) { + margin-bottom: 1rem; } + html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { + font-size: 1.25rem; } + html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { + font-size: 1.5rem; } + html.theme--documenter-dark .buttons.has-addons .button:not(:first-child) { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .buttons.has-addons .button:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; + margin-right: -1px; } + html.theme--documenter-dark .buttons.has-addons .button:last-child { + margin-right: 0; } + html.theme--documenter-dark .buttons.has-addons .button:hover, html.theme--documenter-dark .buttons.has-addons .button.is-hovered { + z-index: 2; } + html.theme--documenter-dark .buttons.has-addons .button:focus, html.theme--documenter-dark .buttons.has-addons .button.is-focused, html.theme--documenter-dark .buttons.has-addons .button:active, html.theme--documenter-dark .buttons.has-addons .button.is-active, html.theme--documenter-dark .buttons.has-addons .button.is-selected { + z-index: 3; } + html.theme--documenter-dark .buttons.has-addons .button:focus:hover, html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover, html.theme--documenter-dark .buttons.has-addons .button:active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover { + z-index: 4; } + html.theme--documenter-dark .buttons.has-addons .button.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .buttons.is-centered { + justify-content: center; } + html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + html.theme--documenter-dark .buttons.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + html.theme--documenter-dark .container { + flex-grow: 1; + margin: 0 auto; + position: relative; + width: auto; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .container { + max-width: 992px; } + html.theme--documenter-dark .container.is-fluid { + margin-left: 32px; + margin-right: 32px; + max-width: none; } } + @media screen and (max-width: 1215px) { + html.theme--documenter-dark .container.is-widescreen { + max-width: 1152px; } } + @media screen and (max-width: 1407px) { + html.theme--documenter-dark .container.is-fullhd { + max-width: 1344px; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .container { + max-width: 1152px; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .container { + max-width: 1344px; } } + html.theme--documenter-dark .content li + li { + margin-top: 0.25em; } + html.theme--documenter-dark .content p:not(:last-child), + html.theme--documenter-dark .content dl:not(:last-child), + html.theme--documenter-dark .content ol:not(:last-child), + html.theme--documenter-dark .content ul:not(:last-child), + html.theme--documenter-dark .content blockquote:not(:last-child), + html.theme--documenter-dark .content pre:not(:last-child), + html.theme--documenter-dark .content table:not(:last-child) { + margin-bottom: 1em; } + html.theme--documenter-dark .content h1, + html.theme--documenter-dark .content h2, + html.theme--documenter-dark .content h3, + html.theme--documenter-dark .content h4, + html.theme--documenter-dark .content h5, + html.theme--documenter-dark .content h6 { + color: #cdc3e3; + font-weight: 600; + line-height: 1.125; } + html.theme--documenter-dark .content h1 { + font-size: 2em; + margin-bottom: 0.5em; } + html.theme--documenter-dark .content h1:not(:first-child) { + margin-top: 1em; } + html.theme--documenter-dark .content h2 { + font-size: 1.75em; + margin-bottom: 0.5714em; } + html.theme--documenter-dark .content h2:not(:first-child) { + margin-top: 1.1428em; } + html.theme--documenter-dark .content h3 { + font-size: 1.5em; + margin-bottom: 0.6666em; } + html.theme--documenter-dark .content h3:not(:first-child) { + margin-top: 1.3333em; } + html.theme--documenter-dark .content h4 { + font-size: 1.25em; + margin-bottom: 0.8em; } + html.theme--documenter-dark .content h5 { + font-size: 1.125em; + margin-bottom: 0.8888em; } + html.theme--documenter-dark .content h6 { + font-size: 1em; + margin-bottom: 1em; } + html.theme--documenter-dark .content blockquote { + background-color: whitesmoke; + border-left: 5px solid #dbdbdb; + padding: 1.25em 1.5em; } + html.theme--documenter-dark .content ol { + list-style-position: outside; + margin-left: 2em; + margin-top: 1em; } + html.theme--documenter-dark .content ol:not([type]) { + list-style-type: decimal; } + html.theme--documenter-dark .content ol.is-lower-alpha:not([type]) { + list-style-type: lower-alpha; } + html.theme--documenter-dark .content ol.is-lower-roman:not([type]) { + list-style-type: lower-roman; } + html.theme--documenter-dark .content ol.is-upper-alpha:not([type]) { + list-style-type: upper-alpha; } + html.theme--documenter-dark .content ol.is-upper-roman:not([type]) { + list-style-type: upper-roman; } + html.theme--documenter-dark .content ul { + list-style: disc outside; + margin-left: 2em; + margin-top: 1em; } + html.theme--documenter-dark .content ul ul { + list-style-type: circle; + margin-top: 0.5em; } + html.theme--documenter-dark .content ul ul ul { + list-style-type: square; } + html.theme--documenter-dark .content dd { + margin-left: 2em; } + html.theme--documenter-dark .content figure { + margin-left: 2em; + margin-right: 2em; + text-align: center; } + html.theme--documenter-dark .content figure:not(:first-child) { + margin-top: 2em; } + html.theme--documenter-dark .content figure:not(:last-child) { + margin-bottom: 2em; } + html.theme--documenter-dark .content figure img { + display: inline-block; } + html.theme--documenter-dark .content figure figcaption { + font-style: italic; } + html.theme--documenter-dark .content pre { + -webkit-overflow-scrolling: touch; + overflow-x: auto; + padding: 0; + white-space: pre; + word-wrap: normal; } + html.theme--documenter-dark .content sup, + html.theme--documenter-dark .content sub { + font-size: 75%; } + html.theme--documenter-dark .content table { + width: 100%; } + html.theme--documenter-dark .content table td, + html.theme--documenter-dark .content table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + html.theme--documenter-dark .content table th { + color: #cdc3e3; } + html.theme--documenter-dark .content table th:not([align]) { + text-align: left; } + html.theme--documenter-dark .content table thead td, + html.theme--documenter-dark .content table thead th { + border-width: 0 0 2px; + color: #cdc3e3; } + html.theme--documenter-dark .content table tfoot td, + html.theme--documenter-dark .content table tfoot th { + border-width: 2px 0 0; + color: #cdc3e3; } + html.theme--documenter-dark .content table tbody tr:last-child td, + html.theme--documenter-dark .content table tbody tr:last-child th { + border-bottom-width: 0; } + html.theme--documenter-dark .content .tabs li + li { + margin-top: 0; } + html.theme--documenter-dark .content.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.content { + font-size: 0.75rem; } + html.theme--documenter-dark .content.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .content.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .icon { + align-items: center; + display: inline-flex; + justify-content: center; + height: 1.5rem; + width: 1.5rem; } + html.theme--documenter-dark .icon.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.icon { + height: 1rem; + width: 1rem; } + html.theme--documenter-dark .icon.is-medium { + height: 2rem; + width: 2rem; } + html.theme--documenter-dark .icon.is-large { + height: 3rem; + width: 3rem; } + html.theme--documenter-dark .image, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { + display: block; + position: relative; } + html.theme--documenter-dark .image img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img { + display: block; + height: auto; + width: 100%; } + html.theme--documenter-dark .image img.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img.is-rounded { + border-radius: 290486px; } + html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img, + html.theme--documenter-dark .image.is-square .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img, + html.theme--documenter-dark .image.is-1by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img, + html.theme--documenter-dark .image.is-5by4 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img, + html.theme--documenter-dark .image.is-4by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img, + html.theme--documenter-dark .image.is-3by2 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img, + html.theme--documenter-dark .image.is-5by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img, + html.theme--documenter-dark .image.is-16by9 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img, + html.theme--documenter-dark .image.is-2by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img, + html.theme--documenter-dark .image.is-3by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img, + html.theme--documenter-dark .image.is-4by5 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img, + html.theme--documenter-dark .image.is-3by4 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img, + html.theme--documenter-dark .image.is-2by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img, + html.theme--documenter-dark .image.is-3by5 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img, + html.theme--documenter-dark .image.is-9by16 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img, + html.theme--documenter-dark .image.is-1by2 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img, + html.theme--documenter-dark .image.is-1by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { + height: 100%; + width: 100%; } + html.theme--documenter-dark .image.is-square, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square, html.theme--documenter-dark .image.is-1by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 { + padding-top: 100%; } + html.theme--documenter-dark .image.is-5by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 { + padding-top: 80%; } + html.theme--documenter-dark .image.is-4by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 { + padding-top: 75%; } + html.theme--documenter-dark .image.is-3by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 { + padding-top: 66.6666%; } + html.theme--documenter-dark .image.is-5by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 { + padding-top: 60%; } + html.theme--documenter-dark .image.is-16by9, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 { + padding-top: 56.25%; } + html.theme--documenter-dark .image.is-2by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 { + padding-top: 50%; } + html.theme--documenter-dark .image.is-3by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 { + padding-top: 33.3333%; } + html.theme--documenter-dark .image.is-4by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 { + padding-top: 125%; } + html.theme--documenter-dark .image.is-3by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 { + padding-top: 133.3333%; } + html.theme--documenter-dark .image.is-2by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 { + padding-top: 150%; } + html.theme--documenter-dark .image.is-3by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 { + padding-top: 166.6666%; } + html.theme--documenter-dark .image.is-9by16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 { + padding-top: 177.7777%; } + html.theme--documenter-dark .image.is-1by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 { + padding-top: 200%; } + html.theme--documenter-dark .image.is-1by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 { + padding-top: 300%; } + html.theme--documenter-dark .image.is-16x16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16x16 { + height: 16px; + width: 16px; } + html.theme--documenter-dark .image.is-24x24, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-24x24 { + height: 24px; + width: 24px; } + html.theme--documenter-dark .image.is-32x32, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-32x32 { + height: 32px; + width: 32px; } + html.theme--documenter-dark .image.is-48x48, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-48x48 { + height: 48px; + width: 48px; } + html.theme--documenter-dark .image.is-64x64, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-64x64 { + height: 64px; + width: 64px; } + html.theme--documenter-dark .image.is-96x96, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-96x96 { + height: 96px; + width: 96px; } + html.theme--documenter-dark .image.is-128x128, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-128x128 { + height: 128px; + width: 128px; } + html.theme--documenter-dark .notification { + background-color: whitesmoke; + border-radius: 4px; + padding: 1.25rem 2.5rem 1.25rem 1.5rem; + position: relative; } + html.theme--documenter-dark .notification a:not(.button):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + html.theme--documenter-dark .notification strong { + color: currentColor; } + html.theme--documenter-dark .notification code, + html.theme--documenter-dark .notification pre { + background: white; } + html.theme--documenter-dark .notification pre code { + background: transparent; } + html.theme--documenter-dark .notification > .delete { + position: absolute; + right: 0.5rem; + top: 0.5rem; } + html.theme--documenter-dark .notification .title, + html.theme--documenter-dark .notification .subtitle, + html.theme--documenter-dark .notification .content { + color: currentColor; } + html.theme--documenter-dark .notification.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .notification.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .notification.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .notification.is-dark, html.theme--documenter-dark .content kbd.notification { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .notification.is-primary, html.theme--documenter-dark .docstring > section > a.notification.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .notification.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .notification.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .notification.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .notification.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .notification.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .progress { + -moz-appearance: none; + -webkit-appearance: none; + border: none; + border-radius: 290486px; + display: block; + height: 1rem; + overflow: hidden; + padding: 0; + width: 100%; } + html.theme--documenter-dark .progress::-webkit-progress-bar { + background-color: #dbdbdb; } + html.theme--documenter-dark .progress::-webkit-progress-value { + background-color: #fbfbfb; } + html.theme--documenter-dark .progress::-moz-progress-bar { + background-color: #fbfbfb; } + html.theme--documenter-dark .progress::-ms-fill { + background-color: #fbfbfb; + border: none; } + html.theme--documenter-dark .progress.is-white::-webkit-progress-value { + background-color: white; } + html.theme--documenter-dark .progress.is-white::-moz-progress-bar { + background-color: white; } + html.theme--documenter-dark .progress.is-white::-ms-fill { + background-color: white; } + html.theme--documenter-dark .progress.is-white:indeterminate { + background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-black::-webkit-progress-value { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black::-moz-progress-bar { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black::-ms-fill { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black:indeterminate { + background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-light::-webkit-progress-value { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light::-moz-progress-bar { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light::-ms-fill { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light:indeterminate { + background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-dark::-webkit-progress-value, html.theme--documenter-dark .content kbd.progress::-webkit-progress-value { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark::-moz-progress-bar, html.theme--documenter-dark .content kbd.progress::-moz-progress-bar { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark::-ms-fill, html.theme--documenter-dark .content kbd.progress::-ms-fill { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark:indeterminate, html.theme--documenter-dark .content kbd.progress:indeterminate { + background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-primary::-webkit-progress-value, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary::-moz-progress-bar, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary::-ms-fill, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-ms-fill { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary:indeterminate, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink:indeterminate { + background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-link::-webkit-progress-value { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link::-moz-progress-bar { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link::-ms-fill { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link:indeterminate { + background-image: linear-gradient(to right, #2ad7e6 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-info::-webkit-progress-value { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info::-moz-progress-bar { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info::-ms-fill { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info:indeterminate { + background-image: linear-gradient(to right, #3489da 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-success::-webkit-progress-value { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success::-moz-progress-bar { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success::-ms-fill { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success:indeterminate { + background-image: linear-gradient(to right, #259a12 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-warning::-webkit-progress-value { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning::-moz-progress-bar { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning::-ms-fill { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning:indeterminate { + background-image: linear-gradient(to right, #f4c72f 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-danger::-webkit-progress-value { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger::-moz-progress-bar { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger::-ms-fill { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger:indeterminate { + background-image: linear-gradient(to right, #cb3c33 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress:indeterminate { + animation-duration: 1.5s; + animation-iteration-count: infinite; + animation-name: moveIndeterminate; + animation-timing-function: linear; + background-color: #dbdbdb; + background-image: linear-gradient(to right, #fbfbfb 30%, #dbdbdb 30%); + background-position: top left; + background-repeat: no-repeat; + background-size: 150% 150%; } + html.theme--documenter-dark .progress:indeterminate::-webkit-progress-bar { + background-color: transparent; } + html.theme--documenter-dark .progress:indeterminate::-moz-progress-bar { + background-color: transparent; } + html.theme--documenter-dark .progress.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.progress { + height: 0.75rem; } + html.theme--documenter-dark .progress.is-medium { + height: 1.25rem; } + html.theme--documenter-dark .progress.is-large { + height: 1.5rem; } + +@keyframes moveIndeterminate { + from { + background-position: 200% 0; } + to { + background-position: -200% 0; } } + html.theme--documenter-dark .table { + background-color: white; + color: #363636; } + html.theme--documenter-dark .table td, + html.theme--documenter-dark .table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + html.theme--documenter-dark .table td.is-white, + html.theme--documenter-dark .table th.is-white { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .table td.is-black, + html.theme--documenter-dark .table th.is-black { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .table td.is-light, + html.theme--documenter-dark .table th.is-light { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .table td.is-dark, + html.theme--documenter-dark .table th.is-dark { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .table td.is-primary, + html.theme--documenter-dark .table th.is-primary { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table td.is-link, + html.theme--documenter-dark .table th.is-link { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .table td.is-info, + html.theme--documenter-dark .table th.is-info { + background-color: #3489da; + border-color: #3489da; + color: #fff; } + html.theme--documenter-dark .table td.is-success, + html.theme--documenter-dark .table th.is-success { + background-color: #259a12; + border-color: #259a12; + color: #fff; } + html.theme--documenter-dark .table td.is-warning, + html.theme--documenter-dark .table th.is-warning { + background-color: #f4c72f; + border-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .table td.is-danger, + html.theme--documenter-dark .table th.is-danger { + background-color: #cb3c33; + border-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .table td.is-narrow, + html.theme--documenter-dark .table th.is-narrow { + white-space: nowrap; + width: 1%; } + html.theme--documenter-dark .table td.is-selected, + html.theme--documenter-dark .table th.is-selected { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table td.is-selected a, + html.theme--documenter-dark .table td.is-selected strong, + html.theme--documenter-dark .table th.is-selected a, + html.theme--documenter-dark .table th.is-selected strong { + color: currentColor; } + html.theme--documenter-dark .table th { + color: #cdc3e3; } + html.theme--documenter-dark .table th:not([align]) { + text-align: left; } + html.theme--documenter-dark .table tr.is-selected { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table tr.is-selected a, + html.theme--documenter-dark .table tr.is-selected strong { + color: currentColor; } + html.theme--documenter-dark .table tr.is-selected td, + html.theme--documenter-dark .table tr.is-selected th { + border-color: #fff; + color: currentColor; } + html.theme--documenter-dark .table thead { + background-color: transparent; } + html.theme--documenter-dark .table thead td, + html.theme--documenter-dark .table thead th { + border-width: 0 0 2px; + color: #cdc3e3; } + html.theme--documenter-dark .table tfoot { + background-color: transparent; } + html.theme--documenter-dark .table tfoot td, + html.theme--documenter-dark .table tfoot th { + border-width: 2px 0 0; + color: #cdc3e3; } + html.theme--documenter-dark .table tbody { + background-color: transparent; } + html.theme--documenter-dark .table tbody tr:last-child td, + html.theme--documenter-dark .table tbody tr:last-child th { + border-bottom-width: 0; } + html.theme--documenter-dark .table.is-bordered td, + html.theme--documenter-dark .table.is-bordered th { + border-width: 1px; } + html.theme--documenter-dark .table.is-bordered tr:last-child td, + html.theme--documenter-dark .table.is-bordered tr:last-child th { + border-bottom-width: 1px; } + html.theme--documenter-dark .table.is-fullwidth { + width: 100%; } + html.theme--documenter-dark .table.is-hoverable tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { + background-color: whitesmoke; } + html.theme--documenter-dark .table.is-narrow td, + html.theme--documenter-dark .table.is-narrow th { + padding: 0.25em 0.5em; } + html.theme--documenter-dark .table.is-striped tbody tr:not(.is-selected):nth-child(even) { + background-color: #fafafa; } + html.theme--documenter-dark .table-container { + -webkit-overflow-scrolling: touch; + overflow: auto; + overflow-y: hidden; + max-width: 100%; } + html.theme--documenter-dark .tags { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .tags .tag, html.theme--documenter-dark .tags .content kbd, html.theme--documenter-dark .content .tags kbd, html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .tags .tag:not(:last-child), html.theme--documenter-dark .tags .content kbd:not(:last-child), html.theme--documenter-dark .content .tags kbd:not(:last-child), html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0.5rem; } + html.theme--documenter-dark .tags:last-child { + margin-bottom: -0.5rem; } + html.theme--documenter-dark .tags:not(:last-child) { + margin-bottom: 1rem; } + html.theme--documenter-dark .tags.are-medium .tag:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .content kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .content .tags.are-medium kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { + font-size: 1rem; } + html.theme--documenter-dark .tags.are-large .tag:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .content kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .content .tags.are-large kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { + font-size: 1.25rem; } + html.theme--documenter-dark .tags.is-centered { + justify-content: center; } + html.theme--documenter-dark .tags.is-centered .tag, html.theme--documenter-dark .tags.is-centered .content kbd, html.theme--documenter-dark .content .tags.is-centered kbd, html.theme--documenter-dark .tags.is-centered .docstring > section > a.docs-sourcelink { + margin-right: 0.25rem; + margin-left: 0.25rem; } + html.theme--documenter-dark .tags.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .tags.is-right .tag:not(:first-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:first-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0.5rem; } + html.theme--documenter-dark .tags.is-right .tag:not(:last-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:last-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0; } + html.theme--documenter-dark .tags.has-addons .tag, html.theme--documenter-dark .tags.has-addons .content kbd, html.theme--documenter-dark .content .tags.has-addons kbd, html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink { + margin-right: 0; } + html.theme--documenter-dark .tags.has-addons .tag:not(:first-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:first-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0; + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .tags.has-addons .tag:not(:last-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:last-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .tag:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { + align-items: center; + background-color: whitesmoke; + border-radius: 4px; + color: #fbfbfb; + display: inline-flex; + font-size: 0.75rem; + height: 2em; + justify-content: center; + line-height: 1.5; + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + html.theme--documenter-dark .tag:not(body) .delete, html.theme--documenter-dark .content kbd:not(body) .delete, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .delete { + margin-left: 0.25rem; + margin-right: -0.375rem; } + html.theme--documenter-dark .tag.is-white:not(body), html.theme--documenter-dark .content kbd.is-white:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-white:not(body) { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .tag.is-black:not(body), html.theme--documenter-dark .content kbd.is-black:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-black:not(body) { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .tag.is-light:not(body), html.theme--documenter-dark .content kbd.is-light:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-light:not(body) { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .tag.is-dark:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-dark:not(body), html.theme--documenter-dark .content .docstring > section > kbd:not(body) { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .tag.is-primary:not(body), html.theme--documenter-dark .content kbd.is-primary:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .tag.is-link:not(body), html.theme--documenter-dark .content kbd.is-link:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-link:not(body) { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .tag.is-info:not(body), html.theme--documenter-dark .content kbd.is-info:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-info:not(body) { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .tag.is-success:not(body), html.theme--documenter-dark .content kbd.is-success:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-success:not(body) { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .tag.is-warning:not(body), html.theme--documenter-dark .content kbd.is-warning:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-warning:not(body) { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .tag.is-danger:not(body), html.theme--documenter-dark .content kbd.is-danger:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-danger:not(body) { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .tag.is-normal:not(body), html.theme--documenter-dark .content kbd.is-normal:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-normal:not(body) { + font-size: 0.75rem; } + html.theme--documenter-dark .tag.is-medium:not(body), html.theme--documenter-dark .content kbd.is-medium:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-medium:not(body) { + font-size: 1rem; } + html.theme--documenter-dark .tag.is-large:not(body), html.theme--documenter-dark .content kbd.is-large:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-large:not(body) { + font-size: 1.25rem; } + html.theme--documenter-dark .tag:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .content kbd:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { + margin-left: -0.375em; + margin-right: 0.1875em; } + html.theme--documenter-dark .tag:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .content kbd:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: -0.375em; } + html.theme--documenter-dark .tag:not(body) .icon:first-child:last-child, html.theme--documenter-dark .content kbd:not(body) .icon:first-child:last-child, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { + margin-left: -0.375em; + margin-right: -0.375em; } + html.theme--documenter-dark .tag.is-delete:not(body), html.theme--documenter-dark .content kbd.is-delete:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body) { + margin-left: 1px; + padding: 0; + position: relative; + width: 2em; } + html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + background-color: currentColor; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { + height: 1px; + width: 50%; } + html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + height: 50%; + width: 1px; } + html.theme--documenter-dark .tag.is-delete:not(body):hover, html.theme--documenter-dark .content kbd.is-delete:not(body):hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, html.theme--documenter-dark .tag.is-delete:not(body):focus, html.theme--documenter-dark .content kbd.is-delete:not(body):focus, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { + background-color: #e8e8e8; } + html.theme--documenter-dark .tag.is-delete:not(body):active, html.theme--documenter-dark .content kbd.is-delete:not(body):active, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):active { + background-color: #dbdbdb; } + html.theme--documenter-dark .tag.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:not(body), html.theme--documenter-dark .content kbd.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-rounded:not(body) { + border-radius: 290486px; } + html.theme--documenter-dark a.tag:hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:hover { + text-decoration: underline; } + html.theme--documenter-dark .title, + html.theme--documenter-dark .subtitle { + word-break: break-word; } + html.theme--documenter-dark .title em, + html.theme--documenter-dark .title span, + html.theme--documenter-dark .subtitle em, + html.theme--documenter-dark .subtitle span { + font-weight: inherit; } + html.theme--documenter-dark .title sub, + html.theme--documenter-dark .subtitle sub { + font-size: 0.75em; } + html.theme--documenter-dark .title sup, + html.theme--documenter-dark .subtitle sup { + font-size: 0.75em; } + html.theme--documenter-dark .title .tag, html.theme--documenter-dark .title .content kbd, html.theme--documenter-dark .content .title kbd, html.theme--documenter-dark .title .docstring > section > a.docs-sourcelink, + html.theme--documenter-dark .subtitle .tag, + html.theme--documenter-dark .subtitle .content kbd, + html.theme--documenter-dark .content .subtitle kbd, + html.theme--documenter-dark .subtitle .docstring > section > a.docs-sourcelink { + vertical-align: middle; } + html.theme--documenter-dark .title { + color: #363636; + font-size: 2rem; + font-weight: 600; + line-height: 1.125; } + html.theme--documenter-dark .title strong { + color: inherit; + font-weight: inherit; } + html.theme--documenter-dark .title + .highlight { + margin-top: -0.75rem; } + html.theme--documenter-dark .title:not(.is-spaced) + .subtitle { + margin-top: -1.25rem; } + html.theme--documenter-dark .title.is-1 { + font-size: 3rem; } + html.theme--documenter-dark .title.is-2 { + font-size: 2.5rem; } + html.theme--documenter-dark .title.is-3 { + font-size: 2rem; } + html.theme--documenter-dark .title.is-4 { + font-size: 1.5rem; } + html.theme--documenter-dark .title.is-5 { + font-size: 1.25rem; } + html.theme--documenter-dark .title.is-6 { + font-size: 1rem; } + html.theme--documenter-dark .title.is-7 { + font-size: 0.75rem; } + html.theme--documenter-dark .subtitle { + color: #4a4a4a; + font-size: 1.25rem; + font-weight: 400; + line-height: 1.25; } + html.theme--documenter-dark .subtitle strong { + color: #363636; + font-weight: 600; } + html.theme--documenter-dark .subtitle:not(.is-spaced) + .title { + margin-top: -1.25rem; } + html.theme--documenter-dark .subtitle.is-1 { + font-size: 3rem; } + html.theme--documenter-dark .subtitle.is-2 { + font-size: 2.5rem; } + html.theme--documenter-dark .subtitle.is-3 { + font-size: 2rem; } + html.theme--documenter-dark .subtitle.is-4 { + font-size: 1.5rem; } + html.theme--documenter-dark .subtitle.is-5 { + font-size: 1.25rem; } + html.theme--documenter-dark .subtitle.is-6 { + font-size: 1rem; } + html.theme--documenter-dark .subtitle.is-7 { + font-size: 0.75rem; } + html.theme--documenter-dark .heading { + display: block; + font-size: 11px; + letter-spacing: 1px; + margin-bottom: 5px; + text-transform: uppercase; } + html.theme--documenter-dark .highlight { + font-weight: 400; + max-width: 100%; + overflow: hidden; + padding: 0; } + html.theme--documenter-dark .highlight pre { + overflow: auto; + max-width: 100%; } + html.theme--documenter-dark .number { + align-items: center; + background-color: whitesmoke; + border-radius: 290486px; + display: inline-flex; + font-size: 1.25rem; + height: 2em; + justify-content: center; + margin-right: 1.5rem; + min-width: 2.5em; + padding: 0.25rem 0.5rem; + text-align: center; + vertical-align: top; } + html.theme--documenter-dark .select select, html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + background-color: white; + border-color: #dbdbdb; + border-radius: 4px; + color: #363636; } + html.theme--documenter-dark .select select::-moz-placeholder, html.theme--documenter-dark .textarea::-moz-placeholder, html.theme--documenter-dark .input::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select::-webkit-input-placeholder, html.theme--documenter-dark .textarea::-webkit-input-placeholder, html.theme--documenter-dark .input::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:-moz-placeholder, html.theme--documenter-dark .textarea:-moz-placeholder, html.theme--documenter-dark .input:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:-ms-input-placeholder, html.theme--documenter-dark .textarea:-ms-input-placeholder, html.theme--documenter-dark .input:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:hover, html.theme--documenter-dark .textarea:hover, html.theme--documenter-dark .input:hover, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:hover, html.theme--documenter-dark .select select.is-hovered, html.theme--documenter-dark .is-hovered.textarea, html.theme--documenter-dark .is-hovered.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-hovered { + border-color: #149eaa; } + html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + border-color: #fff; + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] html.theme--documenter-dark .select select, fieldset[disabled] html.theme--documenter-dark .textarea, fieldset[disabled] html.theme--documenter-dark .input, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + background-color: whitesmoke; + border-color: whitesmoke; + box-shadow: none; + color: #7a7a7a; } + html.theme--documenter-dark .select select[disabled]::-moz-placeholder, html.theme--documenter-dark .textarea[disabled]::-moz-placeholder, html.theme--documenter-dark .input[disabled]::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .textarea[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .input[disabled]::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]:-moz-placeholder, html.theme--documenter-dark .textarea[disabled]:-moz-placeholder, html.theme--documenter-dark .input[disabled]:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]:-ms-input-placeholder, html.theme--documenter-dark .textarea[disabled]:-ms-input-placeholder, html.theme--documenter-dark .input[disabled]:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); + max-width: 100%; + width: 100%; } + html.theme--documenter-dark .textarea[readonly], html.theme--documenter-dark .input[readonly], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[readonly] { + box-shadow: none; } + html.theme--documenter-dark .is-white.textarea, html.theme--documenter-dark .is-white.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white { + border-color: white; } + html.theme--documenter-dark .is-white.textarea:focus, html.theme--documenter-dark .is-white.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:focus, html.theme--documenter-dark .is-white.is-focused.textarea, html.theme--documenter-dark .is-white.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-white.textarea:active, html.theme--documenter-dark .is-white.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:active, html.theme--documenter-dark .is-white.is-active.textarea, html.theme--documenter-dark .is-white.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .is-black.textarea, html.theme--documenter-dark .is-black.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black { + border-color: #0a0a0a; } + html.theme--documenter-dark .is-black.textarea:focus, html.theme--documenter-dark .is-black.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:focus, html.theme--documenter-dark .is-black.is-focused.textarea, html.theme--documenter-dark .is-black.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-black.textarea:active, html.theme--documenter-dark .is-black.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:active, html.theme--documenter-dark .is-black.is-active.textarea, html.theme--documenter-dark .is-black.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .is-light.textarea, html.theme--documenter-dark .is-light.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light { + border-color: whitesmoke; } + html.theme--documenter-dark .is-light.textarea:focus, html.theme--documenter-dark .is-light.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:focus, html.theme--documenter-dark .is-light.is-focused.textarea, html.theme--documenter-dark .is-light.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-light.textarea:active, html.theme--documenter-dark .is-light.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:active, html.theme--documenter-dark .is-light.is-active.textarea, html.theme--documenter-dark .is-light.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .is-dark.textarea, html.theme--documenter-dark .content kbd.textarea, html.theme--documenter-dark .is-dark.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark, html.theme--documenter-dark .content kbd.input { + border-color: #363636; } + html.theme--documenter-dark .is-dark.textarea:focus, html.theme--documenter-dark .content kbd.textarea:focus, html.theme--documenter-dark .is-dark.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:focus, html.theme--documenter-dark .content kbd.input:focus, html.theme--documenter-dark .is-dark.is-focused.textarea, html.theme--documenter-dark .content kbd.is-focused.textarea, html.theme--documenter-dark .is-dark.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .content kbd.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-focused, html.theme--documenter-dark .is-dark.textarea:active, html.theme--documenter-dark .content kbd.textarea:active, html.theme--documenter-dark .is-dark.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:active, html.theme--documenter-dark .content kbd.input:active, html.theme--documenter-dark .is-dark.is-active.textarea, html.theme--documenter-dark .content kbd.is-active.textarea, html.theme--documenter-dark .is-dark.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .content kbd.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .is-primary.textarea, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink { + border-color: #4eb5de; } + html.theme--documenter-dark .is-primary.textarea:focus, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:focus, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.is-focused.textarea, html.theme--documenter-dark .docstring > section > a.is-focused.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .docstring > section > a.is-focused.input.docs-sourcelink, html.theme--documenter-dark .is-primary.textarea:active, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:active, html.theme--documenter-dark .is-primary.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:active, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:active, html.theme--documenter-dark .is-primary.is-active.textarea, html.theme--documenter-dark .docstring > section > a.is-active.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .docstring > section > a.is-active.input.docs-sourcelink { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .is-link.textarea, html.theme--documenter-dark .is-link.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link { + border-color: #2ad7e6; } + html.theme--documenter-dark .is-link.textarea:focus, html.theme--documenter-dark .is-link.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:focus, html.theme--documenter-dark .is-link.is-focused.textarea, html.theme--documenter-dark .is-link.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-link.textarea:active, html.theme--documenter-dark .is-link.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:active, html.theme--documenter-dark .is-link.is-active.textarea, html.theme--documenter-dark .is-link.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .is-info.textarea, html.theme--documenter-dark .is-info.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info { + border-color: #3489da; } + html.theme--documenter-dark .is-info.textarea:focus, html.theme--documenter-dark .is-info.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:focus, html.theme--documenter-dark .is-info.is-focused.textarea, html.theme--documenter-dark .is-info.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-info.textarea:active, html.theme--documenter-dark .is-info.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:active, html.theme--documenter-dark .is-info.is-active.textarea, html.theme--documenter-dark .is-info.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .is-success.textarea, html.theme--documenter-dark .is-success.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success { + border-color: #259a12; } + html.theme--documenter-dark .is-success.textarea:focus, html.theme--documenter-dark .is-success.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:focus, html.theme--documenter-dark .is-success.is-focused.textarea, html.theme--documenter-dark .is-success.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-success.textarea:active, html.theme--documenter-dark .is-success.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:active, html.theme--documenter-dark .is-success.is-active.textarea, html.theme--documenter-dark .is-success.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .is-warning.textarea, html.theme--documenter-dark .is-warning.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning { + border-color: #f4c72f; } + html.theme--documenter-dark .is-warning.textarea:focus, html.theme--documenter-dark .is-warning.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:focus, html.theme--documenter-dark .is-warning.is-focused.textarea, html.theme--documenter-dark .is-warning.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-warning.textarea:active, html.theme--documenter-dark .is-warning.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:active, html.theme--documenter-dark .is-warning.is-active.textarea, html.theme--documenter-dark .is-warning.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .is-danger.textarea, html.theme--documenter-dark .is-danger.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger { + border-color: #cb3c33; } + html.theme--documenter-dark .is-danger.textarea:focus, html.theme--documenter-dark .is-danger.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:focus, html.theme--documenter-dark .is-danger.is-focused.textarea, html.theme--documenter-dark .is-danger.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-danger.textarea:active, html.theme--documenter-dark .is-danger.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:active, html.theme--documenter-dark .is-danger.is-active.textarea, html.theme--documenter-dark .is-danger.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .is-small.textarea, html.theme--documenter-dark .is-small.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .is-medium.textarea, html.theme--documenter-dark .is-medium.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .is-large.textarea, html.theme--documenter-dark .is-large.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .is-fullwidth.textarea, html.theme--documenter-dark .is-fullwidth.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-fullwidth { + display: block; + width: 100%; } + html.theme--documenter-dark .is-inline.textarea, html.theme--documenter-dark .is-inline.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-inline { + display: inline; + width: auto; } + html.theme--documenter-dark .input.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + html.theme--documenter-dark .input.is-static, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-static { + background-color: transparent; + border-color: transparent; + box-shadow: none; + padding-left: 0; + padding-right: 0; } + html.theme--documenter-dark .textarea { + display: block; + max-width: 100%; + min-width: 100%; + padding: 0.625em; + resize: vertical; } + html.theme--documenter-dark .textarea:not([rows]) { + max-height: 600px; + min-height: 120px; } + html.theme--documenter-dark .textarea[rows] { + height: initial; } + html.theme--documenter-dark .textarea.has-fixed-size { + resize: none; } + html.theme--documenter-dark .radio, html.theme--documenter-dark .checkbox { + cursor: pointer; + display: inline-block; + line-height: 1.25; + position: relative; } + html.theme--documenter-dark .radio input, html.theme--documenter-dark .checkbox input { + cursor: pointer; } + html.theme--documenter-dark .radio:hover, html.theme--documenter-dark .checkbox:hover { + color: #363636; } + html.theme--documenter-dark .radio[disabled], html.theme--documenter-dark .checkbox[disabled], fieldset[disabled] html.theme--documenter-dark .radio, fieldset[disabled] html.theme--documenter-dark .checkbox { + color: #7a7a7a; + cursor: not-allowed; } + html.theme--documenter-dark .radio + .radio { + margin-left: 0.5em; } + html.theme--documenter-dark .select { + display: inline-block; + max-width: 100%; + position: relative; + vertical-align: top; } + html.theme--documenter-dark .select:not(.is-multiple) { + height: 2.25em; } + html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after { + border-color: #2ad7e6; + right: 1.125em; + z-index: 4; } + html.theme--documenter-dark .select.is-rounded select, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select select { + border-radius: 290486px; + padding-left: 1em; } + html.theme--documenter-dark .select select { + cursor: pointer; + display: block; + font-size: 1em; + max-width: 100%; + outline: none; } + html.theme--documenter-dark .select select::-ms-expand { + display: none; } + html.theme--documenter-dark .select select[disabled]:hover, fieldset[disabled] html.theme--documenter-dark .select select:hover { + border-color: whitesmoke; } + html.theme--documenter-dark .select select:not([multiple]) { + padding-right: 2.5em; } + html.theme--documenter-dark .select select[multiple] { + height: auto; + padding: 0; } + html.theme--documenter-dark .select select[multiple] option { + padding: 0.5em 1em; } + html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading):hover::after { + border-color: #363636; } + html.theme--documenter-dark .select.is-white:not(:hover)::after { + border-color: white; } + html.theme--documenter-dark .select.is-white select { + border-color: white; } + html.theme--documenter-dark .select.is-white select:hover, html.theme--documenter-dark .select.is-white select.is-hovered { + border-color: #f2f2f2; } + html.theme--documenter-dark .select.is-white select:focus, html.theme--documenter-dark .select.is-white select.is-focused, html.theme--documenter-dark .select.is-white select:active, html.theme--documenter-dark .select.is-white select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .select.is-black:not(:hover)::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .select.is-black select { + border-color: #0a0a0a; } + html.theme--documenter-dark .select.is-black select:hover, html.theme--documenter-dark .select.is-black select.is-hovered { + border-color: black; } + html.theme--documenter-dark .select.is-black select:focus, html.theme--documenter-dark .select.is-black select.is-focused, html.theme--documenter-dark .select.is-black select:active, html.theme--documenter-dark .select.is-black select.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .select.is-light:not(:hover)::after { + border-color: whitesmoke; } + html.theme--documenter-dark .select.is-light select { + border-color: whitesmoke; } + html.theme--documenter-dark .select.is-light select:hover, html.theme--documenter-dark .select.is-light select.is-hovered { + border-color: #e8e8e8; } + html.theme--documenter-dark .select.is-light select:focus, html.theme--documenter-dark .select.is-light select.is-focused, html.theme--documenter-dark .select.is-light select:active, html.theme--documenter-dark .select.is-light select.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .select.is-dark:not(:hover)::after, html.theme--documenter-dark .content kbd.select:not(:hover)::after { + border-color: #363636; } + html.theme--documenter-dark .select.is-dark select, html.theme--documenter-dark .content kbd.select select { + border-color: #363636; } + html.theme--documenter-dark .select.is-dark select:hover, html.theme--documenter-dark .content kbd.select select:hover, html.theme--documenter-dark .select.is-dark select.is-hovered, html.theme--documenter-dark .content kbd.select select.is-hovered { + border-color: #292929; } + html.theme--documenter-dark .select.is-dark select:focus, html.theme--documenter-dark .content kbd.select select:focus, html.theme--documenter-dark .select.is-dark select.is-focused, html.theme--documenter-dark .content kbd.select select.is-focused, html.theme--documenter-dark .select.is-dark select:active, html.theme--documenter-dark .content kbd.select select:active, html.theme--documenter-dark .select.is-dark select.is-active, html.theme--documenter-dark .content kbd.select select.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .select.is-primary:not(:hover)::after, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink:not(:hover)::after { + border-color: #4eb5de; } + html.theme--documenter-dark .select.is-primary select, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select { + border-color: #4eb5de; } + html.theme--documenter-dark .select.is-primary select:hover, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:hover, html.theme--documenter-dark .select.is-primary select.is-hovered, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-hovered { + border-color: #39acda; } + html.theme--documenter-dark .select.is-primary select:focus, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:focus, html.theme--documenter-dark .select.is-primary select.is-focused, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-focused, html.theme--documenter-dark .select.is-primary select:active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:active, html.theme--documenter-dark .select.is-primary select.is-active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-active { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .select.is-link:not(:hover)::after { + border-color: #2ad7e6; } + html.theme--documenter-dark .select.is-link select { + border-color: #2ad7e6; } + html.theme--documenter-dark .select.is-link select:hover, html.theme--documenter-dark .select.is-link select.is-hovered { + border-color: #1acddc; } + html.theme--documenter-dark .select.is-link select:focus, html.theme--documenter-dark .select.is-link select.is-focused, html.theme--documenter-dark .select.is-link select:active, html.theme--documenter-dark .select.is-link select.is-active { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .select.is-info:not(:hover)::after { + border-color: #3489da; } + html.theme--documenter-dark .select.is-info select { + border-color: #3489da; } + html.theme--documenter-dark .select.is-info select:hover, html.theme--documenter-dark .select.is-info select.is-hovered { + border-color: #267ccf; } + html.theme--documenter-dark .select.is-info select:focus, html.theme--documenter-dark .select.is-info select.is-focused, html.theme--documenter-dark .select.is-info select:active, html.theme--documenter-dark .select.is-info select.is-active { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .select.is-success:not(:hover)::after { + border-color: #259a12; } + html.theme--documenter-dark .select.is-success select { + border-color: #259a12; } + html.theme--documenter-dark .select.is-success select:hover, html.theme--documenter-dark .select.is-success select.is-hovered { + border-color: #20830f; } + html.theme--documenter-dark .select.is-success select:focus, html.theme--documenter-dark .select.is-success select.is-focused, html.theme--documenter-dark .select.is-success select:active, html.theme--documenter-dark .select.is-success select.is-active { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .select.is-warning:not(:hover)::after { + border-color: #f4c72f; } + html.theme--documenter-dark .select.is-warning select { + border-color: #f4c72f; } + html.theme--documenter-dark .select.is-warning select:hover, html.theme--documenter-dark .select.is-warning select.is-hovered { + border-color: #f3c017; } + html.theme--documenter-dark .select.is-warning select:focus, html.theme--documenter-dark .select.is-warning select.is-focused, html.theme--documenter-dark .select.is-warning select:active, html.theme--documenter-dark .select.is-warning select.is-active { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .select.is-danger:not(:hover)::after { + border-color: #cb3c33; } + html.theme--documenter-dark .select.is-danger select { + border-color: #cb3c33; } + html.theme--documenter-dark .select.is-danger select:hover, html.theme--documenter-dark .select.is-danger select.is-hovered { + border-color: #b7362e; } + html.theme--documenter-dark .select.is-danger select:focus, html.theme--documenter-dark .select.is-danger select.is-focused, html.theme--documenter-dark .select.is-danger select:active, html.theme--documenter-dark .select.is-danger select.is-active { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .select.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .select.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .select.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .select.is-disabled::after { + border-color: #7a7a7a; } + html.theme--documenter-dark .select.is-fullwidth { + width: 100%; } + html.theme--documenter-dark .select.is-fullwidth select { + width: 100%; } + html.theme--documenter-dark .select.is-loading::after { + margin-top: 0; + position: absolute; + right: 0.625em; + top: 0.625em; + transform: none; } + html.theme--documenter-dark .select.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + html.theme--documenter-dark .select.is-loading.is-medium:after { + font-size: 1.25rem; } + html.theme--documenter-dark .select.is-loading.is-large:after { + font-size: 1.5rem; } + html.theme--documenter-dark .file { + align-items: stretch; + display: flex; + justify-content: flex-start; + position: relative; } + html.theme--documenter-dark .file.is-white .file-cta { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:hover .file-cta, html.theme--documenter-dark .file.is-white.is-hovered .file-cta { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:focus .file-cta, html.theme--documenter-dark .file.is-white.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:active .file-cta, html.theme--documenter-dark .file.is-white.is-active .file-cta { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-black .file-cta { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-black:hover .file-cta, html.theme--documenter-dark .file.is-black.is-hovered .file-cta { + background-color: #040404; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-black:focus .file-cta, html.theme--documenter-dark .file.is-black.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); + color: white; } + html.theme--documenter-dark .file.is-black:active .file-cta, html.theme--documenter-dark .file.is-black.is-active .file-cta { + background-color: black; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-light .file-cta { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-light:hover .file-cta, html.theme--documenter-dark .file.is-light.is-hovered .file-cta { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-light:focus .file-cta, html.theme--documenter-dark .file.is-light.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25); + color: #363636; } + html.theme--documenter-dark .file.is-light:active .file-cta, html.theme--documenter-dark .file.is-light.is-active .file-cta { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-dark .file-cta, html.theme--documenter-dark .content kbd.file .file-cta { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:hover .file-cta, html.theme--documenter-dark .content kbd.file:hover .file-cta, html.theme--documenter-dark .file.is-dark.is-hovered .file-cta, html.theme--documenter-dark .content kbd.file.is-hovered .file-cta { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:focus .file-cta, html.theme--documenter-dark .content kbd.file:focus .file-cta, html.theme--documenter-dark .file.is-dark.is-focused .file-cta, html.theme--documenter-dark .content kbd.file.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25); + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:active .file-cta, html.theme--documenter-dark .content kbd.file:active .file-cta, html.theme--documenter-dark .file.is-dark.is-active .file-cta, html.theme--documenter-dark .content kbd.file.is-active .file-cta { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-primary .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink .file-cta { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-primary:hover .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:hover .file-cta, html.theme--documenter-dark .file.is-primary.is-hovered .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-primary:focus .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:focus .file-cta, html.theme--documenter-dark .file.is-primary.is-focused .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-primary:active .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:active .file-cta, html.theme--documenter-dark .file.is-primary.is-active .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-active.docs-sourcelink .file-cta { + background-color: #39acda; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link .file-cta { + background-color: #2ad7e6; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link:hover .file-cta, html.theme--documenter-dark .file.is-link.is-hovered .file-cta { + background-color: #1ed5e5; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link:focus .file-cta, html.theme--documenter-dark .file.is-link.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(42, 215, 230, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-link:active .file-cta, html.theme--documenter-dark .file.is-link.is-active .file-cta { + background-color: #1acddc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info .file-cta { + background-color: #3489da; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info:hover .file-cta, html.theme--documenter-dark .file.is-info.is-hovered .file-cta { + background-color: #2983d8; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info:focus .file-cta, html.theme--documenter-dark .file.is-info.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(52, 137, 218, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-info:active .file-cta, html.theme--documenter-dark .file.is-info.is-active .file-cta { + background-color: #267ccf; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success .file-cta { + background-color: #259a12; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success:hover .file-cta, html.theme--documenter-dark .file.is-success.is-hovered .file-cta { + background-color: #228f11; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success:focus .file-cta, html.theme--documenter-dark .file.is-success.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(37, 154, 18, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-success:active .file-cta, html.theme--documenter-dark .file.is-success.is-active .file-cta { + background-color: #20830f; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-warning .file-cta { + background-color: #f4c72f; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:hover .file-cta, html.theme--documenter-dark .file.is-warning.is-hovered .file-cta { + background-color: #f3c423; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:focus .file-cta, html.theme--documenter-dark .file.is-warning.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(244, 199, 47, 0.25); + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:active .file-cta, html.theme--documenter-dark .file.is-warning.is-active .file-cta { + background-color: #f3c017; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-danger .file-cta { + background-color: #cb3c33; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-danger:hover .file-cta, html.theme--documenter-dark .file.is-danger.is-hovered .file-cta { + background-color: #c13930; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-danger:focus .file-cta, html.theme--documenter-dark .file.is-danger.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(203, 60, 51, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-danger:active .file-cta, html.theme--documenter-dark .file.is-danger.is-active .file-cta { + background-color: #b7362e; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.file { + font-size: 0.75rem; } + html.theme--documenter-dark .file.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .file.is-medium .file-icon .fa { + font-size: 21px; } + html.theme--documenter-dark .file.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .file.is-large .file-icon .fa { + font-size: 28px; } + html.theme--documenter-dark .file.has-name .file-cta { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .file.has-name .file-name { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .file.has-name.is-empty .file-cta { + border-radius: 4px; } + html.theme--documenter-dark .file.has-name.is-empty .file-name { + display: none; } + html.theme--documenter-dark .file.is-boxed .file-label { + flex-direction: column; } + html.theme--documenter-dark .file.is-boxed .file-cta { + flex-direction: column; + height: auto; + padding: 1em 3em; } + html.theme--documenter-dark .file.is-boxed .file-name { + border-width: 0 1px 1px; } + html.theme--documenter-dark .file.is-boxed .file-icon { + height: 1.5em; + width: 1.5em; } + html.theme--documenter-dark .file.is-boxed .file-icon .fa { + font-size: 21px; } + html.theme--documenter-dark .file.is-boxed.is-small .file-icon .fa, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { + font-size: 14px; } + html.theme--documenter-dark .file.is-boxed.is-medium .file-icon .fa { + font-size: 28px; } + html.theme--documenter-dark .file.is-boxed.is-large .file-icon .fa { + font-size: 35px; } + html.theme--documenter-dark .file.is-boxed.has-name .file-cta { + border-radius: 4px 4px 0 0; } + html.theme--documenter-dark .file.is-boxed.has-name .file-name { + border-radius: 0 0 4px 4px; + border-width: 0 1px 1px; } + html.theme--documenter-dark .file.is-centered { + justify-content: center; } + html.theme--documenter-dark .file.is-fullwidth .file-label { + width: 100%; } + html.theme--documenter-dark .file.is-fullwidth .file-name { + flex-grow: 1; + max-width: none; } + html.theme--documenter-dark .file.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .file.is-right .file-cta { + border-radius: 0 4px 4px 0; } + html.theme--documenter-dark .file.is-right .file-name { + border-radius: 4px 0 0 4px; + border-width: 1px 0 1px 1px; + order: -1; } + html.theme--documenter-dark .file-label { + align-items: stretch; + display: flex; + cursor: pointer; + justify-content: flex-start; + overflow: hidden; + position: relative; } + html.theme--documenter-dark .file-label:hover .file-cta { + background-color: #eeeeee; + color: #363636; } + html.theme--documenter-dark .file-label:hover .file-name { + border-color: #d5d5d5; } + html.theme--documenter-dark .file-label:active .file-cta { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .file-label:active .file-name { + border-color: #cfcfcf; } + html.theme--documenter-dark .file-input { + height: 100%; + left: 0; + opacity: 0; + outline: none; + position: absolute; + top: 0; + width: 100%; } + html.theme--documenter-dark .file-cta, + html.theme--documenter-dark .file-name { + border-color: #dbdbdb; + border-radius: 4px; + font-size: 1em; + padding-left: 1em; + padding-right: 1em; + white-space: nowrap; } + html.theme--documenter-dark .file-cta { + background-color: whitesmoke; + color: #4a4a4a; } + html.theme--documenter-dark .file-name { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px 1px 1px 0; + display: block; + max-width: 16em; + overflow: hidden; + text-align: left; + text-overflow: ellipsis; } + html.theme--documenter-dark .file-icon { + align-items: center; + display: flex; + height: 1em; + justify-content: center; + margin-right: 0.5em; + width: 1em; } + html.theme--documenter-dark .file-icon .fa { + font-size: 14px; } + html.theme--documenter-dark .label { + color: #363636; + display: block; + font-size: 1rem; + font-weight: 700; } + html.theme--documenter-dark .label:not(:last-child) { + margin-bottom: 0.5em; } + html.theme--documenter-dark .label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.label { + font-size: 0.75rem; } + html.theme--documenter-dark .label.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .label.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .help { + display: block; + font-size: 0.75rem; + margin-top: 0.25rem; } + html.theme--documenter-dark .help.is-white { + color: white; } + html.theme--documenter-dark .help.is-black { + color: #0a0a0a; } + html.theme--documenter-dark .help.is-light { + color: whitesmoke; } + html.theme--documenter-dark .help.is-dark, html.theme--documenter-dark .content kbd.help { + color: #363636; } + html.theme--documenter-dark .help.is-primary, html.theme--documenter-dark .docstring > section > a.help.docs-sourcelink { + color: #4eb5de; } + html.theme--documenter-dark .help.is-link { + color: #2ad7e6; } + html.theme--documenter-dark .help.is-info { + color: #3489da; } + html.theme--documenter-dark .help.is-success { + color: #259a12; } + html.theme--documenter-dark .help.is-warning { + color: #f4c72f; } + html.theme--documenter-dark .help.is-danger { + color: #cb3c33; } + html.theme--documenter-dark .field:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .field.has-addons { + display: flex; + justify-content: flex-start; } + html.theme--documenter-dark .field.has-addons .control:not(:last-child) { + margin-right: -1px; } + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .button, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .input, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .select select { + border-radius: 0; } + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .button, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .input, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .select select { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .button, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .input, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .select select { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-hovered:not([disabled]) { + z-index: 2; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]), html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]) { + z-index: 3; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus:hover, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active:hover, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]):hover { + z-index: 4; } + html.theme--documenter-dark .field.has-addons .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .field.has-addons.has-addons-centered { + justify-content: center; } + html.theme--documenter-dark .field.has-addons.has-addons-right { + justify-content: flex-end; } + html.theme--documenter-dark .field.has-addons.has-addons-fullwidth .control { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .field.is-grouped { + display: flex; + justify-content: flex-start; } + html.theme--documenter-dark .field.is-grouped > .control { + flex-shrink: 0; } + html.theme--documenter-dark .field.is-grouped > .control:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + html.theme--documenter-dark .field.is-grouped > .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .field.is-grouped.is-grouped-centered { + justify-content: center; } + html.theme--documenter-dark .field.is-grouped.is-grouped-right { + justify-content: flex-end; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline { + flex-wrap: wrap; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:last-child, html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:not(:last-child) { + margin-bottom: 0; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field.is-horizontal { + display: flex; } } + html.theme--documenter-dark .field-label .label { + font-size: inherit; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .field-label { + margin-bottom: 0.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field-label { + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + margin-right: 1.5rem; + text-align: right; } + html.theme--documenter-dark .field-label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.field-label { + font-size: 0.75rem; + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-normal { + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-medium { + font-size: 1.25rem; + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-large { + font-size: 1.5rem; + padding-top: 0.375em; } } + html.theme--documenter-dark .field-body .field .field { + margin-bottom: 0; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field-body { + display: flex; + flex-basis: 0; + flex-grow: 5; + flex-shrink: 1; } + html.theme--documenter-dark .field-body .field { + margin-bottom: 0; } + html.theme--documenter-dark .field-body > .field { + flex-shrink: 1; } + html.theme--documenter-dark .field-body > .field:not(.is-narrow) { + flex-grow: 1; } + html.theme--documenter-dark .field-body > .field:not(:last-child) { + margin-right: 0.75rem; } } + html.theme--documenter-dark .control { + box-sizing: border-box; + clear: both; + font-size: 1rem; + position: relative; + text-align: left; } + html.theme--documenter-dark .control.has-icons-left .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select:focus ~ .icon { + color: #7a7a7a; } + html.theme--documenter-dark .control.has-icons-left .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-small ~ .icon { + font-size: 0.75rem; } + html.theme--documenter-dark .control.has-icons-left .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-medium ~ .icon { + font-size: 1.25rem; } + html.theme--documenter-dark .control.has-icons-left .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-large ~ .icon { + font-size: 1.5rem; } + html.theme--documenter-dark .control.has-icons-left .icon, html.theme--documenter-dark .control.has-icons-right .icon { + color: #dbdbdb; + height: 2.25em; + pointer-events: none; + position: absolute; + top: 0; + width: 2.25em; + z-index: 4; } + html.theme--documenter-dark .control.has-icons-left .input, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, + html.theme--documenter-dark .control.has-icons-left .select select { + padding-left: 2.25em; } + html.theme--documenter-dark .control.has-icons-left .icon.is-left { + left: 0; } + html.theme--documenter-dark .control.has-icons-right .input, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, + html.theme--documenter-dark .control.has-icons-right .select select { + padding-right: 2.25em; } + html.theme--documenter-dark .control.has-icons-right .icon.is-right { + right: 0; } + html.theme--documenter-dark .control.is-loading::after { + position: absolute !important; + right: 0.625em; + top: 0.625em; + z-index: 4; } + html.theme--documenter-dark .control.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + html.theme--documenter-dark .control.is-loading.is-medium:after { + font-size: 1.25rem; } + html.theme--documenter-dark .control.is-loading.is-large:after { + font-size: 1.5rem; } + html.theme--documenter-dark .breadcrumb { + font-size: 1rem; + white-space: nowrap; } + html.theme--documenter-dark .breadcrumb a { + align-items: center; + color: #2ad7e6; + display: flex; + justify-content: center; + padding: 0 0.75em; } + html.theme--documenter-dark .breadcrumb a:hover { + color: #97ebf3; } + html.theme--documenter-dark .breadcrumb li { + align-items: center; + display: flex; } + html.theme--documenter-dark .breadcrumb li:first-child a { + padding-left: 0; } + html.theme--documenter-dark .breadcrumb li.is-active a { + color: #cdc3e3; + cursor: default; + pointer-events: none; } + html.theme--documenter-dark .breadcrumb li + li::before { + color: #b5b5b5; + content: "\0002f"; } + html.theme--documenter-dark .breadcrumb ul, + html.theme--documenter-dark .breadcrumb ol { + align-items: flex-start; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .breadcrumb .icon:first-child { + margin-right: 0.5em; } + html.theme--documenter-dark .breadcrumb .icon:last-child { + margin-left: 0.5em; } + html.theme--documenter-dark .breadcrumb.is-centered ol, + html.theme--documenter-dark .breadcrumb.is-centered ul { + justify-content: center; } + html.theme--documenter-dark .breadcrumb.is-right ol, + html.theme--documenter-dark .breadcrumb.is-right ul { + justify-content: flex-end; } + html.theme--documenter-dark .breadcrumb.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.breadcrumb { + font-size: 0.75rem; } + html.theme--documenter-dark .breadcrumb.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .breadcrumb.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .breadcrumb.has-arrow-separator li + li::before { + content: "\02192"; } + html.theme--documenter-dark .breadcrumb.has-bullet-separator li + li::before { + content: "\02022"; } + html.theme--documenter-dark .breadcrumb.has-dot-separator li + li::before { + content: "\000b7"; } + html.theme--documenter-dark .breadcrumb.has-succeeds-separator li + li::before { + content: "\0227B"; } + html.theme--documenter-dark .card { + background-color: white; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #fbfbfb; + max-width: 100%; + position: relative; } + html.theme--documenter-dark .card-header { + background-color: transparent; + align-items: stretch; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + display: flex; } + html.theme--documenter-dark .card-header-title { + align-items: center; + color: #cdc3e3; + display: flex; + flex-grow: 1; + font-weight: 700; + padding: 0.75rem; } + html.theme--documenter-dark .card-header-title.is-centered { + justify-content: center; } + html.theme--documenter-dark .card-header-icon { + align-items: center; + cursor: pointer; + display: flex; + justify-content: center; + padding: 0.75rem; } + html.theme--documenter-dark .card-image { + display: block; + position: relative; } + html.theme--documenter-dark .card-content { + background-color: transparent; + padding: 1.5rem; } + html.theme--documenter-dark .card-footer { + background-color: transparent; + border-top: 1px solid #dbdbdb; + align-items: stretch; + display: flex; } + html.theme--documenter-dark .card-footer-item { + align-items: center; + display: flex; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + justify-content: center; + padding: 0.75rem; } + html.theme--documenter-dark .card-footer-item:not(:last-child) { + border-right: 1px solid #dbdbdb; } + html.theme--documenter-dark .card .media:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .dropdown { + display: inline-flex; + position: relative; + vertical-align: top; } + html.theme--documenter-dark .dropdown.is-active .dropdown-menu, html.theme--documenter-dark .dropdown.is-hoverable:hover .dropdown-menu { + display: block; } + html.theme--documenter-dark .dropdown.is-right .dropdown-menu { + left: auto; + right: 0; } + html.theme--documenter-dark .dropdown.is-up .dropdown-menu { + bottom: 100%; + padding-bottom: 4px; + padding-top: initial; + top: auto; } + html.theme--documenter-dark .dropdown-menu { + display: none; + left: 0; + min-width: 12rem; + padding-top: 4px; + position: absolute; + top: 100%; + z-index: 20; } + html.theme--documenter-dark .dropdown-content { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + html.theme--documenter-dark .dropdown-item { + color: #4a4a4a; + display: block; + font-size: 0.875rem; + line-height: 1.5; + padding: 0.375rem 1rem; + position: relative; } + html.theme--documenter-dark a.dropdown-item, + html.theme--documenter-dark button.dropdown-item { + padding-right: 3rem; + text-align: left; + white-space: nowrap; + width: 100%; } + html.theme--documenter-dark a.dropdown-item:hover, + html.theme--documenter-dark button.dropdown-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark a.dropdown-item.is-active, + html.theme--documenter-dark button.dropdown-item.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .dropdown-divider { + background-color: #dbdbdb; + border: none; + display: block; + height: 1px; + margin: 0.5rem 0; } + html.theme--documenter-dark .level { + align-items: center; + justify-content: space-between; } + html.theme--documenter-dark .level code { + border-radius: 4px; } + html.theme--documenter-dark .level img { + display: inline-block; + vertical-align: top; } + html.theme--documenter-dark .level.is-mobile { + display: flex; } + html.theme--documenter-dark .level.is-mobile .level-left, + html.theme--documenter-dark .level.is-mobile .level-right { + display: flex; } + html.theme--documenter-dark .level.is-mobile .level-left + .level-right { + margin-top: 0; } + html.theme--documenter-dark .level.is-mobile .level-item:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + html.theme--documenter-dark .level.is-mobile .level-item:not(.is-narrow) { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level { + display: flex; } + html.theme--documenter-dark .level > .level-item:not(.is-narrow) { + flex-grow: 1; } } + html.theme--documenter-dark .level-item { + align-items: center; + display: flex; + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; + justify-content: center; } + html.theme--documenter-dark .level-item .title, + html.theme--documenter-dark .level-item .subtitle { + margin-bottom: 0; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .level-item:not(:last-child) { + margin-bottom: 0.75rem; } } + html.theme--documenter-dark .level-left, + html.theme--documenter-dark .level-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .level-left .level-item.is-flexible, + html.theme--documenter-dark .level-right .level-item.is-flexible { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-left .level-item:not(:last-child), + html.theme--documenter-dark .level-right .level-item:not(:last-child) { + margin-right: 0.75rem; } } + html.theme--documenter-dark .level-left { + align-items: center; + justify-content: flex-start; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .level-left + .level-right { + margin-top: 1.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-left { + display: flex; } } + html.theme--documenter-dark .level-right { + align-items: center; + justify-content: flex-end; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-right { + display: flex; } } + html.theme--documenter-dark .list { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .list-item { + display: block; + padding: 0.5em 1em; } + html.theme--documenter-dark .list-item:not(a) { + color: #fbfbfb; } + html.theme--documenter-dark .list-item:first-child { + border-top-left-radius: 4px; + border-top-right-radius: 4px; } + html.theme--documenter-dark .list-item:last-child { + border-bottom-left-radius: 4px; + border-bottom-right-radius: 4px; } + html.theme--documenter-dark .list-item:not(:last-child) { + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .list-item.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark a.list-item { + background-color: whitesmoke; + cursor: pointer; } + html.theme--documenter-dark .media { + align-items: flex-start; + display: flex; + text-align: left; } + html.theme--documenter-dark .media .content:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .media .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + display: flex; + padding-top: 0.75rem; } + html.theme--documenter-dark .media .media .content:not(:last-child), + html.theme--documenter-dark .media .media .control:not(:last-child) { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .media .media .media { + padding-top: 0.5rem; } + html.theme--documenter-dark .media .media .media + .media { + margin-top: 0.5rem; } + html.theme--documenter-dark .media + .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + margin-top: 1rem; + padding-top: 1rem; } + html.theme--documenter-dark .media.is-large + .media { + margin-top: 1.5rem; + padding-top: 1.5rem; } + html.theme--documenter-dark .media-left, + html.theme--documenter-dark .media-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .media-left { + margin-right: 1rem; } + html.theme--documenter-dark .media-right { + margin-left: 1rem; } + html.theme--documenter-dark .media-content { + flex-basis: auto; + flex-grow: 1; + flex-shrink: 1; + text-align: left; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .media-content { + overflow-x: auto; } } + html.theme--documenter-dark .menu { + font-size: 1rem; } + html.theme--documenter-dark .menu.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.menu { + font-size: 0.75rem; } + html.theme--documenter-dark .menu.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .menu.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .menu-list { + line-height: 1.25; } + html.theme--documenter-dark .menu-list a { + border-radius: 2px; + color: #fbfbfb; + display: block; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .menu-list a:hover { + background-color: whitesmoke; + color: #cdc3e3; } + html.theme--documenter-dark .menu-list a.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .menu-list li ul { + border-left: 1px solid #dbdbdb; + margin: 0.75em; + padding-left: 0.75em; } + html.theme--documenter-dark .menu-label { + color: #7a7a7a; + font-size: 0.75em; + letter-spacing: 0.1em; + text-transform: uppercase; } + html.theme--documenter-dark .menu-label:not(:first-child) { + margin-top: 1em; } + html.theme--documenter-dark .menu-label:not(:last-child) { + margin-bottom: 1em; } + html.theme--documenter-dark .message { + background-color: whitesmoke; + border-radius: 4px; + font-size: 1rem; } + html.theme--documenter-dark .message strong { + color: currentColor; } + html.theme--documenter-dark .message a:not(.button):not(.tag):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + html.theme--documenter-dark .message.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.message { + font-size: 0.75rem; } + html.theme--documenter-dark .message.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .message.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .message.is-white { + background-color: white; } + html.theme--documenter-dark .message.is-white .message-header { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .message.is-white .message-body { + border-color: white; + color: #4d4d4d; } + html.theme--documenter-dark .message.is-black { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-black .message-header { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .message.is-black .message-body { + border-color: #0a0a0a; + color: #090909; } + html.theme--documenter-dark .message.is-light { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-light .message-header { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .message.is-light .message-body { + border-color: whitesmoke; + color: #505050; } + html.theme--documenter-dark .message.is-dark, html.theme--documenter-dark .content kbd.message { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-dark .message-header, html.theme--documenter-dark .content kbd.message .message-header { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .message.is-dark .message-body, html.theme--documenter-dark .content kbd.message .message-body { + border-color: #363636; + color: #2a2a2a; } + html.theme--documenter-dark .message.is-primary, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink { + background-color: #f6fbfd; } + html.theme--documenter-dark .message.is-primary .message-header, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-header { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .message.is-primary .message-body, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-body { + border-color: #4eb5de; + color: #1f556a; } + html.theme--documenter-dark .message.is-link { + background-color: #f6fdfe; } + html.theme--documenter-dark .message.is-link .message-header { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .message.is-link .message-body { + border-color: #2ad7e6; + color: #0c2f32; } + html.theme--documenter-dark .message.is-info { + background-color: #f6fafd; } + html.theme--documenter-dark .message.is-info .message-header { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .message.is-info .message-body { + border-color: #3489da; + color: #215485; } + html.theme--documenter-dark .message.is-success { + background-color: #f7fef6; } + html.theme--documenter-dark .message.is-success .message-header { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .message.is-success .message-body { + border-color: #259a12; + color: #113b0a; } + html.theme--documenter-dark .message.is-warning { + background-color: #fefcf5; } + html.theme--documenter-dark .message.is-warning .message-header { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .message.is-warning .message-body { + border-color: #f4c72f; + color: #332909; } + html.theme--documenter-dark .message.is-danger { + background-color: #fdf7f7; } + html.theme--documenter-dark .message.is-danger .message-header { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .message.is-danger .message-body { + border-color: #cb3c33; + color: #8d302a; } + html.theme--documenter-dark .message-header { + align-items: center; + background-color: #fbfbfb; + border-radius: 4px 4px 0 0; + color: rgba(0, 0, 0, 0.7); + display: flex; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.75em 1em; + position: relative; } + html.theme--documenter-dark .message-header .delete { + flex-grow: 0; + flex-shrink: 0; + margin-left: 0.75em; } + html.theme--documenter-dark .message-header + .message-body { + border-width: 0; + border-top-left-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .message-body { + border-color: #dbdbdb; + border-radius: 4px; + border-style: solid; + border-width: 0 0 0 4px; + color: #fbfbfb; + padding: 1.25em 1.5em; } + html.theme--documenter-dark .message-body code, + html.theme--documenter-dark .message-body pre { + background-color: white; } + html.theme--documenter-dark .message-body pre code { + background-color: transparent; } + html.theme--documenter-dark .modal { + align-items: center; + display: none; + flex-direction: column; + justify-content: center; + overflow: hidden; + position: fixed; + z-index: 40; } + html.theme--documenter-dark .modal.is-active { + display: flex; } + html.theme--documenter-dark .modal-background { + background-color: rgba(10, 10, 10, 0.86); } + html.theme--documenter-dark .modal-content, + html.theme--documenter-dark .modal-card { + margin: 0 20px; + max-height: calc(100vh - 160px); + overflow: auto; + position: relative; + width: 100%; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .modal-content, + html.theme--documenter-dark .modal-card { + margin: 0 auto; + max-height: calc(100vh - 40px); + width: 640px; } } + html.theme--documenter-dark .modal-close { + background: none; + height: 40px; + position: fixed; + right: 20px; + top: 20px; + width: 40px; } + html.theme--documenter-dark .modal-card { + display: flex; + flex-direction: column; + max-height: calc(100vh - 40px); + overflow: hidden; + -ms-overflow-y: visible; } + html.theme--documenter-dark .modal-card-head, + html.theme--documenter-dark .modal-card-foot { + align-items: center; + background-color: whitesmoke; + display: flex; + flex-shrink: 0; + justify-content: flex-start; + padding: 20px; + position: relative; } + html.theme--documenter-dark .modal-card-head { + border-bottom: 1px solid #dbdbdb; + border-top-left-radius: 6px; + border-top-right-radius: 6px; } + html.theme--documenter-dark .modal-card-title { + color: #cdc3e3; + flex-grow: 1; + flex-shrink: 0; + font-size: 1.5rem; + line-height: 1; } + html.theme--documenter-dark .modal-card-foot { + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark .modal-card-foot .button:not(:last-child) { + margin-right: 0.5em; } + html.theme--documenter-dark .modal-card-body { + -webkit-overflow-scrolling: touch; + background-color: white; + flex-grow: 1; + flex-shrink: 1; + overflow: auto; + padding: 20px; } + html.theme--documenter-dark .navbar { + background-color: white; + min-height: 3.25rem; + position: relative; + z-index: 30; } + html.theme--documenter-dark .navbar.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link { + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-burger { + color: #0a0a0a; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-white .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link { + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-dropdown a.navbar-item.is-active { + background-color: white; + color: #0a0a0a; } } + html.theme--documenter-dark .navbar.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link { + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link::after { + border-color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-burger { + color: white; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-black .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link { + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link::after { + border-color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-dropdown a.navbar-item.is-active { + background-color: #0a0a0a; + color: white; } } + html.theme--documenter-dark .navbar.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link { + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link::after { + border-color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-burger { + color: #363636; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-light .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link { + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link::after { + border-color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #363636; } } + html.theme--documenter-dark .navbar.is-dark, html.theme--documenter-dark .content kbd.navbar { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link { + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link::after { + border-color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-burger, html.theme--documenter-dark .content kbd.navbar .navbar-burger { + color: whitesmoke; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-dark .navbar-start > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-end > .navbar-item, + html.theme--documenter-dark .content kbd.navbar .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link { + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link::after, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link::after { + border-color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { + background-color: #363636; + color: whitesmoke; } } + html.theme--documenter-dark .navbar.is-primary, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-burger, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-primary .navbar-start > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-end > .navbar-item, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link::after, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { + background-color: #4eb5de; + color: #fff; } } + html.theme--documenter-dark .navbar.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-link .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-dropdown a.navbar-item.is-active { + background-color: #2ad7e6; + color: #fff; } } + html.theme--documenter-dark .navbar.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-info .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-dropdown a.navbar-item.is-active { + background-color: #3489da; + color: #fff; } } + html.theme--documenter-dark .navbar.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-success .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-dropdown a.navbar-item.is-active { + background-color: #259a12; + color: #fff; } } + html.theme--documenter-dark .navbar.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-burger { + color: rgba(0, 0, 0, 0.7); } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-warning .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } } + html.theme--documenter-dark .navbar.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-danger .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { + background-color: #cb3c33; + color: #fff; } } + html.theme--documenter-dark .navbar > .container { + align-items: stretch; + display: flex; + min-height: 3.25rem; + width: 100%; } + html.theme--documenter-dark .navbar.has-shadow { + box-shadow: 0 2px 0 0 whitesmoke; } + html.theme--documenter-dark .navbar.is-fixed-bottom, html.theme--documenter-dark .navbar.is-fixed-top { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom.has-shadow { + box-shadow: 0 -2px 0 0 whitesmoke; } + html.theme--documenter-dark .navbar.is-fixed-top { + top: 0; } + html.theme--documenter-dark html.has-navbar-fixed-top, + html.theme--documenter-dark body.has-navbar-fixed-top { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom, + html.theme--documenter-dark body.has-navbar-fixed-bottom { + padding-bottom: 3.25rem; } + html.theme--documenter-dark .navbar-brand, + html.theme--documenter-dark .navbar-tabs { + align-items: stretch; + display: flex; + flex-shrink: 0; + min-height: 3.25rem; } + html.theme--documenter-dark .navbar-brand a.navbar-item:focus, html.theme--documenter-dark .navbar-brand a.navbar-item:hover { + background-color: transparent; } + html.theme--documenter-dark .navbar-tabs { + -webkit-overflow-scrolling: touch; + max-width: 100vw; + overflow-x: auto; + overflow-y: hidden; } + html.theme--documenter-dark .navbar-burger { + color: #4a4a4a; + cursor: pointer; + display: block; + height: 3.25rem; + position: relative; + width: 3.25rem; + margin-left: auto; } + html.theme--documenter-dark .navbar-burger span { + background-color: currentColor; + display: block; + height: 1px; + left: calc(50% - 8px); + position: absolute; + transform-origin: center; + transition-duration: 86ms; + transition-property: background-color, opacity, transform; + transition-timing-function: ease-out; + width: 16px; } + html.theme--documenter-dark .navbar-burger span:nth-child(1) { + top: calc(50% - 6px); } + html.theme--documenter-dark .navbar-burger span:nth-child(2) { + top: calc(50% - 1px); } + html.theme--documenter-dark .navbar-burger span:nth-child(3) { + top: calc(50% + 4px); } + html.theme--documenter-dark .navbar-burger:hover { + background-color: rgba(0, 0, 0, 0.05); } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(1) { + transform: translateY(5px) rotate(45deg); } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(2) { + opacity: 0; } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(3) { + transform: translateY(-5px) rotate(-45deg); } + html.theme--documenter-dark .navbar-menu { + display: none; } + html.theme--documenter-dark .navbar-item, + html.theme--documenter-dark .navbar-link { + color: #4a4a4a; + display: block; + line-height: 1.5; + padding: 0.5rem 0.75rem; + position: relative; } + html.theme--documenter-dark .navbar-item .icon:only-child, + html.theme--documenter-dark .navbar-link .icon:only-child { + margin-left: -0.25rem; + margin-right: -0.25rem; } + html.theme--documenter-dark a.navbar-item, + html.theme--documenter-dark .navbar-link { + cursor: pointer; } + html.theme--documenter-dark a.navbar-item:focus, html.theme--documenter-dark a.navbar-item:focus-within, html.theme--documenter-dark a.navbar-item:hover, html.theme--documenter-dark a.navbar-item.is-active, + html.theme--documenter-dark .navbar-link:focus, + html.theme--documenter-dark .navbar-link:focus-within, + html.theme--documenter-dark .navbar-link:hover, + html.theme--documenter-dark .navbar-link.is-active { + background-color: #fafafa; + color: #2ad7e6; } + html.theme--documenter-dark .navbar-item { + display: block; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .navbar-item img { + max-height: 1.75rem; } + html.theme--documenter-dark .navbar-item.has-dropdown { + padding: 0; } + html.theme--documenter-dark .navbar-item.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .navbar-item.is-tab { + border-bottom: 1px solid transparent; + min-height: 3.25rem; + padding-bottom: calc(0.5rem - 1px); } + html.theme--documenter-dark .navbar-item.is-tab:focus, html.theme--documenter-dark .navbar-item.is-tab:hover { + background-color: transparent; + border-bottom-color: #2ad7e6; } + html.theme--documenter-dark .navbar-item.is-tab.is-active { + background-color: transparent; + border-bottom-color: #2ad7e6; + border-bottom-style: solid; + border-bottom-width: 3px; + color: #2ad7e6; + padding-bottom: calc(0.5rem - 3px); } + html.theme--documenter-dark .navbar-content { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .navbar-link:not(.is-arrowless) { + padding-right: 2.5em; } + html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after { + border-color: #2ad7e6; + margin-top: -0.375em; + right: 1.125em; } + html.theme--documenter-dark .navbar-dropdown { + font-size: 0.875rem; + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + html.theme--documenter-dark .navbar-dropdown .navbar-item { + padding-left: 1.5rem; + padding-right: 1.5rem; } + html.theme--documenter-dark .navbar-divider { + background-color: whitesmoke; + border: none; + display: none; + height: 2px; + margin: 0.5rem 0; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .navbar > .container { + display: block; } + html.theme--documenter-dark .navbar-brand .navbar-item, + html.theme--documenter-dark .navbar-tabs .navbar-item { + align-items: center; + display: flex; } + html.theme--documenter-dark .navbar-link::after { + display: none; } + html.theme--documenter-dark .navbar-menu { + background-color: white; + box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); + padding: 0.5rem 0; } + html.theme--documenter-dark .navbar-menu.is-active { + display: block; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch, html.theme--documenter-dark .navbar.is-fixed-top-touch { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .navbar.is-fixed-top-touch { + top: 0; } + html.theme--documenter-dark .navbar.is-fixed-top .navbar-menu, html.theme--documenter-dark .navbar.is-fixed-top-touch .navbar-menu { + -webkit-overflow-scrolling: touch; + max-height: calc(100vh - 3.25rem); + overflow: auto; } + html.theme--documenter-dark html.has-navbar-fixed-top-touch, + html.theme--documenter-dark body.has-navbar-fixed-top-touch { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom-touch, + html.theme--documenter-dark body.has-navbar-fixed-bottom-touch { + padding-bottom: 3.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar, + html.theme--documenter-dark .navbar-menu, + html.theme--documenter-dark .navbar-start, + html.theme--documenter-dark .navbar-end { + align-items: stretch; + display: flex; } + html.theme--documenter-dark .navbar { + min-height: 3.25rem; } + html.theme--documenter-dark .navbar.is-spaced { + padding: 1rem 2rem; } + html.theme--documenter-dark .navbar.is-spaced .navbar-start, + html.theme--documenter-dark .navbar.is-spaced .navbar-end { + align-items: center; } + html.theme--documenter-dark .navbar.is-spaced a.navbar-item, + html.theme--documenter-dark .navbar.is-spaced .navbar-link { + border-radius: 4px; } + html.theme--documenter-dark .navbar.is-transparent a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent a.navbar-item:hover, html.theme--documenter-dark .navbar.is-transparent a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-transparent .navbar-link:focus, + html.theme--documenter-dark .navbar.is-transparent .navbar-link:hover, + html.theme--documenter-dark .navbar.is-transparent .navbar-link.is-active { + background-color: transparent !important; } + html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { + background-color: transparent !important; } + html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #2ad7e6; } + html.theme--documenter-dark .navbar-burger { + display: none; } + html.theme--documenter-dark .navbar-item, + html.theme--documenter-dark .navbar-link { + align-items: center; + display: flex; } + html.theme--documenter-dark .navbar-item { + display: flex; } + html.theme--documenter-dark .navbar-item.has-dropdown { + align-items: stretch; } + html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-link::after { + transform: rotate(135deg) translate(0.25em, -0.25em); } + html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-dropdown { + border-bottom: 2px solid #dbdbdb; + border-radius: 6px 6px 0 0; + border-top: none; + bottom: 100%; + box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); + top: auto; } + html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown { + display: block; } + .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { + opacity: 1; + pointer-events: auto; + transform: translateY(0); } + html.theme--documenter-dark .navbar-menu { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .navbar-start { + justify-content: flex-start; + margin-right: auto; } + html.theme--documenter-dark .navbar-end { + justify-content: flex-end; + margin-left: auto; } + html.theme--documenter-dark .navbar-dropdown { + background-color: white; + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 2px solid #dbdbdb; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); + display: none; + font-size: 0.875rem; + left: 0; + min-width: 100%; + position: absolute; + top: 100%; + z-index: 20; } + html.theme--documenter-dark .navbar-dropdown .navbar-item { + padding: 0.375rem 1rem; + white-space: nowrap; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item { + padding-right: 3rem; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #2ad7e6; } + .navbar.is-spaced html.theme--documenter-dark .navbar-dropdown, html.theme--documenter-dark .navbar-dropdown.is-boxed { + border-radius: 6px; + border-top: none; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + display: block; + opacity: 0; + pointer-events: none; + top: calc(100% + (-4px)); + transform: translateY(-5px); + transition-duration: 86ms; + transition-property: opacity, transform; } + html.theme--documenter-dark .navbar-dropdown.is-right { + left: auto; + right: 0; } + html.theme--documenter-dark .navbar-divider { + display: block; } + html.theme--documenter-dark .navbar > .container .navbar-brand, + html.theme--documenter-dark .container > .navbar .navbar-brand { + margin-left: -.75rem; } + html.theme--documenter-dark .navbar > .container .navbar-menu, + html.theme--documenter-dark .container > .navbar .navbar-menu { + margin-right: -.75rem; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop, html.theme--documenter-dark .navbar.is-fixed-top-desktop { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .navbar.is-fixed-top-desktop { + top: 0; } + html.theme--documenter-dark html.has-navbar-fixed-top-desktop, + html.theme--documenter-dark body.has-navbar-fixed-top-desktop { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop, + html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop { + padding-bottom: 3.25rem; } + html.theme--documenter-dark html.has-spaced-navbar-fixed-top, + html.theme--documenter-dark body.has-spaced-navbar-fixed-top { + padding-top: 5.25rem; } + html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom, + html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom { + padding-bottom: 5.25rem; } + html.theme--documenter-dark a.navbar-item.is-active, + html.theme--documenter-dark .navbar-link.is-active { + color: #0a0a0a; } + html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover), + html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover) { + background-color: transparent; } + html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #fafafa; } } + html.theme--documenter-dark .hero.is-fullheight-with-navbar { + min-height: calc(100vh - 3.25rem); } + html.theme--documenter-dark .pagination { + font-size: 1rem; + margin: -0.25rem; } + html.theme--documenter-dark .pagination.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination { + font-size: 0.75rem; } + html.theme--documenter-dark .pagination.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .pagination.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .pagination.is-rounded .pagination-previous, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, + html.theme--documenter-dark .pagination.is-rounded .pagination-next, + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { + padding-left: 1em; + padding-right: 1em; + border-radius: 290486px; } + html.theme--documenter-dark .pagination.is-rounded .pagination-link, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { + border-radius: 290486px; } + html.theme--documenter-dark .pagination, + html.theme--documenter-dark .pagination-list { + align-items: center; + display: flex; + justify-content: center; + text-align: center; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark .pagination-link, + html.theme--documenter-dark .pagination-ellipsis { + font-size: 1em; + justify-content: center; + margin: 0.25rem; + padding-left: 0.5em; + padding-right: 0.5em; + text-align: center; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark .pagination-link { + border-color: #dbdbdb; + color: #363636; + min-width: 2.25em; } + html.theme--documenter-dark .pagination-previous:hover, + html.theme--documenter-dark .pagination-next:hover, + html.theme--documenter-dark .pagination-link:hover { + border-color: #b5b5b5; + color: #97ebf3; } + html.theme--documenter-dark .pagination-previous:focus, + html.theme--documenter-dark .pagination-next:focus, + html.theme--documenter-dark .pagination-link:focus { + border-color: #3c5dcd; } + html.theme--documenter-dark .pagination-previous:active, + html.theme--documenter-dark .pagination-next:active, + html.theme--documenter-dark .pagination-link:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } + html.theme--documenter-dark .pagination-previous[disabled], + html.theme--documenter-dark .pagination-next[disabled], + html.theme--documenter-dark .pagination-link[disabled] { + background-color: #dbdbdb; + border-color: #dbdbdb; + box-shadow: none; + color: #7a7a7a; + opacity: 0.5; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next { + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + html.theme--documenter-dark .pagination-link.is-current { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .pagination-ellipsis { + color: #b5b5b5; + pointer-events: none; } + html.theme--documenter-dark .pagination-list { + flex-wrap: wrap; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .pagination { + flex-wrap: wrap; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .pagination-list li { + flex-grow: 1; + flex-shrink: 1; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .pagination-list { + flex-grow: 1; + flex-shrink: 1; + justify-content: flex-start; + order: 1; } + html.theme--documenter-dark .pagination-previous { + order: 2; } + html.theme--documenter-dark .pagination-next { + order: 3; } + html.theme--documenter-dark .pagination { + justify-content: space-between; } + html.theme--documenter-dark .pagination.is-centered .pagination-previous { + order: 1; } + html.theme--documenter-dark .pagination.is-centered .pagination-list { + justify-content: center; + order: 2; } + html.theme--documenter-dark .pagination.is-centered .pagination-next { + order: 3; } + html.theme--documenter-dark .pagination.is-right .pagination-previous { + order: 1; } + html.theme--documenter-dark .pagination.is-right .pagination-next { + order: 2; } + html.theme--documenter-dark .pagination.is-right .pagination-list { + justify-content: flex-end; + order: 3; } } + html.theme--documenter-dark .panel { + font-size: 1rem; } + html.theme--documenter-dark .panel:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .panel-heading, + html.theme--documenter-dark .panel-tabs, + html.theme--documenter-dark .panel-block { + border-bottom: 1px solid #dbdbdb; + border-left: 1px solid #dbdbdb; + border-right: 1px solid #dbdbdb; } + html.theme--documenter-dark .panel-heading:first-child, + html.theme--documenter-dark .panel-tabs:first-child, + html.theme--documenter-dark .panel-block:first-child { + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark .panel-heading { + background-color: whitesmoke; + border-radius: 4px 4px 0 0; + color: #cdc3e3; + font-size: 1.25em; + font-weight: 300; + line-height: 1.25; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .panel-tabs { + align-items: flex-end; + display: flex; + font-size: 0.875em; + justify-content: center; } + html.theme--documenter-dark .panel-tabs a { + border-bottom: 1px solid #dbdbdb; + margin-bottom: -1px; + padding: 0.5em; } + html.theme--documenter-dark .panel-tabs a.is-active { + border-bottom-color: #4a4a4a; + color: #363636; } + html.theme--documenter-dark .panel-list a { + color: #fbfbfb; } + html.theme--documenter-dark .panel-list a:hover { + color: #2ad7e6; } + html.theme--documenter-dark .panel-block { + align-items: center; + color: #cdc3e3; + display: flex; + justify-content: flex-start; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .panel-block input[type="checkbox"] { + margin-right: 0.75em; } + html.theme--documenter-dark .panel-block > .control { + flex-grow: 1; + flex-shrink: 1; + width: 100%; } + html.theme--documenter-dark .panel-block.is-wrapped { + flex-wrap: wrap; } + html.theme--documenter-dark .panel-block.is-active { + border-left-color: #2ad7e6; + color: #363636; } + html.theme--documenter-dark .panel-block.is-active .panel-icon { + color: #2ad7e6; } + html.theme--documenter-dark a.panel-block, + html.theme--documenter-dark label.panel-block { + cursor: pointer; } + html.theme--documenter-dark a.panel-block:hover, + html.theme--documenter-dark label.panel-block:hover { + background-color: whitesmoke; } + html.theme--documenter-dark .panel-icon { + display: inline-block; + font-size: 14px; + height: 1em; + line-height: 1em; + text-align: center; + vertical-align: top; + width: 1em; + color: #7a7a7a; + margin-right: 0.75em; } + html.theme--documenter-dark .panel-icon .fa { + font-size: inherit; + line-height: inherit; } + html.theme--documenter-dark .tabs { + -webkit-overflow-scrolling: touch; + align-items: stretch; + display: flex; + font-size: 1rem; + justify-content: space-between; + overflow: hidden; + overflow-x: auto; + white-space: nowrap; } + html.theme--documenter-dark .tabs a { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + color: #fbfbfb; + display: flex; + justify-content: center; + margin-bottom: -1px; + padding: 0.5em 1em; + vertical-align: top; } + html.theme--documenter-dark .tabs a:hover { + border-bottom-color: #cdc3e3; + color: #cdc3e3; } + html.theme--documenter-dark .tabs li { + display: block; } + html.theme--documenter-dark .tabs li.is-active a { + border-bottom-color: #2ad7e6; + color: #2ad7e6; } + html.theme--documenter-dark .tabs ul { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + display: flex; + flex-grow: 1; + flex-shrink: 0; + justify-content: flex-start; } + html.theme--documenter-dark .tabs ul.is-left { + padding-right: 0.75em; } + html.theme--documenter-dark .tabs ul.is-center { + flex: none; + justify-content: center; + padding-left: 0.75em; + padding-right: 0.75em; } + html.theme--documenter-dark .tabs ul.is-right { + justify-content: flex-end; + padding-left: 0.75em; } + html.theme--documenter-dark .tabs .icon:first-child { + margin-right: 0.5em; } + html.theme--documenter-dark .tabs .icon:last-child { + margin-left: 0.5em; } + html.theme--documenter-dark .tabs.is-centered ul { + justify-content: center; } + html.theme--documenter-dark .tabs.is-right ul { + justify-content: flex-end; } + html.theme--documenter-dark .tabs.is-boxed a { + border: 1px solid transparent; + border-radius: 4px 4px 0 0; } + html.theme--documenter-dark .tabs.is-boxed a:hover { + background-color: whitesmoke; + border-bottom-color: #dbdbdb; } + html.theme--documenter-dark .tabs.is-boxed li.is-active a { + background-color: white; + border-color: #dbdbdb; + border-bottom-color: transparent !important; } + html.theme--documenter-dark .tabs.is-fullwidth li { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .tabs.is-toggle a { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px; + margin-bottom: 0; + position: relative; } + html.theme--documenter-dark .tabs.is-toggle a:hover { + background-color: whitesmoke; + border-color: #b5b5b5; + z-index: 2; } + html.theme--documenter-dark .tabs.is-toggle li + li { + margin-left: -1px; } + html.theme--documenter-dark .tabs.is-toggle li:first-child a { + border-radius: 4px 0 0 4px; } + html.theme--documenter-dark .tabs.is-toggle li:last-child a { + border-radius: 0 4px 4px 0; } + html.theme--documenter-dark .tabs.is-toggle li.is-active a { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; + z-index: 1; } + html.theme--documenter-dark .tabs.is-toggle ul { + border-bottom: none; } + html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:first-child a { + border-bottom-left-radius: 290486px; + border-top-left-radius: 290486px; + padding-left: 1.25em; } + html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:last-child a { + border-bottom-right-radius: 290486px; + border-top-right-radius: 290486px; + padding-right: 1.25em; } + html.theme--documenter-dark .tabs.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.tabs { + font-size: 0.75rem; } + html.theme--documenter-dark .tabs.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .tabs.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .column { + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + padding: 0.75rem; } + .columns.is-mobile > html.theme--documenter-dark .column.is-narrow { + flex: none; } + .columns.is-mobile > html.theme--documenter-dark .column.is-full { + flex: none; + width: 100%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-three-quarters { + flex: none; + width: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-two-thirds { + flex: none; + width: 66.6666%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-half { + flex: none; + width: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-third { + flex: none; + width: 33.3333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-quarter { + flex: none; + width: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-fifth { + flex: none; + width: 20%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-two-fifths { + flex: none; + width: 40%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-three-fifths { + flex: none; + width: 60%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-four-fifths { + flex: none; + width: 80%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-quarters { + margin-left: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-thirds { + margin-left: 66.6666%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-half { + margin-left: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-third { + margin-left: 33.3333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-quarter { + margin-left: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-fifth { + margin-left: 20%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-fifths { + margin-left: 40%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-fifths { + margin-left: 60%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-four-fifths { + margin-left: 80%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-0 { + flex: none; + width: 0%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-0 { + margin-left: 0%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-1 { + flex: none; + width: 8.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-1 { + margin-left: 8.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-2 { + flex: none; + width: 16.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-2 { + margin-left: 16.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-3 { + flex: none; + width: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-3 { + margin-left: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-4 { + flex: none; + width: 33.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-4 { + margin-left: 33.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-5 { + flex: none; + width: 41.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-5 { + margin-left: 41.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-6 { + flex: none; + width: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-6 { + margin-left: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-7 { + flex: none; + width: 58.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-7 { + margin-left: 58.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-8 { + flex: none; + width: 66.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-8 { + margin-left: 66.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-9 { + flex: none; + width: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-9 { + margin-left: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-10 { + flex: none; + width: 83.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-10 { + margin-left: 83.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-11 { + flex: none; + width: 91.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-11 { + margin-left: 91.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-12 { + flex: none; + width: 100%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-12 { + margin-left: 100%; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .column.is-narrow-mobile { + flex: none; } + html.theme--documenter-dark .column.is-full-mobile { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-mobile { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-mobile { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-mobile { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-mobile { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-mobile { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-mobile { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-mobile { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-mobile { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-mobile { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-mobile { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-mobile { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-mobile { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-mobile { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-mobile { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-mobile { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-mobile { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-mobile { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-mobile { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-mobile { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-mobile { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-mobile { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-mobile { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-mobile { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-mobile { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-mobile { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-mobile { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-mobile { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-mobile { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-mobile { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-mobile { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-mobile { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-mobile { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-mobile { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-mobile { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-mobile { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-mobile { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-mobile { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-mobile { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-mobile { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-mobile { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-mobile { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-mobile { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-mobile { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-mobile { + margin-left: 100%; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .column.is-narrow, html.theme--documenter-dark .column.is-narrow-tablet { + flex: none; } + html.theme--documenter-dark .column.is-full, html.theme--documenter-dark .column.is-full-tablet { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters, html.theme--documenter-dark .column.is-three-quarters-tablet { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds, html.theme--documenter-dark .column.is-two-thirds-tablet { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half, html.theme--documenter-dark .column.is-half-tablet { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third, html.theme--documenter-dark .column.is-one-third-tablet { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter, html.theme--documenter-dark .column.is-one-quarter-tablet { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth, html.theme--documenter-dark .column.is-one-fifth-tablet { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths, html.theme--documenter-dark .column.is-two-fifths-tablet { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths, html.theme--documenter-dark .column.is-three-fifths-tablet { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths, html.theme--documenter-dark .column.is-four-fifths-tablet { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters, html.theme--documenter-dark .column.is-offset-three-quarters-tablet { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds, html.theme--documenter-dark .column.is-offset-two-thirds-tablet { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half, html.theme--documenter-dark .column.is-offset-half-tablet { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third, html.theme--documenter-dark .column.is-offset-one-third-tablet { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter, html.theme--documenter-dark .column.is-offset-one-quarter-tablet { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth, html.theme--documenter-dark .column.is-offset-one-fifth-tablet { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths, html.theme--documenter-dark .column.is-offset-two-fifths-tablet { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths, html.theme--documenter-dark .column.is-offset-three-fifths-tablet { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths, html.theme--documenter-dark .column.is-offset-four-fifths-tablet { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0, html.theme--documenter-dark .column.is-0-tablet { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0, html.theme--documenter-dark .column.is-offset-0-tablet { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1, html.theme--documenter-dark .column.is-1-tablet { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1, html.theme--documenter-dark .column.is-offset-1-tablet { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2, html.theme--documenter-dark .column.is-2-tablet { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2, html.theme--documenter-dark .column.is-offset-2-tablet { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3, html.theme--documenter-dark .column.is-3-tablet { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3, html.theme--documenter-dark .column.is-offset-3-tablet { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4, html.theme--documenter-dark .column.is-4-tablet { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4, html.theme--documenter-dark .column.is-offset-4-tablet { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5, html.theme--documenter-dark .column.is-5-tablet { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5, html.theme--documenter-dark .column.is-offset-5-tablet { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6, html.theme--documenter-dark .column.is-6-tablet { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6, html.theme--documenter-dark .column.is-offset-6-tablet { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7, html.theme--documenter-dark .column.is-7-tablet { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7, html.theme--documenter-dark .column.is-offset-7-tablet { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8, html.theme--documenter-dark .column.is-8-tablet { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8, html.theme--documenter-dark .column.is-offset-8-tablet { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9, html.theme--documenter-dark .column.is-9-tablet { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9, html.theme--documenter-dark .column.is-offset-9-tablet { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10, html.theme--documenter-dark .column.is-10-tablet { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10, html.theme--documenter-dark .column.is-offset-10-tablet { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11, html.theme--documenter-dark .column.is-11-tablet { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11, html.theme--documenter-dark .column.is-offset-11-tablet { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12, html.theme--documenter-dark .column.is-12-tablet { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12, html.theme--documenter-dark .column.is-offset-12-tablet { + margin-left: 100%; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .column.is-narrow-touch { + flex: none; } + html.theme--documenter-dark .column.is-full-touch { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-touch { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-touch { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-touch { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-touch { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-touch { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-touch { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-touch { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-touch { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-touch { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-touch { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-touch { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-touch { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-touch { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-touch { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-touch { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-touch { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-touch { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-touch { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-touch { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-touch { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-touch { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-touch { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-touch { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-touch { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-touch { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-touch { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-touch { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-touch { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-touch { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-touch { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-touch { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-touch { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-touch { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-touch { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-touch { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-touch { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-touch { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-touch { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-touch { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-touch { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-touch { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-touch { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-touch { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-touch { + margin-left: 100%; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .column.is-narrow-desktop { + flex: none; } + html.theme--documenter-dark .column.is-full-desktop { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-desktop { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-desktop { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-desktop { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-desktop { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-desktop { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-desktop { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-desktop { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-desktop { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-desktop { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-desktop { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-desktop { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-desktop { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-desktop { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-desktop { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-desktop { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-desktop { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-desktop { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-desktop { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-desktop { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-desktop { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-desktop { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-desktop { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-desktop { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-desktop { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-desktop { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-desktop { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-desktop { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-desktop { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-desktop { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-desktop { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-desktop { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-desktop { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-desktop { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-desktop { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-desktop { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-desktop { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-desktop { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-desktop { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-desktop { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-desktop { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-desktop { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-desktop { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-desktop { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-desktop { + margin-left: 100%; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .column.is-narrow-widescreen { + flex: none; } + html.theme--documenter-dark .column.is-full-widescreen { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-widescreen { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-widescreen { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-widescreen { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-widescreen { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-widescreen { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-widescreen { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-widescreen { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-widescreen { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-widescreen { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-widescreen { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-widescreen { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-widescreen { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-widescreen { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-widescreen { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-widescreen { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-widescreen { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-widescreen { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-widescreen { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-widescreen { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-widescreen { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-widescreen { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-widescreen { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-widescreen { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-widescreen { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-widescreen { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-widescreen { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-widescreen { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-widescreen { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-widescreen { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-widescreen { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-widescreen { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-widescreen { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-widescreen { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-widescreen { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-widescreen { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-widescreen { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-widescreen { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-widescreen { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-widescreen { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-widescreen { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-widescreen { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-widescreen { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-widescreen { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-widescreen { + margin-left: 100%; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .column.is-narrow-fullhd { + flex: none; } + html.theme--documenter-dark .column.is-full-fullhd { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-fullhd { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-fullhd { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-fullhd { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-fullhd { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-fullhd { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-fullhd { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-fullhd { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-fullhd { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-fullhd { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-fullhd { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-fullhd { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-fullhd { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-fullhd { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-fullhd { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-fullhd { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-fullhd { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-fullhd { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-fullhd { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-fullhd { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-fullhd { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-fullhd { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-fullhd { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-fullhd { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-fullhd { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-fullhd { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-fullhd { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-fullhd { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-fullhd { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-fullhd { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-fullhd { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-fullhd { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-fullhd { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-fullhd { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-fullhd { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-fullhd { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-fullhd { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-fullhd { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-fullhd { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-fullhd { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-fullhd { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-fullhd { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-fullhd { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-fullhd { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-fullhd { + margin-left: 100%; } } + html.theme--documenter-dark .columns { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + html.theme--documenter-dark .columns:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .columns:not(:last-child) { + margin-bottom: calc(1.5rem - 0.75rem); } + html.theme--documenter-dark .columns.is-centered { + justify-content: center; } + html.theme--documenter-dark .columns.is-gapless { + margin-left: 0; + margin-right: 0; + margin-top: 0; } + html.theme--documenter-dark .columns.is-gapless > .column { + margin: 0; + padding: 0 !important; } + html.theme--documenter-dark .columns.is-gapless:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .columns.is-gapless:last-child { + margin-bottom: 0; } + html.theme--documenter-dark .columns.is-mobile { + display: flex; } + html.theme--documenter-dark .columns.is-multiline { + flex-wrap: wrap; } + html.theme--documenter-dark .columns.is-vcentered { + align-items: center; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns:not(.is-desktop) { + display: flex; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-desktop { + display: flex; } } + html.theme--documenter-dark .columns.is-variable { + --columnGap: 0.75rem; + margin-left: calc(-1 * var(--columnGap)); + margin-right: calc(-1 * var(--columnGap)); } + html.theme--documenter-dark .columns.is-variable .column { + padding-left: var(--columnGap); + padding-right: var(--columnGap); } + html.theme--documenter-dark .columns.is-variable.is-0 { + --columnGap: 0rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-0-mobile { + --columnGap: 0rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-0-tablet { + --columnGap: 0rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-0-tablet-only { + --columnGap: 0rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-0-touch { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-0-desktop { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-0-desktop-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-0-widescreen { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-0-widescreen-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-0-fullhd { + --columnGap: 0rem; } } + html.theme--documenter-dark .columns.is-variable.is-1 { + --columnGap: 0.25rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-1-mobile { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-1-tablet { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-1-tablet-only { + --columnGap: 0.25rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-1-touch { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-1-desktop { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-1-desktop-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-1-widescreen { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-1-widescreen-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-1-fullhd { + --columnGap: 0.25rem; } } + html.theme--documenter-dark .columns.is-variable.is-2 { + --columnGap: 0.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-2-mobile { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-2-tablet { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-2-tablet-only { + --columnGap: 0.5rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-2-touch { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-2-desktop { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-2-desktop-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-2-widescreen { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-2-widescreen-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-2-fullhd { + --columnGap: 0.5rem; } } + html.theme--documenter-dark .columns.is-variable.is-3 { + --columnGap: 0.75rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-3-mobile { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-3-tablet { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-3-tablet-only { + --columnGap: 0.75rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-3-touch { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-3-desktop { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-3-desktop-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-3-widescreen { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-3-widescreen-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-3-fullhd { + --columnGap: 0.75rem; } } + html.theme--documenter-dark .columns.is-variable.is-4 { + --columnGap: 1rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-4-mobile { + --columnGap: 1rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-4-tablet { + --columnGap: 1rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-4-tablet-only { + --columnGap: 1rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-4-touch { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-4-desktop { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-4-desktop-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-4-widescreen { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-4-widescreen-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-4-fullhd { + --columnGap: 1rem; } } + html.theme--documenter-dark .columns.is-variable.is-5 { + --columnGap: 1.25rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-5-mobile { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-5-tablet { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-5-tablet-only { + --columnGap: 1.25rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-5-touch { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-5-desktop { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-5-desktop-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-5-widescreen { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-5-widescreen-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-5-fullhd { + --columnGap: 1.25rem; } } + html.theme--documenter-dark .columns.is-variable.is-6 { + --columnGap: 1.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-6-mobile { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-6-tablet { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-6-tablet-only { + --columnGap: 1.5rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-6-touch { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-6-desktop { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-6-desktop-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-6-widescreen { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-6-widescreen-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-6-fullhd { + --columnGap: 1.5rem; } } + html.theme--documenter-dark .columns.is-variable.is-7 { + --columnGap: 1.75rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-7-mobile { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-7-tablet { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-7-tablet-only { + --columnGap: 1.75rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-7-touch { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-7-desktop { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-7-desktop-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-7-widescreen { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-7-fullhd { + --columnGap: 1.75rem; } } + html.theme--documenter-dark .columns.is-variable.is-8 { + --columnGap: 2rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-8-mobile { + --columnGap: 2rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-8-tablet { + --columnGap: 2rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-8-tablet-only { + --columnGap: 2rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-8-touch { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-8-desktop { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-8-desktop-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-8-widescreen { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-8-widescreen-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-8-fullhd { + --columnGap: 2rem; } } + html.theme--documenter-dark .tile { + align-items: stretch; + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + min-height: min-content; } + html.theme--documenter-dark .tile.is-ancestor { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + html.theme--documenter-dark .tile.is-ancestor:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .tile.is-ancestor:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .tile.is-child { + margin: 0 !important; } + html.theme--documenter-dark .tile.is-parent { + padding: 0.75rem; } + html.theme--documenter-dark .tile.is-vertical { + flex-direction: column; } + html.theme--documenter-dark .tile.is-vertical > .tile.is-child:not(:last-child) { + margin-bottom: 1.5rem !important; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .tile:not(.is-child) { + display: flex; } + html.theme--documenter-dark .tile.is-1 { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .tile.is-2 { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .tile.is-3 { + flex: none; + width: 25%; } + html.theme--documenter-dark .tile.is-4 { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .tile.is-5 { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .tile.is-6 { + flex: none; + width: 50%; } + html.theme--documenter-dark .tile.is-7 { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .tile.is-8 { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .tile.is-9 { + flex: none; + width: 75%; } + html.theme--documenter-dark .tile.is-10 { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .tile.is-11 { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .tile.is-12 { + flex: none; + width: 100%; } } + html.theme--documenter-dark .hero { + align-items: stretch; + display: flex; + flex-direction: column; + justify-content: space-between; } + html.theme--documenter-dark .hero .navbar { + background: none; } + html.theme--documenter-dark .hero .tabs ul { + border-bottom: none; } + html.theme--documenter-dark .hero.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-white strong { + color: inherit; } + html.theme--documenter-dark .hero.is-white .title { + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .subtitle { + color: rgba(10, 10, 10, 0.9); } + html.theme--documenter-dark .hero.is-white .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-white .subtitle strong { + color: #0a0a0a; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-white .navbar-menu { + background-color: white; } } + html.theme--documenter-dark .hero.is-white .navbar-item, + html.theme--documenter-dark .hero.is-white .navbar-link { + color: rgba(10, 10, 10, 0.7); } + html.theme--documenter-dark .hero.is-white a.navbar-item:hover, html.theme--documenter-dark .hero.is-white a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-white .navbar-link:hover, + html.theme--documenter-dark .hero.is-white .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .tabs a { + color: #0a0a0a; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-white .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-white .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a { + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a:hover { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .hero.is-white.is-bold { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-white.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } + html.theme--documenter-dark .hero.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-black strong { + color: inherit; } + html.theme--documenter-dark .hero.is-black .title { + color: white; } + html.theme--documenter-dark .hero.is-black .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-black .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-black .subtitle strong { + color: white; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-black .navbar-menu { + background-color: #0a0a0a; } } + html.theme--documenter-dark .hero.is-black .navbar-item, + html.theme--documenter-dark .hero.is-black .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-black a.navbar-item:hover, html.theme--documenter-dark .hero.is-black a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-black .navbar-link:hover, + html.theme--documenter-dark .hero.is-black .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .hero.is-black .tabs a { + color: white; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-black .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-black .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a { + color: white; } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a:hover { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-black.is-bold { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-black.is-bold .navbar-menu { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } + html.theme--documenter-dark .hero.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-light strong { + color: inherit; } + html.theme--documenter-dark .hero.is-light .title { + color: #363636; } + html.theme--documenter-dark .hero.is-light .subtitle { + color: rgba(54, 54, 54, 0.9); } + html.theme--documenter-dark .hero.is-light .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-light .subtitle strong { + color: #363636; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-light .navbar-menu { + background-color: whitesmoke; } } + html.theme--documenter-dark .hero.is-light .navbar-item, + html.theme--documenter-dark .hero.is-light .navbar-link { + color: rgba(54, 54, 54, 0.7); } + html.theme--documenter-dark .hero.is-light a.navbar-item:hover, html.theme--documenter-dark .hero.is-light a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-light .navbar-link:hover, + html.theme--documenter-dark .hero.is-light .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .hero.is-light .tabs a { + color: #363636; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-light .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-light .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a { + color: #363636; } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a:hover { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-light.is-bold { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-light.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } } + html.theme--documenter-dark .hero.is-dark, html.theme--documenter-dark .content kbd.hero { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-dark strong, + html.theme--documenter-dark .content kbd.hero strong { + color: inherit; } + html.theme--documenter-dark .hero.is-dark .title, html.theme--documenter-dark .content kbd.hero .title { + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .subtitle, html.theme--documenter-dark .content kbd.hero .subtitle { + color: rgba(245, 245, 245, 0.9); } + html.theme--documenter-dark .hero.is-dark .subtitle a:not(.button), html.theme--documenter-dark .content kbd.hero .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-dark .subtitle strong, + html.theme--documenter-dark .content kbd.hero .subtitle strong { + color: whitesmoke; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-dark .navbar-menu, html.theme--documenter-dark .content kbd.hero .navbar-menu { + background-color: #363636; } } + html.theme--documenter-dark .hero.is-dark .navbar-item, html.theme--documenter-dark .content kbd.hero .navbar-item, + html.theme--documenter-dark .hero.is-dark .navbar-link, + html.theme--documenter-dark .content kbd.hero .navbar-link { + color: rgba(245, 245, 245, 0.7); } + html.theme--documenter-dark .hero.is-dark a.navbar-item:hover, html.theme--documenter-dark .content kbd.hero a.navbar-item:hover, html.theme--documenter-dark .hero.is-dark a.navbar-item.is-active, html.theme--documenter-dark .content kbd.hero a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-dark .navbar-link:hover, + html.theme--documenter-dark .content kbd.hero .navbar-link:hover, + html.theme--documenter-dark .hero.is-dark .navbar-link.is-active, + html.theme--documenter-dark .content kbd.hero .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .tabs a, html.theme--documenter-dark .content kbd.hero .tabs a { + color: whitesmoke; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-dark .tabs a:hover, html.theme--documenter-dark .content kbd.hero .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-dark .tabs li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a { + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a:hover { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .hero.is-dark.is-bold, html.theme--documenter-dark .content kbd.hero.is-bold { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-dark.is-bold .navbar-menu, html.theme--documenter-dark .content kbd.hero.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } } + html.theme--documenter-dark .hero.is-primary, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-primary strong, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink strong { + color: inherit; } + html.theme--documenter-dark .hero.is-primary .title, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .title { + color: #fff; } + html.theme--documenter-dark .hero.is-primary .subtitle, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-primary .subtitle a:not(.button), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-primary .subtitle strong, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-primary .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-menu { + background-color: #4eb5de; } } + html.theme--documenter-dark .hero.is-primary .navbar-item, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-item, + html.theme--documenter-dark .hero.is-primary .navbar-link, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-primary a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, html.theme--documenter-dark .hero.is-primary a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-primary .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, + html.theme--documenter-dark .hero.is-primary .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .hero.is-primary .tabs a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-primary .tabs a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-primary .tabs li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .hero.is-primary.is-bold, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-primary.is-bold .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } } + html.theme--documenter-dark .hero.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-link strong { + color: inherit; } + html.theme--documenter-dark .hero.is-link .title { + color: #fff; } + html.theme--documenter-dark .hero.is-link .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-link .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-link .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-link .navbar-menu { + background-color: #2ad7e6; } } + html.theme--documenter-dark .hero.is-link .navbar-item, + html.theme--documenter-dark .hero.is-link .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-link a.navbar-item:hover, html.theme--documenter-dark .hero.is-link a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-link .navbar-link:hover, + html.theme--documenter-dark .hero.is-link .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .hero.is-link .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-link .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-link .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .hero.is-link.is-bold { + background-image: linear-gradient(141deg, #0cd0bf 0%, #2ad7e6 71%, #3bc2ee 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-link.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #0cd0bf 0%, #2ad7e6 71%, #3bc2ee 100%); } } + html.theme--documenter-dark .hero.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-info strong { + color: inherit; } + html.theme--documenter-dark .hero.is-info .title { + color: #fff; } + html.theme--documenter-dark .hero.is-info .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-info .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-info .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-info .navbar-menu { + background-color: #3489da; } } + html.theme--documenter-dark .hero.is-info .navbar-item, + html.theme--documenter-dark .hero.is-info .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-info a.navbar-item:hover, html.theme--documenter-dark .hero.is-info a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-info .navbar-link:hover, + html.theme--documenter-dark .hero.is-info .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .hero.is-info .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-info .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-info .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #3489da; } + html.theme--documenter-dark .hero.is-info.is-bold { + background-image: linear-gradient(141deg, #178cc4 0%, #3489da 71%, #447be3 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-info.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #178cc4 0%, #3489da 71%, #447be3 100%); } } + html.theme--documenter-dark .hero.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-success strong { + color: inherit; } + html.theme--documenter-dark .hero.is-success .title { + color: #fff; } + html.theme--documenter-dark .hero.is-success .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-success .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-success .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-success .navbar-menu { + background-color: #259a12; } } + html.theme--documenter-dark .hero.is-success .navbar-item, + html.theme--documenter-dark .hero.is-success .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-success a.navbar-item:hover, html.theme--documenter-dark .hero.is-success a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-success .navbar-link:hover, + html.theme--documenter-dark .hero.is-success .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .hero.is-success .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-success .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-success .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #259a12; } + html.theme--documenter-dark .hero.is-success.is-bold { + background-image: linear-gradient(141deg, #287207 0%, #259a12 71%, #10b614 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-success.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #287207 0%, #259a12 71%, #10b614 100%); } } + html.theme--documenter-dark .hero.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-warning strong { + color: inherit; } + html.theme--documenter-dark .hero.is-warning .title { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .subtitle { + color: rgba(0, 0, 0, 0.9); } + html.theme--documenter-dark .hero.is-warning .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-warning .subtitle strong { + color: rgba(0, 0, 0, 0.7); } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-warning .navbar-menu { + background-color: #f4c72f; } } + html.theme--documenter-dark .hero.is-warning .navbar-item, + html.theme--documenter-dark .hero.is-warning .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning a.navbar-item:hover, html.theme--documenter-dark .hero.is-warning a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-warning .navbar-link:hover, + html.theme--documenter-dark .hero.is-warning .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .tabs a { + color: rgba(0, 0, 0, 0.7); + opacity: 0.9; } + html.theme--documenter-dark .hero.is-warning .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-warning .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a:hover { + background-color: rgba(0, 0, 0, 0.7); + border-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .hero.is-warning.is-bold { + background-image: linear-gradient(141deg, #f09100 0%, #f4c72f 71%, #faef42 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-warning.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #f09100 0%, #f4c72f 71%, #faef42 100%); } } + html.theme--documenter-dark .hero.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-danger strong { + color: inherit; } + html.theme--documenter-dark .hero.is-danger .title { + color: #fff; } + html.theme--documenter-dark .hero.is-danger .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-danger .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-danger .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-danger .navbar-menu { + background-color: #cb3c33; } } + html.theme--documenter-dark .hero.is-danger .navbar-item, + html.theme--documenter-dark .hero.is-danger .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-danger a.navbar-item:hover, html.theme--documenter-dark .hero.is-danger a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-danger .navbar-link:hover, + html.theme--documenter-dark .hero.is-danger .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .hero.is-danger .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-danger .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-danger .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .hero.is-danger.is-bold { + background-image: linear-gradient(141deg, #ac1f2e 0%, #cb3c33 71%, #d66341 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-danger.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #ac1f2e 0%, #cb3c33 71%, #d66341 100%); } } + html.theme--documenter-dark .hero.is-small .hero-body, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.hero .hero-body { + padding-bottom: 1.5rem; + padding-top: 1.5rem; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero.is-medium .hero-body { + padding-bottom: 9rem; + padding-top: 9rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero.is-large .hero-body { + padding-bottom: 18rem; + padding-top: 18rem; } } + html.theme--documenter-dark .hero.is-halfheight .hero-body, html.theme--documenter-dark .hero.is-fullheight .hero-body, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body { + align-items: center; + display: flex; } + html.theme--documenter-dark .hero.is-halfheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body > .container { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .hero.is-halfheight { + min-height: 50vh; } + html.theme--documenter-dark .hero.is-fullheight { + min-height: 100vh; } + html.theme--documenter-dark .hero-video { + overflow: hidden; } + html.theme--documenter-dark .hero-video video { + left: 50%; + min-height: 100%; + min-width: 100%; + position: absolute; + top: 50%; + transform: translate3d(-50%, -50%, 0); } + html.theme--documenter-dark .hero-video.is-transparent { + opacity: 0.3; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero-video { + display: none; } } + html.theme--documenter-dark .hero-buttons { + margin-top: 1.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero-buttons .button { + display: flex; } + html.theme--documenter-dark .hero-buttons .button:not(:last-child) { + margin-bottom: 0.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero-buttons { + display: flex; + justify-content: center; } + html.theme--documenter-dark .hero-buttons .button:not(:last-child) { + margin-right: 1.5rem; } } + html.theme--documenter-dark .hero-head, + html.theme--documenter-dark .hero-foot { + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .hero-body { + flex-grow: 1; + flex-shrink: 0; + padding: 3rem 1.5rem; } + html.theme--documenter-dark .section { + padding: 3rem 1.5rem; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .section.is-medium { + padding: 9rem 1.5rem; } + html.theme--documenter-dark .section.is-large { + padding: 18rem 1.5rem; } } + html.theme--documenter-dark .footer { + background-color: #fafafa; + padding: 3rem 1.5rem 6rem; } + html.theme--documenter-dark h1 .docs-heading-anchor, html.theme--documenter-dark h1 .docs-heading-anchor:hover, html.theme--documenter-dark h1 .docs-heading-anchor:visited, html.theme--documenter-dark h2 .docs-heading-anchor, html.theme--documenter-dark h2 .docs-heading-anchor:hover, html.theme--documenter-dark h2 .docs-heading-anchor:visited, html.theme--documenter-dark h3 .docs-heading-anchor, html.theme--documenter-dark h3 .docs-heading-anchor:hover, html.theme--documenter-dark h3 .docs-heading-anchor:visited, html.theme--documenter-dark h4 .docs-heading-anchor, html.theme--documenter-dark h4 .docs-heading-anchor:hover, html.theme--documenter-dark h4 .docs-heading-anchor:visited, html.theme--documenter-dark h5 .docs-heading-anchor, html.theme--documenter-dark h5 .docs-heading-anchor:hover, html.theme--documenter-dark h5 .docs-heading-anchor:visited, html.theme--documenter-dark h6 .docs-heading-anchor, html.theme--documenter-dark h6 .docs-heading-anchor:hover, html.theme--documenter-dark h6 .docs-heading-anchor:visited { + color: #cdc3e3; } + html.theme--documenter-dark h1 .docs-heading-anchor-permalink, html.theme--documenter-dark h2 .docs-heading-anchor-permalink, html.theme--documenter-dark h3 .docs-heading-anchor-permalink, html.theme--documenter-dark h4 .docs-heading-anchor-permalink, html.theme--documenter-dark h5 .docs-heading-anchor-permalink, html.theme--documenter-dark h6 .docs-heading-anchor-permalink { + visibility: hidden; + vertical-align: middle; + margin-left: 0.5em; + font-size: 0.7rem; } + html.theme--documenter-dark h1 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h2 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h3 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h4 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h5 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h6 .docs-heading-anchor-permalink::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f0c1"; } + html.theme--documenter-dark h1:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h2:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h3:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h4:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h5:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h6:hover .docs-heading-anchor-permalink { + visibility: visible; } + html.theme--documenter-dark .docs-light-only { + display: none !important; } + html.theme--documenter-dark pre { + position: relative; + overflow: hidden; } + html.theme--documenter-dark pre code, html.theme--documenter-dark pre code.hljs { + padding: 0 0.75rem !important; + overflow: auto; + display: block; } + html.theme--documenter-dark pre code:first-of-type, html.theme--documenter-dark pre code.hljs:first-of-type { + padding-top: 0.5rem !important; } + html.theme--documenter-dark pre code:last-of-type, html.theme--documenter-dark pre code.hljs:last-of-type { + padding-bottom: 0.5rem !important; } + html.theme--documenter-dark pre .copy-button { + opacity: 0.2; + transition: opacity 0.2s; + position: absolute; + right: 0em; + top: 0em; + padding: 0.5em; + width: 2.5em; + height: 2.5em; + background: transparent; + border: none; + font-family: "Font Awesome 5 Free"; + color: #fbfbfb; + cursor: pointer; + text-align: center; } + html.theme--documenter-dark pre .copy-button:focus, html.theme--documenter-dark pre .copy-button:hover { + opacity: 1; + background: rgba(251, 251, 251, 0.1); + color: #2ad7e6; } + html.theme--documenter-dark pre .copy-button.success { + color: #259a12; + opacity: 1; } + html.theme--documenter-dark pre .copy-button.error { + color: #cb3c33; + opacity: 1; } + html.theme--documenter-dark pre:hover .copy-button { + opacity: 1; } + html.theme--documenter-dark .admonition { + background-color: #28282b; + border-style: solid; + border-width: 1px; + border-color: #ba3f1f; + border-radius: 4px; + font-size: 1rem; } + html.theme--documenter-dark .admonition strong { + color: currentColor; } + html.theme--documenter-dark .admonition.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.admonition { + font-size: 0.75rem; } + html.theme--documenter-dark .admonition.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .admonition.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .admonition.is-default { + background-color: #28282b; + border-color: #ba3f1f; } + html.theme--documenter-dark .admonition.is-default > .admonition-header { + background-color: #ba3f1f; } + html.theme--documenter-dark .admonition.is-info { + background-color: #28282b; + border-color: #28c; } + html.theme--documenter-dark .admonition.is-info > .admonition-header { + background-color: #28c; } + html.theme--documenter-dark .admonition.is-success { + background-color: #28282b; + border-color: #42ac68; } + html.theme--documenter-dark .admonition.is-success > .admonition-header { + background-color: #42ac68; } + html.theme--documenter-dark .admonition.is-warning { + background-color: #28282b; + border-color: #a88b17; } + html.theme--documenter-dark .admonition.is-warning > .admonition-header { + background-color: #a88b17; } + html.theme--documenter-dark .admonition.is-danger { + background-color: #28282b; + border-color: #c7524c; } + html.theme--documenter-dark .admonition.is-danger > .admonition-header { + background-color: #c7524c; } + html.theme--documenter-dark .admonition.is-compat { + background-color: #28282b; + border-color: #00a1b7; } + html.theme--documenter-dark .admonition.is-compat > .admonition-header { + background-color: #00a1b7; } + html.theme--documenter-dark .admonition-header { + background-color: #ba3f1f; + align-items: center; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.5rem 0.75rem; + position: relative; } + html.theme--documenter-dark .admonition-header:before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + margin-right: 0.75rem; + content: "\f06a"; } + html.theme--documenter-dark .admonition-body { + color: #fbfbfb; + padding: 0.5rem 0.75rem; } + html.theme--documenter-dark .admonition-body pre { + background-color: #312550; } + html.theme--documenter-dark .admonition-body code { + background-color: #312550; } + html.theme--documenter-dark .docstring { + margin-bottom: 1em; + background-color: transparent; + border: 1px solid #dbdbdb; + box-shadow: 3px 3px 4px #444444; + max-width: 100%; } + html.theme--documenter-dark .docstring > header { + display: flex; + flex-grow: 1; + align-items: stretch; + padding: 0.5rem 0.75rem; + background-color: #28282b; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + box-shadow: none; + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .docstring > header code { + background-color: transparent; } + html.theme--documenter-dark .docstring > header .docstring-binding { + margin-right: 0.3em; } + html.theme--documenter-dark .docstring > header .docstring-category { + margin-left: 0.3em; } + html.theme--documenter-dark .docstring > section { + position: relative; + padding: 0.75rem 0.75rem; + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .docstring > section:last-child { + border-bottom: none; } + html.theme--documenter-dark .docstring > section > a.docs-sourcelink { + transition: opacity 0.3s; + opacity: 0; + position: absolute; + right: 0.375rem; + bottom: 0.375rem; } + html.theme--documenter-dark .docstring > section > a.docs-sourcelink:focus { + opacity: 1 !important; } + html.theme--documenter-dark .docstring:hover > section > a.docs-sourcelink { + opacity: 0.2; } + html.theme--documenter-dark .docstring:focus-within > section > a.docs-sourcelink { + opacity: 0.2; } + html.theme--documenter-dark .docstring > section:hover a.docs-sourcelink { + opacity: 1; } + html.theme--documenter-dark .documenter-example-output { + background-color: #1e1e20; } + html.theme--documenter-dark .outdated-warning-overlay { + position: fixed; + top: 0; + left: 0; + right: 0; + box-shadow: 0 0 10px rgba(0, 0, 0, 0.3); + z-index: 999; + background-color: #28282b; + border-bottom: 3px solid #c7524c; + padding: 10px 35px; + text-align: center; + font-size: 15px; } + html.theme--documenter-dark .outdated-warning-overlay .outdated-warning-closer { + position: absolute; + top: calc(50% - 10px); + right: 18px; + cursor: pointer; + width: 12px; } + html.theme--documenter-dark .outdated-warning-overlay a { + color: #2ad7e6; } + html.theme--documenter-dark .outdated-warning-overlay a:hover { + color: #97ebf3; } + html.theme--documenter-dark .content pre { + border: 1px solid #dbdbdb; } + html.theme--documenter-dark .content code { + font-weight: inherit; } + html.theme--documenter-dark .content a code { + color: #2ad7e6; } + html.theme--documenter-dark .content h1 code, html.theme--documenter-dark .content h2 code, html.theme--documenter-dark .content h3 code, html.theme--documenter-dark .content h4 code, html.theme--documenter-dark .content h5 code, html.theme--documenter-dark .content h6 code { + color: #cdc3e3; } + html.theme--documenter-dark .content table { + display: block; + width: initial; + max-width: 100%; + overflow-x: auto; } + html.theme--documenter-dark .content blockquote > ul:first-child, html.theme--documenter-dark .content blockquote > ol:first-child, html.theme--documenter-dark .content .admonition-body > ul:first-child, html.theme--documenter-dark .content .admonition-body > ol:first-child { + margin-top: 0; } + html.theme--documenter-dark pre, html.theme--documenter-dark code { + font-variant-ligatures: no-contextual; } + html.theme--documenter-dark .breadcrumb a.is-disabled { + cursor: default; + pointer-events: none; } + html.theme--documenter-dark .breadcrumb a.is-disabled, html.theme--documenter-dark .breadcrumb a.is-disabled:hover { + color: #cdc3e3; } + html.theme--documenter-dark .hljs { + background: initial !important; } + html.theme--documenter-dark .katex .katex-mathml { + top: 0; + right: 0; } + html.theme--documenter-dark .katex-display, html.theme--documenter-dark mjx-container, html.theme--documenter-dark .MathJax_Display { + margin: 0.5em 0 !important; } + html.theme--documenter-dark html { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; } + html.theme--documenter-dark li.no-marker { + list-style: none; } + html.theme--documenter-dark #documenter .docs-main > article { + overflow-wrap: break-word; } + html.theme--documenter-dark #documenter .docs-main > article .math-container { + overflow-x: auto; + overflow-y: hidden; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-main { + max-width: 52rem; + margin-left: 20rem; + padding-right: 1rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main { + width: 100%; } + html.theme--documenter-dark #documenter .docs-main > article { + max-width: 52rem; + margin-left: auto; + margin-right: auto; + margin-bottom: 1rem; + padding: 0 1rem; } + html.theme--documenter-dark #documenter .docs-main > header, html.theme--documenter-dark #documenter .docs-main > nav { + max-width: 100%; + width: 100%; + margin: 0; } } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar { + background-color: #1e1e20; + border-bottom: 1px solid #dbdbdb; + z-index: 2; + min-height: 4rem; + margin-bottom: 1rem; + display: flex; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .breadcrumb { + flex-grow: 1; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right { + display: flex; + white-space: nowrap; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-icon, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + display: inline-block; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label { + padding: 0; + margin-left: 0.3em; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button { + margin: auto 0 auto 1rem; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + font-size: 1.5rem; + margin: auto 0 auto 1rem; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar > * { + margin: auto 0; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main header.docs-navbar { + position: sticky; + top: 0; + padding: 0 1rem; + /* For Headroom.js */ + transition-property: top, box-shadow; + -webkit-transition-property: top, box-shadow; + /* Safari */ + transition-duration: 0.3s; + -webkit-transition-duration: 0.3s; + /* Safari */ } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--not-top { + box-shadow: 0.2rem 0rem 0.4rem #bbb; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { + top: -4.5rem; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } } + html.theme--documenter-dark #documenter .docs-main section.footnotes { + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-main section.footnotes li .tag:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .content kbd:first-child, html.theme--documenter-dark .content #documenter .docs-main section.footnotes li kbd:first-child { + margin-right: 1em; + margin-bottom: 0.4em; } + html.theme--documenter-dark #documenter .docs-main .docs-footer { + display: flex; + flex-wrap: wrap; + margin-left: 0; + margin-right: 0; + border-top: 1px solid #dbdbdb; + padding-top: 1rem; + padding-bottom: 1rem; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main .docs-footer { + padding-left: 1rem; + padding-right: 1rem; } } + html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage, html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-prevpage { + flex-grow: 1; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage { + text-align: right; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .flexbox-break { + flex-basis: 100%; + height: 0; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .footer-message { + font-size: 0.8em; + margin: 0.5em auto 0 auto; + text-align: center; } + html.theme--documenter-dark #documenter .docs-sidebar { + display: flex; + flex-direction: column; + color: #fbfbfb; + background-color: #503c82; + border-right: 1px solid #dbdbdb; + padding: 0; + flex: 0 0 18rem; + z-index: 5; + font-size: 1rem; + position: fixed; + left: -18rem; + width: 18rem; + height: 100%; + transition: left 0.3s; + /* Setting up a nicer theme style for the scrollbar */ } + html.theme--documenter-dark #documenter .docs-sidebar.visible { + left: 0; + box-shadow: 0.4rem 0rem 0.8rem #bbb; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar.visible { + box-shadow: none; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar { + left: 0; + top: 0; } } + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo { + margin-top: 1rem; + padding: 0 1rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { + max-height: 6rem; + margin: auto; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name { + flex-shrink: 0; + font-size: 1.5rem; + font-weight: 700; + text-align: center; + white-space: nowrap; + overflow: hidden; + padding: 0.5rem 0; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name .docs-autofit { + max-width: 16.2rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a, html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a:hover { + color: #fbfbfb; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector { + border-top: 1px solid #dbdbdb; + display: none; + padding: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector.visible { + display: flex; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { + flex-grow: 1; + user-select: none; + border-top: 1px solid #dbdbdb; + padding-bottom: 1.5rem; + /* Managing collapsible submenus */ } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li > .tocitem { + font-weight: bold; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li li { + font-size: 0.95rem; + margin-left: 1em; + border-left: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input.collapse-toggle { + display: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.collapsed { + display: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed { + display: block; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem { + display: flex; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label { + flex-grow: 2; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron { + display: inline-block; + font-style: normal; + font-variant: normal; + text-rendering: auto; + line-height: 1; + font-size: 0.75rem; + margin-left: 1rem; + margin-top: auto; + margin-bottom: auto; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f054"; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before { + content: "\f078"; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem { + display: block; + padding: 0.5rem 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem:hover { + color: #fbfbfb; + background: #503c82; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem:hover { + color: #fbfbfb; + background-color: #3c2d60; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active { + border-top: 1px solid #dbdbdb; + border-bottom: 1px solid #dbdbdb; + background-color: #1e1e20; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover { + background-color: #1e1e20; + color: #fff; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover { + background-color: #3f2f66; + color: #fff; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child { + border-top: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal { + margin: 0 0.5rem 0.5rem; + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal li { + font-size: 0.85rem; + border-left: none; + margin-left: 0; + margin-top: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem { + width: 100%; + padding: 0; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before { + content: "⚬"; + margin-right: 0.4em; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search { + margin: auto; + margin-top: 0.5rem; + margin-bottom: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + width: 14.4rem; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar { + width: .3rem; + background: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #3f2f66; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover { + background: #2e224a; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-sidebar { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar { + width: .3rem; + background: none; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #3f2f66; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover { + background: #2e224a; } } + html.theme--documenter-dark #documenter .docs-main #documenter-search-info { + margin-bottom: 1rem; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results { + list-style-type: circle; + list-style-position: outside; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results li { + margin-left: 2rem; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results .docs-highlight { + background-color: yellow; } + html.theme--documenter-dark { + background-color: #1e1e20; + font-size: 16px; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + html.theme--documenter-dark #documenter .docs-sidebar { + border-right: none; + box-shadow: 0.24rem 0rem 0.4rem #444444; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + color: #fff; + background-color: #3f2f66; + border-color: #2e224a; + margin-top: 1.0rem; + margin-bottom: 1.0rem; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::placeholder { + color: #fff; } + html.theme--documenter-dark .hljs { + background: #2b2b2b; + color: #f8f8f2; } + html.theme--documenter-dark .hljs-comment, + html.theme--documenter-dark .hljs-quote { + color: #d4d0ab; } + html.theme--documenter-dark .hljs-variable, + html.theme--documenter-dark .hljs-template-variable, + html.theme--documenter-dark .hljs-tag, + html.theme--documenter-dark .hljs-name, + html.theme--documenter-dark .hljs-selector-id, + html.theme--documenter-dark .hljs-selector-class, + html.theme--documenter-dark .hljs-regexp, + html.theme--documenter-dark .hljs-deletion { + color: #ffa07a; } + html.theme--documenter-dark .hljs-number, + html.theme--documenter-dark .hljs-built_in, + html.theme--documenter-dark .hljs-literal, + html.theme--documenter-dark .hljs-type, + html.theme--documenter-dark .hljs-params, + html.theme--documenter-dark .hljs-meta, + html.theme--documenter-dark .hljs-link { + color: #f5ab35; } + html.theme--documenter-dark .hljs-attribute { + color: #ffd700; } + html.theme--documenter-dark .hljs-string, + html.theme--documenter-dark .hljs-symbol, + html.theme--documenter-dark .hljs-bullet, + html.theme--documenter-dark .hljs-addition { + color: #abe338; } + html.theme--documenter-dark .hljs-title, + html.theme--documenter-dark .hljs-section { + color: #00e0e0; } + html.theme--documenter-dark .hljs-keyword, + html.theme--documenter-dark .hljs-selector-tag { + color: #dcc6e0; } + html.theme--documenter-dark .hljs-emphasis { + font-style: italic; } + html.theme--documenter-dark .hljs-strong { + font-weight: bold; } + @media screen and (-ms-high-contrast: active) { + html.theme--documenter-dark .hljs-addition, + html.theme--documenter-dark .hljs-attribute, + html.theme--documenter-dark .hljs-built_in, + html.theme--documenter-dark .hljs-bullet, + html.theme--documenter-dark .hljs-comment, + html.theme--documenter-dark .hljs-link, + html.theme--documenter-dark .hljs-literal, + html.theme--documenter-dark .hljs-meta, + html.theme--documenter-dark .hljs-number, + html.theme--documenter-dark .hljs-params, + html.theme--documenter-dark .hljs-string, + html.theme--documenter-dark .hljs-symbol, + html.theme--documenter-dark .hljs-type, + html.theme--documenter-dark .hljs-quote { + color: highlight; } + html.theme--documenter-dark .hljs-keyword, + html.theme--documenter-dark .hljs-selector-tag { + font-weight: bold; } } + html.theme--documenter-dark .hljs-subst { + color: #f8f8f2; } diff --git a/previews/PR17/assets/themes/documenter-light.css b/previews/PR17/assets/themes/documenter-light.css new file mode 100644 index 00000000..e2c74638 --- /dev/null +++ b/previews/PR17/assets/themes/documenter-light.css @@ -0,0 +1,7750 @@ +@charset "UTF-8"; +/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */ +@keyframes spinAround { + from { + transform: rotate(0deg); } + to { + transform: rotate(359deg); } } + +.tabs, .pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis, .breadcrumb, .file, .button, .is-unselectable, .modal-close, .delete { + -webkit-touch-callout: none; + -webkit-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; } + +.navbar-link:not(.is-arrowless)::after, .select:not(.is-multiple):not(.is-loading)::after { + border: 3px solid transparent; + border-radius: 2px; + border-right: 0; + border-top: 0; + content: " "; + display: block; + height: 0.625em; + margin-top: -0.4375em; + pointer-events: none; + position: absolute; + top: 50%; + transform: rotate(-45deg); + transform-origin: center; + width: 0.625em; } + +.admonition:not(:last-child), .tabs:not(:last-child), .message:not(:last-child), .list:not(:last-child), .level:not(:last-child), .breadcrumb:not(:last-child), .highlight:not(:last-child), .block:not(:last-child), .title:not(:last-child), +.subtitle:not(:last-child), .table-container:not(:last-child), .table:not(:last-child), .progress:not(:last-child), .notification:not(:last-child), .content:not(:last-child), .box:not(:last-child) { + margin-bottom: 1.5rem; } + +.modal-close, .delete { + -moz-appearance: none; + -webkit-appearance: none; + background-color: rgba(10, 10, 10, 0.2); + border: none; + border-radius: 290486px; + cursor: pointer; + pointer-events: auto; + display: inline-block; + flex-grow: 0; + flex-shrink: 0; + font-size: 0; + height: 20px; + max-height: 20px; + max-width: 20px; + min-height: 20px; + min-width: 20px; + outline: none; + position: relative; + vertical-align: top; + width: 20px; } + .modal-close::before, .delete::before, .modal-close::after, .delete::after { + background-color: white; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + .modal-close::before, .delete::before { + height: 2px; + width: 50%; } + .modal-close::after, .delete::after { + height: 50%; + width: 2px; } + .modal-close:hover, .delete:hover, .modal-close:focus, .delete:focus { + background-color: rgba(10, 10, 10, 0.3); } + .modal-close:active, .delete:active { + background-color: rgba(10, 10, 10, 0.4); } + .is-small.modal-close, #documenter .docs-sidebar form.docs-search > input.modal-close, .is-small.delete, #documenter .docs-sidebar form.docs-search > input.delete { + height: 16px; + max-height: 16px; + max-width: 16px; + min-height: 16px; + min-width: 16px; + width: 16px; } + .is-medium.modal-close, .is-medium.delete { + height: 24px; + max-height: 24px; + max-width: 24px; + min-height: 24px; + min-width: 24px; + width: 24px; } + .is-large.modal-close, .is-large.delete { + height: 32px; + max-height: 32px; + max-width: 32px; + min-height: 32px; + min-width: 32px; + width: 32px; } + +.control.is-loading::after, .select.is-loading::after, .loader, .button.is-loading::after { + animation: spinAround 500ms infinite linear; + border: 2px solid #dbdbdb; + border-radius: 290486px; + border-right-color: transparent; + border-top-color: transparent; + content: ""; + display: block; + height: 1em; + position: relative; + width: 1em; } + +.hero-video, .modal-background, .modal, .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img, +.image.is-square .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img, +.image.is-1by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img, +.image.is-5by4 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img, +.image.is-4by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img, +.image.is-3by2 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img, +.image.is-5by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img, +.image.is-16by9 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img, +.image.is-2by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img, +.image.is-3by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img, +.image.is-4by5 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img, +.image.is-3by4 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img, +.image.is-2by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img, +.image.is-3by5 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img, +.image.is-9by16 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img, +.image.is-1by2 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img, +.image.is-1by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, .is-overlay { + bottom: 0; + left: 0; + position: absolute; + right: 0; + top: 0; } + +.pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis, .file-cta, +.file-name, .select select, .textarea, .input, #documenter .docs-sidebar form.docs-search > input, .button { + -moz-appearance: none; + -webkit-appearance: none; + align-items: center; + border: 1px solid transparent; + border-radius: 4px; + box-shadow: none; + display: inline-flex; + font-size: 1rem; + height: 2.25em; + justify-content: flex-start; + line-height: 1.5; + padding-bottom: calc(0.375em - 1px); + padding-left: calc(0.625em - 1px); + padding-right: calc(0.625em - 1px); + padding-top: calc(0.375em - 1px); + position: relative; + vertical-align: top; } + .pagination-previous:focus, + .pagination-next:focus, + .pagination-link:focus, + .pagination-ellipsis:focus, .file-cta:focus, + .file-name:focus, .select select:focus, .textarea:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .button:focus, .is-focused.pagination-previous, + .is-focused.pagination-next, + .is-focused.pagination-link, + .is-focused.pagination-ellipsis, .is-focused.file-cta, + .is-focused.file-name, .select select.is-focused, .is-focused.textarea, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-focused.button, .pagination-previous:active, + .pagination-next:active, + .pagination-link:active, + .pagination-ellipsis:active, .file-cta:active, + .file-name:active, .select select:active, .textarea:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .button:active, .is-active.pagination-previous, + .is-active.pagination-next, + .is-active.pagination-link, + .is-active.pagination-ellipsis, .is-active.file-cta, + .is-active.file-name, .select select.is-active, .is-active.textarea, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .is-active.button { + outline: none; } + .pagination-previous[disabled], + .pagination-next[disabled], + .pagination-link[disabled], + .pagination-ellipsis[disabled], .file-cta[disabled], + .file-name[disabled], .select select[disabled], .textarea[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], .button[disabled], fieldset[disabled] .pagination-previous, + fieldset[disabled] .pagination-next, + fieldset[disabled] .pagination-link, + fieldset[disabled] .pagination-ellipsis, fieldset[disabled] .file-cta, + fieldset[disabled] .file-name, fieldset[disabled] .select select, .select fieldset[disabled] select, fieldset[disabled] .textarea, fieldset[disabled] .input, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input, fieldset[disabled] .button { + cursor: not-allowed; } + +/*! minireset.css v0.0.4 | MIT License | github.com/jgthms/minireset.css */ +html, +body, +p, +ol, +ul, +li, +dl, +dt, +dd, +blockquote, +figure, +fieldset, +legend, +textarea, +pre, +iframe, +hr, +h1, +h2, +h3, +h4, +h5, +h6 { + margin: 0; + padding: 0; } + +h1, +h2, +h3, +h4, +h5, +h6 { + font-size: 100%; + font-weight: normal; } + +ul { + list-style: none; } + +button, +input, +select, +textarea { + margin: 0; } + +html { + box-sizing: border-box; } + +*, *::before, *::after { + box-sizing: inherit; } + +img, +embed, +iframe, +object, +video { + height: auto; + max-width: 100%; } + +audio { + max-width: 100%; } + +iframe { + border: 0; } + +table { + border-collapse: collapse; + border-spacing: 0; } + +td, +th { + padding: 0; } + td:not([align]), + th:not([align]) { + text-align: left; } + +html { + background-color: #fff; + font-size: 16px; + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + +article, +aside, +figure, +footer, +header, +hgroup, +section { + display: block; } + +body, +button, +input, +select, +textarea { + font-family: "Montserrat", sans-serif; } + +code, +pre { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; + font-family: "Source Code Pro", monospace; } + +body { + color: #202020; + font-size: 1em; + font-weight: 400; + line-height: 1.5; } + +a { + color: #149eaa; + cursor: pointer; + text-decoration: none; } + a strong { + color: currentColor; } + a:hover { + color: #107c85; } + +code { + background-color: #ebe8f4; + color: #000000; + font-size: 0.875em; + font-weight: normal; + padding: 0.1em; } + +hr { + background-color: whitesmoke; + border: none; + display: block; + height: 2px; + margin: 1.5rem 0; } + +img { + height: auto; + max-width: 100%; } + +input[type="checkbox"], +input[type="radio"] { + vertical-align: baseline; } + +small { + font-size: 0.875em; } + +span { + font-style: inherit; + font-weight: inherit; } + +strong { + color: #654ca3; + font-weight: 700; } + +fieldset { + border: none; } + +pre { + -webkit-overflow-scrolling: touch; + background-color: #ebe8f4; + color: #202020; + font-size: 0.875em; + overflow-x: auto; + padding: 1.25rem 1.5rem; + white-space: pre; + word-wrap: normal; } + pre code { + background-color: transparent; + color: currentColor; + font-size: 1em; + padding: 0; } + +table td, +table th { + vertical-align: top; } + table td:not([align]), + table th:not([align]) { + text-align: left; } + +table th { + color: #654ca3; } + +.is-clearfix::after { + clear: both; + content: " "; + display: table; } + +.is-pulled-left { + float: left !important; } + +.is-pulled-right { + float: right !important; } + +.is-clipped { + overflow: hidden !important; } + +.is-size-1 { + font-size: 3rem !important; } + +.is-size-2 { + font-size: 2.5rem !important; } + +.is-size-3 { + font-size: 2rem !important; } + +.is-size-4 { + font-size: 1.5rem !important; } + +.is-size-5 { + font-size: 1.25rem !important; } + +.is-size-6 { + font-size: 1rem !important; } + +.is-size-7, .docstring > section > a.docs-sourcelink { + font-size: 0.75rem !important; } + +@media screen and (max-width: 768px) { + .is-size-1-mobile { + font-size: 3rem !important; } + .is-size-2-mobile { + font-size: 2.5rem !important; } + .is-size-3-mobile { + font-size: 2rem !important; } + .is-size-4-mobile { + font-size: 1.5rem !important; } + .is-size-5-mobile { + font-size: 1.25rem !important; } + .is-size-6-mobile { + font-size: 1rem !important; } + .is-size-7-mobile { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 769px), print { + .is-size-1-tablet { + font-size: 3rem !important; } + .is-size-2-tablet { + font-size: 2.5rem !important; } + .is-size-3-tablet { + font-size: 2rem !important; } + .is-size-4-tablet { + font-size: 1.5rem !important; } + .is-size-5-tablet { + font-size: 1.25rem !important; } + .is-size-6-tablet { + font-size: 1rem !important; } + .is-size-7-tablet { + font-size: 0.75rem !important; } } + +@media screen and (max-width: 1055px) { + .is-size-1-touch { + font-size: 3rem !important; } + .is-size-2-touch { + font-size: 2.5rem !important; } + .is-size-3-touch { + font-size: 2rem !important; } + .is-size-4-touch { + font-size: 1.5rem !important; } + .is-size-5-touch { + font-size: 1.25rem !important; } + .is-size-6-touch { + font-size: 1rem !important; } + .is-size-7-touch { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1056px) { + .is-size-1-desktop { + font-size: 3rem !important; } + .is-size-2-desktop { + font-size: 2.5rem !important; } + .is-size-3-desktop { + font-size: 2rem !important; } + .is-size-4-desktop { + font-size: 1.5rem !important; } + .is-size-5-desktop { + font-size: 1.25rem !important; } + .is-size-6-desktop { + font-size: 1rem !important; } + .is-size-7-desktop { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1216px) { + .is-size-1-widescreen { + font-size: 3rem !important; } + .is-size-2-widescreen { + font-size: 2.5rem !important; } + .is-size-3-widescreen { + font-size: 2rem !important; } + .is-size-4-widescreen { + font-size: 1.5rem !important; } + .is-size-5-widescreen { + font-size: 1.25rem !important; } + .is-size-6-widescreen { + font-size: 1rem !important; } + .is-size-7-widescreen { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1408px) { + .is-size-1-fullhd { + font-size: 3rem !important; } + .is-size-2-fullhd { + font-size: 2.5rem !important; } + .is-size-3-fullhd { + font-size: 2rem !important; } + .is-size-4-fullhd { + font-size: 1.5rem !important; } + .is-size-5-fullhd { + font-size: 1.25rem !important; } + .is-size-6-fullhd { + font-size: 1rem !important; } + .is-size-7-fullhd { + font-size: 0.75rem !important; } } + +.has-text-centered { + text-align: center !important; } + +.has-text-justified { + text-align: justify !important; } + +.has-text-left { + text-align: left !important; } + +.has-text-right { + text-align: right !important; } + +@media screen and (max-width: 768px) { + .has-text-centered-mobile { + text-align: center !important; } } + +@media screen and (min-width: 769px), print { + .has-text-centered-tablet { + text-align: center !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-centered-tablet-only { + text-align: center !important; } } + +@media screen and (max-width: 1055px) { + .has-text-centered-touch { + text-align: center !important; } } + +@media screen and (min-width: 1056px) { + .has-text-centered-desktop { + text-align: center !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-centered-desktop-only { + text-align: center !important; } } + +@media screen and (min-width: 1216px) { + .has-text-centered-widescreen { + text-align: center !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-centered-widescreen-only { + text-align: center !important; } } + +@media screen and (min-width: 1408px) { + .has-text-centered-fullhd { + text-align: center !important; } } + +@media screen and (max-width: 768px) { + .has-text-justified-mobile { + text-align: justify !important; } } + +@media screen and (min-width: 769px), print { + .has-text-justified-tablet { + text-align: justify !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-justified-tablet-only { + text-align: justify !important; } } + +@media screen and (max-width: 1055px) { + .has-text-justified-touch { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) { + .has-text-justified-desktop { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-justified-desktop-only { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) { + .has-text-justified-widescreen { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-justified-widescreen-only { + text-align: justify !important; } } + +@media screen and (min-width: 1408px) { + .has-text-justified-fullhd { + text-align: justify !important; } } + +@media screen and (max-width: 768px) { + .has-text-left-mobile { + text-align: left !important; } } + +@media screen and (min-width: 769px), print { + .has-text-left-tablet { + text-align: left !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-left-tablet-only { + text-align: left !important; } } + +@media screen and (max-width: 1055px) { + .has-text-left-touch { + text-align: left !important; } } + +@media screen and (min-width: 1056px) { + .has-text-left-desktop { + text-align: left !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-left-desktop-only { + text-align: left !important; } } + +@media screen and (min-width: 1216px) { + .has-text-left-widescreen { + text-align: left !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-left-widescreen-only { + text-align: left !important; } } + +@media screen and (min-width: 1408px) { + .has-text-left-fullhd { + text-align: left !important; } } + +@media screen and (max-width: 768px) { + .has-text-right-mobile { + text-align: right !important; } } + +@media screen and (min-width: 769px), print { + .has-text-right-tablet { + text-align: right !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-right-tablet-only { + text-align: right !important; } } + +@media screen and (max-width: 1055px) { + .has-text-right-touch { + text-align: right !important; } } + +@media screen and (min-width: 1056px) { + .has-text-right-desktop { + text-align: right !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-right-desktop-only { + text-align: right !important; } } + +@media screen and (min-width: 1216px) { + .has-text-right-widescreen { + text-align: right !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-right-widescreen-only { + text-align: right !important; } } + +@media screen and (min-width: 1408px) { + .has-text-right-fullhd { + text-align: right !important; } } + +.is-capitalized { + text-transform: capitalize !important; } + +.is-lowercase { + text-transform: lowercase !important; } + +.is-uppercase { + text-transform: uppercase !important; } + +.is-italic { + font-style: italic !important; } + +.has-text-white { + color: white !important; } + +a.has-text-white:hover, a.has-text-white:focus { + color: #e6e6e6 !important; } + +.has-background-white { + background-color: white !important; } + +.has-text-black { + color: #0a0a0a !important; } + +a.has-text-black:hover, a.has-text-black:focus { + color: black !important; } + +.has-background-black { + background-color: #0a0a0a !important; } + +.has-text-light { + color: whitesmoke !important; } + +a.has-text-light:hover, a.has-text-light:focus { + color: #dbdbdb !important; } + +.has-background-light { + background-color: whitesmoke !important; } + +.has-text-dark { + color: #363636 !important; } + +a.has-text-dark:hover, a.has-text-dark:focus { + color: #1c1c1c !important; } + +.has-background-dark { + background-color: #363636 !important; } + +.has-text-primary { + color: #4eb5de !important; } + +a.has-text-primary:hover, a.has-text-primary:focus { + color: #27a1d2 !important; } + +.has-background-primary { + background-color: #4eb5de !important; } + +.has-text-link { + color: #149eaa !important; } + +a.has-text-link:hover, a.has-text-link:focus { + color: #0f747c !important; } + +.has-background-link { + background-color: #149eaa !important; } + +.has-text-info { + color: #209cee !important; } + +a.has-text-info:hover, a.has-text-info:focus { + color: #1081cb !important; } + +.has-background-info { + background-color: #209cee !important; } + +.has-text-success { + color: #22c35b !important; } + +a.has-text-success:hover, a.has-text-success:focus { + color: #1a9847 !important; } + +.has-background-success { + background-color: #22c35b !important; } + +.has-text-warning { + color: #ffdd57 !important; } + +a.has-text-warning:hover, a.has-text-warning:focus { + color: #ffd324 !important; } + +.has-background-warning { + background-color: #ffdd57 !important; } + +.has-text-danger { + color: #da0b00 !important; } + +a.has-text-danger:hover, a.has-text-danger:focus { + color: #a70800 !important; } + +.has-background-danger { + background-color: #da0b00 !important; } + +.has-text-black-bis { + color: #121212 !important; } + +.has-background-black-bis { + background-color: #121212 !important; } + +.has-text-black-ter { + color: #242424 !important; } + +.has-background-black-ter { + background-color: #242424 !important; } + +.has-text-grey-darker { + color: #363636 !important; } + +.has-background-grey-darker { + background-color: #363636 !important; } + +.has-text-grey-dark { + color: #4a4a4a !important; } + +.has-background-grey-dark { + background-color: #4a4a4a !important; } + +.has-text-grey { + color: #6b6b6b !important; } + +.has-background-grey { + background-color: #6b6b6b !important; } + +.has-text-grey-light { + color: #b5b5b5 !important; } + +.has-background-grey-light { + background-color: #b5b5b5 !important; } + +.has-text-grey-lighter { + color: #dbdbdb !important; } + +.has-background-grey-lighter { + background-color: #dbdbdb !important; } + +.has-text-white-ter { + color: whitesmoke !important; } + +.has-background-white-ter { + background-color: whitesmoke !important; } + +.has-text-white-bis { + color: #fafafa !important; } + +.has-background-white-bis { + background-color: #fafafa !important; } + +.has-text-weight-light { + font-weight: 300 !important; } + +.has-text-weight-normal { + font-weight: 400 !important; } + +.has-text-weight-medium { + font-weight: 500 !important; } + +.has-text-weight-semibold { + font-weight: 600 !important; } + +.has-text-weight-bold { + font-weight: 700 !important; } + +.is-family-primary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-secondary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-sans-serif { + font-family: "Montserrat", sans-serif !important; } + +.is-family-monospace { + font-family: "Source Code Pro", monospace !important; } + +.is-family-code { + font-family: "Source Code Pro", monospace !important; } + +.is-block { + display: block !important; } + +@media screen and (max-width: 768px) { + .is-block-mobile { + display: block !important; } } + +@media screen and (min-width: 769px), print { + .is-block-tablet { + display: block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-block-tablet-only { + display: block !important; } } + +@media screen and (max-width: 1055px) { + .is-block-touch { + display: block !important; } } + +@media screen and (min-width: 1056px) { + .is-block-desktop { + display: block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-block-desktop-only { + display: block !important; } } + +@media screen and (min-width: 1216px) { + .is-block-widescreen { + display: block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-block-widescreen-only { + display: block !important; } } + +@media screen and (min-width: 1408px) { + .is-block-fullhd { + display: block !important; } } + +.is-flex { + display: flex !important; } + +@media screen and (max-width: 768px) { + .is-flex-mobile { + display: flex !important; } } + +@media screen and (min-width: 769px), print { + .is-flex-tablet { + display: flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-flex-tablet-only { + display: flex !important; } } + +@media screen and (max-width: 1055px) { + .is-flex-touch { + display: flex !important; } } + +@media screen and (min-width: 1056px) { + .is-flex-desktop { + display: flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-flex-desktop-only { + display: flex !important; } } + +@media screen and (min-width: 1216px) { + .is-flex-widescreen { + display: flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-flex-widescreen-only { + display: flex !important; } } + +@media screen and (min-width: 1408px) { + .is-flex-fullhd { + display: flex !important; } } + +.is-inline { + display: inline !important; } + +@media screen and (max-width: 768px) { + .is-inline-mobile { + display: inline !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-tablet { + display: inline !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-tablet-only { + display: inline !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-touch { + display: inline !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-desktop { + display: inline !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-desktop-only { + display: inline !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-widescreen { + display: inline !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-widescreen-only { + display: inline !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-fullhd { + display: inline !important; } } + +.is-inline-block { + display: inline-block !important; } + +@media screen and (max-width: 768px) { + .is-inline-block-mobile { + display: inline-block !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-block-tablet { + display: inline-block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-block-tablet-only { + display: inline-block !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-block-touch { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-block-desktop { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-block-desktop-only { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-block-widescreen { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-block-widescreen-only { + display: inline-block !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-block-fullhd { + display: inline-block !important; } } + +.is-inline-flex { + display: inline-flex !important; } + +@media screen and (max-width: 768px) { + .is-inline-flex-mobile { + display: inline-flex !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-flex-tablet { + display: inline-flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-flex-tablet-only { + display: inline-flex !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-flex-touch { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-flex-desktop { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-flex-desktop-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-flex-widescreen { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-flex-widescreen-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-flex-fullhd { + display: inline-flex !important; } } + +.is-hidden { + display: none !important; } + +.is-sr-only { + border: none !important; + clip: rect(0, 0, 0, 0) !important; + height: 0.01em !important; + overflow: hidden !important; + padding: 0 !important; + position: absolute !important; + white-space: nowrap !important; + width: 0.01em !important; } + +@media screen and (max-width: 768px) { + .is-hidden-mobile { + display: none !important; } } + +@media screen and (min-width: 769px), print { + .is-hidden-tablet { + display: none !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-hidden-tablet-only { + display: none !important; } } + +@media screen and (max-width: 1055px) { + .is-hidden-touch { + display: none !important; } } + +@media screen and (min-width: 1056px) { + .is-hidden-desktop { + display: none !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-hidden-desktop-only { + display: none !important; } } + +@media screen and (min-width: 1216px) { + .is-hidden-widescreen { + display: none !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-hidden-widescreen-only { + display: none !important; } } + +@media screen and (min-width: 1408px) { + .is-hidden-fullhd { + display: none !important; } } + +.is-invisible { + visibility: hidden !important; } + +@media screen and (max-width: 768px) { + .is-invisible-mobile { + visibility: hidden !important; } } + +@media screen and (min-width: 769px), print { + .is-invisible-tablet { + visibility: hidden !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-invisible-tablet-only { + visibility: hidden !important; } } + +@media screen and (max-width: 1055px) { + .is-invisible-touch { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) { + .is-invisible-desktop { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-invisible-desktop-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) { + .is-invisible-widescreen { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-invisible-widescreen-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1408px) { + .is-invisible-fullhd { + visibility: hidden !important; } } + +.is-marginless { + margin: 0 !important; } + +.is-paddingless { + padding: 0 !important; } + +.is-radiusless { + border-radius: 0 !important; } + +.is-shadowless { + box-shadow: none !important; } + +.is-relative { + position: relative !important; } + +.box { + background-color: white; + border-radius: 6px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #202020; + display: block; + padding: 1.25rem; } + +a.box:hover, a.box:focus { + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #149eaa; } + +a.box:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #149eaa; } + +.button { + background-color: white; + border-color: #dbdbdb; + border-width: 1px; + color: #363636; + cursor: pointer; + justify-content: center; + padding-bottom: calc(0.375em - 1px); + padding-left: 0.75em; + padding-right: 0.75em; + padding-top: calc(0.375em - 1px); + text-align: center; + white-space: nowrap; } + .button strong { + color: inherit; } + .button .icon, .button .icon.is-small, .button #documenter .docs-sidebar form.docs-search > input.icon, #documenter .docs-sidebar .button form.docs-search > input.icon, .button .icon.is-medium, .button .icon.is-large { + height: 1.5em; + width: 1.5em; } + .button .icon:first-child:not(:last-child) { + margin-left: calc(-0.375em - 1px); + margin-right: 0.1875em; } + .button .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: calc(-0.375em - 1px); } + .button .icon:first-child:last-child { + margin-left: calc(-0.375em - 1px); + margin-right: calc(-0.375em - 1px); } + .button:hover, .button.is-hovered { + border-color: #b5b5b5; + color: #107c85; } + .button:focus, .button.is-focused { + border-color: #3c5dcd; + color: #363636; } + .button:focus:not(:active), .button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .button:active, .button.is-active { + border-color: #4a4a4a; + color: #363636; } + .button.is-text { + background-color: transparent; + border-color: transparent; + color: #202020; + text-decoration: underline; } + .button.is-text:hover, .button.is-text.is-hovered, .button.is-text:focus, .button.is-text.is-focused { + background-color: whitesmoke; + color: #654ca3; } + .button.is-text:active, .button.is-text.is-active { + background-color: #e8e8e8; + color: #654ca3; } + .button.is-text[disabled], fieldset[disabled] .button.is-text { + background-color: transparent; + border-color: transparent; + box-shadow: none; } + .button.is-white { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + .button.is-white:hover, .button.is-white.is-hovered { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + .button.is-white:focus, .button.is-white.is-focused { + border-color: transparent; + color: #0a0a0a; } + .button.is-white:focus:not(:active), .button.is-white.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .button.is-white:active, .button.is-white.is-active { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + .button.is-white[disabled], fieldset[disabled] .button.is-white { + background-color: white; + border-color: transparent; + box-shadow: none; } + .button.is-white.is-inverted { + background-color: #0a0a0a; + color: white; } + .button.is-white.is-inverted:hover, .button.is-white.is-inverted.is-hovered { + background-color: black; } + .button.is-white.is-inverted[disabled], fieldset[disabled] .button.is-white.is-inverted { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; + color: white; } + .button.is-white.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + .button.is-white.is-outlined:hover, .button.is-white.is-outlined.is-hovered, .button.is-white.is-outlined:focus, .button.is-white.is-outlined.is-focused { + background-color: white; + border-color: white; + color: #0a0a0a; } + .button.is-white.is-outlined.is-loading::after { + border-color: transparent transparent white white !important; } + .button.is-white.is-outlined.is-loading:hover::after, .button.is-white.is-outlined.is-loading.is-hovered::after, .button.is-white.is-outlined.is-loading:focus::after, .button.is-white.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-white.is-outlined[disabled], fieldset[disabled] .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + .button.is-white.is-inverted.is-outlined:hover, .button.is-white.is-inverted.is-outlined.is-hovered, .button.is-white.is-inverted.is-outlined:focus, .button.is-white.is-inverted.is-outlined.is-focused { + background-color: #0a0a0a; + color: white; } + .button.is-white.is-inverted.is-outlined.is-loading:hover::after, .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-white.is-inverted.is-outlined.is-loading:focus::after, .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + .button.is-white.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + .button.is-black:hover, .button.is-black.is-hovered { + background-color: #040404; + border-color: transparent; + color: white; } + .button.is-black:focus, .button.is-black.is-focused { + border-color: transparent; + color: white; } + .button.is-black:focus:not(:active), .button.is-black.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .button.is-black:active, .button.is-black.is-active { + background-color: black; + border-color: transparent; + color: white; } + .button.is-black[disabled], fieldset[disabled] .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; } + .button.is-black.is-inverted { + background-color: white; + color: #0a0a0a; } + .button.is-black.is-inverted:hover, .button.is-black.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-black.is-inverted[disabled], fieldset[disabled] .button.is-black.is-inverted { + background-color: white; + border-color: transparent; + box-shadow: none; + color: #0a0a0a; } + .button.is-black.is-loading::after { + border-color: transparent transparent white white !important; } + .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + .button.is-black.is-outlined:hover, .button.is-black.is-outlined.is-hovered, .button.is-black.is-outlined:focus, .button.is-black.is-outlined.is-focused { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .button.is-black.is-outlined.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-black.is-outlined.is-loading:hover::after, .button.is-black.is-outlined.is-loading.is-hovered::after, .button.is-black.is-outlined.is-loading:focus::after, .button.is-black.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + .button.is-black.is-outlined[disabled], fieldset[disabled] .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + .button.is-black.is-inverted.is-outlined:hover, .button.is-black.is-inverted.is-outlined.is-hovered, .button.is-black.is-inverted.is-outlined:focus, .button.is-black.is-inverted.is-outlined.is-focused { + background-color: white; + color: #0a0a0a; } + .button.is-black.is-inverted.is-outlined.is-loading:hover::after, .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-black.is-inverted.is-outlined.is-loading:focus::after, .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + .button.is-light { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + .button.is-light:hover, .button.is-light.is-hovered { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + .button.is-light:focus, .button.is-light.is-focused { + border-color: transparent; + color: #363636; } + .button.is-light:focus:not(:active), .button.is-light.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .button.is-light:active, .button.is-light.is-active { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + .button.is-light[disabled], fieldset[disabled] .button.is-light { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; } + .button.is-light.is-inverted { + background-color: #363636; + color: whitesmoke; } + .button.is-light.is-inverted:hover, .button.is-light.is-inverted.is-hovered { + background-color: #292929; } + .button.is-light.is-inverted[disabled], fieldset[disabled] .button.is-light.is-inverted { + background-color: #363636; + border-color: transparent; + box-shadow: none; + color: whitesmoke; } + .button.is-light.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + .button.is-light.is-outlined:hover, .button.is-light.is-outlined.is-hovered, .button.is-light.is-outlined:focus, .button.is-light.is-outlined.is-focused { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .button.is-light.is-outlined.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-light.is-outlined.is-loading:hover::after, .button.is-light.is-outlined.is-loading.is-hovered::after, .button.is-light.is-outlined.is-loading:focus::after, .button.is-light.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-light.is-outlined[disabled], fieldset[disabled] .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + .button.is-light.is-inverted.is-outlined:hover, .button.is-light.is-inverted.is-outlined.is-hovered, .button.is-light.is-inverted.is-outlined:focus, .button.is-light.is-inverted.is-outlined.is-focused { + background-color: #363636; + color: whitesmoke; } + .button.is-light.is-inverted.is-outlined.is-loading:hover::after, .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-light.is-inverted.is-outlined.is-loading:focus::after, .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + .button.is-dark, .content kbd.button { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + .button.is-dark:hover, .content kbd.button:hover, .button.is-dark.is-hovered, .content kbd.button.is-hovered { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + .button.is-dark:focus, .content kbd.button:focus, .button.is-dark.is-focused, .content kbd.button.is-focused { + border-color: transparent; + color: whitesmoke; } + .button.is-dark:focus:not(:active), .content kbd.button:focus:not(:active), .button.is-dark.is-focused:not(:active), .content kbd.button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .button.is-dark:active, .content kbd.button:active, .button.is-dark.is-active, .content kbd.button.is-active { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + .button.is-dark[disabled], .content kbd.button[disabled], fieldset[disabled] .button.is-dark, fieldset[disabled] .content kbd.button, .content fieldset[disabled] kbd.button { + background-color: #363636; + border-color: transparent; + box-shadow: none; } + .button.is-dark.is-inverted, .content kbd.button.is-inverted { + background-color: whitesmoke; + color: #363636; } + .button.is-dark.is-inverted:hover, .content kbd.button.is-inverted:hover, .button.is-dark.is-inverted.is-hovered, .content kbd.button.is-inverted.is-hovered { + background-color: #e8e8e8; } + .button.is-dark.is-inverted[disabled], .content kbd.button.is-inverted[disabled], fieldset[disabled] .button.is-dark.is-inverted, fieldset[disabled] .content kbd.button.is-inverted, .content fieldset[disabled] kbd.button.is-inverted { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; + color: #363636; } + .button.is-dark.is-loading::after, .content kbd.button.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-dark.is-outlined, .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + .button.is-dark.is-outlined:hover, .content kbd.button.is-outlined:hover, .button.is-dark.is-outlined.is-hovered, .content kbd.button.is-outlined.is-hovered, .button.is-dark.is-outlined:focus, .content kbd.button.is-outlined:focus, .button.is-dark.is-outlined.is-focused, .content kbd.button.is-outlined.is-focused { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .button.is-dark.is-outlined.is-loading::after, .content kbd.button.is-outlined.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-dark.is-outlined.is-loading:hover::after, .content kbd.button.is-outlined.is-loading:hover::after, .button.is-dark.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-outlined.is-loading:focus::after, .content kbd.button.is-outlined.is-loading:focus::after, .button.is-dark.is-outlined.is-loading.is-focused::after, .content kbd.button.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-dark.is-outlined[disabled], .content kbd.button.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-outlined, fieldset[disabled] .content kbd.button.is-outlined, .content fieldset[disabled] kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + .button.is-dark.is-inverted.is-outlined, .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + .button.is-dark.is-inverted.is-outlined:hover, .content kbd.button.is-inverted.is-outlined:hover, .button.is-dark.is-inverted.is-outlined.is-hovered, .content kbd.button.is-inverted.is-outlined.is-hovered, .button.is-dark.is-inverted.is-outlined:focus, .content kbd.button.is-inverted.is-outlined:focus, .button.is-dark.is-inverted.is-outlined.is-focused, .content kbd.button.is-inverted.is-outlined.is-focused { + background-color: whitesmoke; + color: #363636; } + .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-dark.is-inverted.is-outlined[disabled], .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-inverted.is-outlined, fieldset[disabled] .content kbd.button.is-inverted.is-outlined, .content fieldset[disabled] kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + .button.is-primary, .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + .button.is-primary:hover, .docstring > section > a.button.docs-sourcelink:hover, .button.is-primary.is-hovered, .docstring > section > a.button.is-hovered.docs-sourcelink { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + .button.is-primary:focus, .docstring > section > a.button.docs-sourcelink:focus, .button.is-primary.is-focused, .docstring > section > a.button.is-focused.docs-sourcelink { + border-color: transparent; + color: #fff; } + .button.is-primary:focus:not(:active), .docstring > section > a.button.docs-sourcelink:focus:not(:active), .button.is-primary.is-focused:not(:active), .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .button.is-primary:active, .docstring > section > a.button.docs-sourcelink:active, .button.is-primary.is-active, .docstring > section > a.button.is-active.docs-sourcelink { + background-color: #39acda; + border-color: transparent; + color: #fff; } + .button.is-primary[disabled], .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary, fieldset[disabled] .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + box-shadow: none; } + .button.is-primary.is-inverted, .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + .button.is-primary.is-inverted:hover, .docstring > section > a.button.is-inverted.docs-sourcelink:hover, .button.is-primary.is-inverted.is-hovered, .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { + background-color: #f2f2f2; } + .button.is-primary.is-inverted[disabled], .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted, fieldset[disabled] .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #4eb5de; } + .button.is-primary.is-loading::after, .docstring > section > a.button.is-loading.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-primary.is-outlined, .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + color: #4eb5de; } + .button.is-primary.is-outlined:hover, .docstring > section > a.button.is-outlined.docs-sourcelink:hover, .button.is-primary.is-outlined.is-hovered, .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-outlined:focus, .docstring > section > a.button.is-outlined.docs-sourcelink:focus, .button.is-primary.is-outlined.is-focused, .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + .button.is-primary.is-outlined.is-loading::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + .button.is-primary.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-primary.is-outlined[disabled], .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-outlined, fieldset[disabled] .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + box-shadow: none; + color: #4eb5de; } + .button.is-primary.is-inverted.is-outlined, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-primary.is-inverted.is-outlined:hover, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, .button.is-primary.is-inverted.is-outlined.is-hovered, .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-inverted.is-outlined:focus, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, .button.is-primary.is-inverted.is-outlined.is-focused, .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + .button.is-primary.is-inverted.is-outlined[disabled], .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted.is-outlined, fieldset[disabled] .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-link { + background-color: #149eaa; + border-color: transparent; + color: #fff; } + .button.is-link:hover, .button.is-link.is-hovered { + background-color: #13939f; + border-color: transparent; + color: #fff; } + .button.is-link:focus, .button.is-link.is-focused { + border-color: transparent; + color: #fff; } + .button.is-link:focus:not(:active), .button.is-link.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .button.is-link:active, .button.is-link.is-active { + background-color: #118993; + border-color: transparent; + color: #fff; } + .button.is-link[disabled], fieldset[disabled] .button.is-link { + background-color: #149eaa; + border-color: transparent; + box-shadow: none; } + .button.is-link.is-inverted { + background-color: #fff; + color: #149eaa; } + .button.is-link.is-inverted:hover, .button.is-link.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-link.is-inverted[disabled], fieldset[disabled] .button.is-link.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #149eaa; } + .button.is-link.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-link.is-outlined { + background-color: transparent; + border-color: #149eaa; + color: #149eaa; } + .button.is-link.is-outlined:hover, .button.is-link.is-outlined.is-hovered, .button.is-link.is-outlined:focus, .button.is-link.is-outlined.is-focused { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + .button.is-link.is-outlined.is-loading::after { + border-color: transparent transparent #149eaa #149eaa !important; } + .button.is-link.is-outlined.is-loading:hover::after, .button.is-link.is-outlined.is-loading.is-hovered::after, .button.is-link.is-outlined.is-loading:focus::after, .button.is-link.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-link.is-outlined[disabled], fieldset[disabled] .button.is-link.is-outlined { + background-color: transparent; + border-color: #149eaa; + box-shadow: none; + color: #149eaa; } + .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-link.is-inverted.is-outlined:hover, .button.is-link.is-inverted.is-outlined.is-hovered, .button.is-link.is-inverted.is-outlined:focus, .button.is-link.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #149eaa; } + .button.is-link.is-inverted.is-outlined.is-loading:hover::after, .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-link.is-inverted.is-outlined.is-loading:focus::after, .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #149eaa #149eaa !important; } + .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-info { + background-color: #209cee; + border-color: transparent; + color: #fff; } + .button.is-info:hover, .button.is-info.is-hovered { + background-color: #1497ed; + border-color: transparent; + color: #fff; } + .button.is-info:focus, .button.is-info.is-focused { + border-color: transparent; + color: #fff; } + .button.is-info:focus:not(:active), .button.is-info.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .button.is-info:active, .button.is-info.is-active { + background-color: #1190e3; + border-color: transparent; + color: #fff; } + .button.is-info[disabled], fieldset[disabled] .button.is-info { + background-color: #209cee; + border-color: transparent; + box-shadow: none; } + .button.is-info.is-inverted { + background-color: #fff; + color: #209cee; } + .button.is-info.is-inverted:hover, .button.is-info.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-info.is-inverted[disabled], fieldset[disabled] .button.is-info.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #209cee; } + .button.is-info.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-info.is-outlined { + background-color: transparent; + border-color: #209cee; + color: #209cee; } + .button.is-info.is-outlined:hover, .button.is-info.is-outlined.is-hovered, .button.is-info.is-outlined:focus, .button.is-info.is-outlined.is-focused { + background-color: #209cee; + border-color: #209cee; + color: #fff; } + .button.is-info.is-outlined.is-loading::after { + border-color: transparent transparent #209cee #209cee !important; } + .button.is-info.is-outlined.is-loading:hover::after, .button.is-info.is-outlined.is-loading.is-hovered::after, .button.is-info.is-outlined.is-loading:focus::after, .button.is-info.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-info.is-outlined[disabled], fieldset[disabled] .button.is-info.is-outlined { + background-color: transparent; + border-color: #209cee; + box-shadow: none; + color: #209cee; } + .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-info.is-inverted.is-outlined:hover, .button.is-info.is-inverted.is-outlined.is-hovered, .button.is-info.is-inverted.is-outlined:focus, .button.is-info.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #209cee; } + .button.is-info.is-inverted.is-outlined.is-loading:hover::after, .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-info.is-inverted.is-outlined.is-loading:focus::after, .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #209cee #209cee !important; } + .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-success { + background-color: #22c35b; + border-color: transparent; + color: #fff; } + .button.is-success:hover, .button.is-success.is-hovered { + background-color: #20b856; + border-color: transparent; + color: #fff; } + .button.is-success:focus, .button.is-success.is-focused { + border-color: transparent; + color: #fff; } + .button.is-success:focus:not(:active), .button.is-success.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .button.is-success:active, .button.is-success.is-active { + background-color: #1ead51; + border-color: transparent; + color: #fff; } + .button.is-success[disabled], fieldset[disabled] .button.is-success { + background-color: #22c35b; + border-color: transparent; + box-shadow: none; } + .button.is-success.is-inverted { + background-color: #fff; + color: #22c35b; } + .button.is-success.is-inverted:hover, .button.is-success.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-success.is-inverted[disabled], fieldset[disabled] .button.is-success.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #22c35b; } + .button.is-success.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-success.is-outlined { + background-color: transparent; + border-color: #22c35b; + color: #22c35b; } + .button.is-success.is-outlined:hover, .button.is-success.is-outlined.is-hovered, .button.is-success.is-outlined:focus, .button.is-success.is-outlined.is-focused { + background-color: #22c35b; + border-color: #22c35b; + color: #fff; } + .button.is-success.is-outlined.is-loading::after { + border-color: transparent transparent #22c35b #22c35b !important; } + .button.is-success.is-outlined.is-loading:hover::after, .button.is-success.is-outlined.is-loading.is-hovered::after, .button.is-success.is-outlined.is-loading:focus::after, .button.is-success.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-success.is-outlined[disabled], fieldset[disabled] .button.is-success.is-outlined { + background-color: transparent; + border-color: #22c35b; + box-shadow: none; + color: #22c35b; } + .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-success.is-inverted.is-outlined:hover, .button.is-success.is-inverted.is-outlined.is-hovered, .button.is-success.is-inverted.is-outlined:focus, .button.is-success.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #22c35b; } + .button.is-success.is-inverted.is-outlined.is-loading:hover::after, .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-success.is-inverted.is-outlined.is-loading:focus::after, .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #22c35b #22c35b !important; } + .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-warning { + background-color: #ffdd57; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:hover, .button.is-warning.is-hovered { + background-color: #ffda4a; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:focus, .button.is-warning.is-focused { + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:focus:not(:active), .button.is-warning.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .button.is-warning:active, .button.is-warning.is-active { + background-color: #ffd83e; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning[disabled], fieldset[disabled] .button.is-warning { + background-color: #ffdd57; + border-color: transparent; + box-shadow: none; } + .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .button.is-warning.is-inverted:hover, .button.is-warning.is-inverted.is-hovered { + background-color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-inverted[disabled], fieldset[disabled] .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + border-color: transparent; + box-shadow: none; + color: #ffdd57; } + .button.is-warning.is-loading::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + .button.is-warning.is-outlined { + background-color: transparent; + border-color: #ffdd57; + color: #ffdd57; } + .button.is-warning.is-outlined:hover, .button.is-warning.is-outlined.is-hovered, .button.is-warning.is-outlined:focus, .button.is-warning.is-outlined.is-focused { + background-color: #ffdd57; + border-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-outlined.is-loading::after { + border-color: transparent transparent #ffdd57 #ffdd57 !important; } + .button.is-warning.is-outlined.is-loading:hover::after, .button.is-warning.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-outlined.is-loading:focus::after, .button.is-warning.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + .button.is-warning.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-outlined { + background-color: transparent; + border-color: #ffdd57; + box-shadow: none; + color: #ffdd57; } + .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-inverted.is-outlined:hover, .button.is-warning.is-inverted.is-outlined.is-hovered, .button.is-warning.is-inverted.is-outlined:focus, .button.is-warning.is-inverted.is-outlined.is-focused { + background-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #ffdd57 #ffdd57 !important; } + .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + box-shadow: none; + color: rgba(0, 0, 0, 0.7); } + .button.is-danger { + background-color: #da0b00; + border-color: transparent; + color: #fff; } + .button.is-danger:hover, .button.is-danger.is-hovered { + background-color: #cd0a00; + border-color: transparent; + color: #fff; } + .button.is-danger:focus, .button.is-danger.is-focused { + border-color: transparent; + color: #fff; } + .button.is-danger:focus:not(:active), .button.is-danger.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .button.is-danger:active, .button.is-danger.is-active { + background-color: #c10a00; + border-color: transparent; + color: #fff; } + .button.is-danger[disabled], fieldset[disabled] .button.is-danger { + background-color: #da0b00; + border-color: transparent; + box-shadow: none; } + .button.is-danger.is-inverted { + background-color: #fff; + color: #da0b00; } + .button.is-danger.is-inverted:hover, .button.is-danger.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-danger.is-inverted[disabled], fieldset[disabled] .button.is-danger.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #da0b00; } + .button.is-danger.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-danger.is-outlined { + background-color: transparent; + border-color: #da0b00; + color: #da0b00; } + .button.is-danger.is-outlined:hover, .button.is-danger.is-outlined.is-hovered, .button.is-danger.is-outlined:focus, .button.is-danger.is-outlined.is-focused { + background-color: #da0b00; + border-color: #da0b00; + color: #fff; } + .button.is-danger.is-outlined.is-loading::after { + border-color: transparent transparent #da0b00 #da0b00 !important; } + .button.is-danger.is-outlined.is-loading:hover::after, .button.is-danger.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-outlined.is-loading:focus::after, .button.is-danger.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-danger.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-outlined { + background-color: transparent; + border-color: #da0b00; + box-shadow: none; + color: #da0b00; } + .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-danger.is-inverted.is-outlined:hover, .button.is-danger.is-inverted.is-outlined.is-hovered, .button.is-danger.is-inverted.is-outlined:focus, .button.is-danger.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #da0b00; } + .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #da0b00 #da0b00 !important; } + .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-small, #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 2px; + font-size: 0.75rem; } + .button.is-normal { + font-size: 1rem; } + .button.is-medium { + font-size: 1.25rem; } + .button.is-large { + font-size: 1.5rem; } + .button[disabled], fieldset[disabled] .button { + background-color: white; + border-color: #dbdbdb; + box-shadow: none; + opacity: 0.5; } + .button.is-fullwidth { + display: flex; + width: 100%; } + .button.is-loading { + color: transparent !important; + pointer-events: none; } + .button.is-loading::after { + position: absolute; + left: calc(50% - (1em / 2)); + top: calc(50% - (1em / 2)); + position: absolute !important; } + .button.is-static { + background-color: whitesmoke; + border-color: #dbdbdb; + color: #6b6b6b; + box-shadow: none; + pointer-events: none; } + .button.is-rounded, #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + +.buttons { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .buttons .button { + margin-bottom: 0.5rem; } + .buttons .button:not(:last-child):not(.is-fullwidth) { + margin-right: 0.5rem; } + .buttons:last-child { + margin-bottom: -0.5rem; } + .buttons:not(:last-child) { + margin-bottom: 1rem; } + .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { + border-radius: 2px; + font-size: 0.75rem; } + .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { + font-size: 1.25rem; } + .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { + font-size: 1.5rem; } + .buttons.has-addons .button:not(:first-child) { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .buttons.has-addons .button:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; + margin-right: -1px; } + .buttons.has-addons .button:last-child { + margin-right: 0; } + .buttons.has-addons .button:hover, .buttons.has-addons .button.is-hovered { + z-index: 2; } + .buttons.has-addons .button:focus, .buttons.has-addons .button.is-focused, .buttons.has-addons .button:active, .buttons.has-addons .button.is-active, .buttons.has-addons .button.is-selected { + z-index: 3; } + .buttons.has-addons .button:focus:hover, .buttons.has-addons .button.is-focused:hover, .buttons.has-addons .button:active:hover, .buttons.has-addons .button.is-active:hover, .buttons.has-addons .button.is-selected:hover { + z-index: 4; } + .buttons.has-addons .button.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .buttons.is-centered { + justify-content: center; } + .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + .buttons.is-right { + justify-content: flex-end; } + .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + +.container { + flex-grow: 1; + margin: 0 auto; + position: relative; + width: auto; } + @media screen and (min-width: 1056px) { + .container { + max-width: 992px; } + .container.is-fluid { + margin-left: 32px; + margin-right: 32px; + max-width: none; } } + @media screen and (max-width: 1215px) { + .container.is-widescreen { + max-width: 1152px; } } + @media screen and (max-width: 1407px) { + .container.is-fullhd { + max-width: 1344px; } } + @media screen and (min-width: 1216px) { + .container { + max-width: 1152px; } } + @media screen and (min-width: 1408px) { + .container { + max-width: 1344px; } } +.content li + li { + margin-top: 0.25em; } + +.content p:not(:last-child), +.content dl:not(:last-child), +.content ol:not(:last-child), +.content ul:not(:last-child), +.content blockquote:not(:last-child), +.content pre:not(:last-child), +.content table:not(:last-child) { + margin-bottom: 1em; } + +.content h1, +.content h2, +.content h3, +.content h4, +.content h5, +.content h6 { + color: #654ca3; + font-weight: 600; + line-height: 1.125; } + +.content h1 { + font-size: 2em; + margin-bottom: 0.5em; } + .content h1:not(:first-child) { + margin-top: 1em; } + +.content h2 { + font-size: 1.75em; + margin-bottom: 0.5714em; } + .content h2:not(:first-child) { + margin-top: 1.1428em; } + +.content h3 { + font-size: 1.5em; + margin-bottom: 0.6666em; } + .content h3:not(:first-child) { + margin-top: 1.3333em; } + +.content h4 { + font-size: 1.25em; + margin-bottom: 0.8em; } + +.content h5 { + font-size: 1.125em; + margin-bottom: 0.8888em; } + +.content h6 { + font-size: 1em; + margin-bottom: 1em; } + +.content blockquote { + background-color: whitesmoke; + border-left: 5px solid #dbdbdb; + padding: 1.25em 1.5em; } + +.content ol { + list-style-position: outside; + margin-left: 2em; + margin-top: 1em; } + .content ol:not([type]) { + list-style-type: decimal; } + .content ol.is-lower-alpha:not([type]) { + list-style-type: lower-alpha; } + .content ol.is-lower-roman:not([type]) { + list-style-type: lower-roman; } + .content ol.is-upper-alpha:not([type]) { + list-style-type: upper-alpha; } + .content ol.is-upper-roman:not([type]) { + list-style-type: upper-roman; } + +.content ul { + list-style: disc outside; + margin-left: 2em; + margin-top: 1em; } + .content ul ul { + list-style-type: circle; + margin-top: 0.5em; } + .content ul ul ul { + list-style-type: square; } + +.content dd { + margin-left: 2em; } + +.content figure { + margin-left: 2em; + margin-right: 2em; + text-align: center; } + .content figure:not(:first-child) { + margin-top: 2em; } + .content figure:not(:last-child) { + margin-bottom: 2em; } + .content figure img { + display: inline-block; } + .content figure figcaption { + font-style: italic; } + +.content pre { + -webkit-overflow-scrolling: touch; + overflow-x: auto; + padding: 0; + white-space: pre; + word-wrap: normal; } + +.content sup, +.content sub { + font-size: 75%; } + +.content table { + width: 100%; } + .content table td, + .content table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + .content table th { + color: #654ca3; } + .content table th:not([align]) { + text-align: left; } + .content table thead td, + .content table thead th { + border-width: 0 0 2px; + color: #654ca3; } + .content table tfoot td, + .content table tfoot th { + border-width: 2px 0 0; + color: #654ca3; } + .content table tbody tr:last-child td, + .content table tbody tr:last-child th { + border-bottom-width: 0; } + +.content .tabs li + li { + margin-top: 0; } + +.content.is-small, #documenter .docs-sidebar form.docs-search > input.content { + font-size: 0.75rem; } + +.content.is-medium { + font-size: 1.25rem; } + +.content.is-large { + font-size: 1.5rem; } + +.icon { + align-items: center; + display: inline-flex; + justify-content: center; + height: 1.5rem; + width: 1.5rem; } + .icon.is-small, #documenter .docs-sidebar form.docs-search > input.icon { + height: 1rem; + width: 1rem; } + .icon.is-medium { + height: 2rem; + width: 2rem; } + .icon.is-large { + height: 3rem; + width: 3rem; } + +.image, #documenter .docs-sidebar .docs-logo > img { + display: block; + position: relative; } + .image img, #documenter .docs-sidebar .docs-logo > img img { + display: block; + height: auto; + width: 100%; } + .image img.is-rounded, #documenter .docs-sidebar .docs-logo > img img.is-rounded { + border-radius: 290486px; } + .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img, + .image.is-square .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img, + .image.is-1by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img, + .image.is-5by4 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img, + .image.is-4by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img, + .image.is-3by2 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img, + .image.is-5by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img, + .image.is-16by9 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img, + .image.is-2by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img, + .image.is-3by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img, + .image.is-4by5 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img, + .image.is-3by4 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img, + .image.is-2by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img, + .image.is-3by5 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img, + .image.is-9by16 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img, + .image.is-1by2 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img, + .image.is-1by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { + height: 100%; + width: 100%; } + .image.is-square, #documenter .docs-sidebar .docs-logo > img.is-square, .image.is-1by1, #documenter .docs-sidebar .docs-logo > img.is-1by1 { + padding-top: 100%; } + .image.is-5by4, #documenter .docs-sidebar .docs-logo > img.is-5by4 { + padding-top: 80%; } + .image.is-4by3, #documenter .docs-sidebar .docs-logo > img.is-4by3 { + padding-top: 75%; } + .image.is-3by2, #documenter .docs-sidebar .docs-logo > img.is-3by2 { + padding-top: 66.6666%; } + .image.is-5by3, #documenter .docs-sidebar .docs-logo > img.is-5by3 { + padding-top: 60%; } + .image.is-16by9, #documenter .docs-sidebar .docs-logo > img.is-16by9 { + padding-top: 56.25%; } + .image.is-2by1, #documenter .docs-sidebar .docs-logo > img.is-2by1 { + padding-top: 50%; } + .image.is-3by1, #documenter .docs-sidebar .docs-logo > img.is-3by1 { + padding-top: 33.3333%; } + .image.is-4by5, #documenter .docs-sidebar .docs-logo > img.is-4by5 { + padding-top: 125%; } + .image.is-3by4, #documenter .docs-sidebar .docs-logo > img.is-3by4 { + padding-top: 133.3333%; } + .image.is-2by3, #documenter .docs-sidebar .docs-logo > img.is-2by3 { + padding-top: 150%; } + .image.is-3by5, #documenter .docs-sidebar .docs-logo > img.is-3by5 { + padding-top: 166.6666%; } + .image.is-9by16, #documenter .docs-sidebar .docs-logo > img.is-9by16 { + padding-top: 177.7777%; } + .image.is-1by2, #documenter .docs-sidebar .docs-logo > img.is-1by2 { + padding-top: 200%; } + .image.is-1by3, #documenter .docs-sidebar .docs-logo > img.is-1by3 { + padding-top: 300%; } + .image.is-16x16, #documenter .docs-sidebar .docs-logo > img.is-16x16 { + height: 16px; + width: 16px; } + .image.is-24x24, #documenter .docs-sidebar .docs-logo > img.is-24x24 { + height: 24px; + width: 24px; } + .image.is-32x32, #documenter .docs-sidebar .docs-logo > img.is-32x32 { + height: 32px; + width: 32px; } + .image.is-48x48, #documenter .docs-sidebar .docs-logo > img.is-48x48 { + height: 48px; + width: 48px; } + .image.is-64x64, #documenter .docs-sidebar .docs-logo > img.is-64x64 { + height: 64px; + width: 64px; } + .image.is-96x96, #documenter .docs-sidebar .docs-logo > img.is-96x96 { + height: 96px; + width: 96px; } + .image.is-128x128, #documenter .docs-sidebar .docs-logo > img.is-128x128 { + height: 128px; + width: 128px; } + +.notification { + background-color: whitesmoke; + border-radius: 4px; + padding: 1.25rem 2.5rem 1.25rem 1.5rem; + position: relative; } + .notification a:not(.button):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + .notification strong { + color: currentColor; } + .notification code, + .notification pre { + background: white; } + .notification pre code { + background: transparent; } + .notification > .delete { + position: absolute; + right: 0.5rem; + top: 0.5rem; } + .notification .title, + .notification .subtitle, + .notification .content { + color: currentColor; } + .notification.is-white { + background-color: white; + color: #0a0a0a; } + .notification.is-black { + background-color: #0a0a0a; + color: white; } + .notification.is-light { + background-color: whitesmoke; + color: #363636; } + .notification.is-dark, .content kbd.notification { + background-color: #363636; + color: whitesmoke; } + .notification.is-primary, .docstring > section > a.notification.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .notification.is-link { + background-color: #149eaa; + color: #fff; } + .notification.is-info { + background-color: #209cee; + color: #fff; } + .notification.is-success { + background-color: #22c35b; + color: #fff; } + .notification.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .notification.is-danger { + background-color: #da0b00; + color: #fff; } + +.progress { + -moz-appearance: none; + -webkit-appearance: none; + border: none; + border-radius: 290486px; + display: block; + height: 1rem; + overflow: hidden; + padding: 0; + width: 100%; } + .progress::-webkit-progress-bar { + background-color: #dbdbdb; } + .progress::-webkit-progress-value { + background-color: #202020; } + .progress::-moz-progress-bar { + background-color: #202020; } + .progress::-ms-fill { + background-color: #202020; + border: none; } + .progress.is-white::-webkit-progress-value { + background-color: white; } + .progress.is-white::-moz-progress-bar { + background-color: white; } + .progress.is-white::-ms-fill { + background-color: white; } + .progress.is-white:indeterminate { + background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); } + .progress.is-black::-webkit-progress-value { + background-color: #0a0a0a; } + .progress.is-black::-moz-progress-bar { + background-color: #0a0a0a; } + .progress.is-black::-ms-fill { + background-color: #0a0a0a; } + .progress.is-black:indeterminate { + background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); } + .progress.is-light::-webkit-progress-value { + background-color: whitesmoke; } + .progress.is-light::-moz-progress-bar { + background-color: whitesmoke; } + .progress.is-light::-ms-fill { + background-color: whitesmoke; } + .progress.is-light:indeterminate { + background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); } + .progress.is-dark::-webkit-progress-value, .content kbd.progress::-webkit-progress-value { + background-color: #363636; } + .progress.is-dark::-moz-progress-bar, .content kbd.progress::-moz-progress-bar { + background-color: #363636; } + .progress.is-dark::-ms-fill, .content kbd.progress::-ms-fill { + background-color: #363636; } + .progress.is-dark:indeterminate, .content kbd.progress:indeterminate { + background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); } + .progress.is-primary::-webkit-progress-value, .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { + background-color: #4eb5de; } + .progress.is-primary::-moz-progress-bar, .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { + background-color: #4eb5de; } + .progress.is-primary::-ms-fill, .docstring > section > a.progress.docs-sourcelink::-ms-fill { + background-color: #4eb5de; } + .progress.is-primary:indeterminate, .docstring > section > a.progress.docs-sourcelink:indeterminate { + background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); } + .progress.is-link::-webkit-progress-value { + background-color: #149eaa; } + .progress.is-link::-moz-progress-bar { + background-color: #149eaa; } + .progress.is-link::-ms-fill { + background-color: #149eaa; } + .progress.is-link:indeterminate { + background-image: linear-gradient(to right, #149eaa 30%, #dbdbdb 30%); } + .progress.is-info::-webkit-progress-value { + background-color: #209cee; } + .progress.is-info::-moz-progress-bar { + background-color: #209cee; } + .progress.is-info::-ms-fill { + background-color: #209cee; } + .progress.is-info:indeterminate { + background-image: linear-gradient(to right, #209cee 30%, #dbdbdb 30%); } + .progress.is-success::-webkit-progress-value { + background-color: #22c35b; } + .progress.is-success::-moz-progress-bar { + background-color: #22c35b; } + .progress.is-success::-ms-fill { + background-color: #22c35b; } + .progress.is-success:indeterminate { + background-image: linear-gradient(to right, #22c35b 30%, #dbdbdb 30%); } + .progress.is-warning::-webkit-progress-value { + background-color: #ffdd57; } + .progress.is-warning::-moz-progress-bar { + background-color: #ffdd57; } + .progress.is-warning::-ms-fill { + background-color: #ffdd57; } + .progress.is-warning:indeterminate { + background-image: linear-gradient(to right, #ffdd57 30%, #dbdbdb 30%); } + .progress.is-danger::-webkit-progress-value { + background-color: #da0b00; } + .progress.is-danger::-moz-progress-bar { + background-color: #da0b00; } + .progress.is-danger::-ms-fill { + background-color: #da0b00; } + .progress.is-danger:indeterminate { + background-image: linear-gradient(to right, #da0b00 30%, #dbdbdb 30%); } + .progress:indeterminate { + animation-duration: 1.5s; + animation-iteration-count: infinite; + animation-name: moveIndeterminate; + animation-timing-function: linear; + background-color: #dbdbdb; + background-image: linear-gradient(to right, #202020 30%, #dbdbdb 30%); + background-position: top left; + background-repeat: no-repeat; + background-size: 150% 150%; } + .progress:indeterminate::-webkit-progress-bar { + background-color: transparent; } + .progress:indeterminate::-moz-progress-bar { + background-color: transparent; } + .progress.is-small, #documenter .docs-sidebar form.docs-search > input.progress { + height: 0.75rem; } + .progress.is-medium { + height: 1.25rem; } + .progress.is-large { + height: 1.5rem; } + +@keyframes moveIndeterminate { + from { + background-position: 200% 0; } + to { + background-position: -200% 0; } } + +.table { + background-color: white; + color: #363636; } + .table td, + .table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + .table td.is-white, + .table th.is-white { + background-color: white; + border-color: white; + color: #0a0a0a; } + .table td.is-black, + .table th.is-black { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .table td.is-light, + .table th.is-light { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .table td.is-dark, + .table th.is-dark { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .table td.is-primary, + .table th.is-primary { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + .table td.is-link, + .table th.is-link { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + .table td.is-info, + .table th.is-info { + background-color: #209cee; + border-color: #209cee; + color: #fff; } + .table td.is-success, + .table th.is-success { + background-color: #22c35b; + border-color: #22c35b; + color: #fff; } + .table td.is-warning, + .table th.is-warning { + background-color: #ffdd57; + border-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .table td.is-danger, + .table th.is-danger { + background-color: #da0b00; + border-color: #da0b00; + color: #fff; } + .table td.is-narrow, + .table th.is-narrow { + white-space: nowrap; + width: 1%; } + .table td.is-selected, + .table th.is-selected { + background-color: #4eb5de; + color: #fff; } + .table td.is-selected a, + .table td.is-selected strong, + .table th.is-selected a, + .table th.is-selected strong { + color: currentColor; } + .table th { + color: #654ca3; } + .table th:not([align]) { + text-align: left; } + .table tr.is-selected { + background-color: #4eb5de; + color: #fff; } + .table tr.is-selected a, + .table tr.is-selected strong { + color: currentColor; } + .table tr.is-selected td, + .table tr.is-selected th { + border-color: #fff; + color: currentColor; } + .table thead { + background-color: transparent; } + .table thead td, + .table thead th { + border-width: 0 0 2px; + color: #654ca3; } + .table tfoot { + background-color: transparent; } + .table tfoot td, + .table tfoot th { + border-width: 2px 0 0; + color: #654ca3; } + .table tbody { + background-color: transparent; } + .table tbody tr:last-child td, + .table tbody tr:last-child th { + border-bottom-width: 0; } + .table.is-bordered td, + .table.is-bordered th { + border-width: 1px; } + .table.is-bordered tr:last-child td, + .table.is-bordered tr:last-child th { + border-bottom-width: 1px; } + .table.is-fullwidth { + width: 100%; } + .table.is-hoverable tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { + background-color: whitesmoke; } + .table.is-narrow td, + .table.is-narrow th { + padding: 0.25em 0.5em; } + .table.is-striped tbody tr:not(.is-selected):nth-child(even) { + background-color: #fafafa; } + +.table-container { + -webkit-overflow-scrolling: touch; + overflow: auto; + overflow-y: hidden; + max-width: 100%; } + +.tags { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .tags .tag, .tags .content kbd, .content .tags kbd, .tags .docstring > section > a.docs-sourcelink { + margin-bottom: 0.5rem; } + .tags .tag:not(:last-child), .tags .content kbd:not(:last-child), .content .tags kbd:not(:last-child), .tags .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0.5rem; } + .tags:last-child { + margin-bottom: -0.5rem; } + .tags:not(:last-child) { + margin-bottom: 1rem; } + .tags.are-medium .tag:not(.is-normal):not(.is-large), .tags.are-medium .content kbd:not(.is-normal):not(.is-large), .content .tags.are-medium kbd:not(.is-normal):not(.is-large), .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { + font-size: 1rem; } + .tags.are-large .tag:not(.is-normal):not(.is-medium), .tags.are-large .content kbd:not(.is-normal):not(.is-medium), .content .tags.are-large kbd:not(.is-normal):not(.is-medium), .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { + font-size: 1.25rem; } + .tags.is-centered { + justify-content: center; } + .tags.is-centered .tag, .tags.is-centered .content kbd, .content .tags.is-centered kbd, .tags.is-centered .docstring > section > a.docs-sourcelink { + margin-right: 0.25rem; + margin-left: 0.25rem; } + .tags.is-right { + justify-content: flex-end; } + .tags.is-right .tag:not(:first-child), .tags.is-right .content kbd:not(:first-child), .content .tags.is-right kbd:not(:first-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0.5rem; } + .tags.is-right .tag:not(:last-child), .tags.is-right .content kbd:not(:last-child), .content .tags.is-right kbd:not(:last-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0; } + .tags.has-addons .tag, .tags.has-addons .content kbd, .content .tags.has-addons kbd, .tags.has-addons .docstring > section > a.docs-sourcelink { + margin-right: 0; } + .tags.has-addons .tag:not(:first-child), .tags.has-addons .content kbd:not(:first-child), .content .tags.has-addons kbd:not(:first-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0; + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .tags.has-addons .tag:not(:last-child), .tags.has-addons .content kbd:not(:last-child), .content .tags.has-addons kbd:not(:last-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + +.tag:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink:not(body) { + align-items: center; + background-color: whitesmoke; + border-radius: 4px; + color: #202020; + display: inline-flex; + font-size: 0.75rem; + height: 2em; + justify-content: center; + line-height: 1.5; + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + .tag:not(body) .delete, .content kbd:not(body) .delete, .docstring > section > a.docs-sourcelink:not(body) .delete { + margin-left: 0.25rem; + margin-right: -0.375rem; } + .tag.is-white:not(body), .content kbd.is-white:not(body), .docstring > section > a.docs-sourcelink.is-white:not(body) { + background-color: white; + color: #0a0a0a; } + .tag.is-black:not(body), .content kbd.is-black:not(body), .docstring > section > a.docs-sourcelink.is-black:not(body) { + background-color: #0a0a0a; + color: white; } + .tag.is-light:not(body), .content kbd.is-light:not(body), .docstring > section > a.docs-sourcelink.is-light:not(body) { + background-color: whitesmoke; + color: #363636; } + .tag.is-dark:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink.is-dark:not(body), .content .docstring > section > kbd:not(body) { + background-color: #363636; + color: whitesmoke; } + .tag.is-primary:not(body), .content kbd.is-primary:not(body), .docstring > section > a.docs-sourcelink:not(body) { + background-color: #4eb5de; + color: #fff; } + .tag.is-link:not(body), .content kbd.is-link:not(body), .docstring > section > a.docs-sourcelink.is-link:not(body) { + background-color: #149eaa; + color: #fff; } + .tag.is-info:not(body), .content kbd.is-info:not(body), .docstring > section > a.docs-sourcelink.is-info:not(body) { + background-color: #209cee; + color: #fff; } + .tag.is-success:not(body), .content kbd.is-success:not(body), .docstring > section > a.docs-sourcelink.is-success:not(body) { + background-color: #22c35b; + color: #fff; } + .tag.is-warning:not(body), .content kbd.is-warning:not(body), .docstring > section > a.docs-sourcelink.is-warning:not(body) { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .tag.is-danger:not(body), .content kbd.is-danger:not(body), .docstring > section > a.docs-sourcelink.is-danger:not(body) { + background-color: #da0b00; + color: #fff; } + .tag.is-normal:not(body), .content kbd.is-normal:not(body), .docstring > section > a.docs-sourcelink.is-normal:not(body) { + font-size: 0.75rem; } + .tag.is-medium:not(body), .content kbd.is-medium:not(body), .docstring > section > a.docs-sourcelink.is-medium:not(body) { + font-size: 1rem; } + .tag.is-large:not(body), .content kbd.is-large:not(body), .docstring > section > a.docs-sourcelink.is-large:not(body) { + font-size: 1.25rem; } + .tag:not(body) .icon:first-child:not(:last-child), .content kbd:not(body) .icon:first-child:not(:last-child), .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { + margin-left: -0.375em; + margin-right: 0.1875em; } + .tag:not(body) .icon:last-child:not(:first-child), .content kbd:not(body) .icon:last-child:not(:first-child), .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: -0.375em; } + .tag:not(body) .icon:first-child:last-child, .content kbd:not(body) .icon:first-child:last-child, .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { + margin-left: -0.375em; + margin-right: -0.375em; } + .tag.is-delete:not(body), .content kbd.is-delete:not(body), .docstring > section > a.docs-sourcelink.is-delete:not(body) { + margin-left: 1px; + padding: 0; + position: relative; + width: 2em; } + .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + background-color: currentColor; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { + height: 1px; + width: 50%; } + .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + height: 50%; + width: 1px; } + .tag.is-delete:not(body):hover, .content kbd.is-delete:not(body):hover, .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, .tag.is-delete:not(body):focus, .content kbd.is-delete:not(body):focus, .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { + background-color: #e8e8e8; } + .tag.is-delete:not(body):active, .content kbd.is-delete:not(body):active, .docstring > section > a.docs-sourcelink.is-delete:not(body):active { + background-color: #dbdbdb; } + .tag.is-rounded:not(body), #documenter .docs-sidebar form.docs-search > input:not(body), .content kbd.is-rounded:not(body), #documenter .docs-sidebar .content form.docs-search > input:not(body), .docstring > section > a.docs-sourcelink.is-rounded:not(body) { + border-radius: 290486px; } + +a.tag:hover, .docstring > section > a.docs-sourcelink:hover { + text-decoration: underline; } + +.title, +.subtitle { + word-break: break-word; } + .title em, + .title span, + .subtitle em, + .subtitle span { + font-weight: inherit; } + .title sub, + .subtitle sub { + font-size: 0.75em; } + .title sup, + .subtitle sup { + font-size: 0.75em; } + .title .tag, .title .content kbd, .content .title kbd, .title .docstring > section > a.docs-sourcelink, + .subtitle .tag, + .subtitle .content kbd, + .content .subtitle kbd, + .subtitle .docstring > section > a.docs-sourcelink { + vertical-align: middle; } + +.title { + color: #363636; + font-size: 2rem; + font-weight: 600; + line-height: 1.125; } + .title strong { + color: inherit; + font-weight: inherit; } + .title + .highlight { + margin-top: -0.75rem; } + .title:not(.is-spaced) + .subtitle { + margin-top: -1.25rem; } + .title.is-1 { + font-size: 3rem; } + .title.is-2 { + font-size: 2.5rem; } + .title.is-3 { + font-size: 2rem; } + .title.is-4 { + font-size: 1.5rem; } + .title.is-5 { + font-size: 1.25rem; } + .title.is-6 { + font-size: 1rem; } + .title.is-7 { + font-size: 0.75rem; } + +.subtitle { + color: #4a4a4a; + font-size: 1.25rem; + font-weight: 400; + line-height: 1.25; } + .subtitle strong { + color: #363636; + font-weight: 600; } + .subtitle:not(.is-spaced) + .title { + margin-top: -1.25rem; } + .subtitle.is-1 { + font-size: 3rem; } + .subtitle.is-2 { + font-size: 2.5rem; } + .subtitle.is-3 { + font-size: 2rem; } + .subtitle.is-4 { + font-size: 1.5rem; } + .subtitle.is-5 { + font-size: 1.25rem; } + .subtitle.is-6 { + font-size: 1rem; } + .subtitle.is-7 { + font-size: 0.75rem; } + +.heading { + display: block; + font-size: 11px; + letter-spacing: 1px; + margin-bottom: 5px; + text-transform: uppercase; } + +.highlight { + font-weight: 400; + max-width: 100%; + overflow: hidden; + padding: 0; } + .highlight pre { + overflow: auto; + max-width: 100%; } + +.number { + align-items: center; + background-color: whitesmoke; + border-radius: 290486px; + display: inline-flex; + font-size: 1.25rem; + height: 2em; + justify-content: center; + margin-right: 1.5rem; + min-width: 2.5em; + padding: 0.25rem 0.5rem; + text-align: center; + vertical-align: top; } + +.select select, .textarea, .input, #documenter .docs-sidebar form.docs-search > input { + background-color: white; + border-color: #dbdbdb; + border-radius: 4px; + color: #363636; } + .select select::-moz-placeholder, .textarea::-moz-placeholder, .input::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select::-webkit-input-placeholder, .textarea::-webkit-input-placeholder, .input::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:-moz-placeholder, .textarea:-moz-placeholder, .input:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:-ms-input-placeholder, .textarea:-ms-input-placeholder, .input:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:hover, .textarea:hover, .input:hover, #documenter .docs-sidebar form.docs-search > input:hover, .select select.is-hovered, .is-hovered.textarea, .is-hovered.input, #documenter .docs-sidebar form.docs-search > input.is-hovered { + border-color: #149eaa; } + .select select:focus, .textarea:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .select select.is-focused, .is-focused.textarea, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .select select:active, .textarea:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .select select.is-active, .is-active.textarea, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + border-color: #fff; + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .select select[disabled], .textarea[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] .select select, .select fieldset[disabled] select, fieldset[disabled] .textarea, fieldset[disabled] .input, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input { + background-color: whitesmoke; + border-color: whitesmoke; + box-shadow: none; + color: #6b6b6b; } + .select select[disabled]::-moz-placeholder, .textarea[disabled]::-moz-placeholder, .input[disabled]::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] .select select::-moz-placeholder, .select fieldset[disabled] select::-moz-placeholder, fieldset[disabled] .textarea::-moz-placeholder, fieldset[disabled] .input::-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-moz-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]::-webkit-input-placeholder, .textarea[disabled]::-webkit-input-placeholder, .input[disabled]::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] .select select::-webkit-input-placeholder, .select fieldset[disabled] select::-webkit-input-placeholder, fieldset[disabled] .textarea::-webkit-input-placeholder, fieldset[disabled] .input::-webkit-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-webkit-input-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]:-moz-placeholder, .textarea[disabled]:-moz-placeholder, .input[disabled]:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] .select select:-moz-placeholder, .select fieldset[disabled] select:-moz-placeholder, fieldset[disabled] .textarea:-moz-placeholder, fieldset[disabled] .input:-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-moz-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]:-ms-input-placeholder, .textarea[disabled]:-ms-input-placeholder, .input[disabled]:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] .select select:-ms-input-placeholder, .select fieldset[disabled] select:-ms-input-placeholder, fieldset[disabled] .textarea:-ms-input-placeholder, fieldset[disabled] .input:-ms-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-ms-input-placeholder { + color: rgba(107, 107, 107, 0.3); } + +.textarea, .input, #documenter .docs-sidebar form.docs-search > input { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); + max-width: 100%; + width: 100%; } + .textarea[readonly], .input[readonly], #documenter .docs-sidebar form.docs-search > input[readonly] { + box-shadow: none; } + .is-white.textarea, .is-white.input, #documenter .docs-sidebar form.docs-search > input.is-white { + border-color: white; } + .is-white.textarea:focus, .is-white.input:focus, #documenter .docs-sidebar form.docs-search > input.is-white:focus, .is-white.is-focused.textarea, .is-white.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-white.textarea:active, .is-white.input:active, #documenter .docs-sidebar form.docs-search > input.is-white:active, .is-white.is-active.textarea, .is-white.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .is-black.textarea, .is-black.input, #documenter .docs-sidebar form.docs-search > input.is-black { + border-color: #0a0a0a; } + .is-black.textarea:focus, .is-black.input:focus, #documenter .docs-sidebar form.docs-search > input.is-black:focus, .is-black.is-focused.textarea, .is-black.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-black.textarea:active, .is-black.input:active, #documenter .docs-sidebar form.docs-search > input.is-black:active, .is-black.is-active.textarea, .is-black.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .is-light.textarea, .is-light.input, #documenter .docs-sidebar form.docs-search > input.is-light { + border-color: whitesmoke; } + .is-light.textarea:focus, .is-light.input:focus, #documenter .docs-sidebar form.docs-search > input.is-light:focus, .is-light.is-focused.textarea, .is-light.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-light.textarea:active, .is-light.input:active, #documenter .docs-sidebar form.docs-search > input.is-light:active, .is-light.is-active.textarea, .is-light.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .is-dark.textarea, .content kbd.textarea, .is-dark.input, #documenter .docs-sidebar form.docs-search > input.is-dark, .content kbd.input { + border-color: #363636; } + .is-dark.textarea:focus, .content kbd.textarea:focus, .is-dark.input:focus, #documenter .docs-sidebar form.docs-search > input.is-dark:focus, .content kbd.input:focus, .is-dark.is-focused.textarea, .content kbd.is-focused.textarea, .is-dark.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .content kbd.is-focused.input, #documenter .docs-sidebar .content form.docs-search > input.is-focused, .is-dark.textarea:active, .content kbd.textarea:active, .is-dark.input:active, #documenter .docs-sidebar form.docs-search > input.is-dark:active, .content kbd.input:active, .is-dark.is-active.textarea, .content kbd.is-active.textarea, .is-dark.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .content kbd.is-active.input, #documenter .docs-sidebar .content form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .is-primary.textarea, .docstring > section > a.textarea.docs-sourcelink, .is-primary.input, #documenter .docs-sidebar form.docs-search > input.is-primary, .docstring > section > a.input.docs-sourcelink { + border-color: #4eb5de; } + .is-primary.textarea:focus, .docstring > section > a.textarea.docs-sourcelink:focus, .is-primary.input:focus, #documenter .docs-sidebar form.docs-search > input.is-primary:focus, .docstring > section > a.input.docs-sourcelink:focus, .is-primary.is-focused.textarea, .docstring > section > a.is-focused.textarea.docs-sourcelink, .is-primary.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .docstring > section > a.is-focused.input.docs-sourcelink, .is-primary.textarea:active, .docstring > section > a.textarea.docs-sourcelink:active, .is-primary.input:active, #documenter .docs-sidebar form.docs-search > input.is-primary:active, .docstring > section > a.input.docs-sourcelink:active, .is-primary.is-active.textarea, .docstring > section > a.is-active.textarea.docs-sourcelink, .is-primary.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .docstring > section > a.is-active.input.docs-sourcelink { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .is-link.textarea, .is-link.input, #documenter .docs-sidebar form.docs-search > input.is-link { + border-color: #149eaa; } + .is-link.textarea:focus, .is-link.input:focus, #documenter .docs-sidebar form.docs-search > input.is-link:focus, .is-link.is-focused.textarea, .is-link.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-link.textarea:active, .is-link.input:active, #documenter .docs-sidebar form.docs-search > input.is-link:active, .is-link.is-active.textarea, .is-link.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .is-info.textarea, .is-info.input, #documenter .docs-sidebar form.docs-search > input.is-info { + border-color: #209cee; } + .is-info.textarea:focus, .is-info.input:focus, #documenter .docs-sidebar form.docs-search > input.is-info:focus, .is-info.is-focused.textarea, .is-info.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-info.textarea:active, .is-info.input:active, #documenter .docs-sidebar form.docs-search > input.is-info:active, .is-info.is-active.textarea, .is-info.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .is-success.textarea, .is-success.input, #documenter .docs-sidebar form.docs-search > input.is-success { + border-color: #22c35b; } + .is-success.textarea:focus, .is-success.input:focus, #documenter .docs-sidebar form.docs-search > input.is-success:focus, .is-success.is-focused.textarea, .is-success.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-success.textarea:active, .is-success.input:active, #documenter .docs-sidebar form.docs-search > input.is-success:active, .is-success.is-active.textarea, .is-success.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .is-warning.textarea, .is-warning.input, #documenter .docs-sidebar form.docs-search > input.is-warning { + border-color: #ffdd57; } + .is-warning.textarea:focus, .is-warning.input:focus, #documenter .docs-sidebar form.docs-search > input.is-warning:focus, .is-warning.is-focused.textarea, .is-warning.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-warning.textarea:active, .is-warning.input:active, #documenter .docs-sidebar form.docs-search > input.is-warning:active, .is-warning.is-active.textarea, .is-warning.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .is-danger.textarea, .is-danger.input, #documenter .docs-sidebar form.docs-search > input.is-danger { + border-color: #da0b00; } + .is-danger.textarea:focus, .is-danger.input:focus, #documenter .docs-sidebar form.docs-search > input.is-danger:focus, .is-danger.is-focused.textarea, .is-danger.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-danger.textarea:active, .is-danger.input:active, #documenter .docs-sidebar form.docs-search > input.is-danger:active, .is-danger.is-active.textarea, .is-danger.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .is-small.textarea, .is-small.input, #documenter .docs-sidebar form.docs-search > input { + border-radius: 2px; + font-size: 0.75rem; } + .is-medium.textarea, .is-medium.input, #documenter .docs-sidebar form.docs-search > input.is-medium { + font-size: 1.25rem; } + .is-large.textarea, .is-large.input, #documenter .docs-sidebar form.docs-search > input.is-large { + font-size: 1.5rem; } + .is-fullwidth.textarea, .is-fullwidth.input, #documenter .docs-sidebar form.docs-search > input.is-fullwidth { + display: block; + width: 100%; } + .is-inline.textarea, .is-inline.input, #documenter .docs-sidebar form.docs-search > input.is-inline { + display: inline; + width: auto; } + +.input.is-rounded, #documenter .docs-sidebar form.docs-search > input { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + +.input.is-static, #documenter .docs-sidebar form.docs-search > input.is-static { + background-color: transparent; + border-color: transparent; + box-shadow: none; + padding-left: 0; + padding-right: 0; } + +.textarea { + display: block; + max-width: 100%; + min-width: 100%; + padding: 0.625em; + resize: vertical; } + .textarea:not([rows]) { + max-height: 600px; + min-height: 120px; } + .textarea[rows] { + height: initial; } + .textarea.has-fixed-size { + resize: none; } + +.radio, .checkbox { + cursor: pointer; + display: inline-block; + line-height: 1.25; + position: relative; } + .radio input, .checkbox input { + cursor: pointer; } + .radio:hover, .checkbox:hover { + color: #363636; } + .radio[disabled], .checkbox[disabled], fieldset[disabled] .radio, fieldset[disabled] .checkbox { + color: #6b6b6b; + cursor: not-allowed; } + +.radio + .radio { + margin-left: 0.5em; } + +.select { + display: inline-block; + max-width: 100%; + position: relative; + vertical-align: top; } + .select:not(.is-multiple) { + height: 2.25em; } + .select:not(.is-multiple):not(.is-loading)::after { + border-color: #149eaa; + right: 1.125em; + z-index: 4; } + .select.is-rounded select, #documenter .docs-sidebar form.docs-search > input.select select { + border-radius: 290486px; + padding-left: 1em; } + .select select { + cursor: pointer; + display: block; + font-size: 1em; + max-width: 100%; + outline: none; } + .select select::-ms-expand { + display: none; } + .select select[disabled]:hover, fieldset[disabled] .select select:hover { + border-color: whitesmoke; } + .select select:not([multiple]) { + padding-right: 2.5em; } + .select select[multiple] { + height: auto; + padding: 0; } + .select select[multiple] option { + padding: 0.5em 1em; } + .select:not(.is-multiple):not(.is-loading):hover::after { + border-color: #363636; } + .select.is-white:not(:hover)::after { + border-color: white; } + .select.is-white select { + border-color: white; } + .select.is-white select:hover, .select.is-white select.is-hovered { + border-color: #f2f2f2; } + .select.is-white select:focus, .select.is-white select.is-focused, .select.is-white select:active, .select.is-white select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .select.is-black:not(:hover)::after { + border-color: #0a0a0a; } + .select.is-black select { + border-color: #0a0a0a; } + .select.is-black select:hover, .select.is-black select.is-hovered { + border-color: black; } + .select.is-black select:focus, .select.is-black select.is-focused, .select.is-black select:active, .select.is-black select.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .select.is-light:not(:hover)::after { + border-color: whitesmoke; } + .select.is-light select { + border-color: whitesmoke; } + .select.is-light select:hover, .select.is-light select.is-hovered { + border-color: #e8e8e8; } + .select.is-light select:focus, .select.is-light select.is-focused, .select.is-light select:active, .select.is-light select.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .select.is-dark:not(:hover)::after, .content kbd.select:not(:hover)::after { + border-color: #363636; } + .select.is-dark select, .content kbd.select select { + border-color: #363636; } + .select.is-dark select:hover, .content kbd.select select:hover, .select.is-dark select.is-hovered, .content kbd.select select.is-hovered { + border-color: #292929; } + .select.is-dark select:focus, .content kbd.select select:focus, .select.is-dark select.is-focused, .content kbd.select select.is-focused, .select.is-dark select:active, .content kbd.select select:active, .select.is-dark select.is-active, .content kbd.select select.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .select.is-primary:not(:hover)::after, .docstring > section > a.select.docs-sourcelink:not(:hover)::after { + border-color: #4eb5de; } + .select.is-primary select, .docstring > section > a.select.docs-sourcelink select { + border-color: #4eb5de; } + .select.is-primary select:hover, .docstring > section > a.select.docs-sourcelink select:hover, .select.is-primary select.is-hovered, .docstring > section > a.select.docs-sourcelink select.is-hovered { + border-color: #39acda; } + .select.is-primary select:focus, .docstring > section > a.select.docs-sourcelink select:focus, .select.is-primary select.is-focused, .docstring > section > a.select.docs-sourcelink select.is-focused, .select.is-primary select:active, .docstring > section > a.select.docs-sourcelink select:active, .select.is-primary select.is-active, .docstring > section > a.select.docs-sourcelink select.is-active { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .select.is-link:not(:hover)::after { + border-color: #149eaa; } + .select.is-link select { + border-color: #149eaa; } + .select.is-link select:hover, .select.is-link select.is-hovered { + border-color: #118993; } + .select.is-link select:focus, .select.is-link select.is-focused, .select.is-link select:active, .select.is-link select.is-active { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .select.is-info:not(:hover)::after { + border-color: #209cee; } + .select.is-info select { + border-color: #209cee; } + .select.is-info select:hover, .select.is-info select.is-hovered { + border-color: #1190e3; } + .select.is-info select:focus, .select.is-info select.is-focused, .select.is-info select:active, .select.is-info select.is-active { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .select.is-success:not(:hover)::after { + border-color: #22c35b; } + .select.is-success select { + border-color: #22c35b; } + .select.is-success select:hover, .select.is-success select.is-hovered { + border-color: #1ead51; } + .select.is-success select:focus, .select.is-success select.is-focused, .select.is-success select:active, .select.is-success select.is-active { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .select.is-warning:not(:hover)::after { + border-color: #ffdd57; } + .select.is-warning select { + border-color: #ffdd57; } + .select.is-warning select:hover, .select.is-warning select.is-hovered { + border-color: #ffd83e; } + .select.is-warning select:focus, .select.is-warning select.is-focused, .select.is-warning select:active, .select.is-warning select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .select.is-danger:not(:hover)::after { + border-color: #da0b00; } + .select.is-danger select { + border-color: #da0b00; } + .select.is-danger select:hover, .select.is-danger select.is-hovered { + border-color: #c10a00; } + .select.is-danger select:focus, .select.is-danger select.is-focused, .select.is-danger select:active, .select.is-danger select.is-active { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .select.is-small, #documenter .docs-sidebar form.docs-search > input.select { + border-radius: 2px; + font-size: 0.75rem; } + .select.is-medium { + font-size: 1.25rem; } + .select.is-large { + font-size: 1.5rem; } + .select.is-disabled::after { + border-color: #6b6b6b; } + .select.is-fullwidth { + width: 100%; } + .select.is-fullwidth select { + width: 100%; } + .select.is-loading::after { + margin-top: 0; + position: absolute; + right: 0.625em; + top: 0.625em; + transform: none; } + .select.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + .select.is-loading.is-medium:after { + font-size: 1.25rem; } + .select.is-loading.is-large:after { + font-size: 1.5rem; } + +.file { + align-items: stretch; + display: flex; + justify-content: flex-start; + position: relative; } + .file.is-white .file-cta { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + .file.is-white:hover .file-cta, .file.is-white.is-hovered .file-cta { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + .file.is-white:focus .file-cta, .file.is-white.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); + color: #0a0a0a; } + .file.is-white:active .file-cta, .file.is-white.is-active .file-cta { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + .file.is-black .file-cta { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + .file.is-black:hover .file-cta, .file.is-black.is-hovered .file-cta { + background-color: #040404; + border-color: transparent; + color: white; } + .file.is-black:focus .file-cta, .file.is-black.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); + color: white; } + .file.is-black:active .file-cta, .file.is-black.is-active .file-cta { + background-color: black; + border-color: transparent; + color: white; } + .file.is-light .file-cta { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + .file.is-light:hover .file-cta, .file.is-light.is-hovered .file-cta { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + .file.is-light:focus .file-cta, .file.is-light.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25); + color: #363636; } + .file.is-light:active .file-cta, .file.is-light.is-active .file-cta { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + .file.is-dark .file-cta, .content kbd.file .file-cta { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + .file.is-dark:hover .file-cta, .content kbd.file:hover .file-cta, .file.is-dark.is-hovered .file-cta, .content kbd.file.is-hovered .file-cta { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + .file.is-dark:focus .file-cta, .content kbd.file:focus .file-cta, .file.is-dark.is-focused .file-cta, .content kbd.file.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25); + color: whitesmoke; } + .file.is-dark:active .file-cta, .content kbd.file:active .file-cta, .file.is-dark.is-active .file-cta, .content kbd.file.is-active .file-cta { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + .file.is-primary .file-cta, .docstring > section > a.file.docs-sourcelink .file-cta { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + .file.is-primary:hover .file-cta, .docstring > section > a.file.docs-sourcelink:hover .file-cta, .file.is-primary.is-hovered .file-cta, .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + .file.is-primary:focus .file-cta, .docstring > section > a.file.docs-sourcelink:focus .file-cta, .file.is-primary.is-focused .file-cta, .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25); + color: #fff; } + .file.is-primary:active .file-cta, .docstring > section > a.file.docs-sourcelink:active .file-cta, .file.is-primary.is-active .file-cta, .docstring > section > a.file.is-active.docs-sourcelink .file-cta { + background-color: #39acda; + border-color: transparent; + color: #fff; } + .file.is-link .file-cta { + background-color: #149eaa; + border-color: transparent; + color: #fff; } + .file.is-link:hover .file-cta, .file.is-link.is-hovered .file-cta { + background-color: #13939f; + border-color: transparent; + color: #fff; } + .file.is-link:focus .file-cta, .file.is-link.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(20, 158, 170, 0.25); + color: #fff; } + .file.is-link:active .file-cta, .file.is-link.is-active .file-cta { + background-color: #118993; + border-color: transparent; + color: #fff; } + .file.is-info .file-cta { + background-color: #209cee; + border-color: transparent; + color: #fff; } + .file.is-info:hover .file-cta, .file.is-info.is-hovered .file-cta { + background-color: #1497ed; + border-color: transparent; + color: #fff; } + .file.is-info:focus .file-cta, .file.is-info.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(32, 156, 238, 0.25); + color: #fff; } + .file.is-info:active .file-cta, .file.is-info.is-active .file-cta { + background-color: #1190e3; + border-color: transparent; + color: #fff; } + .file.is-success .file-cta { + background-color: #22c35b; + border-color: transparent; + color: #fff; } + .file.is-success:hover .file-cta, .file.is-success.is-hovered .file-cta { + background-color: #20b856; + border-color: transparent; + color: #fff; } + .file.is-success:focus .file-cta, .file.is-success.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(34, 195, 91, 0.25); + color: #fff; } + .file.is-success:active .file-cta, .file.is-success.is-active .file-cta { + background-color: #1ead51; + border-color: transparent; + color: #fff; } + .file.is-warning .file-cta { + background-color: #ffdd57; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:hover .file-cta, .file.is-warning.is-hovered .file-cta { + background-color: #ffda4a; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:focus .file-cta, .file.is-warning.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 221, 87, 0.25); + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:active .file-cta, .file.is-warning.is-active .file-cta { + background-color: #ffd83e; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-danger .file-cta { + background-color: #da0b00; + border-color: transparent; + color: #fff; } + .file.is-danger:hover .file-cta, .file.is-danger.is-hovered .file-cta { + background-color: #cd0a00; + border-color: transparent; + color: #fff; } + .file.is-danger:focus .file-cta, .file.is-danger.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(218, 11, 0, 0.25); + color: #fff; } + .file.is-danger:active .file-cta, .file.is-danger.is-active .file-cta { + background-color: #c10a00; + border-color: transparent; + color: #fff; } + .file.is-small, #documenter .docs-sidebar form.docs-search > input.file { + font-size: 0.75rem; } + .file.is-medium { + font-size: 1.25rem; } + .file.is-medium .file-icon .fa { + font-size: 21px; } + .file.is-large { + font-size: 1.5rem; } + .file.is-large .file-icon .fa { + font-size: 28px; } + .file.has-name .file-cta { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + .file.has-name .file-name { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .file.has-name.is-empty .file-cta { + border-radius: 4px; } + .file.has-name.is-empty .file-name { + display: none; } + .file.is-boxed .file-label { + flex-direction: column; } + .file.is-boxed .file-cta { + flex-direction: column; + height: auto; + padding: 1em 3em; } + .file.is-boxed .file-name { + border-width: 0 1px 1px; } + .file.is-boxed .file-icon { + height: 1.5em; + width: 1.5em; } + .file.is-boxed .file-icon .fa { + font-size: 21px; } + .file.is-boxed.is-small .file-icon .fa, #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { + font-size: 14px; } + .file.is-boxed.is-medium .file-icon .fa { + font-size: 28px; } + .file.is-boxed.is-large .file-icon .fa { + font-size: 35px; } + .file.is-boxed.has-name .file-cta { + border-radius: 4px 4px 0 0; } + .file.is-boxed.has-name .file-name { + border-radius: 0 0 4px 4px; + border-width: 0 1px 1px; } + .file.is-centered { + justify-content: center; } + .file.is-fullwidth .file-label { + width: 100%; } + .file.is-fullwidth .file-name { + flex-grow: 1; + max-width: none; } + .file.is-right { + justify-content: flex-end; } + .file.is-right .file-cta { + border-radius: 0 4px 4px 0; } + .file.is-right .file-name { + border-radius: 4px 0 0 4px; + border-width: 1px 0 1px 1px; + order: -1; } + +.file-label { + align-items: stretch; + display: flex; + cursor: pointer; + justify-content: flex-start; + overflow: hidden; + position: relative; } + .file-label:hover .file-cta { + background-color: #eeeeee; + color: #363636; } + .file-label:hover .file-name { + border-color: #d5d5d5; } + .file-label:active .file-cta { + background-color: #e8e8e8; + color: #363636; } + .file-label:active .file-name { + border-color: #cfcfcf; } + +.file-input { + height: 100%; + left: 0; + opacity: 0; + outline: none; + position: absolute; + top: 0; + width: 100%; } + +.file-cta, +.file-name { + border-color: #dbdbdb; + border-radius: 4px; + font-size: 1em; + padding-left: 1em; + padding-right: 1em; + white-space: nowrap; } + +.file-cta { + background-color: whitesmoke; + color: #4a4a4a; } + +.file-name { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px 1px 1px 0; + display: block; + max-width: 16em; + overflow: hidden; + text-align: left; + text-overflow: ellipsis; } + +.file-icon { + align-items: center; + display: flex; + height: 1em; + justify-content: center; + margin-right: 0.5em; + width: 1em; } + .file-icon .fa { + font-size: 14px; } + +.label { + color: #363636; + display: block; + font-size: 1rem; + font-weight: 700; } + .label:not(:last-child) { + margin-bottom: 0.5em; } + .label.is-small, #documenter .docs-sidebar form.docs-search > input.label { + font-size: 0.75rem; } + .label.is-medium { + font-size: 1.25rem; } + .label.is-large { + font-size: 1.5rem; } + +.help { + display: block; + font-size: 0.75rem; + margin-top: 0.25rem; } + .help.is-white { + color: white; } + .help.is-black { + color: #0a0a0a; } + .help.is-light { + color: whitesmoke; } + .help.is-dark, .content kbd.help { + color: #363636; } + .help.is-primary, .docstring > section > a.help.docs-sourcelink { + color: #4eb5de; } + .help.is-link { + color: #149eaa; } + .help.is-info { + color: #209cee; } + .help.is-success { + color: #22c35b; } + .help.is-warning { + color: #ffdd57; } + .help.is-danger { + color: #da0b00; } + +.field:not(:last-child) { + margin-bottom: 0.75rem; } + +.field.has-addons { + display: flex; + justify-content: flex-start; } + .field.has-addons .control:not(:last-child) { + margin-right: -1px; } + .field.has-addons .control:not(:first-child):not(:last-child) .button, + .field.has-addons .control:not(:first-child):not(:last-child) .input, + .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, + .field.has-addons .control:not(:first-child):not(:last-child) .select select { + border-radius: 0; } + .field.has-addons .control:first-child:not(:only-child) .button, + .field.has-addons .control:first-child:not(:only-child) .input, + .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, + .field.has-addons .control:first-child:not(:only-child) .select select { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + .field.has-addons .control:last-child:not(:only-child) .button, + .field.has-addons .control:last-child:not(:only-child) .input, + .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, + .field.has-addons .control:last-child:not(:only-child) .select select { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .field.has-addons .control .button:not([disabled]):hover, .field.has-addons .control .button.is-hovered:not([disabled]), + .field.has-addons .control .input:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, + .field.has-addons .control .input.is-hovered:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), + .field.has-addons .control .select select:not([disabled]):hover, + .field.has-addons .control .select select.is-hovered:not([disabled]) { + z-index: 2; } + .field.has-addons .control .button:not([disabled]):focus, .field.has-addons .control .button.is-focused:not([disabled]), .field.has-addons .control .button:not([disabled]):active, .field.has-addons .control .button.is-active:not([disabled]), + .field.has-addons .control .input:not([disabled]):focus, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, + .field.has-addons .control .input.is-focused:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), + .field.has-addons .control .input:not([disabled]):active, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, + .field.has-addons .control .input.is-active:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), + .field.has-addons .control .select select:not([disabled]):focus, + .field.has-addons .control .select select.is-focused:not([disabled]), + .field.has-addons .control .select select:not([disabled]):active, + .field.has-addons .control .select select.is-active:not([disabled]) { + z-index: 3; } + .field.has-addons .control .button:not([disabled]):focus:hover, .field.has-addons .control .button.is-focused:not([disabled]):hover, .field.has-addons .control .button:not([disabled]):active:hover, .field.has-addons .control .button.is-active:not([disabled]):hover, + .field.has-addons .control .input:not([disabled]):focus:hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, + .field.has-addons .control .input.is-focused:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, + .field.has-addons .control .input:not([disabled]):active:hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, + .field.has-addons .control .input.is-active:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, + .field.has-addons .control .select select:not([disabled]):focus:hover, + .field.has-addons .control .select select.is-focused:not([disabled]):hover, + .field.has-addons .control .select select:not([disabled]):active:hover, + .field.has-addons .control .select select.is-active:not([disabled]):hover { + z-index: 4; } + .field.has-addons .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .field.has-addons.has-addons-centered { + justify-content: center; } + .field.has-addons.has-addons-right { + justify-content: flex-end; } + .field.has-addons.has-addons-fullwidth .control { + flex-grow: 1; + flex-shrink: 0; } + +.field.is-grouped { + display: flex; + justify-content: flex-start; } + .field.is-grouped > .control { + flex-shrink: 0; } + .field.is-grouped > .control:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + .field.is-grouped > .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .field.is-grouped.is-grouped-centered { + justify-content: center; } + .field.is-grouped.is-grouped-right { + justify-content: flex-end; } + .field.is-grouped.is-grouped-multiline { + flex-wrap: wrap; } + .field.is-grouped.is-grouped-multiline > .control:last-child, .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { + margin-bottom: 0.75rem; } + .field.is-grouped.is-grouped-multiline:last-child { + margin-bottom: -0.75rem; } + .field.is-grouped.is-grouped-multiline:not(:last-child) { + margin-bottom: 0; } + +@media screen and (min-width: 769px), print { + .field.is-horizontal { + display: flex; } } + +.field-label .label { + font-size: inherit; } + +@media screen and (max-width: 768px) { + .field-label { + margin-bottom: 0.5rem; } } + +@media screen and (min-width: 769px), print { + .field-label { + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + margin-right: 1.5rem; + text-align: right; } + .field-label.is-small, #documenter .docs-sidebar form.docs-search > input.field-label { + font-size: 0.75rem; + padding-top: 0.375em; } + .field-label.is-normal { + padding-top: 0.375em; } + .field-label.is-medium { + font-size: 1.25rem; + padding-top: 0.375em; } + .field-label.is-large { + font-size: 1.5rem; + padding-top: 0.375em; } } + +.field-body .field .field { + margin-bottom: 0; } + +@media screen and (min-width: 769px), print { + .field-body { + display: flex; + flex-basis: 0; + flex-grow: 5; + flex-shrink: 1; } + .field-body .field { + margin-bottom: 0; } + .field-body > .field { + flex-shrink: 1; } + .field-body > .field:not(.is-narrow) { + flex-grow: 1; } + .field-body > .field:not(:last-child) { + margin-right: 0.75rem; } } + +.control { + box-sizing: border-box; + clear: both; + font-size: 1rem; + position: relative; + text-align: left; } + .control.has-icons-left .input:focus ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, + .control.has-icons-left .select:focus ~ .icon, .control.has-icons-right .input:focus ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, + .control.has-icons-right .select:focus ~ .icon { + color: #6b6b6b; } + .control.has-icons-left .input.is-small ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, + .control.has-icons-left .select.is-small ~ .icon, .control.has-icons-right .input.is-small ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, + .control.has-icons-right .select.is-small ~ .icon { + font-size: 0.75rem; } + .control.has-icons-left .input.is-medium ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, + .control.has-icons-left .select.is-medium ~ .icon, .control.has-icons-right .input.is-medium ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, + .control.has-icons-right .select.is-medium ~ .icon { + font-size: 1.25rem; } + .control.has-icons-left .input.is-large ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, + .control.has-icons-left .select.is-large ~ .icon, .control.has-icons-right .input.is-large ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, + .control.has-icons-right .select.is-large ~ .icon { + font-size: 1.5rem; } + .control.has-icons-left .icon, .control.has-icons-right .icon { + color: #dbdbdb; + height: 2.25em; + pointer-events: none; + position: absolute; + top: 0; + width: 2.25em; + z-index: 4; } + .control.has-icons-left .input, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, + .control.has-icons-left .select select { + padding-left: 2.25em; } + .control.has-icons-left .icon.is-left { + left: 0; } + .control.has-icons-right .input, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, + .control.has-icons-right .select select { + padding-right: 2.25em; } + .control.has-icons-right .icon.is-right { + right: 0; } + .control.is-loading::after { + position: absolute !important; + right: 0.625em; + top: 0.625em; + z-index: 4; } + .control.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + .control.is-loading.is-medium:after { + font-size: 1.25rem; } + .control.is-loading.is-large:after { + font-size: 1.5rem; } + +.breadcrumb { + font-size: 1rem; + white-space: nowrap; } + .breadcrumb a { + align-items: center; + color: #149eaa; + display: flex; + justify-content: center; + padding: 0 0.75em; } + .breadcrumb a:hover { + color: #107c85; } + .breadcrumb li { + align-items: center; + display: flex; } + .breadcrumb li:first-child a { + padding-left: 0; } + .breadcrumb li.is-active a { + color: #654ca3; + cursor: default; + pointer-events: none; } + .breadcrumb li + li::before { + color: #b5b5b5; + content: "\0002f"; } + .breadcrumb ul, + .breadcrumb ol { + align-items: flex-start; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .breadcrumb .icon:first-child { + margin-right: 0.5em; } + .breadcrumb .icon:last-child { + margin-left: 0.5em; } + .breadcrumb.is-centered ol, + .breadcrumb.is-centered ul { + justify-content: center; } + .breadcrumb.is-right ol, + .breadcrumb.is-right ul { + justify-content: flex-end; } + .breadcrumb.is-small, #documenter .docs-sidebar form.docs-search > input.breadcrumb { + font-size: 0.75rem; } + .breadcrumb.is-medium { + font-size: 1.25rem; } + .breadcrumb.is-large { + font-size: 1.5rem; } + .breadcrumb.has-arrow-separator li + li::before { + content: "\02192"; } + .breadcrumb.has-bullet-separator li + li::before { + content: "\02022"; } + .breadcrumb.has-dot-separator li + li::before { + content: "\000b7"; } + .breadcrumb.has-succeeds-separator li + li::before { + content: "\0227B"; } + +.card { + background-color: white; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #202020; + max-width: 100%; + position: relative; } + +.card-header { + background-color: transparent; + align-items: stretch; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + display: flex; } + +.card-header-title { + align-items: center; + color: #654ca3; + display: flex; + flex-grow: 1; + font-weight: 700; + padding: 0.75rem; } + .card-header-title.is-centered { + justify-content: center; } + +.card-header-icon { + align-items: center; + cursor: pointer; + display: flex; + justify-content: center; + padding: 0.75rem; } + +.card-image { + display: block; + position: relative; } + +.card-content { + background-color: transparent; + padding: 1.5rem; } + +.card-footer { + background-color: transparent; + border-top: 1px solid #dbdbdb; + align-items: stretch; + display: flex; } + +.card-footer-item { + align-items: center; + display: flex; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + justify-content: center; + padding: 0.75rem; } + .card-footer-item:not(:last-child) { + border-right: 1px solid #dbdbdb; } + +.card .media:not(:last-child) { + margin-bottom: 1.5rem; } + +.dropdown { + display: inline-flex; + position: relative; + vertical-align: top; } + .dropdown.is-active .dropdown-menu, .dropdown.is-hoverable:hover .dropdown-menu { + display: block; } + .dropdown.is-right .dropdown-menu { + left: auto; + right: 0; } + .dropdown.is-up .dropdown-menu { + bottom: 100%; + padding-bottom: 4px; + padding-top: initial; + top: auto; } + +.dropdown-menu { + display: none; + left: 0; + min-width: 12rem; + padding-top: 4px; + position: absolute; + top: 100%; + z-index: 20; } + +.dropdown-content { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + +.dropdown-item { + color: #4a4a4a; + display: block; + font-size: 0.875rem; + line-height: 1.5; + padding: 0.375rem 1rem; + position: relative; } + +a.dropdown-item, +button.dropdown-item { + padding-right: 3rem; + text-align: left; + white-space: nowrap; + width: 100%; } + a.dropdown-item:hover, + button.dropdown-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + a.dropdown-item.is-active, + button.dropdown-item.is-active { + background-color: #149eaa; + color: #fff; } + +.dropdown-divider { + background-color: #dbdbdb; + border: none; + display: block; + height: 1px; + margin: 0.5rem 0; } + +.level { + align-items: center; + justify-content: space-between; } + .level code { + border-radius: 4px; } + .level img { + display: inline-block; + vertical-align: top; } + .level.is-mobile { + display: flex; } + .level.is-mobile .level-left, + .level.is-mobile .level-right { + display: flex; } + .level.is-mobile .level-left + .level-right { + margin-top: 0; } + .level.is-mobile .level-item:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + .level.is-mobile .level-item:not(.is-narrow) { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + .level { + display: flex; } + .level > .level-item:not(.is-narrow) { + flex-grow: 1; } } +.level-item { + align-items: center; + display: flex; + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; + justify-content: center; } + .level-item .title, + .level-item .subtitle { + margin-bottom: 0; } + @media screen and (max-width: 768px) { + .level-item:not(:last-child) { + margin-bottom: 0.75rem; } } +.level-left, +.level-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + .level-left .level-item.is-flexible, + .level-right .level-item.is-flexible { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + .level-left .level-item:not(:last-child), + .level-right .level-item:not(:last-child) { + margin-right: 0.75rem; } } +.level-left { + align-items: center; + justify-content: flex-start; } + @media screen and (max-width: 768px) { + .level-left + .level-right { + margin-top: 1.5rem; } } + @media screen and (min-width: 769px), print { + .level-left { + display: flex; } } +.level-right { + align-items: center; + justify-content: flex-end; } + @media screen and (min-width: 769px), print { + .level-right { + display: flex; } } +.list { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } + +.list-item { + display: block; + padding: 0.5em 1em; } + .list-item:not(a) { + color: #202020; } + .list-item:first-child { + border-top-left-radius: 4px; + border-top-right-radius: 4px; } + .list-item:last-child { + border-bottom-left-radius: 4px; + border-bottom-right-radius: 4px; } + .list-item:not(:last-child) { + border-bottom: 1px solid #dbdbdb; } + .list-item.is-active { + background-color: #149eaa; + color: #fff; } + +a.list-item { + background-color: whitesmoke; + cursor: pointer; } + +.media { + align-items: flex-start; + display: flex; + text-align: left; } + .media .content:not(:last-child) { + margin-bottom: 0.75rem; } + .media .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + display: flex; + padding-top: 0.75rem; } + .media .media .content:not(:last-child), + .media .media .control:not(:last-child) { + margin-bottom: 0.5rem; } + .media .media .media { + padding-top: 0.5rem; } + .media .media .media + .media { + margin-top: 0.5rem; } + .media + .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + margin-top: 1rem; + padding-top: 1rem; } + .media.is-large + .media { + margin-top: 1.5rem; + padding-top: 1.5rem; } + +.media-left, +.media-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + +.media-left { + margin-right: 1rem; } + +.media-right { + margin-left: 1rem; } + +.media-content { + flex-basis: auto; + flex-grow: 1; + flex-shrink: 1; + text-align: left; } + +@media screen and (max-width: 768px) { + .media-content { + overflow-x: auto; } } + +.menu { + font-size: 1rem; } + .menu.is-small, #documenter .docs-sidebar form.docs-search > input.menu { + font-size: 0.75rem; } + .menu.is-medium { + font-size: 1.25rem; } + .menu.is-large { + font-size: 1.5rem; } + +.menu-list { + line-height: 1.25; } + .menu-list a { + border-radius: 2px; + color: #202020; + display: block; + padding: 0.5em 0.75em; } + .menu-list a:hover { + background-color: whitesmoke; + color: #654ca3; } + .menu-list a.is-active { + background-color: #149eaa; + color: #fff; } + .menu-list li ul { + border-left: 1px solid #dbdbdb; + margin: 0.75em; + padding-left: 0.75em; } + +.menu-label { + color: #6b6b6b; + font-size: 0.75em; + letter-spacing: 0.1em; + text-transform: uppercase; } + .menu-label:not(:first-child) { + margin-top: 1em; } + .menu-label:not(:last-child) { + margin-bottom: 1em; } + +.message { + background-color: whitesmoke; + border-radius: 4px; + font-size: 1rem; } + .message strong { + color: currentColor; } + .message a:not(.button):not(.tag):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + .message.is-small, #documenter .docs-sidebar form.docs-search > input.message { + font-size: 0.75rem; } + .message.is-medium { + font-size: 1.25rem; } + .message.is-large { + font-size: 1.5rem; } + .message.is-white { + background-color: white; } + .message.is-white .message-header { + background-color: white; + color: #0a0a0a; } + .message.is-white .message-body { + border-color: white; + color: #4d4d4d; } + .message.is-black { + background-color: #fafafa; } + .message.is-black .message-header { + background-color: #0a0a0a; + color: white; } + .message.is-black .message-body { + border-color: #0a0a0a; + color: #090909; } + .message.is-light { + background-color: #fafafa; } + .message.is-light .message-header { + background-color: whitesmoke; + color: #363636; } + .message.is-light .message-body { + border-color: whitesmoke; + color: #505050; } + .message.is-dark, .content kbd.message { + background-color: #fafafa; } + .message.is-dark .message-header, .content kbd.message .message-header { + background-color: #363636; + color: whitesmoke; } + .message.is-dark .message-body, .content kbd.message .message-body { + border-color: #363636; + color: #2a2a2a; } + .message.is-primary, .docstring > section > a.message.docs-sourcelink { + background-color: #f6fbfd; } + .message.is-primary .message-header, .docstring > section > a.message.docs-sourcelink .message-header { + background-color: #4eb5de; + color: #fff; } + .message.is-primary .message-body, .docstring > section > a.message.docs-sourcelink .message-body { + border-color: #4eb5de; + color: #1f556a; } + .message.is-link { + background-color: #f6fdfe; } + .message.is-link .message-header { + background-color: #149eaa; + color: #fff; } + .message.is-link .message-body { + border-color: #149eaa; + color: #0b393d; } + .message.is-info { + background-color: #f6fbfe; } + .message.is-info .message-header { + background-color: #209cee; + color: #fff; } + .message.is-info .message-body { + border-color: #209cee; + color: #12537d; } + .message.is-success { + background-color: #f6fdf9; } + .message.is-success .message-header { + background-color: #22c35b; + color: #fff; } + .message.is-success .message-body { + border-color: #22c35b; + color: #0f361d; } + .message.is-warning { + background-color: #fffdf5; } + .message.is-warning .message-header { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .message.is-warning .message-body { + border-color: #ffdd57; + color: #3c3108; } + .message.is-danger { + background-color: #fff5f5; } + .message.is-danger .message-header { + background-color: #da0b00; + color: #fff; } + .message.is-danger .message-body { + border-color: #da0b00; + color: #9b0c04; } + +.message-header { + align-items: center; + background-color: #202020; + border-radius: 4px 4px 0 0; + color: #fff; + display: flex; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.75em 1em; + position: relative; } + .message-header .delete { + flex-grow: 0; + flex-shrink: 0; + margin-left: 0.75em; } + .message-header + .message-body { + border-width: 0; + border-top-left-radius: 0; + border-top-right-radius: 0; } + +.message-body { + border-color: #dbdbdb; + border-radius: 4px; + border-style: solid; + border-width: 0 0 0 4px; + color: #202020; + padding: 1.25em 1.5em; } + .message-body code, + .message-body pre { + background-color: white; } + .message-body pre code { + background-color: transparent; } + +.modal { + align-items: center; + display: none; + flex-direction: column; + justify-content: center; + overflow: hidden; + position: fixed; + z-index: 40; } + .modal.is-active { + display: flex; } + +.modal-background { + background-color: rgba(10, 10, 10, 0.86); } + +.modal-content, +.modal-card { + margin: 0 20px; + max-height: calc(100vh - 160px); + overflow: auto; + position: relative; + width: 100%; } + @media screen and (min-width: 769px), print { + .modal-content, + .modal-card { + margin: 0 auto; + max-height: calc(100vh - 40px); + width: 640px; } } +.modal-close { + background: none; + height: 40px; + position: fixed; + right: 20px; + top: 20px; + width: 40px; } + +.modal-card { + display: flex; + flex-direction: column; + max-height: calc(100vh - 40px); + overflow: hidden; + -ms-overflow-y: visible; } + +.modal-card-head, +.modal-card-foot { + align-items: center; + background-color: whitesmoke; + display: flex; + flex-shrink: 0; + justify-content: flex-start; + padding: 20px; + position: relative; } + +.modal-card-head { + border-bottom: 1px solid #dbdbdb; + border-top-left-radius: 6px; + border-top-right-radius: 6px; } + +.modal-card-title { + color: #654ca3; + flex-grow: 1; + flex-shrink: 0; + font-size: 1.5rem; + line-height: 1; } + +.modal-card-foot { + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 1px solid #dbdbdb; } + .modal-card-foot .button:not(:last-child) { + margin-right: 0.5em; } + +.modal-card-body { + -webkit-overflow-scrolling: touch; + background-color: white; + flex-grow: 1; + flex-shrink: 1; + overflow: auto; + padding: 20px; } + +.navbar { + background-color: white; + min-height: 3.25rem; + position: relative; + z-index: 30; } + .navbar.is-white { + background-color: white; + color: #0a0a0a; } + .navbar.is-white .navbar-brand > .navbar-item, + .navbar.is-white .navbar-brand .navbar-link { + color: #0a0a0a; } + .navbar.is-white .navbar-brand > a.navbar-item:focus, .navbar.is-white .navbar-brand > a.navbar-item:hover, .navbar.is-white .navbar-brand > a.navbar-item.is-active, + .navbar.is-white .navbar-brand .navbar-link:focus, + .navbar.is-white .navbar-brand .navbar-link:hover, + .navbar.is-white .navbar-brand .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-brand .navbar-link::after { + border-color: #0a0a0a; } + .navbar.is-white .navbar-burger { + color: #0a0a0a; } + @media screen and (min-width: 1056px) { + .navbar.is-white .navbar-start > .navbar-item, + .navbar.is-white .navbar-start .navbar-link, + .navbar.is-white .navbar-end > .navbar-item, + .navbar.is-white .navbar-end .navbar-link { + color: #0a0a0a; } + .navbar.is-white .navbar-start > a.navbar-item:focus, .navbar.is-white .navbar-start > a.navbar-item:hover, .navbar.is-white .navbar-start > a.navbar-item.is-active, + .navbar.is-white .navbar-start .navbar-link:focus, + .navbar.is-white .navbar-start .navbar-link:hover, + .navbar.is-white .navbar-start .navbar-link.is-active, + .navbar.is-white .navbar-end > a.navbar-item:focus, + .navbar.is-white .navbar-end > a.navbar-item:hover, + .navbar.is-white .navbar-end > a.navbar-item.is-active, + .navbar.is-white .navbar-end .navbar-link:focus, + .navbar.is-white .navbar-end .navbar-link:hover, + .navbar.is-white .navbar-end .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-start .navbar-link::after, + .navbar.is-white .navbar-end .navbar-link::after { + border-color: #0a0a0a; } + .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-dropdown a.navbar-item.is-active { + background-color: white; + color: #0a0a0a; } } + .navbar.is-black { + background-color: #0a0a0a; + color: white; } + .navbar.is-black .navbar-brand > .navbar-item, + .navbar.is-black .navbar-brand .navbar-link { + color: white; } + .navbar.is-black .navbar-brand > a.navbar-item:focus, .navbar.is-black .navbar-brand > a.navbar-item:hover, .navbar.is-black .navbar-brand > a.navbar-item.is-active, + .navbar.is-black .navbar-brand .navbar-link:focus, + .navbar.is-black .navbar-brand .navbar-link:hover, + .navbar.is-black .navbar-brand .navbar-link.is-active { + background-color: black; + color: white; } + .navbar.is-black .navbar-brand .navbar-link::after { + border-color: white; } + .navbar.is-black .navbar-burger { + color: white; } + @media screen and (min-width: 1056px) { + .navbar.is-black .navbar-start > .navbar-item, + .navbar.is-black .navbar-start .navbar-link, + .navbar.is-black .navbar-end > .navbar-item, + .navbar.is-black .navbar-end .navbar-link { + color: white; } + .navbar.is-black .navbar-start > a.navbar-item:focus, .navbar.is-black .navbar-start > a.navbar-item:hover, .navbar.is-black .navbar-start > a.navbar-item.is-active, + .navbar.is-black .navbar-start .navbar-link:focus, + .navbar.is-black .navbar-start .navbar-link:hover, + .navbar.is-black .navbar-start .navbar-link.is-active, + .navbar.is-black .navbar-end > a.navbar-item:focus, + .navbar.is-black .navbar-end > a.navbar-item:hover, + .navbar.is-black .navbar-end > a.navbar-item.is-active, + .navbar.is-black .navbar-end .navbar-link:focus, + .navbar.is-black .navbar-end .navbar-link:hover, + .navbar.is-black .navbar-end .navbar-link.is-active { + background-color: black; + color: white; } + .navbar.is-black .navbar-start .navbar-link::after, + .navbar.is-black .navbar-end .navbar-link::after { + border-color: white; } + .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { + background-color: black; + color: white; } + .navbar.is-black .navbar-dropdown a.navbar-item.is-active { + background-color: #0a0a0a; + color: white; } } + .navbar.is-light { + background-color: whitesmoke; + color: #363636; } + .navbar.is-light .navbar-brand > .navbar-item, + .navbar.is-light .navbar-brand .navbar-link { + color: #363636; } + .navbar.is-light .navbar-brand > a.navbar-item:focus, .navbar.is-light .navbar-brand > a.navbar-item:hover, .navbar.is-light .navbar-brand > a.navbar-item.is-active, + .navbar.is-light .navbar-brand .navbar-link:focus, + .navbar.is-light .navbar-brand .navbar-link:hover, + .navbar.is-light .navbar-brand .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-brand .navbar-link::after { + border-color: #363636; } + .navbar.is-light .navbar-burger { + color: #363636; } + @media screen and (min-width: 1056px) { + .navbar.is-light .navbar-start > .navbar-item, + .navbar.is-light .navbar-start .navbar-link, + .navbar.is-light .navbar-end > .navbar-item, + .navbar.is-light .navbar-end .navbar-link { + color: #363636; } + .navbar.is-light .navbar-start > a.navbar-item:focus, .navbar.is-light .navbar-start > a.navbar-item:hover, .navbar.is-light .navbar-start > a.navbar-item.is-active, + .navbar.is-light .navbar-start .navbar-link:focus, + .navbar.is-light .navbar-start .navbar-link:hover, + .navbar.is-light .navbar-start .navbar-link.is-active, + .navbar.is-light .navbar-end > a.navbar-item:focus, + .navbar.is-light .navbar-end > a.navbar-item:hover, + .navbar.is-light .navbar-end > a.navbar-item.is-active, + .navbar.is-light .navbar-end .navbar-link:focus, + .navbar.is-light .navbar-end .navbar-link:hover, + .navbar.is-light .navbar-end .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-start .navbar-link::after, + .navbar.is-light .navbar-end .navbar-link::after { + border-color: #363636; } + .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #363636; } } + .navbar.is-dark, .content kbd.navbar { + background-color: #363636; + color: whitesmoke; } + .navbar.is-dark .navbar-brand > .navbar-item, .content kbd.navbar .navbar-brand > .navbar-item, + .navbar.is-dark .navbar-brand .navbar-link, + .content kbd.navbar .navbar-brand .navbar-link { + color: whitesmoke; } + .navbar.is-dark .navbar-brand > a.navbar-item:focus, .content kbd.navbar .navbar-brand > a.navbar-item:focus, .navbar.is-dark .navbar-brand > a.navbar-item:hover, .content kbd.navbar .navbar-brand > a.navbar-item:hover, .navbar.is-dark .navbar-brand > a.navbar-item.is-active, .content kbd.navbar .navbar-brand > a.navbar-item.is-active, + .navbar.is-dark .navbar-brand .navbar-link:focus, + .content kbd.navbar .navbar-brand .navbar-link:focus, + .navbar.is-dark .navbar-brand .navbar-link:hover, + .content kbd.navbar .navbar-brand .navbar-link:hover, + .navbar.is-dark .navbar-brand .navbar-link.is-active, + .content kbd.navbar .navbar-brand .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-brand .navbar-link::after, .content kbd.navbar .navbar-brand .navbar-link::after { + border-color: whitesmoke; } + .navbar.is-dark .navbar-burger, .content kbd.navbar .navbar-burger { + color: whitesmoke; } + @media screen and (min-width: 1056px) { + .navbar.is-dark .navbar-start > .navbar-item, .content kbd.navbar .navbar-start > .navbar-item, + .navbar.is-dark .navbar-start .navbar-link, + .content kbd.navbar .navbar-start .navbar-link, + .navbar.is-dark .navbar-end > .navbar-item, + .content kbd.navbar .navbar-end > .navbar-item, + .navbar.is-dark .navbar-end .navbar-link, + .content kbd.navbar .navbar-end .navbar-link { + color: whitesmoke; } + .navbar.is-dark .navbar-start > a.navbar-item:focus, .content kbd.navbar .navbar-start > a.navbar-item:focus, .navbar.is-dark .navbar-start > a.navbar-item:hover, .content kbd.navbar .navbar-start > a.navbar-item:hover, .navbar.is-dark .navbar-start > a.navbar-item.is-active, .content kbd.navbar .navbar-start > a.navbar-item.is-active, + .navbar.is-dark .navbar-start .navbar-link:focus, + .content kbd.navbar .navbar-start .navbar-link:focus, + .navbar.is-dark .navbar-start .navbar-link:hover, + .content kbd.navbar .navbar-start .navbar-link:hover, + .navbar.is-dark .navbar-start .navbar-link.is-active, + .content kbd.navbar .navbar-start .navbar-link.is-active, + .navbar.is-dark .navbar-end > a.navbar-item:focus, + .content kbd.navbar .navbar-end > a.navbar-item:focus, + .navbar.is-dark .navbar-end > a.navbar-item:hover, + .content kbd.navbar .navbar-end > a.navbar-item:hover, + .navbar.is-dark .navbar-end > a.navbar-item.is-active, + .content kbd.navbar .navbar-end > a.navbar-item.is-active, + .navbar.is-dark .navbar-end .navbar-link:focus, + .content kbd.navbar .navbar-end .navbar-link:focus, + .navbar.is-dark .navbar-end .navbar-link:hover, + .content kbd.navbar .navbar-end .navbar-link:hover, + .navbar.is-dark .navbar-end .navbar-link.is-active, + .content kbd.navbar .navbar-end .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-start .navbar-link::after, .content kbd.navbar .navbar-start .navbar-link::after, + .navbar.is-dark .navbar-end .navbar-link::after, + .content kbd.navbar .navbar-end .navbar-link::after { + border-color: whitesmoke; } + .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, + .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, + .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { + background-color: #363636; + color: whitesmoke; } } + .navbar.is-primary, .docstring > section > a.navbar.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .navbar.is-primary .navbar-brand > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, + .navbar.is-primary .navbar-brand .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-primary .navbar-brand > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, .navbar.is-primary .navbar-brand > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, .navbar.is-primary .navbar-brand > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, + .navbar.is-primary .navbar-brand .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, + .navbar.is-primary .navbar-brand .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, + .navbar.is-primary .navbar-brand .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-brand .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-primary .navbar-burger, .docstring > section > a.navbar.docs-sourcelink .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-primary .navbar-start > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, + .navbar.is-primary .navbar-start .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, + .navbar.is-primary .navbar-end > .navbar-item, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, + .navbar.is-primary .navbar-end .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { + color: #fff; } + .navbar.is-primary .navbar-start > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, .navbar.is-primary .navbar-start > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, .navbar.is-primary .navbar-start > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, + .navbar.is-primary .navbar-start .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, + .navbar.is-primary .navbar-start .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, + .navbar.is-primary .navbar-start .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, + .navbar.is-primary .navbar-end > a.navbar-item:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, + .navbar.is-primary .navbar-end > a.navbar-item:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, + .navbar.is-primary .navbar-end > a.navbar-item.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, + .navbar.is-primary .navbar-end .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, + .navbar.is-primary .navbar-end .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, + .navbar.is-primary .navbar-end .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-start .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, + .navbar.is-primary .navbar-end .navbar-link::after, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { + background-color: #4eb5de; + color: #fff; } } + .navbar.is-link { + background-color: #149eaa; + color: #fff; } + .navbar.is-link .navbar-brand > .navbar-item, + .navbar.is-link .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-link .navbar-brand > a.navbar-item:focus, .navbar.is-link .navbar-brand > a.navbar-item:hover, .navbar.is-link .navbar-brand > a.navbar-item.is-active, + .navbar.is-link .navbar-brand .navbar-link:focus, + .navbar.is-link .navbar-brand .navbar-link:hover, + .navbar.is-link .navbar-brand .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-link .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-link .navbar-start > .navbar-item, + .navbar.is-link .navbar-start .navbar-link, + .navbar.is-link .navbar-end > .navbar-item, + .navbar.is-link .navbar-end .navbar-link { + color: #fff; } + .navbar.is-link .navbar-start > a.navbar-item:focus, .navbar.is-link .navbar-start > a.navbar-item:hover, .navbar.is-link .navbar-start > a.navbar-item.is-active, + .navbar.is-link .navbar-start .navbar-link:focus, + .navbar.is-link .navbar-start .navbar-link:hover, + .navbar.is-link .navbar-start .navbar-link.is-active, + .navbar.is-link .navbar-end > a.navbar-item:focus, + .navbar.is-link .navbar-end > a.navbar-item:hover, + .navbar.is-link .navbar-end > a.navbar-item.is-active, + .navbar.is-link .navbar-end .navbar-link:focus, + .navbar.is-link .navbar-end .navbar-link:hover, + .navbar.is-link .navbar-end .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-start .navbar-link::after, + .navbar.is-link .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-dropdown a.navbar-item.is-active { + background-color: #149eaa; + color: #fff; } } + .navbar.is-info { + background-color: #209cee; + color: #fff; } + .navbar.is-info .navbar-brand > .navbar-item, + .navbar.is-info .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-info .navbar-brand > a.navbar-item:focus, .navbar.is-info .navbar-brand > a.navbar-item:hover, .navbar.is-info .navbar-brand > a.navbar-item.is-active, + .navbar.is-info .navbar-brand .navbar-link:focus, + .navbar.is-info .navbar-brand .navbar-link:hover, + .navbar.is-info .navbar-brand .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-info .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-info .navbar-start > .navbar-item, + .navbar.is-info .navbar-start .navbar-link, + .navbar.is-info .navbar-end > .navbar-item, + .navbar.is-info .navbar-end .navbar-link { + color: #fff; } + .navbar.is-info .navbar-start > a.navbar-item:focus, .navbar.is-info .navbar-start > a.navbar-item:hover, .navbar.is-info .navbar-start > a.navbar-item.is-active, + .navbar.is-info .navbar-start .navbar-link:focus, + .navbar.is-info .navbar-start .navbar-link:hover, + .navbar.is-info .navbar-start .navbar-link.is-active, + .navbar.is-info .navbar-end > a.navbar-item:focus, + .navbar.is-info .navbar-end > a.navbar-item:hover, + .navbar.is-info .navbar-end > a.navbar-item.is-active, + .navbar.is-info .navbar-end .navbar-link:focus, + .navbar.is-info .navbar-end .navbar-link:hover, + .navbar.is-info .navbar-end .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-start .navbar-link::after, + .navbar.is-info .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-dropdown a.navbar-item.is-active { + background-color: #209cee; + color: #fff; } } + .navbar.is-success { + background-color: #22c35b; + color: #fff; } + .navbar.is-success .navbar-brand > .navbar-item, + .navbar.is-success .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-success .navbar-brand > a.navbar-item:focus, .navbar.is-success .navbar-brand > a.navbar-item:hover, .navbar.is-success .navbar-brand > a.navbar-item.is-active, + .navbar.is-success .navbar-brand .navbar-link:focus, + .navbar.is-success .navbar-brand .navbar-link:hover, + .navbar.is-success .navbar-brand .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-success .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-success .navbar-start > .navbar-item, + .navbar.is-success .navbar-start .navbar-link, + .navbar.is-success .navbar-end > .navbar-item, + .navbar.is-success .navbar-end .navbar-link { + color: #fff; } + .navbar.is-success .navbar-start > a.navbar-item:focus, .navbar.is-success .navbar-start > a.navbar-item:hover, .navbar.is-success .navbar-start > a.navbar-item.is-active, + .navbar.is-success .navbar-start .navbar-link:focus, + .navbar.is-success .navbar-start .navbar-link:hover, + .navbar.is-success .navbar-start .navbar-link.is-active, + .navbar.is-success .navbar-end > a.navbar-item:focus, + .navbar.is-success .navbar-end > a.navbar-item:hover, + .navbar.is-success .navbar-end > a.navbar-item.is-active, + .navbar.is-success .navbar-end .navbar-link:focus, + .navbar.is-success .navbar-end .navbar-link:hover, + .navbar.is-success .navbar-end .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-start .navbar-link::after, + .navbar.is-success .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-dropdown a.navbar-item.is-active { + background-color: #22c35b; + color: #fff; } } + .navbar.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand > .navbar-item, + .navbar.is-warning .navbar-brand .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand > a.navbar-item:focus, .navbar.is-warning .navbar-brand > a.navbar-item:hover, .navbar.is-warning .navbar-brand > a.navbar-item.is-active, + .navbar.is-warning .navbar-brand .navbar-link:focus, + .navbar.is-warning .navbar-brand .navbar-link:hover, + .navbar.is-warning .navbar-brand .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-burger { + color: rgba(0, 0, 0, 0.7); } + @media screen and (min-width: 1056px) { + .navbar.is-warning .navbar-start > .navbar-item, + .navbar.is-warning .navbar-start .navbar-link, + .navbar.is-warning .navbar-end > .navbar-item, + .navbar.is-warning .navbar-end .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-start > a.navbar-item:focus, .navbar.is-warning .navbar-start > a.navbar-item:hover, .navbar.is-warning .navbar-start > a.navbar-item.is-active, + .navbar.is-warning .navbar-start .navbar-link:focus, + .navbar.is-warning .navbar-start .navbar-link:hover, + .navbar.is-warning .navbar-start .navbar-link.is-active, + .navbar.is-warning .navbar-end > a.navbar-item:focus, + .navbar.is-warning .navbar-end > a.navbar-item:hover, + .navbar.is-warning .navbar-end > a.navbar-item.is-active, + .navbar.is-warning .navbar-end .navbar-link:focus, + .navbar.is-warning .navbar-end .navbar-link:hover, + .navbar.is-warning .navbar-end .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-start .navbar-link::after, + .navbar.is-warning .navbar-end .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } } + .navbar.is-danger { + background-color: #da0b00; + color: #fff; } + .navbar.is-danger .navbar-brand > .navbar-item, + .navbar.is-danger .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-danger .navbar-brand > a.navbar-item:focus, .navbar.is-danger .navbar-brand > a.navbar-item:hover, .navbar.is-danger .navbar-brand > a.navbar-item.is-active, + .navbar.is-danger .navbar-brand .navbar-link:focus, + .navbar.is-danger .navbar-brand .navbar-link:hover, + .navbar.is-danger .navbar-brand .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-danger .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-danger .navbar-start > .navbar-item, + .navbar.is-danger .navbar-start .navbar-link, + .navbar.is-danger .navbar-end > .navbar-item, + .navbar.is-danger .navbar-end .navbar-link { + color: #fff; } + .navbar.is-danger .navbar-start > a.navbar-item:focus, .navbar.is-danger .navbar-start > a.navbar-item:hover, .navbar.is-danger .navbar-start > a.navbar-item.is-active, + .navbar.is-danger .navbar-start .navbar-link:focus, + .navbar.is-danger .navbar-start .navbar-link:hover, + .navbar.is-danger .navbar-start .navbar-link.is-active, + .navbar.is-danger .navbar-end > a.navbar-item:focus, + .navbar.is-danger .navbar-end > a.navbar-item:hover, + .navbar.is-danger .navbar-end > a.navbar-item.is-active, + .navbar.is-danger .navbar-end .navbar-link:focus, + .navbar.is-danger .navbar-end .navbar-link:hover, + .navbar.is-danger .navbar-end .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-start .navbar-link::after, + .navbar.is-danger .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { + background-color: #da0b00; + color: #fff; } } + .navbar > .container { + align-items: stretch; + display: flex; + min-height: 3.25rem; + width: 100%; } + .navbar.has-shadow { + box-shadow: 0 2px 0 0 whitesmoke; } + .navbar.is-fixed-bottom, .navbar.is-fixed-top { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom { + bottom: 0; } + .navbar.is-fixed-bottom.has-shadow { + box-shadow: 0 -2px 0 0 whitesmoke; } + .navbar.is-fixed-top { + top: 0; } + +html.has-navbar-fixed-top, +body.has-navbar-fixed-top { + padding-top: 3.25rem; } + +html.has-navbar-fixed-bottom, +body.has-navbar-fixed-bottom { + padding-bottom: 3.25rem; } + +.navbar-brand, +.navbar-tabs { + align-items: stretch; + display: flex; + flex-shrink: 0; + min-height: 3.25rem; } + +.navbar-brand a.navbar-item:focus, .navbar-brand a.navbar-item:hover { + background-color: transparent; } + +.navbar-tabs { + -webkit-overflow-scrolling: touch; + max-width: 100vw; + overflow-x: auto; + overflow-y: hidden; } + +.navbar-burger { + color: #4a4a4a; + cursor: pointer; + display: block; + height: 3.25rem; + position: relative; + width: 3.25rem; + margin-left: auto; } + .navbar-burger span { + background-color: currentColor; + display: block; + height: 1px; + left: calc(50% - 8px); + position: absolute; + transform-origin: center; + transition-duration: 86ms; + transition-property: background-color, opacity, transform; + transition-timing-function: ease-out; + width: 16px; } + .navbar-burger span:nth-child(1) { + top: calc(50% - 6px); } + .navbar-burger span:nth-child(2) { + top: calc(50% - 1px); } + .navbar-burger span:nth-child(3) { + top: calc(50% + 4px); } + .navbar-burger:hover { + background-color: rgba(0, 0, 0, 0.05); } + .navbar-burger.is-active span:nth-child(1) { + transform: translateY(5px) rotate(45deg); } + .navbar-burger.is-active span:nth-child(2) { + opacity: 0; } + .navbar-burger.is-active span:nth-child(3) { + transform: translateY(-5px) rotate(-45deg); } + +.navbar-menu { + display: none; } + +.navbar-item, +.navbar-link { + color: #4a4a4a; + display: block; + line-height: 1.5; + padding: 0.5rem 0.75rem; + position: relative; } + .navbar-item .icon:only-child, + .navbar-link .icon:only-child { + margin-left: -0.25rem; + margin-right: -0.25rem; } + +a.navbar-item, +.navbar-link { + cursor: pointer; } + a.navbar-item:focus, a.navbar-item:focus-within, a.navbar-item:hover, a.navbar-item.is-active, + .navbar-link:focus, + .navbar-link:focus-within, + .navbar-link:hover, + .navbar-link.is-active { + background-color: #fafafa; + color: #149eaa; } + +.navbar-item { + display: block; + flex-grow: 0; + flex-shrink: 0; } + .navbar-item img { + max-height: 1.75rem; } + .navbar-item.has-dropdown { + padding: 0; } + .navbar-item.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .navbar-item.is-tab { + border-bottom: 1px solid transparent; + min-height: 3.25rem; + padding-bottom: calc(0.5rem - 1px); } + .navbar-item.is-tab:focus, .navbar-item.is-tab:hover { + background-color: transparent; + border-bottom-color: #149eaa; } + .navbar-item.is-tab.is-active { + background-color: transparent; + border-bottom-color: #149eaa; + border-bottom-style: solid; + border-bottom-width: 3px; + color: #149eaa; + padding-bottom: calc(0.5rem - 3px); } + +.navbar-content { + flex-grow: 1; + flex-shrink: 1; } + +.navbar-link:not(.is-arrowless) { + padding-right: 2.5em; } + .navbar-link:not(.is-arrowless)::after { + border-color: #149eaa; + margin-top: -0.375em; + right: 1.125em; } + +.navbar-dropdown { + font-size: 0.875rem; + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + .navbar-dropdown .navbar-item { + padding-left: 1.5rem; + padding-right: 1.5rem; } + +.navbar-divider { + background-color: whitesmoke; + border: none; + display: none; + height: 2px; + margin: 0.5rem 0; } + +@media screen and (max-width: 1055px) { + .navbar > .container { + display: block; } + .navbar-brand .navbar-item, + .navbar-tabs .navbar-item { + align-items: center; + display: flex; } + .navbar-link::after { + display: none; } + .navbar-menu { + background-color: white; + box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); + padding: 0.5rem 0; } + .navbar-menu.is-active { + display: block; } + .navbar.is-fixed-bottom-touch, .navbar.is-fixed-top-touch { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom-touch { + bottom: 0; } + .navbar.is-fixed-bottom-touch.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + .navbar.is-fixed-top-touch { + top: 0; } + .navbar.is-fixed-top .navbar-menu, .navbar.is-fixed-top-touch .navbar-menu { + -webkit-overflow-scrolling: touch; + max-height: calc(100vh - 3.25rem); + overflow: auto; } + html.has-navbar-fixed-top-touch, + body.has-navbar-fixed-top-touch { + padding-top: 3.25rem; } + html.has-navbar-fixed-bottom-touch, + body.has-navbar-fixed-bottom-touch { + padding-bottom: 3.25rem; } } + +@media screen and (min-width: 1056px) { + .navbar, + .navbar-menu, + .navbar-start, + .navbar-end { + align-items: stretch; + display: flex; } + .navbar { + min-height: 3.25rem; } + .navbar.is-spaced { + padding: 1rem 2rem; } + .navbar.is-spaced .navbar-start, + .navbar.is-spaced .navbar-end { + align-items: center; } + .navbar.is-spaced a.navbar-item, + .navbar.is-spaced .navbar-link { + border-radius: 4px; } + .navbar.is-transparent a.navbar-item:focus, .navbar.is-transparent a.navbar-item:hover, .navbar.is-transparent a.navbar-item.is-active, + .navbar.is-transparent .navbar-link:focus, + .navbar.is-transparent .navbar-link:hover, + .navbar.is-transparent .navbar-link.is-active { + background-color: transparent !important; } + .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { + background-color: transparent !important; } + .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #149eaa; } + .navbar-burger { + display: none; } + .navbar-item, + .navbar-link { + align-items: center; + display: flex; } + .navbar-item { + display: flex; } + .navbar-item.has-dropdown { + align-items: stretch; } + .navbar-item.has-dropdown-up .navbar-link::after { + transform: rotate(135deg) translate(0.25em, -0.25em); } + .navbar-item.has-dropdown-up .navbar-dropdown { + border-bottom: 2px solid #dbdbdb; + border-radius: 6px 6px 0 0; + border-top: none; + bottom: 100%; + box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); + top: auto; } + .navbar-item.is-active .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown { + display: block; } + .navbar.is-spaced .navbar-item.is-active .navbar-dropdown, .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:hover .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { + opacity: 1; + pointer-events: auto; + transform: translateY(0); } + .navbar-menu { + flex-grow: 1; + flex-shrink: 0; } + .navbar-start { + justify-content: flex-start; + margin-right: auto; } + .navbar-end { + justify-content: flex-end; + margin-left: auto; } + .navbar-dropdown { + background-color: white; + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 2px solid #dbdbdb; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); + display: none; + font-size: 0.875rem; + left: 0; + min-width: 100%; + position: absolute; + top: 100%; + z-index: 20; } + .navbar-dropdown .navbar-item { + padding: 0.375rem 1rem; + white-space: nowrap; } + .navbar-dropdown a.navbar-item { + padding-right: 3rem; } + .navbar-dropdown a.navbar-item:focus, .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #149eaa; } + .navbar.is-spaced .navbar-dropdown, .navbar-dropdown.is-boxed { + border-radius: 6px; + border-top: none; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + display: block; + opacity: 0; + pointer-events: none; + top: calc(100% + (-4px)); + transform: translateY(-5px); + transition-duration: 86ms; + transition-property: opacity, transform; } + .navbar-dropdown.is-right { + left: auto; + right: 0; } + .navbar-divider { + display: block; } + .navbar > .container .navbar-brand, + .container > .navbar .navbar-brand { + margin-left: -.75rem; } + .navbar > .container .navbar-menu, + .container > .navbar .navbar-menu { + margin-right: -.75rem; } + .navbar.is-fixed-bottom-desktop, .navbar.is-fixed-top-desktop { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom-desktop { + bottom: 0; } + .navbar.is-fixed-bottom-desktop.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + .navbar.is-fixed-top-desktop { + top: 0; } + html.has-navbar-fixed-top-desktop, + body.has-navbar-fixed-top-desktop { + padding-top: 3.25rem; } + html.has-navbar-fixed-bottom-desktop, + body.has-navbar-fixed-bottom-desktop { + padding-bottom: 3.25rem; } + html.has-spaced-navbar-fixed-top, + body.has-spaced-navbar-fixed-top { + padding-top: 5.25rem; } + html.has-spaced-navbar-fixed-bottom, + body.has-spaced-navbar-fixed-bottom { + padding-bottom: 5.25rem; } + a.navbar-item.is-active, + .navbar-link.is-active { + color: #0a0a0a; } + a.navbar-item.is-active:not(:focus):not(:hover), + .navbar-link.is-active:not(:focus):not(:hover) { + background-color: transparent; } + .navbar-item.has-dropdown:focus .navbar-link, .navbar-item.has-dropdown:hover .navbar-link, .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #fafafa; } } + +.hero.is-fullheight-with-navbar { + min-height: calc(100vh - 3.25rem); } + +.pagination { + font-size: 1rem; + margin: -0.25rem; } + .pagination.is-small, #documenter .docs-sidebar form.docs-search > input.pagination { + font-size: 0.75rem; } + .pagination.is-medium { + font-size: 1.25rem; } + .pagination.is-large { + font-size: 1.5rem; } + .pagination.is-rounded .pagination-previous, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, + .pagination.is-rounded .pagination-next, + #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { + padding-left: 1em; + padding-right: 1em; + border-radius: 290486px; } + .pagination.is-rounded .pagination-link, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { + border-radius: 290486px; } + +.pagination, +.pagination-list { + align-items: center; + display: flex; + justify-content: center; + text-align: center; } + +.pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis { + font-size: 1em; + justify-content: center; + margin: 0.25rem; + padding-left: 0.5em; + padding-right: 0.5em; + text-align: center; } + +.pagination-previous, +.pagination-next, +.pagination-link { + border-color: #dbdbdb; + color: #363636; + min-width: 2.25em; } + .pagination-previous:hover, + .pagination-next:hover, + .pagination-link:hover { + border-color: #b5b5b5; + color: #107c85; } + .pagination-previous:focus, + .pagination-next:focus, + .pagination-link:focus { + border-color: #3c5dcd; } + .pagination-previous:active, + .pagination-next:active, + .pagination-link:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } + .pagination-previous[disabled], + .pagination-next[disabled], + .pagination-link[disabled] { + background-color: #dbdbdb; + border-color: #dbdbdb; + box-shadow: none; + color: #6b6b6b; + opacity: 0.5; } + +.pagination-previous, +.pagination-next { + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + +.pagination-link.is-current { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + +.pagination-ellipsis { + color: #b5b5b5; + pointer-events: none; } + +.pagination-list { + flex-wrap: wrap; } + +@media screen and (max-width: 768px) { + .pagination { + flex-wrap: wrap; } + .pagination-previous, + .pagination-next { + flex-grow: 1; + flex-shrink: 1; } + .pagination-list li { + flex-grow: 1; + flex-shrink: 1; } } + +@media screen and (min-width: 769px), print { + .pagination-list { + flex-grow: 1; + flex-shrink: 1; + justify-content: flex-start; + order: 1; } + .pagination-previous { + order: 2; } + .pagination-next { + order: 3; } + .pagination { + justify-content: space-between; } + .pagination.is-centered .pagination-previous { + order: 1; } + .pagination.is-centered .pagination-list { + justify-content: center; + order: 2; } + .pagination.is-centered .pagination-next { + order: 3; } + .pagination.is-right .pagination-previous { + order: 1; } + .pagination.is-right .pagination-next { + order: 2; } + .pagination.is-right .pagination-list { + justify-content: flex-end; + order: 3; } } + +.panel { + font-size: 1rem; } + .panel:not(:last-child) { + margin-bottom: 1.5rem; } + +.panel-heading, +.panel-tabs, +.panel-block { + border-bottom: 1px solid #dbdbdb; + border-left: 1px solid #dbdbdb; + border-right: 1px solid #dbdbdb; } + .panel-heading:first-child, + .panel-tabs:first-child, + .panel-block:first-child { + border-top: 1px solid #dbdbdb; } + +.panel-heading { + background-color: whitesmoke; + border-radius: 4px 4px 0 0; + color: #654ca3; + font-size: 1.25em; + font-weight: 300; + line-height: 1.25; + padding: 0.5em 0.75em; } + +.panel-tabs { + align-items: flex-end; + display: flex; + font-size: 0.875em; + justify-content: center; } + .panel-tabs a { + border-bottom: 1px solid #dbdbdb; + margin-bottom: -1px; + padding: 0.5em; } + .panel-tabs a.is-active { + border-bottom-color: #4a4a4a; + color: #363636; } + +.panel-list a { + color: #202020; } + .panel-list a:hover { + color: #149eaa; } + +.panel-block { + align-items: center; + color: #654ca3; + display: flex; + justify-content: flex-start; + padding: 0.5em 0.75em; } + .panel-block input[type="checkbox"] { + margin-right: 0.75em; } + .panel-block > .control { + flex-grow: 1; + flex-shrink: 1; + width: 100%; } + .panel-block.is-wrapped { + flex-wrap: wrap; } + .panel-block.is-active { + border-left-color: #149eaa; + color: #363636; } + .panel-block.is-active .panel-icon { + color: #149eaa; } + +a.panel-block, +label.panel-block { + cursor: pointer; } + a.panel-block:hover, + label.panel-block:hover { + background-color: whitesmoke; } + +.panel-icon { + display: inline-block; + font-size: 14px; + height: 1em; + line-height: 1em; + text-align: center; + vertical-align: top; + width: 1em; + color: #6b6b6b; + margin-right: 0.75em; } + .panel-icon .fa { + font-size: inherit; + line-height: inherit; } + +.tabs { + -webkit-overflow-scrolling: touch; + align-items: stretch; + display: flex; + font-size: 1rem; + justify-content: space-between; + overflow: hidden; + overflow-x: auto; + white-space: nowrap; } + .tabs a { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + color: #202020; + display: flex; + justify-content: center; + margin-bottom: -1px; + padding: 0.5em 1em; + vertical-align: top; } + .tabs a:hover { + border-bottom-color: #654ca3; + color: #654ca3; } + .tabs li { + display: block; } + .tabs li.is-active a { + border-bottom-color: #149eaa; + color: #149eaa; } + .tabs ul { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + display: flex; + flex-grow: 1; + flex-shrink: 0; + justify-content: flex-start; } + .tabs ul.is-left { + padding-right: 0.75em; } + .tabs ul.is-center { + flex: none; + justify-content: center; + padding-left: 0.75em; + padding-right: 0.75em; } + .tabs ul.is-right { + justify-content: flex-end; + padding-left: 0.75em; } + .tabs .icon:first-child { + margin-right: 0.5em; } + .tabs .icon:last-child { + margin-left: 0.5em; } + .tabs.is-centered ul { + justify-content: center; } + .tabs.is-right ul { + justify-content: flex-end; } + .tabs.is-boxed a { + border: 1px solid transparent; + border-radius: 4px 4px 0 0; } + .tabs.is-boxed a:hover { + background-color: whitesmoke; + border-bottom-color: #dbdbdb; } + .tabs.is-boxed li.is-active a { + background-color: white; + border-color: #dbdbdb; + border-bottom-color: transparent !important; } + .tabs.is-fullwidth li { + flex-grow: 1; + flex-shrink: 0; } + .tabs.is-toggle a { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px; + margin-bottom: 0; + position: relative; } + .tabs.is-toggle a:hover { + background-color: whitesmoke; + border-color: #b5b5b5; + z-index: 2; } + .tabs.is-toggle li + li { + margin-left: -1px; } + .tabs.is-toggle li:first-child a { + border-radius: 4px 0 0 4px; } + .tabs.is-toggle li:last-child a { + border-radius: 0 4px 4px 0; } + .tabs.is-toggle li.is-active a { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; + z-index: 1; } + .tabs.is-toggle ul { + border-bottom: none; } + .tabs.is-toggle.is-toggle-rounded li:first-child a { + border-bottom-left-radius: 290486px; + border-top-left-radius: 290486px; + padding-left: 1.25em; } + .tabs.is-toggle.is-toggle-rounded li:last-child a { + border-bottom-right-radius: 290486px; + border-top-right-radius: 290486px; + padding-right: 1.25em; } + .tabs.is-small, #documenter .docs-sidebar form.docs-search > input.tabs { + font-size: 0.75rem; } + .tabs.is-medium { + font-size: 1.25rem; } + .tabs.is-large { + font-size: 1.5rem; } + +.column { + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + padding: 0.75rem; } + .columns.is-mobile > .column.is-narrow { + flex: none; } + .columns.is-mobile > .column.is-full { + flex: none; + width: 100%; } + .columns.is-mobile > .column.is-three-quarters { + flex: none; + width: 75%; } + .columns.is-mobile > .column.is-two-thirds { + flex: none; + width: 66.6666%; } + .columns.is-mobile > .column.is-half { + flex: none; + width: 50%; } + .columns.is-mobile > .column.is-one-third { + flex: none; + width: 33.3333%; } + .columns.is-mobile > .column.is-one-quarter { + flex: none; + width: 25%; } + .columns.is-mobile > .column.is-one-fifth { + flex: none; + width: 20%; } + .columns.is-mobile > .column.is-two-fifths { + flex: none; + width: 40%; } + .columns.is-mobile > .column.is-three-fifths { + flex: none; + width: 60%; } + .columns.is-mobile > .column.is-four-fifths { + flex: none; + width: 80%; } + .columns.is-mobile > .column.is-offset-three-quarters { + margin-left: 75%; } + .columns.is-mobile > .column.is-offset-two-thirds { + margin-left: 66.6666%; } + .columns.is-mobile > .column.is-offset-half { + margin-left: 50%; } + .columns.is-mobile > .column.is-offset-one-third { + margin-left: 33.3333%; } + .columns.is-mobile > .column.is-offset-one-quarter { + margin-left: 25%; } + .columns.is-mobile > .column.is-offset-one-fifth { + margin-left: 20%; } + .columns.is-mobile > .column.is-offset-two-fifths { + margin-left: 40%; } + .columns.is-mobile > .column.is-offset-three-fifths { + margin-left: 60%; } + .columns.is-mobile > .column.is-offset-four-fifths { + margin-left: 80%; } + .columns.is-mobile > .column.is-0 { + flex: none; + width: 0%; } + .columns.is-mobile > .column.is-offset-0 { + margin-left: 0%; } + .columns.is-mobile > .column.is-1 { + flex: none; + width: 8.3333333333%; } + .columns.is-mobile > .column.is-offset-1 { + margin-left: 8.3333333333%; } + .columns.is-mobile > .column.is-2 { + flex: none; + width: 16.6666666667%; } + .columns.is-mobile > .column.is-offset-2 { + margin-left: 16.6666666667%; } + .columns.is-mobile > .column.is-3 { + flex: none; + width: 25%; } + .columns.is-mobile > .column.is-offset-3 { + margin-left: 25%; } + .columns.is-mobile > .column.is-4 { + flex: none; + width: 33.3333333333%; } + .columns.is-mobile > .column.is-offset-4 { + margin-left: 33.3333333333%; } + .columns.is-mobile > .column.is-5 { + flex: none; + width: 41.6666666667%; } + .columns.is-mobile > .column.is-offset-5 { + margin-left: 41.6666666667%; } + .columns.is-mobile > .column.is-6 { + flex: none; + width: 50%; } + .columns.is-mobile > .column.is-offset-6 { + margin-left: 50%; } + .columns.is-mobile > .column.is-7 { + flex: none; + width: 58.3333333333%; } + .columns.is-mobile > .column.is-offset-7 { + margin-left: 58.3333333333%; } + .columns.is-mobile > .column.is-8 { + flex: none; + width: 66.6666666667%; } + .columns.is-mobile > .column.is-offset-8 { + margin-left: 66.6666666667%; } + .columns.is-mobile > .column.is-9 { + flex: none; + width: 75%; } + .columns.is-mobile > .column.is-offset-9 { + margin-left: 75%; } + .columns.is-mobile > .column.is-10 { + flex: none; + width: 83.3333333333%; } + .columns.is-mobile > .column.is-offset-10 { + margin-left: 83.3333333333%; } + .columns.is-mobile > .column.is-11 { + flex: none; + width: 91.6666666667%; } + .columns.is-mobile > .column.is-offset-11 { + margin-left: 91.6666666667%; } + .columns.is-mobile > .column.is-12 { + flex: none; + width: 100%; } + .columns.is-mobile > .column.is-offset-12 { + margin-left: 100%; } + @media screen and (max-width: 768px) { + .column.is-narrow-mobile { + flex: none; } + .column.is-full-mobile { + flex: none; + width: 100%; } + .column.is-three-quarters-mobile { + flex: none; + width: 75%; } + .column.is-two-thirds-mobile { + flex: none; + width: 66.6666%; } + .column.is-half-mobile { + flex: none; + width: 50%; } + .column.is-one-third-mobile { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-mobile { + flex: none; + width: 25%; } + .column.is-one-fifth-mobile { + flex: none; + width: 20%; } + .column.is-two-fifths-mobile { + flex: none; + width: 40%; } + .column.is-three-fifths-mobile { + flex: none; + width: 60%; } + .column.is-four-fifths-mobile { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-mobile { + margin-left: 75%; } + .column.is-offset-two-thirds-mobile { + margin-left: 66.6666%; } + .column.is-offset-half-mobile { + margin-left: 50%; } + .column.is-offset-one-third-mobile { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-mobile { + margin-left: 25%; } + .column.is-offset-one-fifth-mobile { + margin-left: 20%; } + .column.is-offset-two-fifths-mobile { + margin-left: 40%; } + .column.is-offset-three-fifths-mobile { + margin-left: 60%; } + .column.is-offset-four-fifths-mobile { + margin-left: 80%; } + .column.is-0-mobile { + flex: none; + width: 0%; } + .column.is-offset-0-mobile { + margin-left: 0%; } + .column.is-1-mobile { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-mobile { + margin-left: 8.3333333333%; } + .column.is-2-mobile { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-mobile { + margin-left: 16.6666666667%; } + .column.is-3-mobile { + flex: none; + width: 25%; } + .column.is-offset-3-mobile { + margin-left: 25%; } + .column.is-4-mobile { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-mobile { + margin-left: 33.3333333333%; } + .column.is-5-mobile { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-mobile { + margin-left: 41.6666666667%; } + .column.is-6-mobile { + flex: none; + width: 50%; } + .column.is-offset-6-mobile { + margin-left: 50%; } + .column.is-7-mobile { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-mobile { + margin-left: 58.3333333333%; } + .column.is-8-mobile { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-mobile { + margin-left: 66.6666666667%; } + .column.is-9-mobile { + flex: none; + width: 75%; } + .column.is-offset-9-mobile { + margin-left: 75%; } + .column.is-10-mobile { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-mobile { + margin-left: 83.3333333333%; } + .column.is-11-mobile { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-mobile { + margin-left: 91.6666666667%; } + .column.is-12-mobile { + flex: none; + width: 100%; } + .column.is-offset-12-mobile { + margin-left: 100%; } } + @media screen and (min-width: 769px), print { + .column.is-narrow, .column.is-narrow-tablet { + flex: none; } + .column.is-full, .column.is-full-tablet { + flex: none; + width: 100%; } + .column.is-three-quarters, .column.is-three-quarters-tablet { + flex: none; + width: 75%; } + .column.is-two-thirds, .column.is-two-thirds-tablet { + flex: none; + width: 66.6666%; } + .column.is-half, .column.is-half-tablet { + flex: none; + width: 50%; } + .column.is-one-third, .column.is-one-third-tablet { + flex: none; + width: 33.3333%; } + .column.is-one-quarter, .column.is-one-quarter-tablet { + flex: none; + width: 25%; } + .column.is-one-fifth, .column.is-one-fifth-tablet { + flex: none; + width: 20%; } + .column.is-two-fifths, .column.is-two-fifths-tablet { + flex: none; + width: 40%; } + .column.is-three-fifths, .column.is-three-fifths-tablet { + flex: none; + width: 60%; } + .column.is-four-fifths, .column.is-four-fifths-tablet { + flex: none; + width: 80%; } + .column.is-offset-three-quarters, .column.is-offset-three-quarters-tablet { + margin-left: 75%; } + .column.is-offset-two-thirds, .column.is-offset-two-thirds-tablet { + margin-left: 66.6666%; } + .column.is-offset-half, .column.is-offset-half-tablet { + margin-left: 50%; } + .column.is-offset-one-third, .column.is-offset-one-third-tablet { + margin-left: 33.3333%; } + .column.is-offset-one-quarter, .column.is-offset-one-quarter-tablet { + margin-left: 25%; } + .column.is-offset-one-fifth, .column.is-offset-one-fifth-tablet { + margin-left: 20%; } + .column.is-offset-two-fifths, .column.is-offset-two-fifths-tablet { + margin-left: 40%; } + .column.is-offset-three-fifths, .column.is-offset-three-fifths-tablet { + margin-left: 60%; } + .column.is-offset-four-fifths, .column.is-offset-four-fifths-tablet { + margin-left: 80%; } + .column.is-0, .column.is-0-tablet { + flex: none; + width: 0%; } + .column.is-offset-0, .column.is-offset-0-tablet { + margin-left: 0%; } + .column.is-1, .column.is-1-tablet { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1, .column.is-offset-1-tablet { + margin-left: 8.3333333333%; } + .column.is-2, .column.is-2-tablet { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2, .column.is-offset-2-tablet { + margin-left: 16.6666666667%; } + .column.is-3, .column.is-3-tablet { + flex: none; + width: 25%; } + .column.is-offset-3, .column.is-offset-3-tablet { + margin-left: 25%; } + .column.is-4, .column.is-4-tablet { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4, .column.is-offset-4-tablet { + margin-left: 33.3333333333%; } + .column.is-5, .column.is-5-tablet { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5, .column.is-offset-5-tablet { + margin-left: 41.6666666667%; } + .column.is-6, .column.is-6-tablet { + flex: none; + width: 50%; } + .column.is-offset-6, .column.is-offset-6-tablet { + margin-left: 50%; } + .column.is-7, .column.is-7-tablet { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7, .column.is-offset-7-tablet { + margin-left: 58.3333333333%; } + .column.is-8, .column.is-8-tablet { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8, .column.is-offset-8-tablet { + margin-left: 66.6666666667%; } + .column.is-9, .column.is-9-tablet { + flex: none; + width: 75%; } + .column.is-offset-9, .column.is-offset-9-tablet { + margin-left: 75%; } + .column.is-10, .column.is-10-tablet { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10, .column.is-offset-10-tablet { + margin-left: 83.3333333333%; } + .column.is-11, .column.is-11-tablet { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11, .column.is-offset-11-tablet { + margin-left: 91.6666666667%; } + .column.is-12, .column.is-12-tablet { + flex: none; + width: 100%; } + .column.is-offset-12, .column.is-offset-12-tablet { + margin-left: 100%; } } + @media screen and (max-width: 1055px) { + .column.is-narrow-touch { + flex: none; } + .column.is-full-touch { + flex: none; + width: 100%; } + .column.is-three-quarters-touch { + flex: none; + width: 75%; } + .column.is-two-thirds-touch { + flex: none; + width: 66.6666%; } + .column.is-half-touch { + flex: none; + width: 50%; } + .column.is-one-third-touch { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-touch { + flex: none; + width: 25%; } + .column.is-one-fifth-touch { + flex: none; + width: 20%; } + .column.is-two-fifths-touch { + flex: none; + width: 40%; } + .column.is-three-fifths-touch { + flex: none; + width: 60%; } + .column.is-four-fifths-touch { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-touch { + margin-left: 75%; } + .column.is-offset-two-thirds-touch { + margin-left: 66.6666%; } + .column.is-offset-half-touch { + margin-left: 50%; } + .column.is-offset-one-third-touch { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-touch { + margin-left: 25%; } + .column.is-offset-one-fifth-touch { + margin-left: 20%; } + .column.is-offset-two-fifths-touch { + margin-left: 40%; } + .column.is-offset-three-fifths-touch { + margin-left: 60%; } + .column.is-offset-four-fifths-touch { + margin-left: 80%; } + .column.is-0-touch { + flex: none; + width: 0%; } + .column.is-offset-0-touch { + margin-left: 0%; } + .column.is-1-touch { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-touch { + margin-left: 8.3333333333%; } + .column.is-2-touch { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-touch { + margin-left: 16.6666666667%; } + .column.is-3-touch { + flex: none; + width: 25%; } + .column.is-offset-3-touch { + margin-left: 25%; } + .column.is-4-touch { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-touch { + margin-left: 33.3333333333%; } + .column.is-5-touch { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-touch { + margin-left: 41.6666666667%; } + .column.is-6-touch { + flex: none; + width: 50%; } + .column.is-offset-6-touch { + margin-left: 50%; } + .column.is-7-touch { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-touch { + margin-left: 58.3333333333%; } + .column.is-8-touch { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-touch { + margin-left: 66.6666666667%; } + .column.is-9-touch { + flex: none; + width: 75%; } + .column.is-offset-9-touch { + margin-left: 75%; } + .column.is-10-touch { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-touch { + margin-left: 83.3333333333%; } + .column.is-11-touch { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-touch { + margin-left: 91.6666666667%; } + .column.is-12-touch { + flex: none; + width: 100%; } + .column.is-offset-12-touch { + margin-left: 100%; } } + @media screen and (min-width: 1056px) { + .column.is-narrow-desktop { + flex: none; } + .column.is-full-desktop { + flex: none; + width: 100%; } + .column.is-three-quarters-desktop { + flex: none; + width: 75%; } + .column.is-two-thirds-desktop { + flex: none; + width: 66.6666%; } + .column.is-half-desktop { + flex: none; + width: 50%; } + .column.is-one-third-desktop { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-desktop { + flex: none; + width: 25%; } + .column.is-one-fifth-desktop { + flex: none; + width: 20%; } + .column.is-two-fifths-desktop { + flex: none; + width: 40%; } + .column.is-three-fifths-desktop { + flex: none; + width: 60%; } + .column.is-four-fifths-desktop { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-desktop { + margin-left: 75%; } + .column.is-offset-two-thirds-desktop { + margin-left: 66.6666%; } + .column.is-offset-half-desktop { + margin-left: 50%; } + .column.is-offset-one-third-desktop { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-desktop { + margin-left: 25%; } + .column.is-offset-one-fifth-desktop { + margin-left: 20%; } + .column.is-offset-two-fifths-desktop { + margin-left: 40%; } + .column.is-offset-three-fifths-desktop { + margin-left: 60%; } + .column.is-offset-four-fifths-desktop { + margin-left: 80%; } + .column.is-0-desktop { + flex: none; + width: 0%; } + .column.is-offset-0-desktop { + margin-left: 0%; } + .column.is-1-desktop { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-desktop { + margin-left: 8.3333333333%; } + .column.is-2-desktop { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-desktop { + margin-left: 16.6666666667%; } + .column.is-3-desktop { + flex: none; + width: 25%; } + .column.is-offset-3-desktop { + margin-left: 25%; } + .column.is-4-desktop { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-desktop { + margin-left: 33.3333333333%; } + .column.is-5-desktop { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-desktop { + margin-left: 41.6666666667%; } + .column.is-6-desktop { + flex: none; + width: 50%; } + .column.is-offset-6-desktop { + margin-left: 50%; } + .column.is-7-desktop { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-desktop { + margin-left: 58.3333333333%; } + .column.is-8-desktop { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-desktop { + margin-left: 66.6666666667%; } + .column.is-9-desktop { + flex: none; + width: 75%; } + .column.is-offset-9-desktop { + margin-left: 75%; } + .column.is-10-desktop { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-desktop { + margin-left: 83.3333333333%; } + .column.is-11-desktop { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-desktop { + margin-left: 91.6666666667%; } + .column.is-12-desktop { + flex: none; + width: 100%; } + .column.is-offset-12-desktop { + margin-left: 100%; } } + @media screen and (min-width: 1216px) { + .column.is-narrow-widescreen { + flex: none; } + .column.is-full-widescreen { + flex: none; + width: 100%; } + .column.is-three-quarters-widescreen { + flex: none; + width: 75%; } + .column.is-two-thirds-widescreen { + flex: none; + width: 66.6666%; } + .column.is-half-widescreen { + flex: none; + width: 50%; } + .column.is-one-third-widescreen { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-widescreen { + flex: none; + width: 25%; } + .column.is-one-fifth-widescreen { + flex: none; + width: 20%; } + .column.is-two-fifths-widescreen { + flex: none; + width: 40%; } + .column.is-three-fifths-widescreen { + flex: none; + width: 60%; } + .column.is-four-fifths-widescreen { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-widescreen { + margin-left: 75%; } + .column.is-offset-two-thirds-widescreen { + margin-left: 66.6666%; } + .column.is-offset-half-widescreen { + margin-left: 50%; } + .column.is-offset-one-third-widescreen { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-widescreen { + margin-left: 25%; } + .column.is-offset-one-fifth-widescreen { + margin-left: 20%; } + .column.is-offset-two-fifths-widescreen { + margin-left: 40%; } + .column.is-offset-three-fifths-widescreen { + margin-left: 60%; } + .column.is-offset-four-fifths-widescreen { + margin-left: 80%; } + .column.is-0-widescreen { + flex: none; + width: 0%; } + .column.is-offset-0-widescreen { + margin-left: 0%; } + .column.is-1-widescreen { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-widescreen { + margin-left: 8.3333333333%; } + .column.is-2-widescreen { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-widescreen { + margin-left: 16.6666666667%; } + .column.is-3-widescreen { + flex: none; + width: 25%; } + .column.is-offset-3-widescreen { + margin-left: 25%; } + .column.is-4-widescreen { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-widescreen { + margin-left: 33.3333333333%; } + .column.is-5-widescreen { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-widescreen { + margin-left: 41.6666666667%; } + .column.is-6-widescreen { + flex: none; + width: 50%; } + .column.is-offset-6-widescreen { + margin-left: 50%; } + .column.is-7-widescreen { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-widescreen { + margin-left: 58.3333333333%; } + .column.is-8-widescreen { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-widescreen { + margin-left: 66.6666666667%; } + .column.is-9-widescreen { + flex: none; + width: 75%; } + .column.is-offset-9-widescreen { + margin-left: 75%; } + .column.is-10-widescreen { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-widescreen { + margin-left: 83.3333333333%; } + .column.is-11-widescreen { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-widescreen { + margin-left: 91.6666666667%; } + .column.is-12-widescreen { + flex: none; + width: 100%; } + .column.is-offset-12-widescreen { + margin-left: 100%; } } + @media screen and (min-width: 1408px) { + .column.is-narrow-fullhd { + flex: none; } + .column.is-full-fullhd { + flex: none; + width: 100%; } + .column.is-three-quarters-fullhd { + flex: none; + width: 75%; } + .column.is-two-thirds-fullhd { + flex: none; + width: 66.6666%; } + .column.is-half-fullhd { + flex: none; + width: 50%; } + .column.is-one-third-fullhd { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-fullhd { + flex: none; + width: 25%; } + .column.is-one-fifth-fullhd { + flex: none; + width: 20%; } + .column.is-two-fifths-fullhd { + flex: none; + width: 40%; } + .column.is-three-fifths-fullhd { + flex: none; + width: 60%; } + .column.is-four-fifths-fullhd { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-fullhd { + margin-left: 75%; } + .column.is-offset-two-thirds-fullhd { + margin-left: 66.6666%; } + .column.is-offset-half-fullhd { + margin-left: 50%; } + .column.is-offset-one-third-fullhd { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-fullhd { + margin-left: 25%; } + .column.is-offset-one-fifth-fullhd { + margin-left: 20%; } + .column.is-offset-two-fifths-fullhd { + margin-left: 40%; } + .column.is-offset-three-fifths-fullhd { + margin-left: 60%; } + .column.is-offset-four-fifths-fullhd { + margin-left: 80%; } + .column.is-0-fullhd { + flex: none; + width: 0%; } + .column.is-offset-0-fullhd { + margin-left: 0%; } + .column.is-1-fullhd { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-fullhd { + margin-left: 8.3333333333%; } + .column.is-2-fullhd { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-fullhd { + margin-left: 16.6666666667%; } + .column.is-3-fullhd { + flex: none; + width: 25%; } + .column.is-offset-3-fullhd { + margin-left: 25%; } + .column.is-4-fullhd { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-fullhd { + margin-left: 33.3333333333%; } + .column.is-5-fullhd { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-fullhd { + margin-left: 41.6666666667%; } + .column.is-6-fullhd { + flex: none; + width: 50%; } + .column.is-offset-6-fullhd { + margin-left: 50%; } + .column.is-7-fullhd { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-fullhd { + margin-left: 58.3333333333%; } + .column.is-8-fullhd { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-fullhd { + margin-left: 66.6666666667%; } + .column.is-9-fullhd { + flex: none; + width: 75%; } + .column.is-offset-9-fullhd { + margin-left: 75%; } + .column.is-10-fullhd { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-fullhd { + margin-left: 83.3333333333%; } + .column.is-11-fullhd { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-fullhd { + margin-left: 91.6666666667%; } + .column.is-12-fullhd { + flex: none; + width: 100%; } + .column.is-offset-12-fullhd { + margin-left: 100%; } } +.columns { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + .columns:last-child { + margin-bottom: -0.75rem; } + .columns:not(:last-child) { + margin-bottom: calc(1.5rem - 0.75rem); } + .columns.is-centered { + justify-content: center; } + .columns.is-gapless { + margin-left: 0; + margin-right: 0; + margin-top: 0; } + .columns.is-gapless > .column { + margin: 0; + padding: 0 !important; } + .columns.is-gapless:not(:last-child) { + margin-bottom: 1.5rem; } + .columns.is-gapless:last-child { + margin-bottom: 0; } + .columns.is-mobile { + display: flex; } + .columns.is-multiline { + flex-wrap: wrap; } + .columns.is-vcentered { + align-items: center; } + @media screen and (min-width: 769px), print { + .columns:not(.is-desktop) { + display: flex; } } + @media screen and (min-width: 1056px) { + .columns.is-desktop { + display: flex; } } +.columns.is-variable { + --columnGap: 0.75rem; + margin-left: calc(-1 * var(--columnGap)); + margin-right: calc(-1 * var(--columnGap)); } + .columns.is-variable .column { + padding-left: var(--columnGap); + padding-right: var(--columnGap); } + .columns.is-variable.is-0 { + --columnGap: 0rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-0-mobile { + --columnGap: 0rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-0-tablet { + --columnGap: 0rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-0-tablet-only { + --columnGap: 0rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-0-touch { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-0-desktop { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-0-desktop-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-0-widescreen { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-0-widescreen-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-0-fullhd { + --columnGap: 0rem; } } + .columns.is-variable.is-1 { + --columnGap: 0.25rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-1-mobile { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-1-tablet { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-1-tablet-only { + --columnGap: 0.25rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-1-touch { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-1-desktop { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-1-desktop-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-1-widescreen { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-1-widescreen-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-1-fullhd { + --columnGap: 0.25rem; } } + .columns.is-variable.is-2 { + --columnGap: 0.5rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-2-mobile { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-2-tablet { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-2-tablet-only { + --columnGap: 0.5rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-2-touch { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-2-desktop { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-2-desktop-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-2-widescreen { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-2-widescreen-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-2-fullhd { + --columnGap: 0.5rem; } } + .columns.is-variable.is-3 { + --columnGap: 0.75rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-3-mobile { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-3-tablet { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-3-tablet-only { + --columnGap: 0.75rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-3-touch { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-3-desktop { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-3-desktop-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-3-widescreen { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-3-widescreen-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-3-fullhd { + --columnGap: 0.75rem; } } + .columns.is-variable.is-4 { + --columnGap: 1rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-4-mobile { + --columnGap: 1rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-4-tablet { + --columnGap: 1rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-4-tablet-only { + --columnGap: 1rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-4-touch { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-4-desktop { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-4-desktop-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-4-widescreen { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-4-widescreen-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-4-fullhd { + --columnGap: 1rem; } } + .columns.is-variable.is-5 { + --columnGap: 1.25rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-5-mobile { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-5-tablet { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-5-tablet-only { + --columnGap: 1.25rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-5-touch { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-5-desktop { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-5-desktop-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-5-widescreen { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-5-widescreen-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-5-fullhd { + --columnGap: 1.25rem; } } + .columns.is-variable.is-6 { + --columnGap: 1.5rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-6-mobile { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-6-tablet { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-6-tablet-only { + --columnGap: 1.5rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-6-touch { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-6-desktop { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-6-desktop-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-6-widescreen { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-6-widescreen-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-6-fullhd { + --columnGap: 1.5rem; } } + .columns.is-variable.is-7 { + --columnGap: 1.75rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-7-mobile { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-7-tablet { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-7-tablet-only { + --columnGap: 1.75rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-7-touch { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-7-desktop { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-7-desktop-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-7-widescreen { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-7-widescreen-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-7-fullhd { + --columnGap: 1.75rem; } } + .columns.is-variable.is-8 { + --columnGap: 2rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-8-mobile { + --columnGap: 2rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-8-tablet { + --columnGap: 2rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-8-tablet-only { + --columnGap: 2rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-8-touch { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-8-desktop { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-8-desktop-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-8-widescreen { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-8-widescreen-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-8-fullhd { + --columnGap: 2rem; } } +.tile { + align-items: stretch; + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + min-height: min-content; } + .tile.is-ancestor { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + .tile.is-ancestor:last-child { + margin-bottom: -0.75rem; } + .tile.is-ancestor:not(:last-child) { + margin-bottom: 0.75rem; } + .tile.is-child { + margin: 0 !important; } + .tile.is-parent { + padding: 0.75rem; } + .tile.is-vertical { + flex-direction: column; } + .tile.is-vertical > .tile.is-child:not(:last-child) { + margin-bottom: 1.5rem !important; } + @media screen and (min-width: 769px), print { + .tile:not(.is-child) { + display: flex; } + .tile.is-1 { + flex: none; + width: 8.3333333333%; } + .tile.is-2 { + flex: none; + width: 16.6666666667%; } + .tile.is-3 { + flex: none; + width: 25%; } + .tile.is-4 { + flex: none; + width: 33.3333333333%; } + .tile.is-5 { + flex: none; + width: 41.6666666667%; } + .tile.is-6 { + flex: none; + width: 50%; } + .tile.is-7 { + flex: none; + width: 58.3333333333%; } + .tile.is-8 { + flex: none; + width: 66.6666666667%; } + .tile.is-9 { + flex: none; + width: 75%; } + .tile.is-10 { + flex: none; + width: 83.3333333333%; } + .tile.is-11 { + flex: none; + width: 91.6666666667%; } + .tile.is-12 { + flex: none; + width: 100%; } } +.hero { + align-items: stretch; + display: flex; + flex-direction: column; + justify-content: space-between; } + .hero .navbar { + background: none; } + .hero .tabs ul { + border-bottom: none; } + .hero.is-white { + background-color: white; + color: #0a0a0a; } + .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-white strong { + color: inherit; } + .hero.is-white .title { + color: #0a0a0a; } + .hero.is-white .subtitle { + color: rgba(10, 10, 10, 0.9); } + .hero.is-white .subtitle a:not(.button), + .hero.is-white .subtitle strong { + color: #0a0a0a; } + @media screen and (max-width: 1055px) { + .hero.is-white .navbar-menu { + background-color: white; } } + .hero.is-white .navbar-item, + .hero.is-white .navbar-link { + color: rgba(10, 10, 10, 0.7); } + .hero.is-white a.navbar-item:hover, .hero.is-white a.navbar-item.is-active, + .hero.is-white .navbar-link:hover, + .hero.is-white .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .hero.is-white .tabs a { + color: #0a0a0a; + opacity: 0.9; } + .hero.is-white .tabs a:hover { + opacity: 1; } + .hero.is-white .tabs li.is-active a { + opacity: 1; } + .hero.is-white .tabs.is-boxed a, .hero.is-white .tabs.is-toggle a { + color: #0a0a0a; } + .hero.is-white .tabs.is-boxed a:hover, .hero.is-white .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-white .tabs.is-boxed li.is-active a, .hero.is-white .tabs.is-boxed li.is-active a:hover, .hero.is-white .tabs.is-toggle li.is-active a, .hero.is-white .tabs.is-toggle li.is-active a:hover { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .hero.is-white.is-bold { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } + @media screen and (max-width: 768px) { + .hero.is-white.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } + .hero.is-black { + background-color: #0a0a0a; + color: white; } + .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-black strong { + color: inherit; } + .hero.is-black .title { + color: white; } + .hero.is-black .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-black .subtitle a:not(.button), + .hero.is-black .subtitle strong { + color: white; } + @media screen and (max-width: 1055px) { + .hero.is-black .navbar-menu { + background-color: #0a0a0a; } } + .hero.is-black .navbar-item, + .hero.is-black .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-black a.navbar-item:hover, .hero.is-black a.navbar-item.is-active, + .hero.is-black .navbar-link:hover, + .hero.is-black .navbar-link.is-active { + background-color: black; + color: white; } + .hero.is-black .tabs a { + color: white; + opacity: 0.9; } + .hero.is-black .tabs a:hover { + opacity: 1; } + .hero.is-black .tabs li.is-active a { + opacity: 1; } + .hero.is-black .tabs.is-boxed a, .hero.is-black .tabs.is-toggle a { + color: white; } + .hero.is-black .tabs.is-boxed a:hover, .hero.is-black .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-black .tabs.is-boxed li.is-active a, .hero.is-black .tabs.is-boxed li.is-active a:hover, .hero.is-black .tabs.is-toggle li.is-active a, .hero.is-black .tabs.is-toggle li.is-active a:hover { + background-color: white; + border-color: white; + color: #0a0a0a; } + .hero.is-black.is-bold { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } + @media screen and (max-width: 768px) { + .hero.is-black.is-bold .navbar-menu { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } + .hero.is-light { + background-color: whitesmoke; + color: #363636; } + .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-light strong { + color: inherit; } + .hero.is-light .title { + color: #363636; } + .hero.is-light .subtitle { + color: rgba(54, 54, 54, 0.9); } + .hero.is-light .subtitle a:not(.button), + .hero.is-light .subtitle strong { + color: #363636; } + @media screen and (max-width: 1055px) { + .hero.is-light .navbar-menu { + background-color: whitesmoke; } } + .hero.is-light .navbar-item, + .hero.is-light .navbar-link { + color: rgba(54, 54, 54, 0.7); } + .hero.is-light a.navbar-item:hover, .hero.is-light a.navbar-item.is-active, + .hero.is-light .navbar-link:hover, + .hero.is-light .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .hero.is-light .tabs a { + color: #363636; + opacity: 0.9; } + .hero.is-light .tabs a:hover { + opacity: 1; } + .hero.is-light .tabs li.is-active a { + opacity: 1; } + .hero.is-light .tabs.is-boxed a, .hero.is-light .tabs.is-toggle a { + color: #363636; } + .hero.is-light .tabs.is-boxed a:hover, .hero.is-light .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-light .tabs.is-boxed li.is-active a, .hero.is-light .tabs.is-boxed li.is-active a:hover, .hero.is-light .tabs.is-toggle li.is-active a, .hero.is-light .tabs.is-toggle li.is-active a:hover { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .hero.is-light.is-bold { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } + @media screen and (max-width: 768px) { + .hero.is-light.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } } + .hero.is-dark, .content kbd.hero { + background-color: #363636; + color: whitesmoke; } + .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-dark strong, + .content kbd.hero strong { + color: inherit; } + .hero.is-dark .title, .content kbd.hero .title { + color: whitesmoke; } + .hero.is-dark .subtitle, .content kbd.hero .subtitle { + color: rgba(245, 245, 245, 0.9); } + .hero.is-dark .subtitle a:not(.button), .content kbd.hero .subtitle a:not(.button), + .hero.is-dark .subtitle strong, + .content kbd.hero .subtitle strong { + color: whitesmoke; } + @media screen and (max-width: 1055px) { + .hero.is-dark .navbar-menu, .content kbd.hero .navbar-menu { + background-color: #363636; } } + .hero.is-dark .navbar-item, .content kbd.hero .navbar-item, + .hero.is-dark .navbar-link, + .content kbd.hero .navbar-link { + color: rgba(245, 245, 245, 0.7); } + .hero.is-dark a.navbar-item:hover, .content kbd.hero a.navbar-item:hover, .hero.is-dark a.navbar-item.is-active, .content kbd.hero a.navbar-item.is-active, + .hero.is-dark .navbar-link:hover, + .content kbd.hero .navbar-link:hover, + .hero.is-dark .navbar-link.is-active, + .content kbd.hero .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .hero.is-dark .tabs a, .content kbd.hero .tabs a { + color: whitesmoke; + opacity: 0.9; } + .hero.is-dark .tabs a:hover, .content kbd.hero .tabs a:hover { + opacity: 1; } + .hero.is-dark .tabs li.is-active a, .content kbd.hero .tabs li.is-active a { + opacity: 1; } + .hero.is-dark .tabs.is-boxed a, .content kbd.hero .tabs.is-boxed a, .hero.is-dark .tabs.is-toggle a, .content kbd.hero .tabs.is-toggle a { + color: whitesmoke; } + .hero.is-dark .tabs.is-boxed a:hover, .content kbd.hero .tabs.is-boxed a:hover, .hero.is-dark .tabs.is-toggle a:hover, .content kbd.hero .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-dark .tabs.is-boxed li.is-active a, .content kbd.hero .tabs.is-boxed li.is-active a, .hero.is-dark .tabs.is-boxed li.is-active a:hover, .hero.is-dark .tabs.is-toggle li.is-active a, .content kbd.hero .tabs.is-toggle li.is-active a, .hero.is-dark .tabs.is-toggle li.is-active a:hover { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .hero.is-dark.is-bold, .content kbd.hero.is-bold { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } + @media screen and (max-width: 768px) { + .hero.is-dark.is-bold .navbar-menu, .content kbd.hero.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } } + .hero.is-primary, .docstring > section > a.hero.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-primary strong, + .docstring > section > a.hero.docs-sourcelink strong { + color: inherit; } + .hero.is-primary .title, .docstring > section > a.hero.docs-sourcelink .title { + color: #fff; } + .hero.is-primary .subtitle, .docstring > section > a.hero.docs-sourcelink .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-primary .subtitle a:not(.button), .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), + .hero.is-primary .subtitle strong, + .docstring > section > a.hero.docs-sourcelink .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-primary .navbar-menu, .docstring > section > a.hero.docs-sourcelink .navbar-menu { + background-color: #4eb5de; } } + .hero.is-primary .navbar-item, .docstring > section > a.hero.docs-sourcelink .navbar-item, + .hero.is-primary .navbar-link, + .docstring > section > a.hero.docs-sourcelink .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-primary a.navbar-item:hover, .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, .hero.is-primary a.navbar-item.is-active, .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, + .hero.is-primary .navbar-link:hover, + .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, + .hero.is-primary .navbar-link.is-active, + .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .hero.is-primary .tabs a, .docstring > section > a.hero.docs-sourcelink .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-primary .tabs a:hover, .docstring > section > a.hero.docs-sourcelink .tabs a:hover { + opacity: 1; } + .hero.is-primary .tabs li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { + opacity: 1; } + .hero.is-primary .tabs.is-boxed a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, .hero.is-primary .tabs.is-toggle a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { + color: #fff; } + .hero.is-primary .tabs.is-boxed a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, .hero.is-primary .tabs.is-toggle a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-primary .tabs.is-boxed li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, .hero.is-primary .tabs.is-boxed li.is-active a:hover, .hero.is-primary .tabs.is-toggle li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, .hero.is-primary .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #4eb5de; } + .hero.is-primary.is-bold, .docstring > section > a.hero.is-bold.docs-sourcelink { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } + @media screen and (max-width: 768px) { + .hero.is-primary.is-bold .navbar-menu, .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } } + .hero.is-link { + background-color: #149eaa; + color: #fff; } + .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-link strong { + color: inherit; } + .hero.is-link .title { + color: #fff; } + .hero.is-link .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-link .subtitle a:not(.button), + .hero.is-link .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-link .navbar-menu { + background-color: #149eaa; } } + .hero.is-link .navbar-item, + .hero.is-link .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-link a.navbar-item:hover, .hero.is-link a.navbar-item.is-active, + .hero.is-link .navbar-link:hover, + .hero.is-link .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .hero.is-link .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-link .tabs a:hover { + opacity: 1; } + .hero.is-link .tabs li.is-active a { + opacity: 1; } + .hero.is-link .tabs.is-boxed a, .hero.is-link .tabs.is-toggle a { + color: #fff; } + .hero.is-link .tabs.is-boxed a:hover, .hero.is-link .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-link .tabs.is-boxed li.is-active a, .hero.is-link .tabs.is-boxed li.is-active a:hover, .hero.is-link .tabs.is-toggle li.is-active a, .hero.is-link .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #149eaa; } + .hero.is-link.is-bold { + background-image: linear-gradient(141deg, #088379 0%, #149eaa 71%, #119ac6 100%); } + @media screen and (max-width: 768px) { + .hero.is-link.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #088379 0%, #149eaa 71%, #119ac6 100%); } } + .hero.is-info { + background-color: #209cee; + color: #fff; } + .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-info strong { + color: inherit; } + .hero.is-info .title { + color: #fff; } + .hero.is-info .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-info .subtitle a:not(.button), + .hero.is-info .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-info .navbar-menu { + background-color: #209cee; } } + .hero.is-info .navbar-item, + .hero.is-info .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-info a.navbar-item:hover, .hero.is-info a.navbar-item.is-active, + .hero.is-info .navbar-link:hover, + .hero.is-info .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .hero.is-info .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-info .tabs a:hover { + opacity: 1; } + .hero.is-info .tabs li.is-active a { + opacity: 1; } + .hero.is-info .tabs.is-boxed a, .hero.is-info .tabs.is-toggle a { + color: #fff; } + .hero.is-info .tabs.is-boxed a:hover, .hero.is-info .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-info .tabs.is-boxed li.is-active a, .hero.is-info .tabs.is-boxed li.is-active a:hover, .hero.is-info .tabs.is-toggle li.is-active a, .hero.is-info .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #209cee; } + .hero.is-info.is-bold { + background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } + @media screen and (max-width: 768px) { + .hero.is-info.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } } + .hero.is-success { + background-color: #22c35b; + color: #fff; } + .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-success strong { + color: inherit; } + .hero.is-success .title { + color: #fff; } + .hero.is-success .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-success .subtitle a:not(.button), + .hero.is-success .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-success .navbar-menu { + background-color: #22c35b; } } + .hero.is-success .navbar-item, + .hero.is-success .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-success a.navbar-item:hover, .hero.is-success a.navbar-item.is-active, + .hero.is-success .navbar-link:hover, + .hero.is-success .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .hero.is-success .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-success .tabs a:hover { + opacity: 1; } + .hero.is-success .tabs li.is-active a { + opacity: 1; } + .hero.is-success .tabs.is-boxed a, .hero.is-success .tabs.is-toggle a { + color: #fff; } + .hero.is-success .tabs.is-boxed a:hover, .hero.is-success .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-success .tabs.is-boxed li.is-active a, .hero.is-success .tabs.is-boxed li.is-active a:hover, .hero.is-success .tabs.is-toggle li.is-active a, .hero.is-success .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #22c35b; } + .hero.is-success.is-bold { + background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } + @media screen and (max-width: 768px) { + .hero.is-success.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } } + .hero.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-warning strong { + color: inherit; } + .hero.is-warning .title { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .subtitle { + color: rgba(0, 0, 0, 0.9); } + .hero.is-warning .subtitle a:not(.button), + .hero.is-warning .subtitle strong { + color: rgba(0, 0, 0, 0.7); } + @media screen and (max-width: 1055px) { + .hero.is-warning .navbar-menu { + background-color: #ffdd57; } } + .hero.is-warning .navbar-item, + .hero.is-warning .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning a.navbar-item:hover, .hero.is-warning a.navbar-item.is-active, + .hero.is-warning .navbar-link:hover, + .hero.is-warning .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .tabs a { + color: rgba(0, 0, 0, 0.7); + opacity: 0.9; } + .hero.is-warning .tabs a:hover { + opacity: 1; } + .hero.is-warning .tabs li.is-active a { + opacity: 1; } + .hero.is-warning .tabs.is-boxed a, .hero.is-warning .tabs.is-toggle a { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .tabs.is-boxed a:hover, .hero.is-warning .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-warning .tabs.is-boxed li.is-active a, .hero.is-warning .tabs.is-boxed li.is-active a:hover, .hero.is-warning .tabs.is-toggle li.is-active a, .hero.is-warning .tabs.is-toggle li.is-active a:hover { + background-color: rgba(0, 0, 0, 0.7); + border-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .hero.is-warning.is-bold { + background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } + @media screen and (max-width: 768px) { + .hero.is-warning.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } } + .hero.is-danger { + background-color: #da0b00; + color: #fff; } + .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-danger strong { + color: inherit; } + .hero.is-danger .title { + color: #fff; } + .hero.is-danger .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-danger .subtitle a:not(.button), + .hero.is-danger .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-danger .navbar-menu { + background-color: #da0b00; } } + .hero.is-danger .navbar-item, + .hero.is-danger .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-danger a.navbar-item:hover, .hero.is-danger a.navbar-item.is-active, + .hero.is-danger .navbar-link:hover, + .hero.is-danger .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .hero.is-danger .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-danger .tabs a:hover { + opacity: 1; } + .hero.is-danger .tabs li.is-active a { + opacity: 1; } + .hero.is-danger .tabs.is-boxed a, .hero.is-danger .tabs.is-toggle a { + color: #fff; } + .hero.is-danger .tabs.is-boxed a:hover, .hero.is-danger .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-danger .tabs.is-boxed li.is-active a, .hero.is-danger .tabs.is-boxed li.is-active a:hover, .hero.is-danger .tabs.is-toggle li.is-active a, .hero.is-danger .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #da0b00; } + .hero.is-danger.is-bold { + background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } + @media screen and (max-width: 768px) { + .hero.is-danger.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } } + .hero.is-small .hero-body, #documenter .docs-sidebar form.docs-search > input.hero .hero-body { + padding-bottom: 1.5rem; + padding-top: 1.5rem; } + @media screen and (min-width: 769px), print { + .hero.is-medium .hero-body { + padding-bottom: 9rem; + padding-top: 9rem; } } + @media screen and (min-width: 769px), print { + .hero.is-large .hero-body { + padding-bottom: 18rem; + padding-top: 18rem; } } + .hero.is-halfheight .hero-body, .hero.is-fullheight .hero-body, .hero.is-fullheight-with-navbar .hero-body { + align-items: center; + display: flex; } + .hero.is-halfheight .hero-body > .container, .hero.is-fullheight .hero-body > .container, .hero.is-fullheight-with-navbar .hero-body > .container { + flex-grow: 1; + flex-shrink: 1; } + .hero.is-halfheight { + min-height: 50vh; } + .hero.is-fullheight { + min-height: 100vh; } + +.hero-video { + overflow: hidden; } + .hero-video video { + left: 50%; + min-height: 100%; + min-width: 100%; + position: absolute; + top: 50%; + transform: translate3d(-50%, -50%, 0); } + .hero-video.is-transparent { + opacity: 0.3; } + @media screen and (max-width: 768px) { + .hero-video { + display: none; } } +.hero-buttons { + margin-top: 1.5rem; } + @media screen and (max-width: 768px) { + .hero-buttons .button { + display: flex; } + .hero-buttons .button:not(:last-child) { + margin-bottom: 0.75rem; } } + @media screen and (min-width: 769px), print { + .hero-buttons { + display: flex; + justify-content: center; } + .hero-buttons .button:not(:last-child) { + margin-right: 1.5rem; } } +.hero-head, +.hero-foot { + flex-grow: 0; + flex-shrink: 0; } + +.hero-body { + flex-grow: 1; + flex-shrink: 0; + padding: 3rem 1.5rem; } + +.section { + padding: 3rem 1.5rem; } + @media screen and (min-width: 1056px) { + .section.is-medium { + padding: 9rem 1.5rem; } + .section.is-large { + padding: 18rem 1.5rem; } } +.footer { + background-color: #fafafa; + padding: 3rem 1.5rem 6rem; } + +h1 .docs-heading-anchor, h1 .docs-heading-anchor:hover, h1 .docs-heading-anchor:visited, h2 .docs-heading-anchor, h2 .docs-heading-anchor:hover, h2 .docs-heading-anchor:visited, h3 .docs-heading-anchor, h3 .docs-heading-anchor:hover, h3 .docs-heading-anchor:visited, h4 .docs-heading-anchor, h4 .docs-heading-anchor:hover, h4 .docs-heading-anchor:visited, h5 .docs-heading-anchor, h5 .docs-heading-anchor:hover, h5 .docs-heading-anchor:visited, h6 .docs-heading-anchor, h6 .docs-heading-anchor:hover, h6 .docs-heading-anchor:visited { + color: #654ca3; } + +h1 .docs-heading-anchor-permalink, h2 .docs-heading-anchor-permalink, h3 .docs-heading-anchor-permalink, h4 .docs-heading-anchor-permalink, h5 .docs-heading-anchor-permalink, h6 .docs-heading-anchor-permalink { + visibility: hidden; + vertical-align: middle; + margin-left: 0.5em; + font-size: 0.7rem; } + h1 .docs-heading-anchor-permalink::before, h2 .docs-heading-anchor-permalink::before, h3 .docs-heading-anchor-permalink::before, h4 .docs-heading-anchor-permalink::before, h5 .docs-heading-anchor-permalink::before, h6 .docs-heading-anchor-permalink::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f0c1"; } + +h1:hover .docs-heading-anchor-permalink, h2:hover .docs-heading-anchor-permalink, h3:hover .docs-heading-anchor-permalink, h4:hover .docs-heading-anchor-permalink, h5:hover .docs-heading-anchor-permalink, h6:hover .docs-heading-anchor-permalink { + visibility: visible; } + +.docs-dark-only { + display: none !important; } + +pre { + position: relative; + overflow: hidden; } + pre code, pre code.hljs { + padding: 0 0.75rem !important; + overflow: auto; + display: block; } + pre code:first-of-type, pre code.hljs:first-of-type { + padding-top: 0.5rem !important; } + pre code:last-of-type, pre code.hljs:last-of-type { + padding-bottom: 0.5rem !important; } + pre .copy-button { + opacity: 0.2; + transition: opacity 0.2s; + position: absolute; + right: 0em; + top: 0em; + padding: 0.5em; + width: 2.5em; + height: 2.5em; + background: transparent; + border: none; + font-family: "Font Awesome 5 Free"; + color: #202020; + cursor: pointer; + text-align: center; } + pre .copy-button:focus, pre .copy-button:hover { + opacity: 1; + background: rgba(32, 32, 32, 0.1); + color: #149eaa; } + pre .copy-button.success { + color: #259a12; + opacity: 1; } + pre .copy-button.error { + color: #cb3c33; + opacity: 1; } + pre:hover .copy-button { + opacity: 1; } + +.admonition { + background-color: #b5b5b5; + border-style: solid; + border-width: 1px; + border-color: #363636; + border-radius: 4px; + font-size: 1rem; } + .admonition strong { + color: currentColor; } + .admonition.is-small, #documenter .docs-sidebar form.docs-search > input.admonition { + font-size: 0.75rem; } + .admonition.is-medium { + font-size: 1.25rem; } + .admonition.is-large { + font-size: 1.5rem; } + .admonition.is-default { + background-color: #b5b5b5; + border-color: #363636; } + .admonition.is-default > .admonition-header { + background-color: #363636; + color: #fff; } + .admonition.is-default > .admonition-body { + color: #fff; } + .admonition.is-info { + background-color: #def0fc; + border-color: #209cee; } + .admonition.is-info > .admonition-header { + background-color: #209cee; + color: #fff; } + .admonition.is-info > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-success { + background-color: #bdf4d1; + border-color: #22c35b; } + .admonition.is-success > .admonition-header { + background-color: #22c35b; + color: #fff; } + .admonition.is-success > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-warning { + background-color: #fff3c5; + border-color: #ffdd57; } + .admonition.is-warning > .admonition-header { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .admonition.is-warning > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-danger { + background-color: #ffaba7; + border-color: #da0b00; } + .admonition.is-danger > .admonition-header { + background-color: #da0b00; + color: #fff; } + .admonition.is-danger > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-compat { + background-color: #bdeff5; + border-color: #1db5c9; } + .admonition.is-compat > .admonition-header { + background-color: #1db5c9; + color: #fff; } + .admonition.is-compat > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + +.admonition-header { + color: #fff; + background-color: #363636; + align-items: center; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.5rem 0.75rem; + position: relative; } + .admonition-header:before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + margin-right: 0.75rem; + content: "\f06a"; } + +.admonition-body { + color: #202020; + padding: 0.5rem 0.75rem; } + .admonition-body pre { + background-color: #ebe8f4; } + .admonition-body code { + background-color: #ebe8f4; } + +.docstring { + margin-bottom: 1em; + background-color: transparent; + border: 1px solid #dbdbdb; + box-shadow: 2px 2px 3px rgba(10, 10, 10, 0.1); + max-width: 100%; } + .docstring > header { + display: flex; + flex-grow: 1; + align-items: stretch; + padding: 0.5rem 0.75rem; + background-color: #f7f7f7; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + box-shadow: none; + border-bottom: 1px solid #dbdbdb; } + .docstring > header code { + background-color: transparent; } + .docstring > header .docstring-binding { + margin-right: 0.3em; } + .docstring > header .docstring-category { + margin-left: 0.3em; } + .docstring > section { + position: relative; + padding: 0.75rem 0.75rem; + border-bottom: 1px solid #dbdbdb; } + .docstring > section:last-child { + border-bottom: none; } + .docstring > section > a.docs-sourcelink { + transition: opacity 0.3s; + opacity: 0; + position: absolute; + right: 0.375rem; + bottom: 0.375rem; } + .docstring > section > a.docs-sourcelink:focus { + opacity: 1 !important; } + .docstring:hover > section > a.docs-sourcelink { + opacity: 0.2; } + .docstring:focus-within > section > a.docs-sourcelink { + opacity: 0.2; } + .docstring > section:hover a.docs-sourcelink { + opacity: 1; } + +.documenter-example-output { + background-color: #fff; } + +.outdated-warning-overlay { + position: fixed; + top: 0; + left: 0; + right: 0; + box-shadow: 0 0 10px rgba(0, 0, 0, 0.3); + z-index: 999; + background-color: #ffaba7; + color: rgba(0, 0, 0, 0.7); + border-bottom: 3px solid #da0b00; + padding: 10px 35px; + text-align: center; + font-size: 15px; } + .outdated-warning-overlay .outdated-warning-closer { + position: absolute; + top: calc(50% - 10px); + right: 18px; + cursor: pointer; + width: 12px; } + .outdated-warning-overlay a { + color: #149eaa; } + .outdated-warning-overlay a:hover { + color: #107c85; } + +.content pre { + border: 1px solid #dbdbdb; } + +.content code { + font-weight: inherit; } + +.content a code { + color: #149eaa; } + +.content h1 code, .content h2 code, .content h3 code, .content h4 code, .content h5 code, .content h6 code { + color: #654ca3; } + +.content table { + display: block; + width: initial; + max-width: 100%; + overflow-x: auto; } + +.content blockquote > ul:first-child, .content blockquote > ol:first-child, .content .admonition-body > ul:first-child, .content .admonition-body > ol:first-child { + margin-top: 0; } + +pre, code { + font-variant-ligatures: no-contextual; } + +.breadcrumb a.is-disabled { + cursor: default; + pointer-events: none; } + .breadcrumb a.is-disabled, .breadcrumb a.is-disabled:hover { + color: #654ca3; } + +.hljs { + background: initial !important; } + +.katex .katex-mathml { + top: 0; + right: 0; } + +.katex-display, mjx-container, .MathJax_Display { + margin: 0.5em 0 !important; } + +html { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; } + +li.no-marker { + list-style: none; } + +/* This file contain the overall layout. + * + * The main container is
    that is identified by id #documenter. + */ +#documenter .docs-main > article { + overflow-wrap: break-word; } + #documenter .docs-main > article .math-container { + overflow-x: auto; + overflow-y: hidden; } + +@media screen and (min-width: 1056px) { + #documenter .docs-main { + max-width: 52rem; + margin-left: 20rem; + padding-right: 1rem; } } + +@media screen and (max-width: 1055px) { + #documenter .docs-main { + width: 100%; } + #documenter .docs-main > article { + max-width: 52rem; + margin-left: auto; + margin-right: auto; + margin-bottom: 1rem; + padding: 0 1rem; } + #documenter .docs-main > header, #documenter .docs-main > nav { + max-width: 100%; + width: 100%; + margin: 0; } } + +#documenter .docs-main header.docs-navbar { + background-color: #fff; + border-bottom: 1px solid #dbdbdb; + z-index: 2; + min-height: 4rem; + margin-bottom: 1rem; + display: flex; } + #documenter .docs-main header.docs-navbar .breadcrumb { + flex-grow: 1; } + #documenter .docs-main header.docs-navbar .docs-right { + display: flex; + white-space: nowrap; } + #documenter .docs-main header.docs-navbar .docs-right .docs-icon, #documenter .docs-main header.docs-navbar .docs-right .docs-label, #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + display: inline-block; } + #documenter .docs-main header.docs-navbar .docs-right .docs-label { + padding: 0; + margin-left: 0.3em; } + #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button { + margin: auto 0 auto 1rem; } + #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + font-size: 1.5rem; + margin: auto 0 auto 1rem; } + #documenter .docs-main header.docs-navbar > * { + margin: auto 0; } + @media screen and (max-width: 1055px) { + #documenter .docs-main header.docs-navbar { + position: sticky; + top: 0; + padding: 0 1rem; + /* For Headroom.js */ + transition-property: top, box-shadow; + -webkit-transition-property: top, box-shadow; + /* Safari */ + transition-duration: 0.3s; + -webkit-transition-duration: 0.3s; + /* Safari */ } + #documenter .docs-main header.docs-navbar.headroom--not-top { + box-shadow: 0.2rem 0rem 0.4rem #bbb; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } + #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { + top: -4.5rem; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } } +#documenter .docs-main section.footnotes { + border-top: 1px solid #dbdbdb; } + #documenter .docs-main section.footnotes li .tag:first-child, #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, #documenter .docs-main section.footnotes li .content kbd:first-child, .content #documenter .docs-main section.footnotes li kbd:first-child { + margin-right: 1em; + margin-bottom: 0.4em; } + +#documenter .docs-main .docs-footer { + display: flex; + flex-wrap: wrap; + margin-left: 0; + margin-right: 0; + border-top: 1px solid #dbdbdb; + padding-top: 1rem; + padding-bottom: 1rem; } + @media screen and (max-width: 1055px) { + #documenter .docs-main .docs-footer { + padding-left: 1rem; + padding-right: 1rem; } } + #documenter .docs-main .docs-footer .docs-footer-nextpage, #documenter .docs-main .docs-footer .docs-footer-prevpage { + flex-grow: 1; } + #documenter .docs-main .docs-footer .docs-footer-nextpage { + text-align: right; } + #documenter .docs-main .docs-footer .flexbox-break { + flex-basis: 100%; + height: 0; } + #documenter .docs-main .docs-footer .footer-message { + font-size: 0.8em; + margin: 0.5em auto 0 auto; + text-align: center; } + +#documenter .docs-sidebar { + display: flex; + flex-direction: column; + color: #fff; + background-color: #654ca3; + border-right: 1px solid #dbdbdb; + padding: 0; + flex: 0 0 18rem; + z-index: 5; + font-size: 1em; + position: fixed; + left: -18rem; + width: 18rem; + height: 100%; + transition: left 0.3s; + /* Setting up a nicer theme style for the scrollbar */ } + #documenter .docs-sidebar.visible { + left: 0; + box-shadow: 0.4rem 0rem 0.8rem #bbb; } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar.visible { + box-shadow: none; } } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar { + left: 0; + top: 0; } } + #documenter .docs-sidebar .docs-logo { + margin-top: 1rem; + padding: 0 1rem; } + #documenter .docs-sidebar .docs-logo > img { + max-height: 6rem; + margin: auto; } + #documenter .docs-sidebar .docs-package-name { + flex-shrink: 0; + font-size: 1.5rem; + font-weight: 700; + text-align: center; + white-space: nowrap; + overflow: hidden; + padding: 0.5rem 0; } + #documenter .docs-sidebar .docs-package-name .docs-autofit { + max-width: 16.2rem; } + #documenter .docs-sidebar .docs-package-name a, #documenter .docs-sidebar .docs-package-name a:hover { + color: #fff; } + #documenter .docs-sidebar .docs-version-selector { + border-top: 1px solid #dbdbdb; + display: none; + padding: 0.5rem; } + #documenter .docs-sidebar .docs-version-selector.visible { + display: flex; } + #documenter .docs-sidebar ul.docs-menu { + flex-grow: 1; + user-select: none; + border-top: 1px solid #dbdbdb; + padding-bottom: 1.5rem; + /* Managing collapsible submenus */ } + #documenter .docs-sidebar ul.docs-menu > li > .tocitem { + font-weight: bold; } + #documenter .docs-sidebar ul.docs-menu > li li { + font-size: 0.95em; + margin-left: 1em; + border-left: 1px solid #dbdbdb; } + #documenter .docs-sidebar ul.docs-menu input.collapse-toggle { + display: none; } + #documenter .docs-sidebar ul.docs-menu ul.collapsed { + display: none; } + #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed { + display: block; } + #documenter .docs-sidebar ul.docs-menu label.tocitem { + display: flex; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label { + flex-grow: 2; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron { + display: inline-block; + font-style: normal; + font-variant: normal; + text-rendering: auto; + line-height: 1; + font-size: 0.75em; + margin-left: 1rem; + margin-top: auto; + margin-bottom: auto; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f054"; } + #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before { + content: "\f078"; } + #documenter .docs-sidebar ul.docs-menu .tocitem { + display: block; + padding: 0.5rem 0.5rem; } + #documenter .docs-sidebar ul.docs-menu .tocitem, #documenter .docs-sidebar ul.docs-menu .tocitem:hover { + color: #fff; + background: #654ca3; } + #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, #documenter .docs-sidebar ul.docs-menu label.tocitem:hover { + color: #fff; + background-color: #4b3979; } + #documenter .docs-sidebar ul.docs-menu li.is-active { + border-top: 1px solid #dbdbdb; + border-bottom: 1px solid #dbdbdb; + background-color: #fff; } + #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover { + background-color: #fff; + color: #202020; } + #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover { + background-color: #ddd7ec; + color: #202020; } + #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child { + border-top: none; } + #documenter .docs-sidebar ul.docs-menu ul.internal { + margin: 0 0.5rem 0.5rem; + border-top: 1px solid #dbdbdb; } + #documenter .docs-sidebar ul.docs-menu ul.internal li { + font-size: 0.85em; + border-left: none; + margin-left: 0; + margin-top: 0.5rem; } + #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem { + width: 100%; + padding: 0; } + #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before { + content: "⚬"; + margin-right: 0.4em; } + #documenter .docs-sidebar form.docs-search { + margin: auto; + margin-top: 0.5rem; + margin-bottom: 0.5rem; } + #documenter .docs-sidebar form.docs-search > input { + width: 14.4rem; } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar ul.docs-menu { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar { + width: .3rem; + background: none; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #543f87; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover { + background: #43326b; } } + @media screen and (max-width: 1055px) { + #documenter .docs-sidebar { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + #documenter .docs-sidebar::-webkit-scrollbar { + width: .3rem; + background: none; } + #documenter .docs-sidebar::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #543f87; } + #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover { + background: #43326b; } } +#documenter .docs-main #documenter-search-info { + margin-bottom: 1rem; } + +#documenter .docs-main #documenter-search-results { + list-style-type: circle; + list-style-position: outside; } + #documenter .docs-main #documenter-search-results li { + margin-left: 2rem; } + #documenter .docs-main #documenter-search-results .docs-highlight { + background-color: yellow; } + +.ansi span.sgr1 { + font-weight: bolder; } + +.ansi span.sgr2 { + font-weight: lighter; } + +.ansi span.sgr3 { + font-style: italic; } + +.ansi span.sgr4 { + text-decoration: underline; } + +.ansi span.sgr7 { + color: #fff; + background-color: #202020; } + +.ansi span.sgr8 { + color: transparent; } + .ansi span.sgr8 span { + color: transparent; } + +.ansi span.sgr9 { + text-decoration: line-through; } + +.ansi span.sgr30 { + color: #242424; } + +.ansi span.sgr31 { + color: #a7201f; } + +.ansi span.sgr32 { + color: #066f00; } + +.ansi span.sgr33 { + color: #856b00; } + +.ansi span.sgr34 { + color: #2149b0; } + +.ansi span.sgr35 { + color: #7d4498; } + +.ansi span.sgr36 { + color: #007989; } + +.ansi span.sgr37 { + color: gray; } + +.ansi span.sgr40 { + background-color: #242424; } + +.ansi span.sgr41 { + background-color: #a7201f; } + +.ansi span.sgr42 { + background-color: #066f00; } + +.ansi span.sgr43 { + background-color: #856b00; } + +.ansi span.sgr44 { + background-color: #2149b0; } + +.ansi span.sgr45 { + background-color: #7d4498; } + +.ansi span.sgr46 { + background-color: #007989; } + +.ansi span.sgr47 { + background-color: gray; } + +.ansi span.sgr90 { + color: #616161; } + +.ansi span.sgr91 { + color: #cb3c33; } + +.ansi span.sgr92 { + color: #0e8300; } + +.ansi span.sgr93 { + color: #a98800; } + +.ansi span.sgr94 { + color: #3c5dcd; } + +.ansi span.sgr95 { + color: #9256af; } + +.ansi span.sgr96 { + color: #008fa3; } + +.ansi span.sgr97 { + color: whitesmoke; } + +.ansi span.sgr100 { + background-color: #616161; } + +.ansi span.sgr101 { + background-color: #cb3c33; } + +.ansi span.sgr102 { + background-color: #0e8300; } + +.ansi span.sgr103 { + background-color: #a98800; } + +.ansi span.sgr104 { + background-color: #3c5dcd; } + +.ansi span.sgr105 { + background-color: #9256af; } + +.ansi span.sgr106 { + background-color: #008fa3; } + +.ansi span.sgr107 { + background-color: whitesmoke; } + +code.language-julia-repl > span.hljs-meta { + color: #066f00; + font-weight: bolder; } + +/*! + Theme: Default + Description: Original highlight.js style + Author: (c) Ivan Sagalaev + Maintainer: @highlightjs/core-team + Website: https://highlightjs.org/ + License: see project LICENSE + Touched: 2021 +*/ +/* +This is left on purpose making default.css the single file that can be lifted +as-is from the repository directly without the need for a build step + +Typically this "required" baseline CSS is added by `makestuff.js` during build. +*/ +pre code.hljs { + display: block; + overflow-x: auto; } + +code.hljs { + padding: 3px 5px; } + +/* end baseline CSS */ +.hljs { + background: #F0F0F0; + color: #444; } + +/* Base color: saturation 0; */ +.hljs-subst { + /* default */ } + +/* purposely ignored */ +.hljs-comment { + color: #888888; } + +.hljs-tag, +.hljs-punctuation { + color: #444a; } + +.hljs-tag .hljs-name, +.hljs-tag .hljs-attr { + color: #444; } + +.hljs-keyword, +.hljs-attribute, +.hljs-selector-tag, +.hljs-meta .hljs-keyword, +.hljs-doctag, +.hljs-name { + font-weight: bold; } + +/* User color: hue: 0 */ +.hljs-type, +.hljs-string, +.hljs-number, +.hljs-selector-id, +.hljs-selector-class, +.hljs-quote, +.hljs-template-tag, +.hljs-deletion { + color: #880000; } + +.hljs-title, +.hljs-section { + color: #880000; + font-weight: bold; } + +.hljs-regexp, +.hljs-symbol, +.hljs-variable, +.hljs-template-variable, +.hljs-link, +.hljs-selector-attr, +.hljs-operator, +.hljs-selector-pseudo { + color: #BC6060; } + +/* Language color: hue: 90; */ +.hljs-literal { + color: #78A960; } + +.hljs-built_in, +.hljs-bullet, +.hljs-code, +.hljs-addition { + color: #397300; } + +/* Meta color: hue: 200 */ +.hljs-meta { + color: #1f7199; } + +.hljs-meta .hljs-string { + color: #4d99bf; } + +/* Misc effects */ +.hljs-emphasis { + font-style: italic; } + +.hljs-strong { + font-weight: bold; } + +#documenter .docs-sidebar { + border-right: none; + box-shadow: 0.24rem 0rem 0.4rem #bbb; } + #documenter .docs-sidebar form.docs-search > input { + color: #fff; + background-color: #543f87; + border-color: #43326b; + margin-top: 1.0rem; + margin-bottom: 1.0rem; } + #documenter .docs-sidebar form.docs-search > input::placeholder { + color: #fff; } diff --git a/previews/PR17/assets/themeswap.js b/previews/PR17/assets/themeswap.js new file mode 100644 index 00000000..c58e993e --- /dev/null +++ b/previews/PR17/assets/themeswap.js @@ -0,0 +1,66 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Intialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if(window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the browser supports user color preference + var darkPreference = false; + // Check if the users preference is for dark color scheme + if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { + darkPreference = true; + } + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; var disabled = []; var darkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if(themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); + // Check if the theme is primary dark theme + var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null); + // If ss is for dark theme then set the value of darkTheme to the name of the theme + if(isDarkTheme) darkTheme = themename; + // If we find a matching theme (and it's not the default), we'll set active to non-null + if(themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if(themename !== theme) disabled.push(ss); + } + if(active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + theme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + else if(darkTheme !== null && darkPreference === true) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + darkTheme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + if (ss.ownerNode.getAttribute("data-theme-name") !== darkTheme) { + ss.disabled = true; + } + }); + } +} +set_theme_from_local_storage(); diff --git a/previews/PR17/assets/warner.js b/previews/PR17/assets/warner.js new file mode 100644 index 00000000..5531c885 --- /dev/null +++ b/previews/PR17/assets/warner.js @@ -0,0 +1,49 @@ +function maybeAddWarning () { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return + }; + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return + }; + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return + }; + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement('meta'); + meta.name = 'robots'; + meta.content = 'noindex'; + + document.getElementsByTagName('head')[0].appendChild(meta); + }; + + const div = document.createElement('div'); + div.classList.add('outdated-warning-overlay'); + const closer = document.createElement('button'); + closer.classList.add('outdated-warning-closer', 'delete'); + closer.addEventListener('click', function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + '/../' + window.DOCUMENTER_STABLE; + div.innerHTML = 'This documentation is not for the latest stable release, but for either the development version or an older release.
    Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/previews/PR17/index.html b/previews/PR17/index.html new file mode 100644 index 00000000..d58fc140 --- /dev/null +++ b/previews/PR17/index.html @@ -0,0 +1,34 @@ + +TransitionIndicators.jl · TransitionIndicators.jl
    Edit on GitHub

    TransitionIndicators.jl

    TransitionIndicators — Module

    TransitionIndicators.jl

    CI codecov Package Downloads

    A Julia package that can estimates indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime Shift Identifiers / Change Point Detectors, or however else you want to call them!

    To install it, run import Pkg; Pkg.add("TransitionIndicators").

    All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

    source

    Example

    using TransitionIndicators
+using Statistics: mean, var
+
+n = 1001
+t = collect(1.0:n)
+x = copy(t)
+p = init_metaanalysis_params(n_surrogates = 100)
+res = analyze_indicators(t, x, [mean, var], ridge_slope, p)
+
+# The trend of mean(windowview) is the stride for x=t
+meantrend_ground_truth = fill(p.wv_indicator_stride, length(res.t_evolution))
+# The trend of var(windowview) is 0 for x any affine function of t.
+vartrend_ground_truth = fill(0.0, length(res.t_evolution))
    201-element Vector{Float64}:
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ ⋮
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0

    API

    TransitionIndicators.analyze_indicators — Function
    analyze_indicators(t, x, indicators, evolution_metrics, p)

    Compute the indicators and their evolution_metrics for a timeseries t, x and its surrogates. If t is not provided, it is simply assumed to be 1:length(x). This meta-analysis is performed based on p::MetaAnalysisParameters.

    source
    diff --git a/previews/PR17/search/index.html b/previews/PR17/search/index.html new file mode 100644 index 00000000..089eae0c --- /dev/null +++ b/previews/PR17/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionIndicators.jl

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      diff --git a/previews/PR17/search_index.js b/previews/PR17/search_index.js new file mode 100644 index 00000000..8c550da1 --- /dev/null +++ b/previews/PR17/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"#TransitionIndicators.jl","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"TransitionIndicators","category":"page"},{"location":"#TransitionIndicators","page":"TransitionIndicators.jl","title":"TransitionIndicators","text":"TransitionIndicators.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimates indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime Shift Identifiers / Change Point Detectors, or however else you want to call them!\n\nTo install it, run import Pkg; Pkg.add(\"TransitionIndicators\").\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"#Example","page":"TransitionIndicators.jl","title":"Example","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"using TransitionIndicators\nusing Statistics: mean, var\n\nn = 1001\nt = collect(1.0:n)\nx = copy(t)\np = init_metaanalysis_params(n_surrogates = 100)\nres = analyze_indicators(t, x, [mean, var], ridge_slope, p)\n\n# The trend of mean(windowview) is the stride for x=t\nmeantrend_ground_truth = fill(p.wv_indicator_stride, length(res.t_evolution))\n# The trend of var(windowview) is 0 for x any affine function of t.\nvartrend_ground_truth = fill(0.0, length(res.t_evolution))","category":"page"},{"location":"#API","page":"TransitionIndicators.jl","title":"API","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"analyze_indicators","category":"page"},{"location":"#TransitionIndicators.analyze_indicators","page":"TransitionIndicators.jl","title":"TransitionIndicators.analyze_indicators","text":"analyze_indicators(t, x, indicators, evolution_metrics, p)\n\nCompute the indicators and their evolution_metrics for a timeseries t, x and its surrogates. If t is not provided, it is simply assumed to be 1:length(x). This meta-analysis is performed based on p::MetaAnalysisParameters.\n\n\n\n\n\n","category":"function"}] +} diff --git a/previews/PR17/siteinfo.js b/previews/PR17/siteinfo.js new file mode 100644 index 00000000..15711260 --- /dev/null +++ b/previews/PR17/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR17"; diff --git a/previews/PR18/assets/documenter.js b/previews/PR18/assets/documenter.js new file mode 100644 index 00000000..6adfbbbf --- /dev/null +++ b/previews/PR18/assets/documenter.js @@ -0,0 +1,331 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fas", "fa-copy"); + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-times"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-times"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); + }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR18/assets/search.js b/previews/PR18/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR18/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
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Can be included in any rule that should render Font Awesome icons. */ +@keyframes spinAround { + from { + transform: rotate(0deg); } + to { + transform: rotate(359deg); } } + +html.theme--documenter-dark .tabs, html.theme--documenter-dark .pagination-previous, +html.theme--documenter-dark .pagination-next, +html.theme--documenter-dark .pagination-link, +html.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .breadcrumb, html.theme--documenter-dark .file, html.theme--documenter-dark .button, .is-unselectable, html.theme--documenter-dark .modal-close, html.theme--documenter-dark .delete { + -webkit-touch-callout: none; + -webkit-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; } + +html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after, html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after { + border: 3px solid transparent; + border-radius: 2px; + border-right: 0; + border-top: 0; + 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html.theme--documenter-dark .content:not(:last-child), html.theme--documenter-dark .box:not(:last-child) { + margin-bottom: 1.5rem; } + +html.theme--documenter-dark .modal-close, html.theme--documenter-dark .delete { + -moz-appearance: none; + -webkit-appearance: none; + background-color: rgba(10, 10, 10, 0.2); + border: none; + border-radius: 290486px; + cursor: pointer; + pointer-events: auto; + display: inline-block; + flex-grow: 0; + flex-shrink: 0; + font-size: 0; + height: 20px; + max-height: 20px; + max-width: 20px; + min-height: 20px; + min-width: 20px; + outline: none; + position: relative; + vertical-align: top; + width: 20px; } + html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::before, html.theme--documenter-dark .modal-close::after, html.theme--documenter-dark .delete::after { + background-color: white; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::before { + height: 2px; + width: 50%; } + html.theme--documenter-dark .modal-close::after, html.theme--documenter-dark .delete::after { + height: 50%; + width: 2px; } + html.theme--documenter-dark .modal-close:hover, html.theme--documenter-dark .delete:hover, html.theme--documenter-dark .modal-close:focus, html.theme--documenter-dark .delete:focus { + background-color: rgba(10, 10, 10, 0.3); } + html.theme--documenter-dark .modal-close:active, html.theme--documenter-dark .delete:active { + background-color: rgba(10, 10, 10, 0.4); } + html.theme--documenter-dark .is-small.modal-close, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.modal-close, html.theme--documenter-dark .is-small.delete, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.delete { + height: 16px; + max-height: 16px; + max-width: 16px; + min-height: 16px; + min-width: 16px; + width: 16px; } + html.theme--documenter-dark .is-medium.modal-close, html.theme--documenter-dark .is-medium.delete { + height: 24px; + max-height: 24px; + max-width: 24px; + min-height: 24px; + min-width: 24px; + width: 24px; } + html.theme--documenter-dark .is-large.modal-close, html.theme--documenter-dark .is-large.delete { + height: 32px; + max-height: 32px; + max-width: 32px; + min-height: 32px; + min-width: 32px; + width: 32px; } + +html.theme--documenter-dark .control.is-loading::after, html.theme--documenter-dark .select.is-loading::after, html.theme--documenter-dark .loader, html.theme--documenter-dark .button.is-loading::after { + animation: spinAround 500ms infinite linear; + border: 2px solid #dbdbdb; + border-radius: 290486px; + border-right-color: transparent; + border-top-color: transparent; + content: ""; + display: block; + height: 1em; + position: relative; + width: 1em; } + +html.theme--documenter-dark .hero-video, html.theme--documenter-dark .modal-background, html.theme--documenter-dark .modal, html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img, +html.theme--documenter-dark .image.is-square .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img, +html.theme--documenter-dark .image.is-1by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img, +html.theme--documenter-dark .image.is-5by4 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img, +html.theme--documenter-dark .image.is-4by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img, +html.theme--documenter-dark .image.is-3by2 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img, +html.theme--documenter-dark .image.is-5by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img, +html.theme--documenter-dark .image.is-16by9 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img, +html.theme--documenter-dark .image.is-2by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img, +html.theme--documenter-dark .image.is-3by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img, +html.theme--documenter-dark .image.is-4by5 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img, +html.theme--documenter-dark .image.is-3by4 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img, +html.theme--documenter-dark .image.is-2by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img, +html.theme--documenter-dark .image.is-3by5 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img, +html.theme--documenter-dark .image.is-9by16 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img, +html.theme--documenter-dark .image.is-1by2 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img, +html.theme--documenter-dark .image.is-1by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, .is-overlay { + bottom: 0; + left: 0; + position: absolute; + right: 0; + top: 0; } + +html.theme--documenter-dark .pagination-previous, +html.theme--documenter-dark .pagination-next, +html.theme--documenter-dark .pagination-link, +html.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .file-cta, +html.theme--documenter-dark .file-name, html.theme--documenter-dark .select select, html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .button { + -moz-appearance: none; + -webkit-appearance: none; + align-items: center; + border: 1px solid transparent; + border-radius: 4px; + box-shadow: none; + display: inline-flex; + font-size: 1rem; + height: 2.25em; + justify-content: flex-start; + line-height: 1.5; + padding-bottom: calc(0.375em - 1px); + padding-left: calc(0.625em - 1px); + padding-right: calc(0.625em - 1px); + padding-top: calc(0.375em - 1px); + position: relative; + vertical-align: top; } + html.theme--documenter-dark .pagination-previous:focus, + html.theme--documenter-dark .pagination-next:focus, + html.theme--documenter-dark .pagination-link:focus, + html.theme--documenter-dark .pagination-ellipsis:focus, html.theme--documenter-dark .file-cta:focus, + html.theme--documenter-dark .file-name:focus, html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .button:focus, html.theme--documenter-dark .is-focused.pagination-previous, + html.theme--documenter-dark .is-focused.pagination-next, + html.theme--documenter-dark .is-focused.pagination-link, + html.theme--documenter-dark .is-focused.pagination-ellipsis, html.theme--documenter-dark .is-focused.file-cta, + html.theme--documenter-dark .is-focused.file-name, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-focused.button, html.theme--documenter-dark .pagination-previous:active, + html.theme--documenter-dark .pagination-next:active, + html.theme--documenter-dark .pagination-link:active, + html.theme--documenter-dark .pagination-ellipsis:active, html.theme--documenter-dark .file-cta:active, + html.theme--documenter-dark .file-name:active, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .button:active, html.theme--documenter-dark .is-active.pagination-previous, + html.theme--documenter-dark .is-active.pagination-next, + html.theme--documenter-dark .is-active.pagination-link, + html.theme--documenter-dark .is-active.pagination-ellipsis, html.theme--documenter-dark .is-active.file-cta, + html.theme--documenter-dark .is-active.file-name, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .is-active.button { + outline: none; } + html.theme--documenter-dark .pagination-previous[disabled], + html.theme--documenter-dark .pagination-next[disabled], + html.theme--documenter-dark .pagination-link[disabled], + html.theme--documenter-dark .pagination-ellipsis[disabled], html.theme--documenter-dark .file-cta[disabled], + html.theme--documenter-dark .file-name[disabled], html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], html.theme--documenter-dark .button[disabled], fieldset[disabled] html.theme--documenter-dark .pagination-previous, html.theme--documenter-dark fieldset[disabled] .pagination-previous, + fieldset[disabled] html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark fieldset[disabled] .pagination-next, + fieldset[disabled] html.theme--documenter-dark .pagination-link, + html.theme--documenter-dark fieldset[disabled] .pagination-link, + fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis, + html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis, fieldset[disabled] html.theme--documenter-dark .file-cta, html.theme--documenter-dark fieldset[disabled] .file-cta, + fieldset[disabled] html.theme--documenter-dark .file-name, + html.theme--documenter-dark fieldset[disabled] .file-name, fieldset[disabled] html.theme--documenter-dark .select select, fieldset[disabled] html.theme--documenter-dark .textarea, fieldset[disabled] html.theme--documenter-dark .input, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark fieldset[disabled] .select select, html.theme--documenter-dark .select fieldset[disabled] select, html.theme--documenter-dark fieldset[disabled] .textarea, html.theme--documenter-dark fieldset[disabled] .input, html.theme--documenter-dark fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search > input, fieldset[disabled] html.theme--documenter-dark .button, html.theme--documenter-dark fieldset[disabled] .button { + cursor: not-allowed; } + +/*! minireset.css v0.0.4 | MIT License | github.com/jgthms/minireset.css */ +html, +body, +p, +ol, +ul, +li, +dl, +dt, +dd, +blockquote, +figure, +fieldset, +legend, +textarea, +pre, +iframe, +hr, +h1, +h2, +h3, +h4, +h5, +h6 { + margin: 0; + padding: 0; } + +h1, +h2, +h3, +h4, +h5, +h6 { + font-size: 100%; + font-weight: normal; } + +ul { + list-style: none; } + +button, +input, +select, +textarea { + margin: 0; } + +html { + box-sizing: border-box; } + +*, *::before, *::after { + box-sizing: inherit; } + +img, +embed, +iframe, +object, +video { + height: auto; + max-width: 100%; } + +audio { + max-width: 100%; } + +iframe { + border: 0; } + +table { + border-collapse: collapse; + border-spacing: 0; } + +td, +th { + padding: 0; } + td:not([align]), + th:not([align]) { + text-align: left; } + +.is-clearfix::after { + clear: both; + content: " "; + display: table; } + +.is-pulled-left { + float: left !important; } + +.is-pulled-right { + float: right !important; } + +.is-clipped { + overflow: hidden !important; } + +.is-size-1 { + font-size: 3rem !important; } + +.is-size-2 { + font-size: 2.5rem !important; } + +.is-size-3 { + font-size: 2rem !important; } + +.is-size-4 { + font-size: 1.5rem !important; } + +.is-size-5 { + font-size: 1.25rem !important; } + +.is-size-6 { + font-size: 1rem !important; } + +.is-size-7, html.theme--documenter-dark .docstring > section > a.docs-sourcelink { + font-size: 0.75rem !important; } + +@media screen and (max-width: 768px) { + .is-size-1-mobile { + font-size: 3rem !important; } + .is-size-2-mobile { + font-size: 2.5rem !important; } + .is-size-3-mobile { + font-size: 2rem !important; } + .is-size-4-mobile { + font-size: 1.5rem !important; } + .is-size-5-mobile { + font-size: 1.25rem !important; } + .is-size-6-mobile { + font-size: 1rem !important; } + .is-size-7-mobile { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 769px), print { + .is-size-1-tablet { + font-size: 3rem !important; } + .is-size-2-tablet { + font-size: 2.5rem !important; } + .is-size-3-tablet { + font-size: 2rem !important; } + .is-size-4-tablet { + font-size: 1.5rem !important; } + .is-size-5-tablet { + font-size: 1.25rem !important; } + .is-size-6-tablet { + font-size: 1rem !important; } + .is-size-7-tablet { + font-size: 0.75rem !important; } } + +@media screen and (max-width: 1055px) { + .is-size-1-touch { + font-size: 3rem !important; } + .is-size-2-touch { + font-size: 2.5rem !important; } + .is-size-3-touch { + font-size: 2rem !important; } + .is-size-4-touch { + font-size: 1.5rem !important; } + .is-size-5-touch { + font-size: 1.25rem !important; } + .is-size-6-touch { + font-size: 1rem !important; } + .is-size-7-touch { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1056px) { + .is-size-1-desktop { + font-size: 3rem !important; } + .is-size-2-desktop { + font-size: 2.5rem !important; } + .is-size-3-desktop { + font-size: 2rem !important; } + .is-size-4-desktop { + font-size: 1.5rem !important; } + .is-size-5-desktop { + font-size: 1.25rem !important; } + .is-size-6-desktop { + font-size: 1rem !important; } + .is-size-7-desktop { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1216px) { + .is-size-1-widescreen { + font-size: 3rem !important; } + .is-size-2-widescreen { + font-size: 2.5rem !important; } + .is-size-3-widescreen { + font-size: 2rem !important; } + .is-size-4-widescreen { + font-size: 1.5rem !important; } + .is-size-5-widescreen { + font-size: 1.25rem !important; } + .is-size-6-widescreen { + font-size: 1rem !important; } + .is-size-7-widescreen { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1408px) { + .is-size-1-fullhd { + font-size: 3rem !important; } + .is-size-2-fullhd { + font-size: 2.5rem !important; } + .is-size-3-fullhd { + font-size: 2rem !important; } + .is-size-4-fullhd { + font-size: 1.5rem !important; } + .is-size-5-fullhd { + font-size: 1.25rem !important; } + .is-size-6-fullhd { + font-size: 1rem !important; } + .is-size-7-fullhd { + font-size: 0.75rem !important; } } + +.has-text-centered { + text-align: center !important; } + +.has-text-justified { + text-align: justify !important; } + +.has-text-left { + text-align: left !important; } + +.has-text-right { + text-align: right !important; } + +@media screen and (max-width: 768px) { + .has-text-centered-mobile { + text-align: center !important; } } + +@media screen and (min-width: 769px), print { + .has-text-centered-tablet { + text-align: center !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-centered-tablet-only { + text-align: center !important; } } + +@media screen and (max-width: 1055px) { + .has-text-centered-touch { + text-align: center !important; } } + +@media screen and (min-width: 1056px) { + .has-text-centered-desktop { + text-align: center !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-centered-desktop-only { + text-align: center !important; } } + +@media screen and (min-width: 1216px) { + .has-text-centered-widescreen { + text-align: center !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-centered-widescreen-only { + text-align: center !important; } } + +@media screen and (min-width: 1408px) { + .has-text-centered-fullhd { + text-align: center !important; } } + +@media screen and (max-width: 768px) { + .has-text-justified-mobile { + text-align: justify !important; } } + +@media screen and (min-width: 769px), print { + .has-text-justified-tablet { + text-align: justify !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-justified-tablet-only { + text-align: justify !important; } } + +@media screen and (max-width: 1055px) { + .has-text-justified-touch { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) { + .has-text-justified-desktop { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-justified-desktop-only { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) { + .has-text-justified-widescreen { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-justified-widescreen-only { + text-align: justify !important; } } + +@media screen and (min-width: 1408px) { + .has-text-justified-fullhd { + text-align: justify !important; } } + +@media screen and (max-width: 768px) { + .has-text-left-mobile { + text-align: left !important; } } + +@media screen and (min-width: 769px), print { + .has-text-left-tablet { + text-align: left !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-left-tablet-only { + text-align: left !important; } } + +@media screen and (max-width: 1055px) { + .has-text-left-touch { + text-align: left !important; } } + +@media screen and (min-width: 1056px) { + .has-text-left-desktop { + text-align: left !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-left-desktop-only { + text-align: left !important; } } + +@media screen and (min-width: 1216px) { + .has-text-left-widescreen { + text-align: left !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-left-widescreen-only { + text-align: left !important; } } + +@media screen and (min-width: 1408px) { + .has-text-left-fullhd { + text-align: left !important; } } + +@media screen and (max-width: 768px) { + .has-text-right-mobile { + text-align: right !important; } } + +@media screen and (min-width: 769px), print { + .has-text-right-tablet { + text-align: right !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-right-tablet-only { + text-align: right !important; } } + +@media screen and (max-width: 1055px) { + .has-text-right-touch { + text-align: right !important; } } + +@media screen and (min-width: 1056px) { + .has-text-right-desktop { + text-align: right !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-right-desktop-only { + text-align: right !important; } } + +@media screen and (min-width: 1216px) { + .has-text-right-widescreen { + text-align: right !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-right-widescreen-only { + text-align: right !important; } } + +@media screen and (min-width: 1408px) { + .has-text-right-fullhd { + text-align: right !important; } } + +.is-capitalized { + text-transform: capitalize !important; } + +.is-lowercase { + text-transform: lowercase !important; } + +.is-uppercase { + text-transform: uppercase !important; } + +.is-italic { + font-style: italic !important; } + +.has-text-white { + color: white !important; } + +a.has-text-white:hover, a.has-text-white:focus { + color: #e6e6e6 !important; } + +.has-background-white { + background-color: white !important; } + +.has-text-black { + color: #0a0a0a !important; } + +a.has-text-black:hover, a.has-text-black:focus { + color: black !important; } + +.has-background-black { + background-color: #0a0a0a !important; } + +.has-text-light { + color: whitesmoke !important; } + +a.has-text-light:hover, a.has-text-light:focus { + color: #dbdbdb !important; } + +.has-background-light { + background-color: whitesmoke !important; } + +.has-text-dark { + color: #363636 !important; } + +a.has-text-dark:hover, a.has-text-dark:focus { + color: #1c1c1c !important; } + +.has-background-dark { + background-color: #363636 !important; } + +.has-text-primary { + color: #4eb5de !important; } + +a.has-text-primary:hover, a.has-text-primary:focus { + color: #27a1d2 !important; } + +.has-background-primary { + background-color: #4eb5de !important; } + +.has-text-link { + color: #2ad7e6 !important; } + +a.has-text-link:hover, a.has-text-link:focus { + color: #17b7c5 !important; } + +.has-background-link { + background-color: #2ad7e6 !important; } + +.has-text-info { + color: #3489da !important; } + +a.has-text-info:hover, a.has-text-info:focus { + color: #226fb9 !important; } + +.has-background-info { + background-color: #3489da !important; } + +.has-text-success { + color: #259a12 !important; } + +a.has-text-success:hover, a.has-text-success:focus { + color: #1a6c0d !important; } + +.has-background-success { + background-color: #259a12 !important; } + +.has-text-warning { + color: #f4c72f !important; } + +a.has-text-warning:hover, a.has-text-warning:focus { + color: #e4b30c !important; } + +.has-background-warning { + background-color: #f4c72f !important; } + +.has-text-danger { + color: #cb3c33 !important; } + +a.has-text-danger:hover, a.has-text-danger:focus { + color: #a23029 !important; } + +.has-background-danger { + background-color: #cb3c33 !important; } + +.has-text-black-bis { + color: #121212 !important; } + +.has-background-black-bis { + background-color: #121212 !important; } + +.has-text-black-ter { + color: #242424 !important; } + +.has-background-black-ter { + background-color: #242424 !important; } + +.has-text-grey-darker { + color: #363636 !important; } + +.has-background-grey-darker { + background-color: #363636 !important; } + +.has-text-grey-dark { + color: #4a4a4a !important; } + +.has-background-grey-dark { + background-color: #4a4a4a !important; } + +.has-text-grey { + color: #7a7a7a !important; } + +.has-background-grey { + background-color: #7a7a7a !important; } + +.has-text-grey-light { + color: #b5b5b5 !important; } + +.has-background-grey-light { + background-color: #b5b5b5 !important; } + +.has-text-grey-lighter { + color: #dbdbdb !important; } + +.has-background-grey-lighter { + background-color: #dbdbdb !important; } + +.has-text-white-ter { + color: whitesmoke !important; } + +.has-background-white-ter { + background-color: whitesmoke !important; } + +.has-text-white-bis { + color: #fafafa !important; } + +.has-background-white-bis { + background-color: #fafafa !important; } + +.has-text-weight-light { + font-weight: 300 !important; } + +.has-text-weight-normal { + font-weight: 400 !important; } + +.has-text-weight-medium { + font-weight: 500 !important; } + +.has-text-weight-semibold { + font-weight: 600 !important; } + +.has-text-weight-bold { + font-weight: 700 !important; } + +.is-family-primary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-secondary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-sans-serif { + font-family: "Montserrat", sans-serif !important; } + +.is-family-monospace { + font-family: "Source Code Pro", monospace !important; } + +.is-family-code { + font-family: "Source Code Pro", monospace !important; } + +.is-block { + display: block !important; } + +@media screen and (max-width: 768px) { + .is-block-mobile { + display: block !important; } } + +@media screen and (min-width: 769px), print { + .is-block-tablet { + display: block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-block-tablet-only { + display: block !important; } } + +@media screen and (max-width: 1055px) { + .is-block-touch { + display: block !important; } } + +@media screen and (min-width: 1056px) { + .is-block-desktop { + display: block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-block-desktop-only { + display: block !important; } } + +@media screen and (min-width: 1216px) { + .is-block-widescreen { + display: block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-block-widescreen-only { + display: block !important; } } + +@media screen and (min-width: 1408px) { + .is-block-fullhd { + display: block !important; } } + +.is-flex { + display: flex !important; } + +@media screen and (max-width: 768px) { + .is-flex-mobile { + display: flex !important; } } + +@media screen and (min-width: 769px), print { + .is-flex-tablet { + display: flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-flex-tablet-only { + display: flex !important; } } + +@media screen and (max-width: 1055px) { + .is-flex-touch { + display: flex !important; } } + +@media screen and (min-width: 1056px) { + .is-flex-desktop { + display: flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-flex-desktop-only { + display: flex !important; } } + +@media screen and (min-width: 1216px) { + .is-flex-widescreen { + display: flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-flex-widescreen-only { + display: flex !important; } } + +@media screen and (min-width: 1408px) { + .is-flex-fullhd { + display: flex !important; } } + +.is-inline { + display: inline !important; } + +@media screen and (max-width: 768px) { + .is-inline-mobile { + display: inline !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-tablet { + display: inline !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-tablet-only { + display: inline !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-touch { + display: inline !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-desktop { + display: inline !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-desktop-only { + display: inline !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-widescreen { + display: inline !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-widescreen-only { + display: inline !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-fullhd { + display: inline !important; } } + +.is-inline-block { + display: inline-block !important; } + +@media screen and (max-width: 768px) { + .is-inline-block-mobile { + display: inline-block !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-block-tablet { + display: inline-block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-block-tablet-only { + display: inline-block !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-block-touch { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-block-desktop { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-block-desktop-only { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-block-widescreen { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-block-widescreen-only { + display: inline-block !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-block-fullhd { + display: inline-block !important; } } + +.is-inline-flex { + display: inline-flex !important; } + +@media screen and (max-width: 768px) { + .is-inline-flex-mobile { + display: inline-flex !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-flex-tablet { + display: inline-flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-flex-tablet-only { + display: inline-flex !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-flex-touch { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-flex-desktop { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-flex-desktop-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-flex-widescreen { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-flex-widescreen-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-flex-fullhd { + display: inline-flex !important; } } + +.is-hidden { + display: none !important; } + +.is-sr-only { + border: none !important; + clip: rect(0, 0, 0, 0) !important; + height: 0.01em !important; + overflow: hidden !important; + padding: 0 !important; + position: absolute !important; + white-space: nowrap !important; + width: 0.01em !important; } + +@media screen and (max-width: 768px) { + .is-hidden-mobile { + display: none !important; } } + +@media screen and (min-width: 769px), print { + .is-hidden-tablet { + display: none !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-hidden-tablet-only { + display: none !important; } } + +@media screen and (max-width: 1055px) { + .is-hidden-touch { + display: none !important; } } + +@media screen and (min-width: 1056px) { + .is-hidden-desktop { + display: none !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-hidden-desktop-only { + display: none !important; } } + +@media screen and (min-width: 1216px) { + .is-hidden-widescreen { + display: none !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-hidden-widescreen-only { + display: none !important; } } + +@media screen and (min-width: 1408px) { + .is-hidden-fullhd { + display: none !important; } } + +.is-invisible { + visibility: hidden !important; } + +@media screen and (max-width: 768px) { + .is-invisible-mobile { + visibility: hidden !important; } } + +@media screen and (min-width: 769px), print { + .is-invisible-tablet { + visibility: hidden !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-invisible-tablet-only { + visibility: hidden !important; } } + +@media screen and (max-width: 1055px) { + .is-invisible-touch { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) { + .is-invisible-desktop { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-invisible-desktop-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) { + .is-invisible-widescreen { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-invisible-widescreen-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1408px) { + .is-invisible-fullhd { + visibility: hidden !important; } } + +.is-marginless { + margin: 0 !important; } + +.is-paddingless { + padding: 0 !important; } + +.is-radiusless { + border-radius: 0 !important; } + +.is-shadowless { + box-shadow: none !important; } + +.is-relative { + position: relative !important; } + +html.theme--documenter-dark { + /* This file contain the overall layout. + * + * The main container is
      that is identified by id #documenter. + */ + /*! + Theme: a11y-dark + Author: @ericwbailey + Maintainer: @ericwbailey + + Based on the Tomorrow Night Eighties theme: https://github.com/isagalaev/highlight.js/blob/master/src/styles/tomorrow-night-eighties.css +*/ + /* Comment */ + /* Red */ + /* Orange */ + /* Yellow */ + /* Green */ + /* Blue */ + /* Purple */ } + html.theme--documenter-dark html { + background-color: #1e1e20; + font-size: 16px; + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + html.theme--documenter-dark article, + html.theme--documenter-dark aside, + html.theme--documenter-dark figure, + html.theme--documenter-dark footer, + html.theme--documenter-dark header, + html.theme--documenter-dark hgroup, + html.theme--documenter-dark section { + display: block; } + html.theme--documenter-dark body, + html.theme--documenter-dark button, + html.theme--documenter-dark input, + html.theme--documenter-dark select, + html.theme--documenter-dark textarea { + font-family: "Montserrat", sans-serif; } + html.theme--documenter-dark code, + html.theme--documenter-dark pre { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; + font-family: "Source Code Pro", monospace; } + html.theme--documenter-dark body { + color: #fbfbfb; + font-size: 1em; + font-weight: 400; + line-height: 1.5; } + html.theme--documenter-dark a { + color: #2ad7e6; + cursor: pointer; + text-decoration: none; } + html.theme--documenter-dark a strong { + color: currentColor; } + html.theme--documenter-dark a:hover { + color: #97ebf3; } + html.theme--documenter-dark code { + background-color: #312550; + color: #fff; + font-size: 0.875em; + font-weight: normal; + padding: 0.1em; } + html.theme--documenter-dark hr { + background-color: whitesmoke; + border: none; + display: block; + height: 2px; + margin: 1.5rem 0; } + html.theme--documenter-dark img { + height: auto; + max-width: 100%; } + html.theme--documenter-dark input[type="checkbox"], + html.theme--documenter-dark input[type="radio"] { + vertical-align: baseline; } + html.theme--documenter-dark small { + font-size: 0.875em; } + html.theme--documenter-dark span { + font-style: inherit; + font-weight: inherit; } + html.theme--documenter-dark strong { + color: #cdc3e3; + font-weight: 700; } + html.theme--documenter-dark fieldset { + border: none; } + html.theme--documenter-dark pre { + -webkit-overflow-scrolling: touch; + background-color: #312550; + color: #fbfbfb; + font-size: 0.875em; + overflow-x: auto; + padding: 1.25rem 1.5rem; + white-space: pre; + word-wrap: normal; } + html.theme--documenter-dark pre code { + background-color: transparent; + color: currentColor; + font-size: 1em; + padding: 0; } + html.theme--documenter-dark table td, + html.theme--documenter-dark table th { + vertical-align: top; } + html.theme--documenter-dark table td:not([align]), + html.theme--documenter-dark table th:not([align]) { + text-align: left; } + html.theme--documenter-dark table th { + color: #cdc3e3; } + html.theme--documenter-dark .box { + background-color: white; + border-radius: 6px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #fbfbfb; + display: block; + padding: 1.25rem; } + html.theme--documenter-dark a.box:hover, html.theme--documenter-dark a.box:focus { + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #2ad7e6; } + html.theme--documenter-dark a.box:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #2ad7e6; } + html.theme--documenter-dark .button { + background-color: white; + border-color: #dbdbdb; + border-width: 1px; + color: #363636; + cursor: pointer; + justify-content: center; + padding-bottom: calc(0.375em - 1px); + padding-left: 0.75em; + padding-right: 0.75em; + padding-top: calc(0.375em - 1px); + text-align: center; + white-space: nowrap; } + html.theme--documenter-dark .button strong { + color: inherit; } + html.theme--documenter-dark .button .icon, html.theme--documenter-dark .button .icon.is-small, html.theme--documenter-dark .button #documenter .docs-sidebar form.docs-search > input.icon, html.theme--documenter-dark #documenter .docs-sidebar .button form.docs-search > input.icon, html.theme--documenter-dark .button .icon.is-medium, html.theme--documenter-dark .button .icon.is-large { + height: 1.5em; + width: 1.5em; } + html.theme--documenter-dark .button .icon:first-child:not(:last-child) { + margin-left: calc(-0.375em - 1px); + margin-right: 0.1875em; } + html.theme--documenter-dark .button .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: calc(-0.375em - 1px); } + html.theme--documenter-dark .button .icon:first-child:last-child { + margin-left: calc(-0.375em - 1px); + margin-right: calc(-0.375em - 1px); } + html.theme--documenter-dark .button:hover, html.theme--documenter-dark .button.is-hovered { + border-color: #b5b5b5; + color: #97ebf3; } + html.theme--documenter-dark .button:focus, html.theme--documenter-dark .button.is-focused { + border-color: #3c5dcd; + color: #363636; } + html.theme--documenter-dark .button:focus:not(:active), html.theme--documenter-dark .button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .button:active, html.theme--documenter-dark .button.is-active { + border-color: #4a4a4a; + color: #363636; } + html.theme--documenter-dark .button.is-text { + background-color: transparent; + border-color: transparent; + color: #fbfbfb; + text-decoration: underline; } + html.theme--documenter-dark .button.is-text:hover, html.theme--documenter-dark .button.is-text.is-hovered, html.theme--documenter-dark .button.is-text:focus, html.theme--documenter-dark .button.is-text.is-focused { + background-color: whitesmoke; + color: #cdc3e3; } + html.theme--documenter-dark .button.is-text:active, html.theme--documenter-dark .button.is-text.is-active { + background-color: #e8e8e8; + color: #cdc3e3; } + html.theme--documenter-dark .button.is-text[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-text { + background-color: transparent; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-white { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:hover, html.theme--documenter-dark .button.is-white.is-hovered { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:focus, html.theme--documenter-dark .button.is-white.is-focused { + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:focus:not(:active), html.theme--documenter-dark .button.is-white.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .button.is-white:active, html.theme--documenter-dark .button.is-white.is-active { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white { + background-color: white; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-white.is-inverted { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-hovered { + background-color: black; } + html.theme--documenter-dark .button.is-white.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-white.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + html.theme--documenter-dark .button.is-white.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-outlined.is-focused { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-white.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:hover, html.theme--documenter-dark .button.is-black.is-hovered { + background-color: #040404; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:focus, html.theme--documenter-dark .button.is-black.is-focused { + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:focus:not(:active), html.theme--documenter-dark .button.is-black.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .button.is-black:active, html.theme--documenter-dark .button.is-black.is-active { + background-color: black; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-black.is-inverted { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-black.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted { + background-color: white; + border-color: transparent; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-loading::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-outlined.is-focused { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-black.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-light { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:hover, html.theme--documenter-dark .button.is-light.is-hovered { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:focus, html.theme--documenter-dark .button.is-light.is-focused { + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:focus:not(:active), html.theme--documenter-dark .button.is-light.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .button.is-light:active, html.theme--documenter-dark .button.is-light.is-active { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-light.is-inverted { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-hovered { + background-color: #292929; } + html.theme--documenter-dark .button.is-light.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted { + background-color: #363636; + border-color: transparent; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-outlined.is-focused { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-light.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark, html.theme--documenter-dark .content kbd.button { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:hover, html.theme--documenter-dark .content kbd.button:hover, html.theme--documenter-dark .button.is-dark.is-hovered, html.theme--documenter-dark .content kbd.button.is-hovered { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:focus, html.theme--documenter-dark .content kbd.button:focus, html.theme--documenter-dark .button.is-dark.is-focused, html.theme--documenter-dark .content kbd.button.is-focused { + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:focus:not(:active), html.theme--documenter-dark .content kbd.button:focus:not(:active), html.theme--documenter-dark .button.is-dark.is-focused:not(:active), html.theme--documenter-dark .content kbd.button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .button.is-dark:active, html.theme--documenter-dark .content kbd.button:active, html.theme--documenter-dark .button.is-dark.is-active, html.theme--documenter-dark .content kbd.button.is-active { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark[disabled], html.theme--documenter-dark .content kbd.button[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark, fieldset[disabled] html.theme--documenter-dark .content kbd.button { + background-color: #363636; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-dark.is-inverted, html.theme--documenter-dark .content kbd.button.is-inverted { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted:hover, html.theme--documenter-dark .content kbd.button.is-inverted:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered { + background-color: #e8e8e8; } + html.theme--documenter-dark .button.is-dark.is-inverted[disabled], html.theme--documenter-dark .content kbd.button.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-loading::after, html.theme--documenter-dark .content kbd.button.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-dark.is-outlined, html.theme--documenter-dark .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-outlined.is-focused { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-dark.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-primary, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:hover, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-hovered.docs-sourcelink { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:focus, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:focus:not(:active), html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus:not(:active), html.theme--documenter-dark .button.is-primary.is-focused:not(:active), html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .button.is-primary:active, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:active, html.theme--documenter-dark .button.is-primary.is-active, html.theme--documenter-dark .docstring > section > a.button.is-active.docs-sourcelink { + background-color: #39acda; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary[disabled], html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-primary.is-inverted, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-primary.is-inverted[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-loading.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-primary.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-primary.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + box-shadow: none; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-link { + background-color: #2ad7e6; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:hover, html.theme--documenter-dark .button.is-link.is-hovered { + background-color: #1ed5e5; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:focus, html.theme--documenter-dark .button.is-link.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:focus:not(:active), html.theme--documenter-dark .button.is-link.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .button.is-link:active, html.theme--documenter-dark .button.is-link.is-active { + background-color: #1acddc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link { + background-color: #2ad7e6; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-link.is-inverted { + background-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-link.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-link.is-outlined { + background-color: transparent; + border-color: #2ad7e6; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-outlined.is-focused { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after { + border-color: transparent transparent #2ad7e6 #2ad7e6 !important; } + html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-link.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined { + background-color: transparent; + border-color: #2ad7e6; + box-shadow: none; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #2ad7e6 #2ad7e6 !important; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-info { + background-color: #3489da; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:hover, html.theme--documenter-dark .button.is-info.is-hovered { + background-color: #2983d8; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:focus, html.theme--documenter-dark .button.is-info.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:focus:not(:active), html.theme--documenter-dark .button.is-info.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .button.is-info:active, html.theme--documenter-dark .button.is-info.is-active { + background-color: #267ccf; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info { + background-color: #3489da; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-info.is-inverted { + background-color: #fff; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-info.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-info.is-outlined { + background-color: transparent; + border-color: #3489da; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-outlined.is-focused { + background-color: #3489da; + border-color: #3489da; + color: #fff; } + html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after { + border-color: transparent transparent #3489da #3489da !important; } + html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-info.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined { + background-color: transparent; + border-color: #3489da; + box-shadow: none; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #3489da #3489da !important; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-success { + background-color: #259a12; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:hover, html.theme--documenter-dark .button.is-success.is-hovered { + background-color: #228f11; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:focus, html.theme--documenter-dark .button.is-success.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:focus:not(:active), html.theme--documenter-dark .button.is-success.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .button.is-success:active, html.theme--documenter-dark .button.is-success.is-active { + background-color: #20830f; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success { + background-color: #259a12; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-success.is-inverted { + background-color: #fff; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-success.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-success.is-outlined { + background-color: transparent; + border-color: #259a12; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-outlined.is-focused { + background-color: #259a12; + border-color: #259a12; + color: #fff; } + html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after { + border-color: transparent transparent #259a12 #259a12 !important; } + html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-success.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined { + background-color: transparent; + border-color: #259a12; + box-shadow: none; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #259a12 #259a12 !important; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-warning { + background-color: #f4c72f; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:hover, html.theme--documenter-dark .button.is-warning.is-hovered { + background-color: #f3c423; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:focus, html.theme--documenter-dark .button.is-warning.is-focused { + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:focus:not(:active), html.theme--documenter-dark .button.is-warning.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .button.is-warning:active, html.theme--documenter-dark .button.is-warning.is-active { + background-color: #f3c017; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning { + background-color: #f4c72f; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered { + background-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + border-color: transparent; + box-shadow: none; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-loading::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + html.theme--documenter-dark .button.is-warning.is-outlined { + background-color: transparent; + border-color: #f4c72f; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-outlined.is-focused { + background-color: #f4c72f; + border-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after { + border-color: transparent transparent #f4c72f #f4c72f !important; } + html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + html.theme--documenter-dark .button.is-warning.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined { + background-color: transparent; + border-color: #f4c72f; + box-shadow: none; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused { + background-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #f4c72f #f4c72f !important; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + box-shadow: none; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-danger { + background-color: #cb3c33; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:hover, html.theme--documenter-dark .button.is-danger.is-hovered { + background-color: #c13930; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:focus, html.theme--documenter-dark .button.is-danger.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:focus:not(:active), html.theme--documenter-dark .button.is-danger.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .button.is-danger:active, html.theme--documenter-dark .button.is-danger.is-active { + background-color: #b7362e; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger { + background-color: #cb3c33; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-danger.is-inverted { + background-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-danger.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-danger.is-outlined { + background-color: transparent; + border-color: #cb3c33; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-outlined.is-focused { + background-color: #cb3c33; + border-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after { + border-color: transparent transparent #cb3c33 #cb3c33 !important; } + html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-danger.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined { + background-color: transparent; + border-color: #cb3c33; + box-shadow: none; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #cb3c33 #cb3c33 !important; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .button.is-normal { + font-size: 1rem; } + html.theme--documenter-dark .button.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .button.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .button[disabled], fieldset[disabled] html.theme--documenter-dark .button { + background-color: white; + border-color: #dbdbdb; + box-shadow: none; + opacity: 0.5; } + html.theme--documenter-dark .button.is-fullwidth { + display: flex; + width: 100%; } + html.theme--documenter-dark .button.is-loading { + color: transparent !important; + pointer-events: none; } + html.theme--documenter-dark .button.is-loading::after { + position: absolute; + left: calc(50% - (1em / 2)); + top: calc(50% - (1em / 2)); + position: absolute !important; } + html.theme--documenter-dark .button.is-static { + background-color: whitesmoke; + border-color: #dbdbdb; + color: #7a7a7a; + box-shadow: none; + pointer-events: none; } + html.theme--documenter-dark .button.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + html.theme--documenter-dark .buttons { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .buttons .button { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth) { + margin-right: 0.5rem; } + html.theme--documenter-dark .buttons:last-child { + margin-bottom: -0.5rem; } + html.theme--documenter-dark .buttons:not(:last-child) { + margin-bottom: 1rem; } + html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { + font-size: 1.25rem; } + html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { + font-size: 1.5rem; } + html.theme--documenter-dark .buttons.has-addons .button:not(:first-child) { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .buttons.has-addons .button:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; + margin-right: -1px; } + html.theme--documenter-dark .buttons.has-addons .button:last-child { + margin-right: 0; } + html.theme--documenter-dark .buttons.has-addons .button:hover, html.theme--documenter-dark .buttons.has-addons .button.is-hovered { + z-index: 2; } + html.theme--documenter-dark .buttons.has-addons .button:focus, html.theme--documenter-dark .buttons.has-addons .button.is-focused, html.theme--documenter-dark .buttons.has-addons .button:active, html.theme--documenter-dark .buttons.has-addons .button.is-active, html.theme--documenter-dark .buttons.has-addons .button.is-selected { + z-index: 3; } + html.theme--documenter-dark .buttons.has-addons .button:focus:hover, html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover, html.theme--documenter-dark .buttons.has-addons .button:active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover { + z-index: 4; } + html.theme--documenter-dark .buttons.has-addons .button.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .buttons.is-centered { + justify-content: center; } + html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + html.theme--documenter-dark .buttons.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + html.theme--documenter-dark .container { + flex-grow: 1; + margin: 0 auto; + position: relative; + width: auto; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .container { + max-width: 992px; } + html.theme--documenter-dark .container.is-fluid { + margin-left: 32px; + margin-right: 32px; + max-width: none; } } + @media screen and (max-width: 1215px) { + html.theme--documenter-dark .container.is-widescreen { + max-width: 1152px; } } + @media screen and (max-width: 1407px) { + html.theme--documenter-dark .container.is-fullhd { + max-width: 1344px; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .container { + max-width: 1152px; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .container { + max-width: 1344px; } } + html.theme--documenter-dark .content li + li { + margin-top: 0.25em; } + html.theme--documenter-dark .content p:not(:last-child), + html.theme--documenter-dark .content dl:not(:last-child), + html.theme--documenter-dark .content ol:not(:last-child), + html.theme--documenter-dark .content ul:not(:last-child), + html.theme--documenter-dark .content blockquote:not(:last-child), + html.theme--documenter-dark .content pre:not(:last-child), + html.theme--documenter-dark .content table:not(:last-child) { + margin-bottom: 1em; } + html.theme--documenter-dark .content h1, + html.theme--documenter-dark .content h2, + html.theme--documenter-dark .content h3, + html.theme--documenter-dark .content h4, + html.theme--documenter-dark .content h5, + html.theme--documenter-dark .content h6 { + color: #cdc3e3; + font-weight: 600; + line-height: 1.125; } + html.theme--documenter-dark .content h1 { + font-size: 2em; + margin-bottom: 0.5em; } + html.theme--documenter-dark .content h1:not(:first-child) { + margin-top: 1em; } + html.theme--documenter-dark .content h2 { + font-size: 1.75em; + margin-bottom: 0.5714em; } + html.theme--documenter-dark .content h2:not(:first-child) { + margin-top: 1.1428em; } + html.theme--documenter-dark .content h3 { + font-size: 1.5em; + margin-bottom: 0.6666em; } + html.theme--documenter-dark .content h3:not(:first-child) { + margin-top: 1.3333em; } + html.theme--documenter-dark .content h4 { + font-size: 1.25em; + margin-bottom: 0.8em; } + html.theme--documenter-dark .content h5 { + font-size: 1.125em; + margin-bottom: 0.8888em; } + html.theme--documenter-dark .content h6 { + font-size: 1em; + margin-bottom: 1em; } + html.theme--documenter-dark .content blockquote { + background-color: whitesmoke; + border-left: 5px solid #dbdbdb; + padding: 1.25em 1.5em; } + html.theme--documenter-dark .content ol { + list-style-position: outside; + margin-left: 2em; + margin-top: 1em; } + html.theme--documenter-dark .content ol:not([type]) { + list-style-type: decimal; } + html.theme--documenter-dark .content ol.is-lower-alpha:not([type]) { + list-style-type: lower-alpha; } + html.theme--documenter-dark .content ol.is-lower-roman:not([type]) { + list-style-type: lower-roman; } + html.theme--documenter-dark .content ol.is-upper-alpha:not([type]) { + list-style-type: upper-alpha; } + html.theme--documenter-dark .content ol.is-upper-roman:not([type]) { + list-style-type: upper-roman; } + html.theme--documenter-dark .content ul { + list-style: disc outside; + margin-left: 2em; + margin-top: 1em; } + html.theme--documenter-dark .content ul ul { + list-style-type: circle; + margin-top: 0.5em; } + html.theme--documenter-dark .content ul ul ul { + list-style-type: square; } + html.theme--documenter-dark .content dd { + margin-left: 2em; } + html.theme--documenter-dark .content figure { + margin-left: 2em; + margin-right: 2em; + text-align: center; } + html.theme--documenter-dark .content figure:not(:first-child) { + margin-top: 2em; } + html.theme--documenter-dark .content figure:not(:last-child) { + margin-bottom: 2em; } + html.theme--documenter-dark .content figure img { + display: inline-block; } + html.theme--documenter-dark .content figure figcaption { + font-style: italic; } + html.theme--documenter-dark .content pre { + -webkit-overflow-scrolling: touch; + overflow-x: auto; + padding: 0; + white-space: pre; + word-wrap: normal; } + html.theme--documenter-dark .content sup, + html.theme--documenter-dark .content sub { + font-size: 75%; } + html.theme--documenter-dark .content table { + width: 100%; } + html.theme--documenter-dark .content table td, + html.theme--documenter-dark .content table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + html.theme--documenter-dark .content table th { + color: #cdc3e3; } + html.theme--documenter-dark .content table th:not([align]) { + text-align: left; } + html.theme--documenter-dark .content table thead td, + html.theme--documenter-dark .content table thead th { + border-width: 0 0 2px; + color: #cdc3e3; } + html.theme--documenter-dark .content table tfoot td, + html.theme--documenter-dark .content table tfoot th { + border-width: 2px 0 0; + color: #cdc3e3; } + html.theme--documenter-dark .content table tbody tr:last-child td, + html.theme--documenter-dark .content table tbody tr:last-child th { + border-bottom-width: 0; } + html.theme--documenter-dark .content .tabs li + li { + margin-top: 0; } + html.theme--documenter-dark .content.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.content { + font-size: 0.75rem; } + html.theme--documenter-dark .content.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .content.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .icon { + align-items: center; + display: inline-flex; + justify-content: center; + height: 1.5rem; + width: 1.5rem; } + html.theme--documenter-dark .icon.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.icon { + height: 1rem; + width: 1rem; } + html.theme--documenter-dark .icon.is-medium { + height: 2rem; + width: 2rem; } + html.theme--documenter-dark .icon.is-large { + height: 3rem; + width: 3rem; } + html.theme--documenter-dark .image, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { + display: block; + position: relative; } + html.theme--documenter-dark .image img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img { + display: block; + height: auto; + width: 100%; } + html.theme--documenter-dark .image img.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img.is-rounded { + border-radius: 290486px; } + html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img, + html.theme--documenter-dark .image.is-square .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img, + html.theme--documenter-dark .image.is-1by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img, + html.theme--documenter-dark .image.is-5by4 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img, + html.theme--documenter-dark .image.is-4by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img, + html.theme--documenter-dark .image.is-3by2 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img, + html.theme--documenter-dark .image.is-5by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img, + html.theme--documenter-dark .image.is-16by9 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img, + html.theme--documenter-dark .image.is-2by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img, + html.theme--documenter-dark .image.is-3by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img, + html.theme--documenter-dark .image.is-4by5 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img, + html.theme--documenter-dark .image.is-3by4 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img, + html.theme--documenter-dark .image.is-2by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img, + html.theme--documenter-dark .image.is-3by5 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img, + html.theme--documenter-dark .image.is-9by16 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img, + html.theme--documenter-dark .image.is-1by2 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img, + html.theme--documenter-dark .image.is-1by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { + height: 100%; + width: 100%; } + html.theme--documenter-dark .image.is-square, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square, html.theme--documenter-dark .image.is-1by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 { + padding-top: 100%; } + html.theme--documenter-dark .image.is-5by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 { + padding-top: 80%; } + html.theme--documenter-dark .image.is-4by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 { + padding-top: 75%; } + html.theme--documenter-dark .image.is-3by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 { + padding-top: 66.6666%; } + html.theme--documenter-dark .image.is-5by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 { + padding-top: 60%; } + html.theme--documenter-dark .image.is-16by9, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 { + padding-top: 56.25%; } + html.theme--documenter-dark .image.is-2by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 { + padding-top: 50%; } + html.theme--documenter-dark .image.is-3by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 { + padding-top: 33.3333%; } + html.theme--documenter-dark .image.is-4by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 { + padding-top: 125%; } + html.theme--documenter-dark .image.is-3by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 { + padding-top: 133.3333%; } + html.theme--documenter-dark .image.is-2by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 { + padding-top: 150%; } + html.theme--documenter-dark .image.is-3by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 { + padding-top: 166.6666%; } + html.theme--documenter-dark .image.is-9by16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 { + padding-top: 177.7777%; } + html.theme--documenter-dark .image.is-1by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 { + padding-top: 200%; } + html.theme--documenter-dark .image.is-1by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 { + padding-top: 300%; } + html.theme--documenter-dark .image.is-16x16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16x16 { + height: 16px; + width: 16px; } + html.theme--documenter-dark .image.is-24x24, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-24x24 { + height: 24px; + width: 24px; } + html.theme--documenter-dark .image.is-32x32, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-32x32 { + height: 32px; + width: 32px; } + html.theme--documenter-dark .image.is-48x48, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-48x48 { + height: 48px; + width: 48px; } + html.theme--documenter-dark .image.is-64x64, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-64x64 { + height: 64px; + width: 64px; } + html.theme--documenter-dark .image.is-96x96, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-96x96 { + height: 96px; + width: 96px; } + html.theme--documenter-dark .image.is-128x128, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-128x128 { + height: 128px; + width: 128px; } + html.theme--documenter-dark .notification { + background-color: whitesmoke; + border-radius: 4px; + padding: 1.25rem 2.5rem 1.25rem 1.5rem; + position: relative; } + html.theme--documenter-dark .notification a:not(.button):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + html.theme--documenter-dark .notification strong { + color: currentColor; } + html.theme--documenter-dark .notification code, + html.theme--documenter-dark .notification pre { + background: white; } + html.theme--documenter-dark .notification pre code { + background: transparent; } + html.theme--documenter-dark .notification > .delete { + position: absolute; + right: 0.5rem; + top: 0.5rem; } + html.theme--documenter-dark .notification .title, + html.theme--documenter-dark .notification .subtitle, + html.theme--documenter-dark .notification .content { + color: currentColor; } + html.theme--documenter-dark .notification.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .notification.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .notification.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .notification.is-dark, html.theme--documenter-dark .content kbd.notification { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .notification.is-primary, html.theme--documenter-dark .docstring > section > a.notification.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .notification.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .notification.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .notification.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .notification.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .notification.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .progress { + -moz-appearance: none; + -webkit-appearance: none; + border: none; + border-radius: 290486px; + display: block; + height: 1rem; + overflow: hidden; + padding: 0; + width: 100%; } + html.theme--documenter-dark .progress::-webkit-progress-bar { + background-color: #dbdbdb; } + html.theme--documenter-dark .progress::-webkit-progress-value { + background-color: #fbfbfb; } + html.theme--documenter-dark .progress::-moz-progress-bar { + background-color: #fbfbfb; } + html.theme--documenter-dark .progress::-ms-fill { + background-color: #fbfbfb; + border: none; } + html.theme--documenter-dark .progress.is-white::-webkit-progress-value { + background-color: white; } + html.theme--documenter-dark .progress.is-white::-moz-progress-bar { + background-color: white; } + html.theme--documenter-dark .progress.is-white::-ms-fill { + background-color: white; } + html.theme--documenter-dark .progress.is-white:indeterminate { + background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-black::-webkit-progress-value { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black::-moz-progress-bar { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black::-ms-fill { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black:indeterminate { + background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-light::-webkit-progress-value { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light::-moz-progress-bar { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light::-ms-fill { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light:indeterminate { + background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-dark::-webkit-progress-value, html.theme--documenter-dark .content kbd.progress::-webkit-progress-value { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark::-moz-progress-bar, html.theme--documenter-dark .content kbd.progress::-moz-progress-bar { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark::-ms-fill, html.theme--documenter-dark .content kbd.progress::-ms-fill { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark:indeterminate, html.theme--documenter-dark .content kbd.progress:indeterminate { + background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-primary::-webkit-progress-value, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary::-moz-progress-bar, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary::-ms-fill, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-ms-fill { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary:indeterminate, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink:indeterminate { + background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-link::-webkit-progress-value { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link::-moz-progress-bar { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link::-ms-fill { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link:indeterminate { + background-image: linear-gradient(to right, #2ad7e6 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-info::-webkit-progress-value { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info::-moz-progress-bar { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info::-ms-fill { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info:indeterminate { + background-image: linear-gradient(to right, #3489da 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-success::-webkit-progress-value { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success::-moz-progress-bar { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success::-ms-fill { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success:indeterminate { + background-image: linear-gradient(to right, #259a12 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-warning::-webkit-progress-value { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning::-moz-progress-bar { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning::-ms-fill { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning:indeterminate { + background-image: linear-gradient(to right, #f4c72f 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-danger::-webkit-progress-value { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger::-moz-progress-bar { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger::-ms-fill { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger:indeterminate { + background-image: linear-gradient(to right, #cb3c33 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress:indeterminate { + animation-duration: 1.5s; + animation-iteration-count: infinite; + animation-name: moveIndeterminate; + animation-timing-function: linear; + background-color: #dbdbdb; + background-image: linear-gradient(to right, #fbfbfb 30%, #dbdbdb 30%); + background-position: top left; + background-repeat: no-repeat; + background-size: 150% 150%; } + html.theme--documenter-dark .progress:indeterminate::-webkit-progress-bar { + background-color: transparent; } + html.theme--documenter-dark .progress:indeterminate::-moz-progress-bar { + background-color: transparent; } + html.theme--documenter-dark .progress.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.progress { + height: 0.75rem; } + html.theme--documenter-dark .progress.is-medium { + height: 1.25rem; } + html.theme--documenter-dark .progress.is-large { + height: 1.5rem; } + +@keyframes moveIndeterminate { + from { + background-position: 200% 0; } + to { + background-position: -200% 0; } } + html.theme--documenter-dark .table { + background-color: white; + color: #363636; } + html.theme--documenter-dark .table td, + html.theme--documenter-dark .table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + html.theme--documenter-dark .table td.is-white, + html.theme--documenter-dark .table th.is-white { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .table td.is-black, + html.theme--documenter-dark .table th.is-black { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .table td.is-light, + html.theme--documenter-dark .table th.is-light { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .table td.is-dark, + html.theme--documenter-dark .table th.is-dark { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .table td.is-primary, + html.theme--documenter-dark .table th.is-primary { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table td.is-link, + html.theme--documenter-dark .table th.is-link { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .table td.is-info, + html.theme--documenter-dark .table th.is-info { + background-color: #3489da; + border-color: #3489da; + color: #fff; } + html.theme--documenter-dark .table td.is-success, + html.theme--documenter-dark .table th.is-success { + background-color: #259a12; + border-color: #259a12; + color: #fff; } + html.theme--documenter-dark .table td.is-warning, + html.theme--documenter-dark .table th.is-warning { + background-color: #f4c72f; + border-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .table td.is-danger, + html.theme--documenter-dark .table th.is-danger { + background-color: #cb3c33; + border-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .table td.is-narrow, + html.theme--documenter-dark .table th.is-narrow { + white-space: nowrap; + width: 1%; } + html.theme--documenter-dark .table td.is-selected, + html.theme--documenter-dark .table th.is-selected { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table td.is-selected a, + html.theme--documenter-dark .table td.is-selected strong, + html.theme--documenter-dark .table th.is-selected a, + html.theme--documenter-dark .table th.is-selected strong { + color: currentColor; } + html.theme--documenter-dark .table th { + color: #cdc3e3; } + html.theme--documenter-dark .table th:not([align]) { + text-align: left; } + html.theme--documenter-dark .table tr.is-selected { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table tr.is-selected a, + html.theme--documenter-dark .table tr.is-selected strong { + color: currentColor; } + html.theme--documenter-dark .table tr.is-selected td, + html.theme--documenter-dark .table tr.is-selected th { + border-color: #fff; + color: currentColor; } + html.theme--documenter-dark .table thead { + background-color: transparent; } + html.theme--documenter-dark .table thead td, + html.theme--documenter-dark .table thead th { + border-width: 0 0 2px; + color: #cdc3e3; } + html.theme--documenter-dark .table tfoot { + background-color: transparent; } + html.theme--documenter-dark .table tfoot td, + html.theme--documenter-dark .table tfoot th { + border-width: 2px 0 0; + color: #cdc3e3; } + html.theme--documenter-dark .table tbody { + background-color: transparent; } + html.theme--documenter-dark .table tbody tr:last-child td, + html.theme--documenter-dark .table tbody tr:last-child th { + border-bottom-width: 0; } + html.theme--documenter-dark .table.is-bordered td, + html.theme--documenter-dark .table.is-bordered th { + border-width: 1px; } + html.theme--documenter-dark .table.is-bordered tr:last-child td, + html.theme--documenter-dark .table.is-bordered tr:last-child th { + border-bottom-width: 1px; } + html.theme--documenter-dark .table.is-fullwidth { + width: 100%; } + html.theme--documenter-dark .table.is-hoverable tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { + background-color: whitesmoke; } + html.theme--documenter-dark .table.is-narrow td, + html.theme--documenter-dark .table.is-narrow th { + padding: 0.25em 0.5em; } + html.theme--documenter-dark .table.is-striped tbody tr:not(.is-selected):nth-child(even) { + background-color: #fafafa; } + html.theme--documenter-dark .table-container { + -webkit-overflow-scrolling: touch; + overflow: auto; + overflow-y: hidden; + max-width: 100%; } + html.theme--documenter-dark .tags { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .tags .tag, html.theme--documenter-dark .tags .content kbd, html.theme--documenter-dark .content .tags kbd, html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .tags .tag:not(:last-child), html.theme--documenter-dark .tags .content kbd:not(:last-child), html.theme--documenter-dark .content .tags kbd:not(:last-child), html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0.5rem; } + html.theme--documenter-dark .tags:last-child { + margin-bottom: -0.5rem; } + html.theme--documenter-dark .tags:not(:last-child) { + margin-bottom: 1rem; } + html.theme--documenter-dark .tags.are-medium .tag:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .content kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .content .tags.are-medium kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { + font-size: 1rem; } + html.theme--documenter-dark .tags.are-large .tag:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .content kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .content .tags.are-large kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { + font-size: 1.25rem; } + html.theme--documenter-dark .tags.is-centered { + justify-content: center; } + html.theme--documenter-dark .tags.is-centered .tag, html.theme--documenter-dark .tags.is-centered .content kbd, html.theme--documenter-dark .content .tags.is-centered kbd, html.theme--documenter-dark .tags.is-centered .docstring > section > a.docs-sourcelink { + margin-right: 0.25rem; + margin-left: 0.25rem; } + html.theme--documenter-dark .tags.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .tags.is-right .tag:not(:first-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:first-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0.5rem; } + html.theme--documenter-dark .tags.is-right .tag:not(:last-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:last-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0; } + html.theme--documenter-dark .tags.has-addons .tag, html.theme--documenter-dark .tags.has-addons .content kbd, html.theme--documenter-dark .content .tags.has-addons kbd, html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink { + margin-right: 0; } + html.theme--documenter-dark .tags.has-addons .tag:not(:first-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:first-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0; + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .tags.has-addons .tag:not(:last-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:last-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .tag:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { + align-items: center; + background-color: whitesmoke; + border-radius: 4px; + color: #fbfbfb; + display: inline-flex; + font-size: 0.75rem; + height: 2em; + justify-content: center; + line-height: 1.5; + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + html.theme--documenter-dark .tag:not(body) .delete, html.theme--documenter-dark .content kbd:not(body) .delete, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .delete { + margin-left: 0.25rem; + margin-right: -0.375rem; } + html.theme--documenter-dark .tag.is-white:not(body), html.theme--documenter-dark .content kbd.is-white:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-white:not(body) { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .tag.is-black:not(body), html.theme--documenter-dark .content kbd.is-black:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-black:not(body) { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .tag.is-light:not(body), html.theme--documenter-dark .content kbd.is-light:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-light:not(body) { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .tag.is-dark:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-dark:not(body), html.theme--documenter-dark .content .docstring > section > kbd:not(body) { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .tag.is-primary:not(body), html.theme--documenter-dark .content kbd.is-primary:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .tag.is-link:not(body), html.theme--documenter-dark .content kbd.is-link:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-link:not(body) { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .tag.is-info:not(body), html.theme--documenter-dark .content kbd.is-info:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-info:not(body) { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .tag.is-success:not(body), html.theme--documenter-dark .content kbd.is-success:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-success:not(body) { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .tag.is-warning:not(body), html.theme--documenter-dark .content kbd.is-warning:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-warning:not(body) { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .tag.is-danger:not(body), html.theme--documenter-dark .content kbd.is-danger:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-danger:not(body) { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .tag.is-normal:not(body), html.theme--documenter-dark .content kbd.is-normal:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-normal:not(body) { + font-size: 0.75rem; } + html.theme--documenter-dark .tag.is-medium:not(body), html.theme--documenter-dark .content kbd.is-medium:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-medium:not(body) { + font-size: 1rem; } + html.theme--documenter-dark .tag.is-large:not(body), html.theme--documenter-dark .content kbd.is-large:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-large:not(body) { + font-size: 1.25rem; } + html.theme--documenter-dark .tag:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .content kbd:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { + margin-left: -0.375em; + margin-right: 0.1875em; } + html.theme--documenter-dark .tag:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .content kbd:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: -0.375em; } + html.theme--documenter-dark .tag:not(body) .icon:first-child:last-child, html.theme--documenter-dark .content kbd:not(body) .icon:first-child:last-child, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { + margin-left: -0.375em; + margin-right: -0.375em; } + html.theme--documenter-dark .tag.is-delete:not(body), html.theme--documenter-dark .content kbd.is-delete:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body) { + margin-left: 1px; + padding: 0; + position: relative; + width: 2em; } + html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + background-color: currentColor; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { + height: 1px; + width: 50%; } + html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + height: 50%; + width: 1px; } + html.theme--documenter-dark .tag.is-delete:not(body):hover, html.theme--documenter-dark .content kbd.is-delete:not(body):hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, html.theme--documenter-dark .tag.is-delete:not(body):focus, html.theme--documenter-dark .content kbd.is-delete:not(body):focus, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { + background-color: #e8e8e8; } + html.theme--documenter-dark .tag.is-delete:not(body):active, html.theme--documenter-dark .content kbd.is-delete:not(body):active, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):active { + background-color: #dbdbdb; } + html.theme--documenter-dark .tag.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:not(body), html.theme--documenter-dark .content kbd.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-rounded:not(body) { + border-radius: 290486px; } + html.theme--documenter-dark a.tag:hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:hover { + text-decoration: underline; } + html.theme--documenter-dark .title, + html.theme--documenter-dark .subtitle { + word-break: break-word; } + html.theme--documenter-dark .title em, + html.theme--documenter-dark .title span, + html.theme--documenter-dark .subtitle em, + html.theme--documenter-dark .subtitle span { + font-weight: inherit; } + html.theme--documenter-dark .title sub, + html.theme--documenter-dark .subtitle sub { + font-size: 0.75em; } + html.theme--documenter-dark .title sup, + html.theme--documenter-dark .subtitle sup { + font-size: 0.75em; } + html.theme--documenter-dark .title .tag, html.theme--documenter-dark .title .content kbd, html.theme--documenter-dark .content .title kbd, html.theme--documenter-dark .title .docstring > section > a.docs-sourcelink, + html.theme--documenter-dark .subtitle .tag, + html.theme--documenter-dark .subtitle .content kbd, + html.theme--documenter-dark .content .subtitle kbd, + html.theme--documenter-dark .subtitle .docstring > section > a.docs-sourcelink { + vertical-align: middle; } + html.theme--documenter-dark .title { + color: #363636; + font-size: 2rem; + font-weight: 600; + line-height: 1.125; } + html.theme--documenter-dark .title strong { + color: inherit; + font-weight: inherit; } + html.theme--documenter-dark .title + .highlight { + margin-top: -0.75rem; } + html.theme--documenter-dark .title:not(.is-spaced) + .subtitle { + margin-top: -1.25rem; } + html.theme--documenter-dark .title.is-1 { + font-size: 3rem; } + html.theme--documenter-dark .title.is-2 { + font-size: 2.5rem; } + html.theme--documenter-dark .title.is-3 { + font-size: 2rem; } + html.theme--documenter-dark .title.is-4 { + font-size: 1.5rem; } + html.theme--documenter-dark .title.is-5 { + font-size: 1.25rem; } + html.theme--documenter-dark .title.is-6 { + font-size: 1rem; } + html.theme--documenter-dark .title.is-7 { + font-size: 0.75rem; } + html.theme--documenter-dark .subtitle { + color: #4a4a4a; + font-size: 1.25rem; + font-weight: 400; + line-height: 1.25; } + html.theme--documenter-dark .subtitle strong { + color: #363636; + font-weight: 600; } + html.theme--documenter-dark .subtitle:not(.is-spaced) + .title { + margin-top: -1.25rem; } + html.theme--documenter-dark .subtitle.is-1 { + font-size: 3rem; } + html.theme--documenter-dark .subtitle.is-2 { + font-size: 2.5rem; } + html.theme--documenter-dark .subtitle.is-3 { + font-size: 2rem; } + html.theme--documenter-dark .subtitle.is-4 { + font-size: 1.5rem; } + html.theme--documenter-dark .subtitle.is-5 { + font-size: 1.25rem; } + html.theme--documenter-dark .subtitle.is-6 { + font-size: 1rem; } + html.theme--documenter-dark .subtitle.is-7 { + font-size: 0.75rem; } + html.theme--documenter-dark .heading { + display: block; + font-size: 11px; + letter-spacing: 1px; + margin-bottom: 5px; + text-transform: uppercase; } + html.theme--documenter-dark .highlight { + font-weight: 400; + max-width: 100%; + overflow: hidden; + padding: 0; } + html.theme--documenter-dark .highlight pre { + overflow: auto; + max-width: 100%; } + html.theme--documenter-dark .number { + align-items: center; + background-color: whitesmoke; + border-radius: 290486px; + display: inline-flex; + font-size: 1.25rem; + height: 2em; + justify-content: center; + margin-right: 1.5rem; + min-width: 2.5em; + padding: 0.25rem 0.5rem; + text-align: center; + vertical-align: top; } + html.theme--documenter-dark .select select, html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + background-color: white; + border-color: #dbdbdb; + border-radius: 4px; + color: #363636; } + html.theme--documenter-dark .select select::-moz-placeholder, html.theme--documenter-dark .textarea::-moz-placeholder, html.theme--documenter-dark .input::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select::-webkit-input-placeholder, html.theme--documenter-dark .textarea::-webkit-input-placeholder, html.theme--documenter-dark .input::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:-moz-placeholder, html.theme--documenter-dark .textarea:-moz-placeholder, html.theme--documenter-dark .input:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:-ms-input-placeholder, html.theme--documenter-dark .textarea:-ms-input-placeholder, html.theme--documenter-dark .input:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:hover, html.theme--documenter-dark .textarea:hover, html.theme--documenter-dark .input:hover, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:hover, html.theme--documenter-dark .select select.is-hovered, html.theme--documenter-dark .is-hovered.textarea, html.theme--documenter-dark .is-hovered.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-hovered { + border-color: #149eaa; } + html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + border-color: #fff; + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] html.theme--documenter-dark .select select, fieldset[disabled] html.theme--documenter-dark .textarea, fieldset[disabled] html.theme--documenter-dark .input, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + background-color: whitesmoke; + border-color: whitesmoke; + box-shadow: none; + color: #7a7a7a; } + html.theme--documenter-dark .select select[disabled]::-moz-placeholder, html.theme--documenter-dark .textarea[disabled]::-moz-placeholder, html.theme--documenter-dark .input[disabled]::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .textarea[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .input[disabled]::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]:-moz-placeholder, html.theme--documenter-dark .textarea[disabled]:-moz-placeholder, html.theme--documenter-dark .input[disabled]:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]:-ms-input-placeholder, html.theme--documenter-dark .textarea[disabled]:-ms-input-placeholder, html.theme--documenter-dark .input[disabled]:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); + max-width: 100%; + width: 100%; } + html.theme--documenter-dark .textarea[readonly], html.theme--documenter-dark .input[readonly], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[readonly] { + box-shadow: none; } + html.theme--documenter-dark .is-white.textarea, html.theme--documenter-dark .is-white.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white { + border-color: white; } + html.theme--documenter-dark .is-white.textarea:focus, html.theme--documenter-dark .is-white.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:focus, html.theme--documenter-dark .is-white.is-focused.textarea, html.theme--documenter-dark .is-white.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-white.textarea:active, html.theme--documenter-dark .is-white.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:active, html.theme--documenter-dark .is-white.is-active.textarea, html.theme--documenter-dark .is-white.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .is-black.textarea, html.theme--documenter-dark .is-black.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black { + border-color: #0a0a0a; } + html.theme--documenter-dark .is-black.textarea:focus, html.theme--documenter-dark .is-black.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:focus, html.theme--documenter-dark .is-black.is-focused.textarea, html.theme--documenter-dark .is-black.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-black.textarea:active, html.theme--documenter-dark .is-black.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:active, html.theme--documenter-dark .is-black.is-active.textarea, html.theme--documenter-dark .is-black.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .is-light.textarea, html.theme--documenter-dark .is-light.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light { + border-color: whitesmoke; } + html.theme--documenter-dark .is-light.textarea:focus, html.theme--documenter-dark .is-light.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:focus, html.theme--documenter-dark .is-light.is-focused.textarea, html.theme--documenter-dark .is-light.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-light.textarea:active, html.theme--documenter-dark .is-light.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:active, html.theme--documenter-dark .is-light.is-active.textarea, html.theme--documenter-dark .is-light.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .is-dark.textarea, html.theme--documenter-dark .content kbd.textarea, html.theme--documenter-dark .is-dark.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark, html.theme--documenter-dark .content kbd.input { + border-color: #363636; } + html.theme--documenter-dark .is-dark.textarea:focus, html.theme--documenter-dark .content kbd.textarea:focus, html.theme--documenter-dark .is-dark.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:focus, html.theme--documenter-dark .content kbd.input:focus, html.theme--documenter-dark .is-dark.is-focused.textarea, html.theme--documenter-dark .content kbd.is-focused.textarea, html.theme--documenter-dark .is-dark.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .content kbd.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-focused, html.theme--documenter-dark .is-dark.textarea:active, html.theme--documenter-dark .content kbd.textarea:active, html.theme--documenter-dark .is-dark.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:active, html.theme--documenter-dark .content kbd.input:active, html.theme--documenter-dark .is-dark.is-active.textarea, html.theme--documenter-dark .content kbd.is-active.textarea, html.theme--documenter-dark .is-dark.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .content kbd.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .is-primary.textarea, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink { + border-color: #4eb5de; } + html.theme--documenter-dark .is-primary.textarea:focus, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:focus, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.is-focused.textarea, html.theme--documenter-dark .docstring > section > a.is-focused.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .docstring > section > a.is-focused.input.docs-sourcelink, html.theme--documenter-dark .is-primary.textarea:active, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:active, html.theme--documenter-dark .is-primary.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:active, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:active, html.theme--documenter-dark .is-primary.is-active.textarea, html.theme--documenter-dark .docstring > section > a.is-active.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .docstring > section > a.is-active.input.docs-sourcelink { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .is-link.textarea, html.theme--documenter-dark .is-link.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link { + border-color: #2ad7e6; } + html.theme--documenter-dark .is-link.textarea:focus, html.theme--documenter-dark .is-link.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:focus, html.theme--documenter-dark .is-link.is-focused.textarea, html.theme--documenter-dark .is-link.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-link.textarea:active, html.theme--documenter-dark .is-link.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:active, html.theme--documenter-dark .is-link.is-active.textarea, html.theme--documenter-dark .is-link.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .is-info.textarea, html.theme--documenter-dark .is-info.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info { + border-color: #3489da; } + html.theme--documenter-dark .is-info.textarea:focus, html.theme--documenter-dark .is-info.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:focus, html.theme--documenter-dark .is-info.is-focused.textarea, html.theme--documenter-dark .is-info.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-info.textarea:active, html.theme--documenter-dark .is-info.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:active, html.theme--documenter-dark .is-info.is-active.textarea, html.theme--documenter-dark .is-info.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .is-success.textarea, html.theme--documenter-dark .is-success.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success { + border-color: #259a12; } + html.theme--documenter-dark .is-success.textarea:focus, html.theme--documenter-dark .is-success.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:focus, html.theme--documenter-dark .is-success.is-focused.textarea, html.theme--documenter-dark .is-success.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-success.textarea:active, html.theme--documenter-dark .is-success.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:active, html.theme--documenter-dark .is-success.is-active.textarea, html.theme--documenter-dark .is-success.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .is-warning.textarea, html.theme--documenter-dark .is-warning.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning { + border-color: #f4c72f; } + html.theme--documenter-dark .is-warning.textarea:focus, html.theme--documenter-dark .is-warning.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:focus, html.theme--documenter-dark .is-warning.is-focused.textarea, html.theme--documenter-dark .is-warning.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-warning.textarea:active, html.theme--documenter-dark .is-warning.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:active, html.theme--documenter-dark .is-warning.is-active.textarea, html.theme--documenter-dark .is-warning.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .is-danger.textarea, html.theme--documenter-dark .is-danger.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger { + border-color: #cb3c33; } + html.theme--documenter-dark .is-danger.textarea:focus, html.theme--documenter-dark .is-danger.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:focus, html.theme--documenter-dark .is-danger.is-focused.textarea, html.theme--documenter-dark .is-danger.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-danger.textarea:active, html.theme--documenter-dark .is-danger.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:active, html.theme--documenter-dark .is-danger.is-active.textarea, html.theme--documenter-dark .is-danger.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .is-small.textarea, html.theme--documenter-dark .is-small.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .is-medium.textarea, html.theme--documenter-dark .is-medium.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .is-large.textarea, html.theme--documenter-dark .is-large.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .is-fullwidth.textarea, html.theme--documenter-dark .is-fullwidth.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-fullwidth { + display: block; + width: 100%; } + html.theme--documenter-dark .is-inline.textarea, html.theme--documenter-dark .is-inline.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-inline { + display: inline; + width: auto; } + html.theme--documenter-dark .input.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + html.theme--documenter-dark .input.is-static, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-static { + background-color: transparent; + border-color: transparent; + box-shadow: none; + padding-left: 0; + padding-right: 0; } + html.theme--documenter-dark .textarea { + display: block; + max-width: 100%; + min-width: 100%; + padding: 0.625em; + resize: vertical; } + html.theme--documenter-dark .textarea:not([rows]) { + max-height: 600px; + min-height: 120px; } + html.theme--documenter-dark .textarea[rows] { + height: initial; } + html.theme--documenter-dark .textarea.has-fixed-size { + resize: none; } + html.theme--documenter-dark .radio, html.theme--documenter-dark .checkbox { + cursor: pointer; + display: inline-block; + line-height: 1.25; + position: relative; } + html.theme--documenter-dark .radio input, html.theme--documenter-dark .checkbox input { + cursor: pointer; } + html.theme--documenter-dark .radio:hover, html.theme--documenter-dark .checkbox:hover { + color: #363636; } + html.theme--documenter-dark .radio[disabled], html.theme--documenter-dark .checkbox[disabled], fieldset[disabled] html.theme--documenter-dark .radio, fieldset[disabled] html.theme--documenter-dark .checkbox { + color: #7a7a7a; + cursor: not-allowed; } + html.theme--documenter-dark .radio + .radio { + margin-left: 0.5em; } + html.theme--documenter-dark .select { + display: inline-block; + max-width: 100%; + position: relative; + vertical-align: top; } + html.theme--documenter-dark .select:not(.is-multiple) { + height: 2.25em; } + html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after { + border-color: #2ad7e6; + right: 1.125em; + z-index: 4; } + html.theme--documenter-dark .select.is-rounded select, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select select { + border-radius: 290486px; + padding-left: 1em; } + html.theme--documenter-dark .select select { + cursor: pointer; + display: block; + font-size: 1em; + max-width: 100%; + outline: none; } + html.theme--documenter-dark .select select::-ms-expand { + display: none; } + html.theme--documenter-dark .select select[disabled]:hover, fieldset[disabled] html.theme--documenter-dark .select select:hover { + border-color: whitesmoke; } + html.theme--documenter-dark .select select:not([multiple]) { + padding-right: 2.5em; } + html.theme--documenter-dark .select select[multiple] { + height: auto; + padding: 0; } + html.theme--documenter-dark .select select[multiple] option { + padding: 0.5em 1em; } + html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading):hover::after { + border-color: #363636; } + html.theme--documenter-dark .select.is-white:not(:hover)::after { + border-color: white; } + html.theme--documenter-dark .select.is-white select { + border-color: white; } + html.theme--documenter-dark .select.is-white select:hover, html.theme--documenter-dark .select.is-white select.is-hovered { + border-color: #f2f2f2; } + html.theme--documenter-dark .select.is-white select:focus, html.theme--documenter-dark .select.is-white select.is-focused, html.theme--documenter-dark .select.is-white select:active, html.theme--documenter-dark .select.is-white select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .select.is-black:not(:hover)::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .select.is-black select { + border-color: #0a0a0a; } + html.theme--documenter-dark .select.is-black select:hover, html.theme--documenter-dark .select.is-black select.is-hovered { + border-color: black; } + html.theme--documenter-dark .select.is-black select:focus, html.theme--documenter-dark .select.is-black select.is-focused, html.theme--documenter-dark .select.is-black select:active, html.theme--documenter-dark .select.is-black select.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .select.is-light:not(:hover)::after { + border-color: whitesmoke; } + html.theme--documenter-dark .select.is-light select { + border-color: whitesmoke; } + html.theme--documenter-dark .select.is-light select:hover, html.theme--documenter-dark .select.is-light select.is-hovered { + border-color: #e8e8e8; } + html.theme--documenter-dark .select.is-light select:focus, html.theme--documenter-dark .select.is-light select.is-focused, html.theme--documenter-dark .select.is-light select:active, html.theme--documenter-dark .select.is-light select.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .select.is-dark:not(:hover)::after, html.theme--documenter-dark .content kbd.select:not(:hover)::after { + border-color: #363636; } + html.theme--documenter-dark .select.is-dark select, html.theme--documenter-dark .content kbd.select select { + border-color: #363636; } + html.theme--documenter-dark .select.is-dark select:hover, html.theme--documenter-dark .content kbd.select select:hover, html.theme--documenter-dark .select.is-dark select.is-hovered, html.theme--documenter-dark .content kbd.select select.is-hovered { + border-color: #292929; } + html.theme--documenter-dark .select.is-dark select:focus, html.theme--documenter-dark .content kbd.select select:focus, html.theme--documenter-dark .select.is-dark select.is-focused, html.theme--documenter-dark .content kbd.select select.is-focused, html.theme--documenter-dark .select.is-dark select:active, html.theme--documenter-dark .content kbd.select select:active, html.theme--documenter-dark .select.is-dark select.is-active, html.theme--documenter-dark .content kbd.select select.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .select.is-primary:not(:hover)::after, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink:not(:hover)::after { + border-color: #4eb5de; } + html.theme--documenter-dark .select.is-primary select, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select { + border-color: #4eb5de; } + html.theme--documenter-dark .select.is-primary select:hover, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:hover, html.theme--documenter-dark .select.is-primary select.is-hovered, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-hovered { + border-color: #39acda; } + html.theme--documenter-dark .select.is-primary select:focus, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:focus, html.theme--documenter-dark .select.is-primary select.is-focused, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-focused, html.theme--documenter-dark .select.is-primary select:active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:active, html.theme--documenter-dark .select.is-primary select.is-active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-active { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .select.is-link:not(:hover)::after { + border-color: #2ad7e6; } + html.theme--documenter-dark .select.is-link select { + border-color: #2ad7e6; } + html.theme--documenter-dark .select.is-link select:hover, html.theme--documenter-dark .select.is-link select.is-hovered { + border-color: #1acddc; } + html.theme--documenter-dark .select.is-link select:focus, html.theme--documenter-dark .select.is-link select.is-focused, html.theme--documenter-dark .select.is-link select:active, html.theme--documenter-dark .select.is-link select.is-active { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .select.is-info:not(:hover)::after { + border-color: #3489da; } + html.theme--documenter-dark .select.is-info select { + border-color: #3489da; } + html.theme--documenter-dark .select.is-info select:hover, html.theme--documenter-dark .select.is-info select.is-hovered { + border-color: #267ccf; } + html.theme--documenter-dark .select.is-info select:focus, html.theme--documenter-dark .select.is-info select.is-focused, html.theme--documenter-dark .select.is-info select:active, html.theme--documenter-dark .select.is-info select.is-active { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .select.is-success:not(:hover)::after { + border-color: #259a12; } + html.theme--documenter-dark .select.is-success select { + border-color: #259a12; } + html.theme--documenter-dark .select.is-success select:hover, html.theme--documenter-dark .select.is-success select.is-hovered { + border-color: #20830f; } + html.theme--documenter-dark .select.is-success select:focus, html.theme--documenter-dark .select.is-success select.is-focused, html.theme--documenter-dark .select.is-success select:active, html.theme--documenter-dark .select.is-success select.is-active { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .select.is-warning:not(:hover)::after { + border-color: #f4c72f; } + html.theme--documenter-dark .select.is-warning select { + border-color: #f4c72f; } + html.theme--documenter-dark .select.is-warning select:hover, html.theme--documenter-dark .select.is-warning select.is-hovered { + border-color: #f3c017; } + html.theme--documenter-dark .select.is-warning select:focus, html.theme--documenter-dark .select.is-warning select.is-focused, html.theme--documenter-dark .select.is-warning select:active, html.theme--documenter-dark .select.is-warning select.is-active { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .select.is-danger:not(:hover)::after { + border-color: #cb3c33; } + html.theme--documenter-dark .select.is-danger select { + border-color: #cb3c33; } + html.theme--documenter-dark .select.is-danger select:hover, html.theme--documenter-dark .select.is-danger select.is-hovered { + border-color: #b7362e; } + html.theme--documenter-dark .select.is-danger select:focus, html.theme--documenter-dark .select.is-danger select.is-focused, html.theme--documenter-dark .select.is-danger select:active, html.theme--documenter-dark .select.is-danger select.is-active { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .select.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .select.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .select.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .select.is-disabled::after { + border-color: #7a7a7a; } + html.theme--documenter-dark .select.is-fullwidth { + width: 100%; } + html.theme--documenter-dark .select.is-fullwidth select { + width: 100%; } + html.theme--documenter-dark .select.is-loading::after { + margin-top: 0; + position: absolute; + right: 0.625em; + top: 0.625em; + transform: none; } + html.theme--documenter-dark .select.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + html.theme--documenter-dark .select.is-loading.is-medium:after { + font-size: 1.25rem; } + html.theme--documenter-dark .select.is-loading.is-large:after { + font-size: 1.5rem; } + html.theme--documenter-dark .file { + align-items: stretch; + display: flex; + justify-content: flex-start; + position: relative; } + html.theme--documenter-dark .file.is-white .file-cta { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:hover .file-cta, html.theme--documenter-dark .file.is-white.is-hovered .file-cta { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:focus .file-cta, html.theme--documenter-dark .file.is-white.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:active .file-cta, html.theme--documenter-dark .file.is-white.is-active .file-cta { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-black .file-cta { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-black:hover .file-cta, html.theme--documenter-dark .file.is-black.is-hovered .file-cta { + background-color: #040404; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-black:focus .file-cta, html.theme--documenter-dark .file.is-black.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); + color: white; } + html.theme--documenter-dark .file.is-black:active .file-cta, html.theme--documenter-dark .file.is-black.is-active .file-cta { + background-color: black; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-light .file-cta { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-light:hover .file-cta, html.theme--documenter-dark .file.is-light.is-hovered .file-cta { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-light:focus .file-cta, html.theme--documenter-dark .file.is-light.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25); + color: #363636; } + html.theme--documenter-dark .file.is-light:active .file-cta, html.theme--documenter-dark .file.is-light.is-active .file-cta { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-dark .file-cta, html.theme--documenter-dark .content kbd.file .file-cta { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:hover .file-cta, html.theme--documenter-dark .content kbd.file:hover .file-cta, html.theme--documenter-dark .file.is-dark.is-hovered .file-cta, html.theme--documenter-dark .content kbd.file.is-hovered .file-cta { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:focus .file-cta, html.theme--documenter-dark .content kbd.file:focus .file-cta, html.theme--documenter-dark .file.is-dark.is-focused .file-cta, html.theme--documenter-dark .content kbd.file.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25); + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:active .file-cta, html.theme--documenter-dark .content kbd.file:active .file-cta, html.theme--documenter-dark .file.is-dark.is-active .file-cta, html.theme--documenter-dark .content kbd.file.is-active .file-cta { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-primary .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink .file-cta { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-primary:hover .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:hover .file-cta, html.theme--documenter-dark .file.is-primary.is-hovered .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-primary:focus .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:focus .file-cta, html.theme--documenter-dark .file.is-primary.is-focused .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-primary:active .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:active .file-cta, html.theme--documenter-dark .file.is-primary.is-active .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-active.docs-sourcelink .file-cta { + background-color: #39acda; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link .file-cta { + background-color: #2ad7e6; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link:hover .file-cta, html.theme--documenter-dark .file.is-link.is-hovered .file-cta { + background-color: #1ed5e5; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link:focus .file-cta, html.theme--documenter-dark .file.is-link.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(42, 215, 230, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-link:active .file-cta, html.theme--documenter-dark .file.is-link.is-active .file-cta { + background-color: #1acddc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info .file-cta { + background-color: #3489da; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info:hover .file-cta, html.theme--documenter-dark .file.is-info.is-hovered .file-cta { + background-color: #2983d8; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info:focus .file-cta, html.theme--documenter-dark .file.is-info.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(52, 137, 218, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-info:active .file-cta, html.theme--documenter-dark .file.is-info.is-active .file-cta { + background-color: #267ccf; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success .file-cta { + background-color: #259a12; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success:hover .file-cta, html.theme--documenter-dark .file.is-success.is-hovered .file-cta { + background-color: #228f11; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success:focus .file-cta, html.theme--documenter-dark .file.is-success.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(37, 154, 18, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-success:active .file-cta, html.theme--documenter-dark .file.is-success.is-active .file-cta { + background-color: #20830f; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-warning .file-cta { + background-color: #f4c72f; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:hover .file-cta, html.theme--documenter-dark .file.is-warning.is-hovered .file-cta { + background-color: #f3c423; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:focus .file-cta, html.theme--documenter-dark .file.is-warning.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(244, 199, 47, 0.25); + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:active .file-cta, html.theme--documenter-dark .file.is-warning.is-active .file-cta { + background-color: #f3c017; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-danger .file-cta { + background-color: #cb3c33; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-danger:hover .file-cta, html.theme--documenter-dark .file.is-danger.is-hovered .file-cta { + background-color: #c13930; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-danger:focus .file-cta, html.theme--documenter-dark .file.is-danger.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(203, 60, 51, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-danger:active .file-cta, html.theme--documenter-dark .file.is-danger.is-active .file-cta { + background-color: #b7362e; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.file { + font-size: 0.75rem; } + html.theme--documenter-dark .file.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .file.is-medium .file-icon .fa { + font-size: 21px; } + html.theme--documenter-dark .file.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .file.is-large .file-icon .fa { + font-size: 28px; } + html.theme--documenter-dark .file.has-name .file-cta { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .file.has-name .file-name { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .file.has-name.is-empty .file-cta { + border-radius: 4px; } + html.theme--documenter-dark .file.has-name.is-empty .file-name { + display: none; } + html.theme--documenter-dark .file.is-boxed .file-label { + flex-direction: column; } + html.theme--documenter-dark .file.is-boxed .file-cta { + flex-direction: column; + height: auto; + padding: 1em 3em; } + html.theme--documenter-dark .file.is-boxed .file-name { + border-width: 0 1px 1px; } + html.theme--documenter-dark .file.is-boxed .file-icon { + height: 1.5em; + width: 1.5em; } + html.theme--documenter-dark .file.is-boxed .file-icon .fa { + font-size: 21px; } + html.theme--documenter-dark .file.is-boxed.is-small .file-icon .fa, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { + font-size: 14px; } + html.theme--documenter-dark .file.is-boxed.is-medium .file-icon .fa { + font-size: 28px; } + html.theme--documenter-dark .file.is-boxed.is-large .file-icon .fa { + font-size: 35px; } + html.theme--documenter-dark .file.is-boxed.has-name .file-cta { + border-radius: 4px 4px 0 0; } + html.theme--documenter-dark .file.is-boxed.has-name .file-name { + border-radius: 0 0 4px 4px; + border-width: 0 1px 1px; } + html.theme--documenter-dark .file.is-centered { + justify-content: center; } + html.theme--documenter-dark .file.is-fullwidth .file-label { + width: 100%; } + html.theme--documenter-dark .file.is-fullwidth .file-name { + flex-grow: 1; + max-width: none; } + html.theme--documenter-dark .file.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .file.is-right .file-cta { + border-radius: 0 4px 4px 0; } + html.theme--documenter-dark .file.is-right .file-name { + border-radius: 4px 0 0 4px; + border-width: 1px 0 1px 1px; + order: -1; } + html.theme--documenter-dark .file-label { + align-items: stretch; + display: flex; + cursor: pointer; + justify-content: flex-start; + overflow: hidden; + position: relative; } + html.theme--documenter-dark .file-label:hover .file-cta { + background-color: #eeeeee; + color: #363636; } + html.theme--documenter-dark .file-label:hover .file-name { + border-color: #d5d5d5; } + html.theme--documenter-dark .file-label:active .file-cta { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .file-label:active .file-name { + border-color: #cfcfcf; } + html.theme--documenter-dark .file-input { + height: 100%; + left: 0; + opacity: 0; + outline: none; + position: absolute; + top: 0; + width: 100%; } + html.theme--documenter-dark .file-cta, + html.theme--documenter-dark .file-name { + border-color: #dbdbdb; + border-radius: 4px; + font-size: 1em; + padding-left: 1em; + padding-right: 1em; + white-space: nowrap; } + html.theme--documenter-dark .file-cta { + background-color: whitesmoke; + color: #4a4a4a; } + html.theme--documenter-dark .file-name { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px 1px 1px 0; + display: block; + max-width: 16em; + overflow: hidden; + text-align: left; + text-overflow: ellipsis; } + html.theme--documenter-dark .file-icon { + align-items: center; + display: flex; + height: 1em; + justify-content: center; + margin-right: 0.5em; + width: 1em; } + html.theme--documenter-dark .file-icon .fa { + font-size: 14px; } + html.theme--documenter-dark .label { + color: #363636; + display: block; + font-size: 1rem; + font-weight: 700; } + html.theme--documenter-dark .label:not(:last-child) { + margin-bottom: 0.5em; } + html.theme--documenter-dark .label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.label { + font-size: 0.75rem; } + html.theme--documenter-dark .label.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .label.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .help { + display: block; + font-size: 0.75rem; + margin-top: 0.25rem; } + html.theme--documenter-dark .help.is-white { + color: white; } + html.theme--documenter-dark .help.is-black { + color: #0a0a0a; } + html.theme--documenter-dark .help.is-light { + color: whitesmoke; } + html.theme--documenter-dark .help.is-dark, html.theme--documenter-dark .content kbd.help { + color: #363636; } + html.theme--documenter-dark .help.is-primary, html.theme--documenter-dark .docstring > section > a.help.docs-sourcelink { + color: #4eb5de; } + html.theme--documenter-dark .help.is-link { + color: #2ad7e6; } + html.theme--documenter-dark .help.is-info { + color: #3489da; } + html.theme--documenter-dark .help.is-success { + color: #259a12; } + html.theme--documenter-dark .help.is-warning { + color: #f4c72f; } + html.theme--documenter-dark .help.is-danger { + color: #cb3c33; } + html.theme--documenter-dark .field:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .field.has-addons { + display: flex; + justify-content: flex-start; } + html.theme--documenter-dark .field.has-addons .control:not(:last-child) { + margin-right: -1px; } + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .button, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .input, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .select select { + border-radius: 0; } + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .button, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .input, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .select select { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .button, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .input, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .select select { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-hovered:not([disabled]) { + z-index: 2; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]), html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]) { + z-index: 3; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus:hover, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active:hover, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]):hover { + z-index: 4; } + html.theme--documenter-dark .field.has-addons .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .field.has-addons.has-addons-centered { + justify-content: center; } + html.theme--documenter-dark .field.has-addons.has-addons-right { + justify-content: flex-end; } + html.theme--documenter-dark .field.has-addons.has-addons-fullwidth .control { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .field.is-grouped { + display: flex; + justify-content: flex-start; } + html.theme--documenter-dark .field.is-grouped > .control { + flex-shrink: 0; } + html.theme--documenter-dark .field.is-grouped > .control:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + html.theme--documenter-dark .field.is-grouped > .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .field.is-grouped.is-grouped-centered { + justify-content: center; } + html.theme--documenter-dark .field.is-grouped.is-grouped-right { + justify-content: flex-end; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline { + flex-wrap: wrap; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:last-child, html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:not(:last-child) { + margin-bottom: 0; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field.is-horizontal { + display: flex; } } + html.theme--documenter-dark .field-label .label { + font-size: inherit; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .field-label { + margin-bottom: 0.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field-label { + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + margin-right: 1.5rem; + text-align: right; } + html.theme--documenter-dark .field-label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.field-label { + font-size: 0.75rem; + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-normal { + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-medium { + font-size: 1.25rem; + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-large { + font-size: 1.5rem; + padding-top: 0.375em; } } + html.theme--documenter-dark .field-body .field .field { + margin-bottom: 0; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field-body { + display: flex; + flex-basis: 0; + flex-grow: 5; + flex-shrink: 1; } + html.theme--documenter-dark .field-body .field { + margin-bottom: 0; } + html.theme--documenter-dark .field-body > .field { + flex-shrink: 1; } + html.theme--documenter-dark .field-body > .field:not(.is-narrow) { + flex-grow: 1; } + html.theme--documenter-dark .field-body > .field:not(:last-child) { + margin-right: 0.75rem; } } + html.theme--documenter-dark .control { + box-sizing: border-box; + clear: both; + font-size: 1rem; + position: relative; + text-align: left; } + html.theme--documenter-dark .control.has-icons-left .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select:focus ~ .icon { + color: #7a7a7a; } + html.theme--documenter-dark .control.has-icons-left .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-small ~ .icon { + font-size: 0.75rem; } + html.theme--documenter-dark .control.has-icons-left .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-medium ~ .icon { + font-size: 1.25rem; } + html.theme--documenter-dark .control.has-icons-left .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-large ~ .icon { + font-size: 1.5rem; } + html.theme--documenter-dark .control.has-icons-left .icon, html.theme--documenter-dark .control.has-icons-right .icon { + color: #dbdbdb; + height: 2.25em; + pointer-events: none; + position: absolute; + top: 0; + width: 2.25em; + z-index: 4; } + html.theme--documenter-dark .control.has-icons-left .input, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, + html.theme--documenter-dark .control.has-icons-left .select select { + padding-left: 2.25em; } + html.theme--documenter-dark .control.has-icons-left .icon.is-left { + left: 0; } + html.theme--documenter-dark .control.has-icons-right .input, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, + html.theme--documenter-dark .control.has-icons-right .select select { + padding-right: 2.25em; } + html.theme--documenter-dark .control.has-icons-right .icon.is-right { + right: 0; } + html.theme--documenter-dark .control.is-loading::after { + position: absolute !important; + right: 0.625em; + top: 0.625em; + z-index: 4; } + html.theme--documenter-dark .control.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + html.theme--documenter-dark .control.is-loading.is-medium:after { + font-size: 1.25rem; } + html.theme--documenter-dark .control.is-loading.is-large:after { + font-size: 1.5rem; } + html.theme--documenter-dark .breadcrumb { + font-size: 1rem; + white-space: nowrap; } + html.theme--documenter-dark .breadcrumb a { + align-items: center; + color: #2ad7e6; + display: flex; + justify-content: center; + padding: 0 0.75em; } + html.theme--documenter-dark .breadcrumb a:hover { + color: #97ebf3; } + html.theme--documenter-dark .breadcrumb li { + align-items: center; + display: flex; } + html.theme--documenter-dark .breadcrumb li:first-child a { + padding-left: 0; } + html.theme--documenter-dark .breadcrumb li.is-active a { + color: #cdc3e3; + cursor: default; + pointer-events: none; } + html.theme--documenter-dark .breadcrumb li + li::before { + color: #b5b5b5; + content: "\0002f"; } + html.theme--documenter-dark .breadcrumb ul, + html.theme--documenter-dark .breadcrumb ol { + align-items: flex-start; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .breadcrumb .icon:first-child { + margin-right: 0.5em; } + html.theme--documenter-dark .breadcrumb .icon:last-child { + margin-left: 0.5em; } + html.theme--documenter-dark .breadcrumb.is-centered ol, + html.theme--documenter-dark .breadcrumb.is-centered ul { + justify-content: center; } + html.theme--documenter-dark .breadcrumb.is-right ol, + html.theme--documenter-dark .breadcrumb.is-right ul { + justify-content: flex-end; } + html.theme--documenter-dark .breadcrumb.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.breadcrumb { + font-size: 0.75rem; } + html.theme--documenter-dark .breadcrumb.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .breadcrumb.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .breadcrumb.has-arrow-separator li + li::before { + content: "\02192"; } + html.theme--documenter-dark .breadcrumb.has-bullet-separator li + li::before { + content: "\02022"; } + html.theme--documenter-dark .breadcrumb.has-dot-separator li + li::before { + content: "\000b7"; } + html.theme--documenter-dark .breadcrumb.has-succeeds-separator li + li::before { + content: "\0227B"; } + html.theme--documenter-dark .card { + background-color: white; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #fbfbfb; + max-width: 100%; + position: relative; } + html.theme--documenter-dark .card-header { + background-color: transparent; + align-items: stretch; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + display: flex; } + html.theme--documenter-dark .card-header-title { + align-items: center; + color: #cdc3e3; + display: flex; + flex-grow: 1; + font-weight: 700; + padding: 0.75rem; } + html.theme--documenter-dark .card-header-title.is-centered { + justify-content: center; } + html.theme--documenter-dark .card-header-icon { + align-items: center; + cursor: pointer; + display: flex; + justify-content: center; + padding: 0.75rem; } + html.theme--documenter-dark .card-image { + display: block; + position: relative; } + html.theme--documenter-dark .card-content { + background-color: transparent; + padding: 1.5rem; } + html.theme--documenter-dark .card-footer { + background-color: transparent; + border-top: 1px solid #dbdbdb; + align-items: stretch; + display: flex; } + html.theme--documenter-dark .card-footer-item { + align-items: center; + display: flex; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + justify-content: center; + padding: 0.75rem; } + html.theme--documenter-dark .card-footer-item:not(:last-child) { + border-right: 1px solid #dbdbdb; } + html.theme--documenter-dark .card .media:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .dropdown { + display: inline-flex; + position: relative; + vertical-align: top; } + html.theme--documenter-dark .dropdown.is-active .dropdown-menu, html.theme--documenter-dark .dropdown.is-hoverable:hover .dropdown-menu { + display: block; } + html.theme--documenter-dark .dropdown.is-right .dropdown-menu { + left: auto; + right: 0; } + html.theme--documenter-dark .dropdown.is-up .dropdown-menu { + bottom: 100%; + padding-bottom: 4px; + padding-top: initial; + top: auto; } + html.theme--documenter-dark .dropdown-menu { + display: none; + left: 0; + min-width: 12rem; + padding-top: 4px; + position: absolute; + top: 100%; + z-index: 20; } + html.theme--documenter-dark .dropdown-content { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + html.theme--documenter-dark .dropdown-item { + color: #4a4a4a; + display: block; + font-size: 0.875rem; + line-height: 1.5; + padding: 0.375rem 1rem; + position: relative; } + html.theme--documenter-dark a.dropdown-item, + html.theme--documenter-dark button.dropdown-item { + padding-right: 3rem; + text-align: left; + white-space: nowrap; + width: 100%; } + html.theme--documenter-dark a.dropdown-item:hover, + html.theme--documenter-dark button.dropdown-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark a.dropdown-item.is-active, + html.theme--documenter-dark button.dropdown-item.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .dropdown-divider { + background-color: #dbdbdb; + border: none; + display: block; + height: 1px; + margin: 0.5rem 0; } + html.theme--documenter-dark .level { + align-items: center; + justify-content: space-between; } + html.theme--documenter-dark .level code { + border-radius: 4px; } + html.theme--documenter-dark .level img { + display: inline-block; + vertical-align: top; } + html.theme--documenter-dark .level.is-mobile { + display: flex; } + html.theme--documenter-dark .level.is-mobile .level-left, + html.theme--documenter-dark .level.is-mobile .level-right { + display: flex; } + html.theme--documenter-dark .level.is-mobile .level-left + .level-right { + margin-top: 0; } + html.theme--documenter-dark .level.is-mobile .level-item:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + html.theme--documenter-dark .level.is-mobile .level-item:not(.is-narrow) { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level { + display: flex; } + html.theme--documenter-dark .level > .level-item:not(.is-narrow) { + flex-grow: 1; } } + html.theme--documenter-dark .level-item { + align-items: center; + display: flex; + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; + justify-content: center; } + html.theme--documenter-dark .level-item .title, + html.theme--documenter-dark .level-item .subtitle { + margin-bottom: 0; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .level-item:not(:last-child) { + margin-bottom: 0.75rem; } } + html.theme--documenter-dark .level-left, + html.theme--documenter-dark .level-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .level-left .level-item.is-flexible, + html.theme--documenter-dark .level-right .level-item.is-flexible { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-left .level-item:not(:last-child), + html.theme--documenter-dark .level-right .level-item:not(:last-child) { + margin-right: 0.75rem; } } + html.theme--documenter-dark .level-left { + align-items: center; + justify-content: flex-start; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .level-left + .level-right { + margin-top: 1.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-left { + display: flex; } } + html.theme--documenter-dark .level-right { + align-items: center; + justify-content: flex-end; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-right { + display: flex; } } + html.theme--documenter-dark .list { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .list-item { + display: block; + padding: 0.5em 1em; } + html.theme--documenter-dark .list-item:not(a) { + color: #fbfbfb; } + html.theme--documenter-dark .list-item:first-child { + border-top-left-radius: 4px; + border-top-right-radius: 4px; } + html.theme--documenter-dark .list-item:last-child { + border-bottom-left-radius: 4px; + border-bottom-right-radius: 4px; } + html.theme--documenter-dark .list-item:not(:last-child) { + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .list-item.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark a.list-item { + background-color: whitesmoke; + cursor: pointer; } + html.theme--documenter-dark .media { + align-items: flex-start; + display: flex; + text-align: left; } + html.theme--documenter-dark .media .content:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .media .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + display: flex; + padding-top: 0.75rem; } + html.theme--documenter-dark .media .media .content:not(:last-child), + html.theme--documenter-dark .media .media .control:not(:last-child) { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .media .media .media { + padding-top: 0.5rem; } + html.theme--documenter-dark .media .media .media + .media { + margin-top: 0.5rem; } + html.theme--documenter-dark .media + .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + margin-top: 1rem; + padding-top: 1rem; } + html.theme--documenter-dark .media.is-large + .media { + margin-top: 1.5rem; + padding-top: 1.5rem; } + html.theme--documenter-dark .media-left, + html.theme--documenter-dark .media-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .media-left { + margin-right: 1rem; } + html.theme--documenter-dark .media-right { + margin-left: 1rem; } + html.theme--documenter-dark .media-content { + flex-basis: auto; + flex-grow: 1; + flex-shrink: 1; + text-align: left; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .media-content { + overflow-x: auto; } } + html.theme--documenter-dark .menu { + font-size: 1rem; } + html.theme--documenter-dark .menu.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.menu { + font-size: 0.75rem; } + html.theme--documenter-dark .menu.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .menu.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .menu-list { + line-height: 1.25; } + html.theme--documenter-dark .menu-list a { + border-radius: 2px; + color: #fbfbfb; + display: block; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .menu-list a:hover { + background-color: whitesmoke; + color: #cdc3e3; } + html.theme--documenter-dark .menu-list a.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .menu-list li ul { + border-left: 1px solid #dbdbdb; + margin: 0.75em; + padding-left: 0.75em; } + html.theme--documenter-dark .menu-label { + color: #7a7a7a; + font-size: 0.75em; + letter-spacing: 0.1em; + text-transform: uppercase; } + html.theme--documenter-dark .menu-label:not(:first-child) { + margin-top: 1em; } + html.theme--documenter-dark .menu-label:not(:last-child) { + margin-bottom: 1em; } + html.theme--documenter-dark .message { + background-color: whitesmoke; + border-radius: 4px; + font-size: 1rem; } + html.theme--documenter-dark .message strong { + color: currentColor; } + html.theme--documenter-dark .message a:not(.button):not(.tag):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + html.theme--documenter-dark .message.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.message { + font-size: 0.75rem; } + html.theme--documenter-dark .message.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .message.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .message.is-white { + background-color: white; } + html.theme--documenter-dark .message.is-white .message-header { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .message.is-white .message-body { + border-color: white; + color: #4d4d4d; } + html.theme--documenter-dark .message.is-black { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-black .message-header { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .message.is-black .message-body { + border-color: #0a0a0a; + color: #090909; } + html.theme--documenter-dark .message.is-light { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-light .message-header { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .message.is-light .message-body { + border-color: whitesmoke; + color: #505050; } + html.theme--documenter-dark .message.is-dark, html.theme--documenter-dark .content kbd.message { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-dark .message-header, html.theme--documenter-dark .content kbd.message .message-header { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .message.is-dark .message-body, html.theme--documenter-dark .content kbd.message .message-body { + border-color: #363636; + color: #2a2a2a; } + html.theme--documenter-dark .message.is-primary, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink { + background-color: #f6fbfd; } + html.theme--documenter-dark .message.is-primary .message-header, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-header { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .message.is-primary .message-body, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-body { + border-color: #4eb5de; + color: #1f556a; } + html.theme--documenter-dark .message.is-link { + background-color: #f6fdfe; } + html.theme--documenter-dark .message.is-link .message-header { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .message.is-link .message-body { + border-color: #2ad7e6; + color: #0c2f32; } + html.theme--documenter-dark .message.is-info { + background-color: #f6fafd; } + html.theme--documenter-dark .message.is-info .message-header { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .message.is-info .message-body { + border-color: #3489da; + color: #215485; } + html.theme--documenter-dark .message.is-success { + background-color: #f7fef6; } + html.theme--documenter-dark .message.is-success .message-header { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .message.is-success .message-body { + border-color: #259a12; + color: #113b0a; } + html.theme--documenter-dark .message.is-warning { + background-color: #fefcf5; } + html.theme--documenter-dark .message.is-warning .message-header { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .message.is-warning .message-body { + border-color: #f4c72f; + color: #332909; } + html.theme--documenter-dark .message.is-danger { + background-color: #fdf7f7; } + html.theme--documenter-dark .message.is-danger .message-header { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .message.is-danger .message-body { + border-color: #cb3c33; + color: #8d302a; } + html.theme--documenter-dark .message-header { + align-items: center; + background-color: #fbfbfb; + border-radius: 4px 4px 0 0; + color: rgba(0, 0, 0, 0.7); + display: flex; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.75em 1em; + position: relative; } + html.theme--documenter-dark .message-header .delete { + flex-grow: 0; + flex-shrink: 0; + margin-left: 0.75em; } + html.theme--documenter-dark .message-header + .message-body { + border-width: 0; + border-top-left-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .message-body { + border-color: #dbdbdb; + border-radius: 4px; + border-style: solid; + border-width: 0 0 0 4px; + color: #fbfbfb; + padding: 1.25em 1.5em; } + html.theme--documenter-dark .message-body code, + html.theme--documenter-dark .message-body pre { + background-color: white; } + html.theme--documenter-dark .message-body pre code { + background-color: transparent; } + html.theme--documenter-dark .modal { + align-items: center; + display: none; + flex-direction: column; + justify-content: center; + overflow: hidden; + position: fixed; + z-index: 40; } + html.theme--documenter-dark .modal.is-active { + display: flex; } + html.theme--documenter-dark .modal-background { + background-color: rgba(10, 10, 10, 0.86); } + html.theme--documenter-dark .modal-content, + html.theme--documenter-dark .modal-card { + margin: 0 20px; + max-height: calc(100vh - 160px); + overflow: auto; + position: relative; + width: 100%; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .modal-content, + html.theme--documenter-dark .modal-card { + margin: 0 auto; + max-height: calc(100vh - 40px); + width: 640px; } } + html.theme--documenter-dark .modal-close { + background: none; + height: 40px; + position: fixed; + right: 20px; + top: 20px; + width: 40px; } + html.theme--documenter-dark .modal-card { + display: flex; + flex-direction: column; + max-height: calc(100vh - 40px); + overflow: hidden; + -ms-overflow-y: visible; } + html.theme--documenter-dark .modal-card-head, + html.theme--documenter-dark .modal-card-foot { + align-items: center; + background-color: whitesmoke; + display: flex; + flex-shrink: 0; + justify-content: flex-start; + padding: 20px; + position: relative; } + html.theme--documenter-dark .modal-card-head { + border-bottom: 1px solid #dbdbdb; + border-top-left-radius: 6px; + border-top-right-radius: 6px; } + html.theme--documenter-dark .modal-card-title { + color: #cdc3e3; + flex-grow: 1; + flex-shrink: 0; + font-size: 1.5rem; + line-height: 1; } + html.theme--documenter-dark .modal-card-foot { + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark .modal-card-foot .button:not(:last-child) { + margin-right: 0.5em; } + html.theme--documenter-dark .modal-card-body { + -webkit-overflow-scrolling: touch; + background-color: white; + flex-grow: 1; + flex-shrink: 1; + overflow: auto; + padding: 20px; } + html.theme--documenter-dark .navbar { + background-color: white; + min-height: 3.25rem; + position: relative; + z-index: 30; } + html.theme--documenter-dark .navbar.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link { + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-burger { + color: #0a0a0a; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-white .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link { + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-dropdown a.navbar-item.is-active { + background-color: white; + color: #0a0a0a; } } + html.theme--documenter-dark .navbar.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link { + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link::after { + border-color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-burger { + color: white; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-black .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link { + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link::after { + border-color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-dropdown a.navbar-item.is-active { + background-color: #0a0a0a; + color: white; } } + html.theme--documenter-dark .navbar.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link { + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link::after { + border-color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-burger { + color: #363636; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-light .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link { + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link::after { + border-color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #363636; } } + html.theme--documenter-dark .navbar.is-dark, html.theme--documenter-dark .content kbd.navbar { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link { + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link::after { + border-color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-burger, html.theme--documenter-dark .content kbd.navbar .navbar-burger { + color: whitesmoke; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-dark .navbar-start > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-end > .navbar-item, + html.theme--documenter-dark .content kbd.navbar .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link { + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link::after, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link::after { + border-color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { + background-color: #363636; + color: whitesmoke; } } + html.theme--documenter-dark .navbar.is-primary, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-burger, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-primary .navbar-start > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-end > .navbar-item, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link::after, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { + background-color: #4eb5de; + color: #fff; } } + html.theme--documenter-dark .navbar.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-link .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-dropdown a.navbar-item.is-active { + background-color: #2ad7e6; + color: #fff; } } + html.theme--documenter-dark .navbar.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-info .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-dropdown a.navbar-item.is-active { + background-color: #3489da; + color: #fff; } } + html.theme--documenter-dark .navbar.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-success .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-dropdown a.navbar-item.is-active { + background-color: #259a12; + color: #fff; } } + html.theme--documenter-dark .navbar.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-burger { + color: rgba(0, 0, 0, 0.7); } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-warning .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } } + html.theme--documenter-dark .navbar.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-danger .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { + background-color: #cb3c33; + color: #fff; } } + html.theme--documenter-dark .navbar > .container { + align-items: stretch; + display: flex; + min-height: 3.25rem; + width: 100%; } + html.theme--documenter-dark .navbar.has-shadow { + box-shadow: 0 2px 0 0 whitesmoke; } + html.theme--documenter-dark .navbar.is-fixed-bottom, html.theme--documenter-dark .navbar.is-fixed-top { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom.has-shadow { + box-shadow: 0 -2px 0 0 whitesmoke; } + html.theme--documenter-dark .navbar.is-fixed-top { + top: 0; } + html.theme--documenter-dark html.has-navbar-fixed-top, + html.theme--documenter-dark body.has-navbar-fixed-top { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom, + html.theme--documenter-dark body.has-navbar-fixed-bottom { + padding-bottom: 3.25rem; } + html.theme--documenter-dark .navbar-brand, + html.theme--documenter-dark .navbar-tabs { + align-items: stretch; + display: flex; + flex-shrink: 0; + min-height: 3.25rem; } + html.theme--documenter-dark .navbar-brand a.navbar-item:focus, html.theme--documenter-dark .navbar-brand a.navbar-item:hover { + background-color: transparent; } + html.theme--documenter-dark .navbar-tabs { + -webkit-overflow-scrolling: touch; + max-width: 100vw; + overflow-x: auto; + overflow-y: hidden; } + html.theme--documenter-dark .navbar-burger { + color: #4a4a4a; + cursor: pointer; + display: block; + height: 3.25rem; + position: relative; + width: 3.25rem; + margin-left: auto; } + html.theme--documenter-dark .navbar-burger span { + background-color: currentColor; + display: block; + height: 1px; + left: calc(50% - 8px); + position: absolute; + transform-origin: center; + transition-duration: 86ms; + transition-property: background-color, opacity, transform; + transition-timing-function: ease-out; + width: 16px; } + html.theme--documenter-dark .navbar-burger span:nth-child(1) { + top: calc(50% - 6px); } + html.theme--documenter-dark .navbar-burger span:nth-child(2) { + top: calc(50% - 1px); } + html.theme--documenter-dark .navbar-burger span:nth-child(3) { + top: calc(50% + 4px); } + html.theme--documenter-dark .navbar-burger:hover { + background-color: rgba(0, 0, 0, 0.05); } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(1) { + transform: translateY(5px) rotate(45deg); } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(2) { + opacity: 0; } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(3) { + transform: translateY(-5px) rotate(-45deg); } + html.theme--documenter-dark .navbar-menu { + display: none; } + html.theme--documenter-dark .navbar-item, + html.theme--documenter-dark .navbar-link { + color: #4a4a4a; + display: block; + line-height: 1.5; + padding: 0.5rem 0.75rem; + position: relative; } + html.theme--documenter-dark .navbar-item .icon:only-child, + html.theme--documenter-dark .navbar-link .icon:only-child { + margin-left: -0.25rem; + margin-right: -0.25rem; } + html.theme--documenter-dark a.navbar-item, + html.theme--documenter-dark .navbar-link { + cursor: pointer; } + html.theme--documenter-dark a.navbar-item:focus, html.theme--documenter-dark a.navbar-item:focus-within, html.theme--documenter-dark a.navbar-item:hover, html.theme--documenter-dark a.navbar-item.is-active, + html.theme--documenter-dark .navbar-link:focus, + html.theme--documenter-dark .navbar-link:focus-within, + html.theme--documenter-dark .navbar-link:hover, + html.theme--documenter-dark .navbar-link.is-active { + background-color: #fafafa; + color: #2ad7e6; } + html.theme--documenter-dark .navbar-item { + display: block; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .navbar-item img { + max-height: 1.75rem; } + html.theme--documenter-dark .navbar-item.has-dropdown { + padding: 0; } + html.theme--documenter-dark .navbar-item.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .navbar-item.is-tab { + border-bottom: 1px solid transparent; + min-height: 3.25rem; + padding-bottom: calc(0.5rem - 1px); } + html.theme--documenter-dark .navbar-item.is-tab:focus, html.theme--documenter-dark .navbar-item.is-tab:hover { + background-color: transparent; + border-bottom-color: #2ad7e6; } + html.theme--documenter-dark .navbar-item.is-tab.is-active { + background-color: transparent; + border-bottom-color: #2ad7e6; + border-bottom-style: solid; + border-bottom-width: 3px; + color: #2ad7e6; + padding-bottom: calc(0.5rem - 3px); } + html.theme--documenter-dark .navbar-content { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .navbar-link:not(.is-arrowless) { + padding-right: 2.5em; } + html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after { + border-color: #2ad7e6; + margin-top: -0.375em; + right: 1.125em; } + html.theme--documenter-dark .navbar-dropdown { + font-size: 0.875rem; + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + html.theme--documenter-dark .navbar-dropdown .navbar-item { + padding-left: 1.5rem; + padding-right: 1.5rem; } + html.theme--documenter-dark .navbar-divider { + background-color: whitesmoke; + border: none; + display: none; + height: 2px; + margin: 0.5rem 0; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .navbar > .container { + display: block; } + html.theme--documenter-dark .navbar-brand .navbar-item, + html.theme--documenter-dark .navbar-tabs .navbar-item { + align-items: center; + display: flex; } + html.theme--documenter-dark .navbar-link::after { + display: none; } + html.theme--documenter-dark .navbar-menu { + background-color: white; + box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); + padding: 0.5rem 0; } + html.theme--documenter-dark .navbar-menu.is-active { + display: block; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch, html.theme--documenter-dark .navbar.is-fixed-top-touch { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .navbar.is-fixed-top-touch { + top: 0; } + html.theme--documenter-dark .navbar.is-fixed-top .navbar-menu, html.theme--documenter-dark .navbar.is-fixed-top-touch .navbar-menu { + -webkit-overflow-scrolling: touch; + max-height: calc(100vh - 3.25rem); + overflow: auto; } + html.theme--documenter-dark html.has-navbar-fixed-top-touch, + html.theme--documenter-dark body.has-navbar-fixed-top-touch { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom-touch, + html.theme--documenter-dark body.has-navbar-fixed-bottom-touch { + padding-bottom: 3.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar, + html.theme--documenter-dark .navbar-menu, + html.theme--documenter-dark .navbar-start, + html.theme--documenter-dark .navbar-end { + align-items: stretch; + display: flex; } + html.theme--documenter-dark .navbar { + min-height: 3.25rem; } + html.theme--documenter-dark .navbar.is-spaced { + padding: 1rem 2rem; } + html.theme--documenter-dark .navbar.is-spaced .navbar-start, + html.theme--documenter-dark .navbar.is-spaced .navbar-end { + align-items: center; } + html.theme--documenter-dark .navbar.is-spaced a.navbar-item, + html.theme--documenter-dark .navbar.is-spaced .navbar-link { + border-radius: 4px; } + html.theme--documenter-dark .navbar.is-transparent a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent a.navbar-item:hover, html.theme--documenter-dark .navbar.is-transparent a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-transparent .navbar-link:focus, + html.theme--documenter-dark .navbar.is-transparent .navbar-link:hover, + html.theme--documenter-dark .navbar.is-transparent .navbar-link.is-active { + background-color: transparent !important; } + html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { + background-color: transparent !important; } + html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #2ad7e6; } + html.theme--documenter-dark .navbar-burger { + display: none; } + html.theme--documenter-dark .navbar-item, + html.theme--documenter-dark .navbar-link { + align-items: center; + display: flex; } + html.theme--documenter-dark .navbar-item { + display: flex; } + html.theme--documenter-dark .navbar-item.has-dropdown { + align-items: stretch; } + html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-link::after { + transform: rotate(135deg) translate(0.25em, -0.25em); } + html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-dropdown { + border-bottom: 2px solid #dbdbdb; + border-radius: 6px 6px 0 0; + border-top: none; + bottom: 100%; + box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); + top: auto; } + html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown { + display: block; } + .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { + opacity: 1; + pointer-events: auto; + transform: translateY(0); } + html.theme--documenter-dark .navbar-menu { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .navbar-start { + justify-content: flex-start; + margin-right: auto; } + html.theme--documenter-dark .navbar-end { + justify-content: flex-end; + margin-left: auto; } + html.theme--documenter-dark .navbar-dropdown { + background-color: white; + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 2px solid #dbdbdb; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); + display: none; + font-size: 0.875rem; + left: 0; + min-width: 100%; + position: absolute; + top: 100%; + z-index: 20; } + html.theme--documenter-dark .navbar-dropdown .navbar-item { + padding: 0.375rem 1rem; + white-space: nowrap; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item { + padding-right: 3rem; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #2ad7e6; } + .navbar.is-spaced html.theme--documenter-dark .navbar-dropdown, html.theme--documenter-dark .navbar-dropdown.is-boxed { + border-radius: 6px; + border-top: none; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + display: block; + opacity: 0; + pointer-events: none; + top: calc(100% + (-4px)); + transform: translateY(-5px); + transition-duration: 86ms; + transition-property: opacity, transform; } + html.theme--documenter-dark .navbar-dropdown.is-right { + left: auto; + right: 0; } + html.theme--documenter-dark .navbar-divider { + display: block; } + html.theme--documenter-dark .navbar > .container .navbar-brand, + html.theme--documenter-dark .container > .navbar .navbar-brand { + margin-left: -.75rem; } + html.theme--documenter-dark .navbar > .container .navbar-menu, + html.theme--documenter-dark .container > .navbar .navbar-menu { + margin-right: -.75rem; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop, html.theme--documenter-dark .navbar.is-fixed-top-desktop { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .navbar.is-fixed-top-desktop { + top: 0; } + html.theme--documenter-dark html.has-navbar-fixed-top-desktop, + html.theme--documenter-dark body.has-navbar-fixed-top-desktop { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop, + html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop { + padding-bottom: 3.25rem; } + html.theme--documenter-dark html.has-spaced-navbar-fixed-top, + html.theme--documenter-dark body.has-spaced-navbar-fixed-top { + padding-top: 5.25rem; } + html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom, + html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom { + padding-bottom: 5.25rem; } + html.theme--documenter-dark a.navbar-item.is-active, + html.theme--documenter-dark .navbar-link.is-active { + color: #0a0a0a; } + html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover), + html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover) { + background-color: transparent; } + html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #fafafa; } } + html.theme--documenter-dark .hero.is-fullheight-with-navbar { + min-height: calc(100vh - 3.25rem); } + html.theme--documenter-dark .pagination { + font-size: 1rem; + margin: -0.25rem; } + html.theme--documenter-dark .pagination.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination { + font-size: 0.75rem; } + html.theme--documenter-dark .pagination.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .pagination.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .pagination.is-rounded .pagination-previous, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, + html.theme--documenter-dark .pagination.is-rounded .pagination-next, + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { + padding-left: 1em; + padding-right: 1em; + border-radius: 290486px; } + html.theme--documenter-dark .pagination.is-rounded .pagination-link, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { + border-radius: 290486px; } + html.theme--documenter-dark .pagination, + html.theme--documenter-dark .pagination-list { + align-items: center; + display: flex; + justify-content: center; + text-align: center; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark .pagination-link, + html.theme--documenter-dark .pagination-ellipsis { + font-size: 1em; + justify-content: center; + margin: 0.25rem; + padding-left: 0.5em; + padding-right: 0.5em; + text-align: center; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark .pagination-link { + border-color: #dbdbdb; + color: #363636; + min-width: 2.25em; } + html.theme--documenter-dark .pagination-previous:hover, + html.theme--documenter-dark .pagination-next:hover, + html.theme--documenter-dark .pagination-link:hover { + border-color: #b5b5b5; + color: #97ebf3; } + html.theme--documenter-dark .pagination-previous:focus, + html.theme--documenter-dark .pagination-next:focus, + html.theme--documenter-dark .pagination-link:focus { + border-color: #3c5dcd; } + html.theme--documenter-dark .pagination-previous:active, + html.theme--documenter-dark .pagination-next:active, + html.theme--documenter-dark .pagination-link:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } + html.theme--documenter-dark .pagination-previous[disabled], + html.theme--documenter-dark .pagination-next[disabled], + html.theme--documenter-dark .pagination-link[disabled] { + background-color: #dbdbdb; + border-color: #dbdbdb; + box-shadow: none; + color: #7a7a7a; + opacity: 0.5; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next { + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + html.theme--documenter-dark .pagination-link.is-current { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .pagination-ellipsis { + color: #b5b5b5; + pointer-events: none; } + html.theme--documenter-dark .pagination-list { + flex-wrap: wrap; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .pagination { + flex-wrap: wrap; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .pagination-list li { + flex-grow: 1; + flex-shrink: 1; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .pagination-list { + flex-grow: 1; + flex-shrink: 1; + justify-content: flex-start; + order: 1; } + html.theme--documenter-dark .pagination-previous { + order: 2; } + html.theme--documenter-dark .pagination-next { + order: 3; } + html.theme--documenter-dark .pagination { + justify-content: space-between; } + html.theme--documenter-dark .pagination.is-centered .pagination-previous { + order: 1; } + html.theme--documenter-dark .pagination.is-centered .pagination-list { + justify-content: center; + order: 2; } + html.theme--documenter-dark .pagination.is-centered .pagination-next { + order: 3; } + html.theme--documenter-dark .pagination.is-right .pagination-previous { + order: 1; } + html.theme--documenter-dark .pagination.is-right .pagination-next { + order: 2; } + html.theme--documenter-dark .pagination.is-right .pagination-list { + justify-content: flex-end; + order: 3; } } + html.theme--documenter-dark .panel { + font-size: 1rem; } + html.theme--documenter-dark .panel:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .panel-heading, + html.theme--documenter-dark .panel-tabs, + html.theme--documenter-dark .panel-block { + border-bottom: 1px solid #dbdbdb; + border-left: 1px solid #dbdbdb; + border-right: 1px solid #dbdbdb; } + html.theme--documenter-dark .panel-heading:first-child, + html.theme--documenter-dark .panel-tabs:first-child, + html.theme--documenter-dark .panel-block:first-child { + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark .panel-heading { + background-color: whitesmoke; + border-radius: 4px 4px 0 0; + color: #cdc3e3; + font-size: 1.25em; + font-weight: 300; + line-height: 1.25; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .panel-tabs { + align-items: flex-end; + display: flex; + font-size: 0.875em; + justify-content: center; } + html.theme--documenter-dark .panel-tabs a { + border-bottom: 1px solid #dbdbdb; + margin-bottom: -1px; + padding: 0.5em; } + html.theme--documenter-dark .panel-tabs a.is-active { + border-bottom-color: #4a4a4a; + color: #363636; } + html.theme--documenter-dark .panel-list a { + color: #fbfbfb; } + html.theme--documenter-dark .panel-list a:hover { + color: #2ad7e6; } + html.theme--documenter-dark .panel-block { + align-items: center; + color: #cdc3e3; + display: flex; + justify-content: flex-start; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .panel-block input[type="checkbox"] { + margin-right: 0.75em; } + html.theme--documenter-dark .panel-block > .control { + flex-grow: 1; + flex-shrink: 1; + width: 100%; } + html.theme--documenter-dark .panel-block.is-wrapped { + flex-wrap: wrap; } + html.theme--documenter-dark .panel-block.is-active { + border-left-color: #2ad7e6; + color: #363636; } + html.theme--documenter-dark .panel-block.is-active .panel-icon { + color: #2ad7e6; } + html.theme--documenter-dark a.panel-block, + html.theme--documenter-dark label.panel-block { + cursor: pointer; } + html.theme--documenter-dark a.panel-block:hover, + html.theme--documenter-dark label.panel-block:hover { + background-color: whitesmoke; } + html.theme--documenter-dark .panel-icon { + display: inline-block; + font-size: 14px; + height: 1em; + line-height: 1em; + text-align: center; + vertical-align: top; + width: 1em; + color: #7a7a7a; + margin-right: 0.75em; } + html.theme--documenter-dark .panel-icon .fa { + font-size: inherit; + line-height: inherit; } + html.theme--documenter-dark .tabs { + -webkit-overflow-scrolling: touch; + align-items: stretch; + display: flex; + font-size: 1rem; + justify-content: space-between; + overflow: hidden; + overflow-x: auto; + white-space: nowrap; } + html.theme--documenter-dark .tabs a { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + color: #fbfbfb; + display: flex; + justify-content: center; + margin-bottom: -1px; + padding: 0.5em 1em; + vertical-align: top; } + html.theme--documenter-dark .tabs a:hover { + border-bottom-color: #cdc3e3; + color: #cdc3e3; } + html.theme--documenter-dark .tabs li { + display: block; } + html.theme--documenter-dark .tabs li.is-active a { + border-bottom-color: #2ad7e6; + color: #2ad7e6; } + html.theme--documenter-dark .tabs ul { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + display: flex; + flex-grow: 1; + flex-shrink: 0; + justify-content: flex-start; } + html.theme--documenter-dark .tabs ul.is-left { + padding-right: 0.75em; } + html.theme--documenter-dark .tabs ul.is-center { + flex: none; + justify-content: center; + padding-left: 0.75em; + padding-right: 0.75em; } + html.theme--documenter-dark .tabs ul.is-right { + justify-content: flex-end; + padding-left: 0.75em; } + html.theme--documenter-dark .tabs .icon:first-child { + margin-right: 0.5em; } + html.theme--documenter-dark .tabs .icon:last-child { + margin-left: 0.5em; } + html.theme--documenter-dark .tabs.is-centered ul { + justify-content: center; } + html.theme--documenter-dark .tabs.is-right ul { + justify-content: flex-end; } + html.theme--documenter-dark .tabs.is-boxed a { + border: 1px solid transparent; + border-radius: 4px 4px 0 0; } + html.theme--documenter-dark .tabs.is-boxed a:hover { + background-color: whitesmoke; + border-bottom-color: #dbdbdb; } + html.theme--documenter-dark .tabs.is-boxed li.is-active a { + background-color: white; + border-color: #dbdbdb; + border-bottom-color: transparent !important; } + html.theme--documenter-dark .tabs.is-fullwidth li { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .tabs.is-toggle a { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px; + margin-bottom: 0; + position: relative; } + html.theme--documenter-dark .tabs.is-toggle a:hover { + background-color: whitesmoke; + border-color: #b5b5b5; + z-index: 2; } + html.theme--documenter-dark .tabs.is-toggle li + li { + margin-left: -1px; } + html.theme--documenter-dark .tabs.is-toggle li:first-child a { + border-radius: 4px 0 0 4px; } + html.theme--documenter-dark .tabs.is-toggle li:last-child a { + border-radius: 0 4px 4px 0; } + html.theme--documenter-dark .tabs.is-toggle li.is-active a { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; + z-index: 1; } + html.theme--documenter-dark .tabs.is-toggle ul { + border-bottom: none; } + html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:first-child a { + border-bottom-left-radius: 290486px; + border-top-left-radius: 290486px; + padding-left: 1.25em; } + html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:last-child a { + border-bottom-right-radius: 290486px; + border-top-right-radius: 290486px; + padding-right: 1.25em; } + html.theme--documenter-dark .tabs.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.tabs { + font-size: 0.75rem; } + html.theme--documenter-dark .tabs.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .tabs.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .column { + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + padding: 0.75rem; } + .columns.is-mobile > html.theme--documenter-dark .column.is-narrow { + flex: none; } + .columns.is-mobile > html.theme--documenter-dark .column.is-full { + flex: none; + width: 100%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-three-quarters { + flex: none; + width: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-two-thirds { + flex: none; + width: 66.6666%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-half { + flex: none; + width: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-third { + flex: none; + width: 33.3333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-quarter { + flex: none; + width: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-fifth { + flex: none; + width: 20%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-two-fifths { + flex: none; + width: 40%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-three-fifths { + flex: none; + width: 60%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-four-fifths { + flex: none; + width: 80%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-quarters { + margin-left: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-thirds { + margin-left: 66.6666%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-half { + margin-left: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-third { + margin-left: 33.3333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-quarter { + margin-left: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-fifth { + margin-left: 20%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-fifths { + margin-left: 40%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-fifths { + margin-left: 60%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-four-fifths { + margin-left: 80%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-0 { + flex: none; + width: 0%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-0 { + margin-left: 0%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-1 { + flex: none; + width: 8.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-1 { + margin-left: 8.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-2 { + flex: none; + width: 16.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-2 { + margin-left: 16.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-3 { + flex: none; + width: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-3 { + margin-left: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-4 { + flex: none; + width: 33.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-4 { + margin-left: 33.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-5 { + flex: none; + width: 41.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-5 { + margin-left: 41.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-6 { + flex: none; + width: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-6 { + margin-left: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-7 { + flex: none; + width: 58.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-7 { + margin-left: 58.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-8 { + flex: none; + width: 66.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-8 { + margin-left: 66.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-9 { + flex: none; + width: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-9 { + margin-left: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-10 { + flex: none; + width: 83.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-10 { + margin-left: 83.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-11 { + flex: none; + width: 91.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-11 { + margin-left: 91.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-12 { + flex: none; + width: 100%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-12 { + margin-left: 100%; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .column.is-narrow-mobile { + flex: none; } + html.theme--documenter-dark .column.is-full-mobile { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-mobile { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-mobile { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-mobile { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-mobile { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-mobile { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-mobile { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-mobile { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-mobile { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-mobile { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-mobile { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-mobile { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-mobile { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-mobile { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-mobile { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-mobile { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-mobile { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-mobile { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-mobile { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-mobile { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-mobile { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-mobile { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-mobile { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-mobile { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-mobile { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-mobile { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-mobile { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-mobile { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-mobile { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-mobile { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-mobile { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-mobile { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-mobile { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-mobile { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-mobile { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-mobile { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-mobile { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-mobile { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-mobile { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-mobile { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-mobile { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-mobile { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-mobile { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-mobile { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-mobile { + margin-left: 100%; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .column.is-narrow, html.theme--documenter-dark .column.is-narrow-tablet { + flex: none; } + html.theme--documenter-dark .column.is-full, html.theme--documenter-dark .column.is-full-tablet { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters, html.theme--documenter-dark .column.is-three-quarters-tablet { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds, html.theme--documenter-dark .column.is-two-thirds-tablet { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half, html.theme--documenter-dark .column.is-half-tablet { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third, html.theme--documenter-dark .column.is-one-third-tablet { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter, html.theme--documenter-dark .column.is-one-quarter-tablet { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth, html.theme--documenter-dark .column.is-one-fifth-tablet { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths, html.theme--documenter-dark .column.is-two-fifths-tablet { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths, html.theme--documenter-dark .column.is-three-fifths-tablet { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths, html.theme--documenter-dark .column.is-four-fifths-tablet { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters, html.theme--documenter-dark .column.is-offset-three-quarters-tablet { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds, html.theme--documenter-dark .column.is-offset-two-thirds-tablet { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half, html.theme--documenter-dark .column.is-offset-half-tablet { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third, html.theme--documenter-dark .column.is-offset-one-third-tablet { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter, html.theme--documenter-dark .column.is-offset-one-quarter-tablet { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth, html.theme--documenter-dark .column.is-offset-one-fifth-tablet { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths, html.theme--documenter-dark .column.is-offset-two-fifths-tablet { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths, html.theme--documenter-dark .column.is-offset-three-fifths-tablet { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths, html.theme--documenter-dark .column.is-offset-four-fifths-tablet { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0, html.theme--documenter-dark .column.is-0-tablet { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0, html.theme--documenter-dark .column.is-offset-0-tablet { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1, html.theme--documenter-dark .column.is-1-tablet { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1, html.theme--documenter-dark .column.is-offset-1-tablet { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2, html.theme--documenter-dark .column.is-2-tablet { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2, html.theme--documenter-dark .column.is-offset-2-tablet { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3, html.theme--documenter-dark .column.is-3-tablet { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3, html.theme--documenter-dark .column.is-offset-3-tablet { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4, html.theme--documenter-dark .column.is-4-tablet { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4, html.theme--documenter-dark .column.is-offset-4-tablet { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5, html.theme--documenter-dark .column.is-5-tablet { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5, html.theme--documenter-dark .column.is-offset-5-tablet { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6, html.theme--documenter-dark .column.is-6-tablet { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6, html.theme--documenter-dark .column.is-offset-6-tablet { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7, html.theme--documenter-dark .column.is-7-tablet { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7, html.theme--documenter-dark .column.is-offset-7-tablet { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8, html.theme--documenter-dark .column.is-8-tablet { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8, html.theme--documenter-dark .column.is-offset-8-tablet { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9, html.theme--documenter-dark .column.is-9-tablet { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9, html.theme--documenter-dark .column.is-offset-9-tablet { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10, html.theme--documenter-dark .column.is-10-tablet { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10, html.theme--documenter-dark .column.is-offset-10-tablet { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11, html.theme--documenter-dark .column.is-11-tablet { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11, html.theme--documenter-dark .column.is-offset-11-tablet { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12, html.theme--documenter-dark .column.is-12-tablet { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12, html.theme--documenter-dark .column.is-offset-12-tablet { + margin-left: 100%; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .column.is-narrow-touch { + flex: none; } + html.theme--documenter-dark .column.is-full-touch { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-touch { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-touch { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-touch { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-touch { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-touch { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-touch { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-touch { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-touch { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-touch { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-touch { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-touch { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-touch { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-touch { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-touch { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-touch { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-touch { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-touch { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-touch { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-touch { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-touch { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-touch { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-touch { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-touch { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-touch { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-touch { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-touch { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-touch { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-touch { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-touch { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-touch { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-touch { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-touch { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-touch { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-touch { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-touch { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-touch { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-touch { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-touch { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-touch { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-touch { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-touch { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-touch { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-touch { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-touch { + margin-left: 100%; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .column.is-narrow-desktop { + flex: none; } + html.theme--documenter-dark .column.is-full-desktop { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-desktop { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-desktop { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-desktop { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-desktop { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-desktop { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-desktop { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-desktop { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-desktop { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-desktop { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-desktop { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-desktop { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-desktop { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-desktop { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-desktop { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-desktop { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-desktop { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-desktop { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-desktop { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-desktop { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-desktop { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-desktop { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-desktop { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-desktop { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-desktop { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-desktop { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-desktop { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-desktop { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-desktop { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-desktop { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-desktop { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-desktop { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-desktop { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-desktop { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-desktop { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-desktop { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-desktop { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-desktop { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-desktop { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-desktop { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-desktop { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-desktop { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-desktop { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-desktop { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-desktop { + margin-left: 100%; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .column.is-narrow-widescreen { + flex: none; } + html.theme--documenter-dark .column.is-full-widescreen { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-widescreen { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-widescreen { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-widescreen { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-widescreen { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-widescreen { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-widescreen { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-widescreen { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-widescreen { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-widescreen { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-widescreen { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-widescreen { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-widescreen { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-widescreen { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-widescreen { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-widescreen { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-widescreen { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-widescreen { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-widescreen { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-widescreen { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-widescreen { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-widescreen { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-widescreen { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-widescreen { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-widescreen { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-widescreen { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-widescreen { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-widescreen { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-widescreen { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-widescreen { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-widescreen { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-widescreen { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-widescreen { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-widescreen { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-widescreen { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-widescreen { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-widescreen { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-widescreen { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-widescreen { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-widescreen { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-widescreen { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-widescreen { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-widescreen { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-widescreen { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-widescreen { + margin-left: 100%; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .column.is-narrow-fullhd { + flex: none; } + html.theme--documenter-dark .column.is-full-fullhd { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-fullhd { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-fullhd { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-fullhd { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-fullhd { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-fullhd { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-fullhd { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-fullhd { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-fullhd { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-fullhd { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-fullhd { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-fullhd { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-fullhd { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-fullhd { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-fullhd { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-fullhd { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-fullhd { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-fullhd { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-fullhd { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-fullhd { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-fullhd { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-fullhd { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-fullhd { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-fullhd { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-fullhd { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-fullhd { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-fullhd { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-fullhd { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-fullhd { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-fullhd { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-fullhd { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-fullhd { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-fullhd { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-fullhd { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-fullhd { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-fullhd { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-fullhd { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-fullhd { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-fullhd { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-fullhd { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-fullhd { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-fullhd { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-fullhd { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-fullhd { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-fullhd { + margin-left: 100%; } } + html.theme--documenter-dark .columns { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + html.theme--documenter-dark .columns:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .columns:not(:last-child) { + margin-bottom: calc(1.5rem - 0.75rem); } + html.theme--documenter-dark .columns.is-centered { + justify-content: center; } + html.theme--documenter-dark .columns.is-gapless { + margin-left: 0; + margin-right: 0; + margin-top: 0; } + html.theme--documenter-dark .columns.is-gapless > .column { + margin: 0; + padding: 0 !important; } + html.theme--documenter-dark .columns.is-gapless:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .columns.is-gapless:last-child { + margin-bottom: 0; } + html.theme--documenter-dark .columns.is-mobile { + display: flex; } + html.theme--documenter-dark .columns.is-multiline { + flex-wrap: wrap; } + html.theme--documenter-dark .columns.is-vcentered { + align-items: center; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns:not(.is-desktop) { + display: flex; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-desktop { + display: flex; } } + html.theme--documenter-dark .columns.is-variable { + --columnGap: 0.75rem; + margin-left: calc(-1 * var(--columnGap)); + margin-right: calc(-1 * var(--columnGap)); } + html.theme--documenter-dark .columns.is-variable .column { + padding-left: var(--columnGap); + padding-right: var(--columnGap); } + html.theme--documenter-dark .columns.is-variable.is-0 { + --columnGap: 0rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-0-mobile { + --columnGap: 0rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-0-tablet { + --columnGap: 0rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-0-tablet-only { + --columnGap: 0rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-0-touch { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-0-desktop { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-0-desktop-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-0-widescreen { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-0-widescreen-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-0-fullhd { + --columnGap: 0rem; } } + html.theme--documenter-dark .columns.is-variable.is-1 { + --columnGap: 0.25rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-1-mobile { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-1-tablet { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-1-tablet-only { + --columnGap: 0.25rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-1-touch { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-1-desktop { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-1-desktop-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-1-widescreen { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-1-widescreen-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-1-fullhd { + --columnGap: 0.25rem; } } + html.theme--documenter-dark .columns.is-variable.is-2 { + --columnGap: 0.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-2-mobile { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-2-tablet { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-2-tablet-only { + --columnGap: 0.5rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-2-touch { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-2-desktop { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-2-desktop-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-2-widescreen { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-2-widescreen-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-2-fullhd { + --columnGap: 0.5rem; } } + html.theme--documenter-dark .columns.is-variable.is-3 { + --columnGap: 0.75rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-3-mobile { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-3-tablet { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-3-tablet-only { + --columnGap: 0.75rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-3-touch { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-3-desktop { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-3-desktop-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-3-widescreen { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-3-widescreen-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-3-fullhd { + --columnGap: 0.75rem; } } + html.theme--documenter-dark .columns.is-variable.is-4 { + --columnGap: 1rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-4-mobile { + --columnGap: 1rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-4-tablet { + --columnGap: 1rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-4-tablet-only { + --columnGap: 1rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-4-touch { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-4-desktop { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-4-desktop-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-4-widescreen { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-4-widescreen-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-4-fullhd { + --columnGap: 1rem; } } + html.theme--documenter-dark .columns.is-variable.is-5 { + --columnGap: 1.25rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-5-mobile { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-5-tablet { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-5-tablet-only { + --columnGap: 1.25rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-5-touch { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-5-desktop { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-5-desktop-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-5-widescreen { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-5-widescreen-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-5-fullhd { + --columnGap: 1.25rem; } } + html.theme--documenter-dark .columns.is-variable.is-6 { + --columnGap: 1.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-6-mobile { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-6-tablet { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-6-tablet-only { + --columnGap: 1.5rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-6-touch { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-6-desktop { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-6-desktop-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-6-widescreen { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-6-widescreen-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-6-fullhd { + --columnGap: 1.5rem; } } + html.theme--documenter-dark .columns.is-variable.is-7 { + --columnGap: 1.75rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-7-mobile { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-7-tablet { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-7-tablet-only { + --columnGap: 1.75rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-7-touch { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-7-desktop { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-7-desktop-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-7-widescreen { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-7-fullhd { + --columnGap: 1.75rem; } } + html.theme--documenter-dark .columns.is-variable.is-8 { + --columnGap: 2rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-8-mobile { + --columnGap: 2rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-8-tablet { + --columnGap: 2rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-8-tablet-only { + --columnGap: 2rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-8-touch { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-8-desktop { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-8-desktop-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-8-widescreen { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-8-widescreen-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-8-fullhd { + --columnGap: 2rem; } } + html.theme--documenter-dark .tile { + align-items: stretch; + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + min-height: min-content; } + html.theme--documenter-dark .tile.is-ancestor { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + html.theme--documenter-dark .tile.is-ancestor:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .tile.is-ancestor:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .tile.is-child { + margin: 0 !important; } + html.theme--documenter-dark .tile.is-parent { + padding: 0.75rem; } + html.theme--documenter-dark .tile.is-vertical { + flex-direction: column; } + html.theme--documenter-dark .tile.is-vertical > .tile.is-child:not(:last-child) { + margin-bottom: 1.5rem !important; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .tile:not(.is-child) { + display: flex; } + html.theme--documenter-dark .tile.is-1 { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .tile.is-2 { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .tile.is-3 { + flex: none; + width: 25%; } + html.theme--documenter-dark .tile.is-4 { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .tile.is-5 { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .tile.is-6 { + flex: none; + width: 50%; } + html.theme--documenter-dark .tile.is-7 { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .tile.is-8 { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .tile.is-9 { + flex: none; + width: 75%; } + html.theme--documenter-dark .tile.is-10 { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .tile.is-11 { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .tile.is-12 { + flex: none; + width: 100%; } } + html.theme--documenter-dark .hero { + align-items: stretch; + display: flex; + flex-direction: column; + justify-content: space-between; } + html.theme--documenter-dark .hero .navbar { + background: none; } + html.theme--documenter-dark .hero .tabs ul { + border-bottom: none; } + html.theme--documenter-dark .hero.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-white strong { + color: inherit; } + html.theme--documenter-dark .hero.is-white .title { + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .subtitle { + color: rgba(10, 10, 10, 0.9); } + html.theme--documenter-dark .hero.is-white .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-white .subtitle strong { + color: #0a0a0a; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-white .navbar-menu { + background-color: white; } } + html.theme--documenter-dark .hero.is-white .navbar-item, + html.theme--documenter-dark .hero.is-white .navbar-link { + color: rgba(10, 10, 10, 0.7); } + html.theme--documenter-dark .hero.is-white a.navbar-item:hover, html.theme--documenter-dark .hero.is-white a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-white .navbar-link:hover, + html.theme--documenter-dark .hero.is-white .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .tabs a { + color: #0a0a0a; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-white .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-white .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a { + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a:hover { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .hero.is-white.is-bold { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-white.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } + html.theme--documenter-dark .hero.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-black strong { + color: inherit; } + html.theme--documenter-dark .hero.is-black .title { + color: white; } + html.theme--documenter-dark .hero.is-black .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-black .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-black .subtitle strong { + color: white; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-black .navbar-menu { + background-color: #0a0a0a; } } + html.theme--documenter-dark .hero.is-black .navbar-item, + html.theme--documenter-dark .hero.is-black .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-black a.navbar-item:hover, html.theme--documenter-dark .hero.is-black a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-black .navbar-link:hover, + html.theme--documenter-dark .hero.is-black .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .hero.is-black .tabs a { + color: white; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-black .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-black .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a { + color: white; } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a:hover { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-black.is-bold { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-black.is-bold .navbar-menu { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } + html.theme--documenter-dark .hero.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-light strong { + color: inherit; } + html.theme--documenter-dark .hero.is-light .title { + color: #363636; } + html.theme--documenter-dark .hero.is-light .subtitle { + color: rgba(54, 54, 54, 0.9); } + html.theme--documenter-dark .hero.is-light .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-light .subtitle strong { + color: #363636; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-light .navbar-menu { + background-color: whitesmoke; } } + html.theme--documenter-dark .hero.is-light .navbar-item, + html.theme--documenter-dark .hero.is-light .navbar-link { + color: rgba(54, 54, 54, 0.7); } + html.theme--documenter-dark .hero.is-light a.navbar-item:hover, html.theme--documenter-dark .hero.is-light a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-light .navbar-link:hover, + html.theme--documenter-dark .hero.is-light .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .hero.is-light .tabs a { + color: #363636; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-light .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-light .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a { + color: #363636; } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a:hover { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-light.is-bold { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-light.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } } + html.theme--documenter-dark .hero.is-dark, html.theme--documenter-dark .content kbd.hero { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-dark strong, + html.theme--documenter-dark .content kbd.hero strong { + color: inherit; } + html.theme--documenter-dark .hero.is-dark .title, html.theme--documenter-dark .content kbd.hero .title { + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .subtitle, html.theme--documenter-dark .content kbd.hero .subtitle { + color: rgba(245, 245, 245, 0.9); } + html.theme--documenter-dark .hero.is-dark .subtitle a:not(.button), html.theme--documenter-dark .content kbd.hero .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-dark .subtitle strong, + html.theme--documenter-dark .content kbd.hero .subtitle strong { + color: whitesmoke; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-dark .navbar-menu, html.theme--documenter-dark .content kbd.hero .navbar-menu { + background-color: #363636; } } + html.theme--documenter-dark .hero.is-dark .navbar-item, html.theme--documenter-dark .content kbd.hero .navbar-item, + html.theme--documenter-dark .hero.is-dark .navbar-link, + html.theme--documenter-dark .content kbd.hero .navbar-link { + color: rgba(245, 245, 245, 0.7); } + html.theme--documenter-dark .hero.is-dark a.navbar-item:hover, html.theme--documenter-dark .content kbd.hero a.navbar-item:hover, html.theme--documenter-dark .hero.is-dark a.navbar-item.is-active, html.theme--documenter-dark .content kbd.hero a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-dark .navbar-link:hover, + html.theme--documenter-dark .content kbd.hero .navbar-link:hover, + html.theme--documenter-dark .hero.is-dark .navbar-link.is-active, + html.theme--documenter-dark .content kbd.hero .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .tabs a, html.theme--documenter-dark .content kbd.hero .tabs a { + color: whitesmoke; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-dark .tabs a:hover, html.theme--documenter-dark .content kbd.hero .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-dark .tabs li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a { + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a:hover { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .hero.is-dark.is-bold, html.theme--documenter-dark .content kbd.hero.is-bold { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-dark.is-bold .navbar-menu, html.theme--documenter-dark .content kbd.hero.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } } + html.theme--documenter-dark .hero.is-primary, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-primary strong, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink strong { + color: inherit; } + html.theme--documenter-dark .hero.is-primary .title, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .title { + color: #fff; } + html.theme--documenter-dark .hero.is-primary .subtitle, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-primary .subtitle a:not(.button), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-primary .subtitle strong, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-primary .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-menu { + background-color: #4eb5de; } } + html.theme--documenter-dark .hero.is-primary .navbar-item, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-item, + html.theme--documenter-dark .hero.is-primary .navbar-link, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-primary a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, html.theme--documenter-dark .hero.is-primary a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-primary .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, + html.theme--documenter-dark .hero.is-primary .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .hero.is-primary .tabs a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-primary .tabs a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-primary .tabs li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .hero.is-primary.is-bold, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-primary.is-bold .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } } + html.theme--documenter-dark .hero.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-link strong { + color: inherit; } + html.theme--documenter-dark .hero.is-link .title { + color: #fff; } + html.theme--documenter-dark .hero.is-link .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-link .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-link .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-link .navbar-menu { + background-color: #2ad7e6; } } + html.theme--documenter-dark .hero.is-link .navbar-item, + html.theme--documenter-dark .hero.is-link .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-link a.navbar-item:hover, html.theme--documenter-dark .hero.is-link a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-link .navbar-link:hover, + html.theme--documenter-dark .hero.is-link .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .hero.is-link .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-link .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-link .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .hero.is-link.is-bold { + background-image: linear-gradient(141deg, #0cd0bf 0%, #2ad7e6 71%, #3bc2ee 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-link.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #0cd0bf 0%, #2ad7e6 71%, #3bc2ee 100%); } } + html.theme--documenter-dark .hero.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-info strong { + color: inherit; } + html.theme--documenter-dark .hero.is-info .title { + color: #fff; } + html.theme--documenter-dark .hero.is-info .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-info .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-info .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-info .navbar-menu { + background-color: #3489da; } } + html.theme--documenter-dark .hero.is-info .navbar-item, + html.theme--documenter-dark .hero.is-info .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-info a.navbar-item:hover, html.theme--documenter-dark .hero.is-info a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-info .navbar-link:hover, + html.theme--documenter-dark .hero.is-info .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .hero.is-info .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-info .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-info .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #3489da; } + html.theme--documenter-dark .hero.is-info.is-bold { + background-image: linear-gradient(141deg, #178cc4 0%, #3489da 71%, #447be3 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-info.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #178cc4 0%, #3489da 71%, #447be3 100%); } } + html.theme--documenter-dark .hero.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-success strong { + color: inherit; } + html.theme--documenter-dark .hero.is-success .title { + color: #fff; } + html.theme--documenter-dark .hero.is-success .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-success .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-success .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-success .navbar-menu { + background-color: #259a12; } } + html.theme--documenter-dark .hero.is-success .navbar-item, + html.theme--documenter-dark .hero.is-success .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-success a.navbar-item:hover, html.theme--documenter-dark .hero.is-success a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-success .navbar-link:hover, + html.theme--documenter-dark .hero.is-success .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .hero.is-success .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-success .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-success .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #259a12; } + html.theme--documenter-dark .hero.is-success.is-bold { + background-image: linear-gradient(141deg, #287207 0%, #259a12 71%, #10b614 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-success.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #287207 0%, #259a12 71%, #10b614 100%); } } + html.theme--documenter-dark .hero.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-warning strong { + color: inherit; } + html.theme--documenter-dark .hero.is-warning .title { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .subtitle { + color: rgba(0, 0, 0, 0.9); } + html.theme--documenter-dark .hero.is-warning .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-warning .subtitle strong { + color: rgba(0, 0, 0, 0.7); } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-warning .navbar-menu { + background-color: #f4c72f; } } + html.theme--documenter-dark .hero.is-warning .navbar-item, + html.theme--documenter-dark .hero.is-warning .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning a.navbar-item:hover, html.theme--documenter-dark .hero.is-warning a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-warning .navbar-link:hover, + html.theme--documenter-dark .hero.is-warning .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .tabs a { + color: rgba(0, 0, 0, 0.7); + opacity: 0.9; } + html.theme--documenter-dark .hero.is-warning .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-warning .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a:hover { + background-color: rgba(0, 0, 0, 0.7); + border-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .hero.is-warning.is-bold { + background-image: linear-gradient(141deg, #f09100 0%, #f4c72f 71%, #faef42 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-warning.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #f09100 0%, #f4c72f 71%, #faef42 100%); } } + html.theme--documenter-dark .hero.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-danger strong { + color: inherit; } + html.theme--documenter-dark .hero.is-danger .title { + color: #fff; } + html.theme--documenter-dark .hero.is-danger .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-danger .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-danger .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-danger .navbar-menu { + background-color: #cb3c33; } } + html.theme--documenter-dark .hero.is-danger .navbar-item, + html.theme--documenter-dark .hero.is-danger .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-danger a.navbar-item:hover, html.theme--documenter-dark .hero.is-danger a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-danger .navbar-link:hover, + html.theme--documenter-dark .hero.is-danger .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .hero.is-danger .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-danger .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-danger .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .hero.is-danger.is-bold { + background-image: linear-gradient(141deg, #ac1f2e 0%, #cb3c33 71%, #d66341 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-danger.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #ac1f2e 0%, #cb3c33 71%, #d66341 100%); } } + html.theme--documenter-dark .hero.is-small .hero-body, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.hero .hero-body { + padding-bottom: 1.5rem; + padding-top: 1.5rem; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero.is-medium .hero-body { + padding-bottom: 9rem; + padding-top: 9rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero.is-large .hero-body { + padding-bottom: 18rem; + padding-top: 18rem; } } + html.theme--documenter-dark .hero.is-halfheight .hero-body, html.theme--documenter-dark .hero.is-fullheight .hero-body, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body { + align-items: center; + display: flex; } + html.theme--documenter-dark .hero.is-halfheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body > .container { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .hero.is-halfheight { + min-height: 50vh; } + html.theme--documenter-dark .hero.is-fullheight { + min-height: 100vh; } + html.theme--documenter-dark .hero-video { + overflow: hidden; } + html.theme--documenter-dark .hero-video video { + left: 50%; + min-height: 100%; + min-width: 100%; + position: absolute; + top: 50%; + transform: translate3d(-50%, -50%, 0); } + html.theme--documenter-dark .hero-video.is-transparent { + opacity: 0.3; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero-video { + display: none; } } + html.theme--documenter-dark .hero-buttons { + margin-top: 1.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero-buttons .button { + display: flex; } + html.theme--documenter-dark .hero-buttons .button:not(:last-child) { + margin-bottom: 0.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero-buttons { + display: flex; + justify-content: center; } + html.theme--documenter-dark .hero-buttons .button:not(:last-child) { + margin-right: 1.5rem; } } + html.theme--documenter-dark .hero-head, + html.theme--documenter-dark .hero-foot { + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .hero-body { + flex-grow: 1; + flex-shrink: 0; + padding: 3rem 1.5rem; } + html.theme--documenter-dark .section { + padding: 3rem 1.5rem; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .section.is-medium { + padding: 9rem 1.5rem; } + html.theme--documenter-dark .section.is-large { + padding: 18rem 1.5rem; } } + html.theme--documenter-dark .footer { + background-color: #fafafa; + padding: 3rem 1.5rem 6rem; } + html.theme--documenter-dark h1 .docs-heading-anchor, html.theme--documenter-dark h1 .docs-heading-anchor:hover, html.theme--documenter-dark h1 .docs-heading-anchor:visited, html.theme--documenter-dark h2 .docs-heading-anchor, html.theme--documenter-dark h2 .docs-heading-anchor:hover, html.theme--documenter-dark h2 .docs-heading-anchor:visited, html.theme--documenter-dark h3 .docs-heading-anchor, html.theme--documenter-dark h3 .docs-heading-anchor:hover, html.theme--documenter-dark h3 .docs-heading-anchor:visited, html.theme--documenter-dark h4 .docs-heading-anchor, html.theme--documenter-dark h4 .docs-heading-anchor:hover, html.theme--documenter-dark h4 .docs-heading-anchor:visited, html.theme--documenter-dark h5 .docs-heading-anchor, html.theme--documenter-dark h5 .docs-heading-anchor:hover, html.theme--documenter-dark h5 .docs-heading-anchor:visited, html.theme--documenter-dark h6 .docs-heading-anchor, html.theme--documenter-dark h6 .docs-heading-anchor:hover, html.theme--documenter-dark h6 .docs-heading-anchor:visited { + color: #cdc3e3; } + html.theme--documenter-dark h1 .docs-heading-anchor-permalink, html.theme--documenter-dark h2 .docs-heading-anchor-permalink, html.theme--documenter-dark h3 .docs-heading-anchor-permalink, html.theme--documenter-dark h4 .docs-heading-anchor-permalink, html.theme--documenter-dark h5 .docs-heading-anchor-permalink, html.theme--documenter-dark h6 .docs-heading-anchor-permalink { + visibility: hidden; + vertical-align: middle; + margin-left: 0.5em; + font-size: 0.7rem; } + html.theme--documenter-dark h1 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h2 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h3 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h4 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h5 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h6 .docs-heading-anchor-permalink::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f0c1"; } + html.theme--documenter-dark h1:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h2:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h3:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h4:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h5:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h6:hover .docs-heading-anchor-permalink { + visibility: visible; } + html.theme--documenter-dark .docs-light-only { + display: none !important; } + html.theme--documenter-dark pre { + position: relative; + overflow: hidden; } + html.theme--documenter-dark pre code, html.theme--documenter-dark pre code.hljs { + padding: 0 0.75rem !important; + overflow: auto; + display: block; } + html.theme--documenter-dark pre code:first-of-type, html.theme--documenter-dark pre code.hljs:first-of-type { + padding-top: 0.5rem !important; } + html.theme--documenter-dark pre code:last-of-type, html.theme--documenter-dark pre code.hljs:last-of-type { + padding-bottom: 0.5rem !important; } + html.theme--documenter-dark pre .copy-button { + opacity: 0.2; + transition: opacity 0.2s; + position: absolute; + right: 0em; + top: 0em; + padding: 0.5em; + width: 2.5em; + height: 2.5em; + background: transparent; + border: none; + font-family: "Font Awesome 5 Free"; + color: #fbfbfb; + cursor: pointer; + text-align: center; } + html.theme--documenter-dark pre .copy-button:focus, html.theme--documenter-dark pre .copy-button:hover { + opacity: 1; + background: rgba(251, 251, 251, 0.1); + color: #2ad7e6; } + html.theme--documenter-dark pre .copy-button.success { + color: #259a12; + opacity: 1; } + html.theme--documenter-dark pre .copy-button.error { + color: #cb3c33; + opacity: 1; } + html.theme--documenter-dark pre:hover .copy-button { + opacity: 1; } + html.theme--documenter-dark .admonition { + background-color: #28282b; + border-style: solid; + border-width: 1px; + border-color: #ba3f1f; + border-radius: 4px; + font-size: 1rem; } + html.theme--documenter-dark .admonition strong { + color: currentColor; } + html.theme--documenter-dark .admonition.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.admonition { + font-size: 0.75rem; } + html.theme--documenter-dark .admonition.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .admonition.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .admonition.is-default { + background-color: #28282b; + border-color: #ba3f1f; } + html.theme--documenter-dark .admonition.is-default > .admonition-header { + background-color: #ba3f1f; } + html.theme--documenter-dark .admonition.is-info { + background-color: #28282b; + border-color: #28c; } + html.theme--documenter-dark .admonition.is-info > .admonition-header { + background-color: #28c; } + html.theme--documenter-dark .admonition.is-success { + background-color: #28282b; + border-color: #42ac68; } + html.theme--documenter-dark .admonition.is-success > .admonition-header { + background-color: #42ac68; } + html.theme--documenter-dark .admonition.is-warning { + background-color: #28282b; + border-color: #a88b17; } + html.theme--documenter-dark .admonition.is-warning > .admonition-header { + background-color: #a88b17; } + html.theme--documenter-dark .admonition.is-danger { + background-color: #28282b; + border-color: #c7524c; } + html.theme--documenter-dark .admonition.is-danger > .admonition-header { + background-color: #c7524c; } + html.theme--documenter-dark .admonition.is-compat { + background-color: #28282b; + border-color: #00a1b7; } + html.theme--documenter-dark .admonition.is-compat > .admonition-header { + background-color: #00a1b7; } + html.theme--documenter-dark .admonition-header { + background-color: #ba3f1f; + align-items: center; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.5rem 0.75rem; + position: relative; } + html.theme--documenter-dark .admonition-header:before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + margin-right: 0.75rem; + content: "\f06a"; } + html.theme--documenter-dark .admonition-body { + color: #fbfbfb; + padding: 0.5rem 0.75rem; } + html.theme--documenter-dark .admonition-body pre { + background-color: #312550; } + html.theme--documenter-dark .admonition-body code { + background-color: #312550; } + html.theme--documenter-dark .docstring { + margin-bottom: 1em; + background-color: transparent; + border: 1px solid #dbdbdb; + box-shadow: 3px 3px 4px #444444; + max-width: 100%; } + html.theme--documenter-dark .docstring > header { + display: flex; + flex-grow: 1; + align-items: stretch; + padding: 0.5rem 0.75rem; + background-color: #28282b; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + box-shadow: none; + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .docstring > header code { + background-color: transparent; } + html.theme--documenter-dark .docstring > header .docstring-binding { + margin-right: 0.3em; } + html.theme--documenter-dark .docstring > header .docstring-category { + margin-left: 0.3em; } + html.theme--documenter-dark .docstring > section { + position: relative; + padding: 0.75rem 0.75rem; + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .docstring > section:last-child { + border-bottom: none; } + html.theme--documenter-dark .docstring > section > a.docs-sourcelink { + transition: opacity 0.3s; + opacity: 0; + position: absolute; + right: 0.375rem; + bottom: 0.375rem; } + html.theme--documenter-dark .docstring > section > a.docs-sourcelink:focus { + opacity: 1 !important; } + html.theme--documenter-dark .docstring:hover > section > a.docs-sourcelink { + opacity: 0.2; } + html.theme--documenter-dark .docstring:focus-within > section > a.docs-sourcelink { + opacity: 0.2; } + html.theme--documenter-dark .docstring > section:hover a.docs-sourcelink { + opacity: 1; } + html.theme--documenter-dark .documenter-example-output { + background-color: #1e1e20; } + html.theme--documenter-dark .outdated-warning-overlay { + position: fixed; + top: 0; + left: 0; + right: 0; + box-shadow: 0 0 10px rgba(0, 0, 0, 0.3); + z-index: 999; + background-color: #28282b; + border-bottom: 3px solid #c7524c; + padding: 10px 35px; + text-align: center; + font-size: 15px; } + html.theme--documenter-dark .outdated-warning-overlay .outdated-warning-closer { + position: absolute; + top: calc(50% - 10px); + right: 18px; + cursor: pointer; + width: 12px; } + html.theme--documenter-dark .outdated-warning-overlay a { + color: #2ad7e6; } + html.theme--documenter-dark .outdated-warning-overlay a:hover { + color: #97ebf3; } + html.theme--documenter-dark .content pre { + border: 1px solid #dbdbdb; } + html.theme--documenter-dark .content code { + font-weight: inherit; } + html.theme--documenter-dark .content a code { + color: #2ad7e6; } + html.theme--documenter-dark .content h1 code, html.theme--documenter-dark .content h2 code, html.theme--documenter-dark .content h3 code, html.theme--documenter-dark .content h4 code, html.theme--documenter-dark .content h5 code, html.theme--documenter-dark .content h6 code { + color: #cdc3e3; } + html.theme--documenter-dark .content table { + display: block; + width: initial; + max-width: 100%; + overflow-x: auto; } + html.theme--documenter-dark .content blockquote > ul:first-child, html.theme--documenter-dark .content blockquote > ol:first-child, html.theme--documenter-dark .content .admonition-body > ul:first-child, html.theme--documenter-dark .content .admonition-body > ol:first-child { + margin-top: 0; } + html.theme--documenter-dark pre, html.theme--documenter-dark code { + font-variant-ligatures: no-contextual; } + html.theme--documenter-dark .breadcrumb a.is-disabled { + cursor: default; + pointer-events: none; } + html.theme--documenter-dark .breadcrumb a.is-disabled, html.theme--documenter-dark .breadcrumb a.is-disabled:hover { + color: #cdc3e3; } + html.theme--documenter-dark .hljs { + background: initial !important; } + html.theme--documenter-dark .katex .katex-mathml { + top: 0; + right: 0; } + html.theme--documenter-dark .katex-display, html.theme--documenter-dark mjx-container, html.theme--documenter-dark .MathJax_Display { + margin: 0.5em 0 !important; } + html.theme--documenter-dark html { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; } + html.theme--documenter-dark li.no-marker { + list-style: none; } + html.theme--documenter-dark #documenter .docs-main > article { + overflow-wrap: break-word; } + html.theme--documenter-dark #documenter .docs-main > article .math-container { + overflow-x: auto; + overflow-y: hidden; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-main { + max-width: 52rem; + margin-left: 20rem; + padding-right: 1rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main { + width: 100%; } + html.theme--documenter-dark #documenter .docs-main > article { + max-width: 52rem; + margin-left: auto; + margin-right: auto; + margin-bottom: 1rem; + padding: 0 1rem; } + html.theme--documenter-dark #documenter .docs-main > header, html.theme--documenter-dark #documenter .docs-main > nav { + max-width: 100%; + width: 100%; + margin: 0; } } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar { + background-color: #1e1e20; + border-bottom: 1px solid #dbdbdb; + z-index: 2; + min-height: 4rem; + margin-bottom: 1rem; + display: flex; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .breadcrumb { + flex-grow: 1; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right { + display: flex; + white-space: nowrap; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-icon, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + display: inline-block; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label { + padding: 0; + margin-left: 0.3em; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button { + margin: auto 0 auto 1rem; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + font-size: 1.5rem; + margin: auto 0 auto 1rem; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar > * { + margin: auto 0; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main header.docs-navbar { + position: sticky; + top: 0; + padding: 0 1rem; + /* For Headroom.js */ + transition-property: top, box-shadow; + -webkit-transition-property: top, box-shadow; + /* Safari */ + transition-duration: 0.3s; + -webkit-transition-duration: 0.3s; + /* Safari */ } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--not-top { + box-shadow: 0.2rem 0rem 0.4rem #bbb; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { + top: -4.5rem; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } } + html.theme--documenter-dark #documenter .docs-main section.footnotes { + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-main section.footnotes li .tag:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .content kbd:first-child, html.theme--documenter-dark .content #documenter .docs-main section.footnotes li kbd:first-child { + margin-right: 1em; + margin-bottom: 0.4em; } + html.theme--documenter-dark #documenter .docs-main .docs-footer { + display: flex; + flex-wrap: wrap; + margin-left: 0; + margin-right: 0; + border-top: 1px solid #dbdbdb; + padding-top: 1rem; + padding-bottom: 1rem; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main .docs-footer { + padding-left: 1rem; + padding-right: 1rem; } } + html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage, html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-prevpage { + flex-grow: 1; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage { + text-align: right; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .flexbox-break { + flex-basis: 100%; + height: 0; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .footer-message { + font-size: 0.8em; + margin: 0.5em auto 0 auto; + text-align: center; } + html.theme--documenter-dark #documenter .docs-sidebar { + display: flex; + flex-direction: column; + color: #fbfbfb; + background-color: #503c82; + border-right: 1px solid #dbdbdb; + padding: 0; + flex: 0 0 18rem; + z-index: 5; + font-size: 1rem; + position: fixed; + left: -18rem; + width: 18rem; + height: 100%; + transition: left 0.3s; + /* Setting up a nicer theme style for the scrollbar */ } + html.theme--documenter-dark #documenter .docs-sidebar.visible { + left: 0; + box-shadow: 0.4rem 0rem 0.8rem #bbb; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar.visible { + box-shadow: none; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar { + left: 0; + top: 0; } } + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo { + margin-top: 1rem; + padding: 0 1rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { + max-height: 6rem; + margin: auto; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name { + flex-shrink: 0; + font-size: 1.5rem; + font-weight: 700; + text-align: center; + white-space: nowrap; + overflow: hidden; + padding: 0.5rem 0; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name .docs-autofit { + max-width: 16.2rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a, html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a:hover { + color: #fbfbfb; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector { + border-top: 1px solid #dbdbdb; + display: none; + padding: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector.visible { + display: flex; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { + flex-grow: 1; + user-select: none; + border-top: 1px solid #dbdbdb; + padding-bottom: 1.5rem; + /* Managing collapsible submenus */ } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li > .tocitem { + font-weight: bold; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li li { + font-size: 0.95rem; + margin-left: 1em; + border-left: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input.collapse-toggle { + display: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.collapsed { + display: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed { + display: block; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem { + display: flex; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label { + flex-grow: 2; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron { + display: inline-block; + font-style: normal; + font-variant: normal; + text-rendering: auto; + line-height: 1; + font-size: 0.75rem; + margin-left: 1rem; + margin-top: auto; + margin-bottom: auto; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f054"; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before { + content: "\f078"; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem { + display: block; + padding: 0.5rem 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem:hover { + color: #fbfbfb; + background: #503c82; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem:hover { + color: #fbfbfb; + background-color: #3c2d60; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active { + border-top: 1px solid #dbdbdb; + border-bottom: 1px solid #dbdbdb; + background-color: #1e1e20; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover { + background-color: #1e1e20; + color: #fff; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover { + background-color: #3f2f66; + color: #fff; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child { + border-top: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal { + margin: 0 0.5rem 0.5rem; + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal li { + font-size: 0.85rem; + border-left: none; + margin-left: 0; + margin-top: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem { + width: 100%; + padding: 0; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before { + content: "⚬"; + margin-right: 0.4em; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search { + margin: auto; + margin-top: 0.5rem; + margin-bottom: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + width: 14.4rem; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar { + width: .3rem; + background: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #3f2f66; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover { + background: #2e224a; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-sidebar { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar { + width: .3rem; + background: none; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #3f2f66; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover { + background: #2e224a; } } + html.theme--documenter-dark #documenter .docs-main #documenter-search-info { + margin-bottom: 1rem; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results { + list-style-type: circle; + list-style-position: outside; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results li { + margin-left: 2rem; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results .docs-highlight { + background-color: yellow; } + html.theme--documenter-dark { + background-color: #1e1e20; + font-size: 16px; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + html.theme--documenter-dark #documenter .docs-sidebar { + border-right: none; + box-shadow: 0.24rem 0rem 0.4rem #444444; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + color: #fff; + background-color: #3f2f66; + border-color: #2e224a; + margin-top: 1.0rem; + margin-bottom: 1.0rem; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::placeholder { + color: #fff; } + html.theme--documenter-dark .hljs { + background: #2b2b2b; + color: #f8f8f2; } + html.theme--documenter-dark .hljs-comment, + html.theme--documenter-dark .hljs-quote { + color: #d4d0ab; } + html.theme--documenter-dark .hljs-variable, + html.theme--documenter-dark .hljs-template-variable, + html.theme--documenter-dark .hljs-tag, + html.theme--documenter-dark .hljs-name, + html.theme--documenter-dark .hljs-selector-id, + html.theme--documenter-dark .hljs-selector-class, + html.theme--documenter-dark .hljs-regexp, + html.theme--documenter-dark .hljs-deletion { + color: #ffa07a; } + html.theme--documenter-dark .hljs-number, + html.theme--documenter-dark .hljs-built_in, + html.theme--documenter-dark .hljs-literal, + html.theme--documenter-dark .hljs-type, + html.theme--documenter-dark .hljs-params, + html.theme--documenter-dark .hljs-meta, + html.theme--documenter-dark .hljs-link { + color: #f5ab35; } + html.theme--documenter-dark .hljs-attribute { + color: #ffd700; } + html.theme--documenter-dark .hljs-string, + html.theme--documenter-dark .hljs-symbol, + html.theme--documenter-dark .hljs-bullet, + html.theme--documenter-dark .hljs-addition { + color: #abe338; } + html.theme--documenter-dark .hljs-title, + html.theme--documenter-dark .hljs-section { + color: #00e0e0; } + html.theme--documenter-dark .hljs-keyword, + html.theme--documenter-dark .hljs-selector-tag { + color: #dcc6e0; } + html.theme--documenter-dark .hljs-emphasis { + font-style: italic; } + html.theme--documenter-dark .hljs-strong { + font-weight: bold; } + @media screen and (-ms-high-contrast: active) { + html.theme--documenter-dark .hljs-addition, + html.theme--documenter-dark .hljs-attribute, + html.theme--documenter-dark .hljs-built_in, + html.theme--documenter-dark .hljs-bullet, + html.theme--documenter-dark .hljs-comment, + html.theme--documenter-dark .hljs-link, + html.theme--documenter-dark .hljs-literal, + html.theme--documenter-dark .hljs-meta, + html.theme--documenter-dark .hljs-number, + html.theme--documenter-dark .hljs-params, + html.theme--documenter-dark .hljs-string, + html.theme--documenter-dark .hljs-symbol, + html.theme--documenter-dark .hljs-type, + html.theme--documenter-dark .hljs-quote { + color: highlight; } + html.theme--documenter-dark .hljs-keyword, + html.theme--documenter-dark .hljs-selector-tag { + font-weight: bold; } } + html.theme--documenter-dark .hljs-subst { + color: #f8f8f2; } diff --git a/previews/PR18/assets/themes/documenter-light.css b/previews/PR18/assets/themes/documenter-light.css new file mode 100644 index 00000000..e2c74638 --- /dev/null +++ b/previews/PR18/assets/themes/documenter-light.css @@ -0,0 +1,7750 @@ +@charset "UTF-8"; +/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */ +@keyframes spinAround { + from { + transform: rotate(0deg); } + to { + transform: rotate(359deg); } } + +.tabs, .pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis, .breadcrumb, .file, .button, .is-unselectable, .modal-close, .delete { + -webkit-touch-callout: none; + -webkit-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; } + +.navbar-link:not(.is-arrowless)::after, .select:not(.is-multiple):not(.is-loading)::after { + border: 3px solid transparent; + border-radius: 2px; + border-right: 0; + border-top: 0; + content: " "; + display: block; + height: 0.625em; + margin-top: -0.4375em; + pointer-events: none; + position: absolute; + top: 50%; + transform: rotate(-45deg); + transform-origin: center; + width: 0.625em; } + +.admonition:not(:last-child), .tabs:not(:last-child), .message:not(:last-child), .list:not(:last-child), .level:not(:last-child), .breadcrumb:not(:last-child), .highlight:not(:last-child), .block:not(:last-child), .title:not(:last-child), +.subtitle:not(:last-child), .table-container:not(:last-child), .table:not(:last-child), .progress:not(:last-child), .notification:not(:last-child), .content:not(:last-child), .box:not(:last-child) { + margin-bottom: 1.5rem; } + +.modal-close, .delete { + -moz-appearance: none; + -webkit-appearance: none; + background-color: rgba(10, 10, 10, 0.2); + border: none; + border-radius: 290486px; + cursor: pointer; + pointer-events: auto; + display: inline-block; + flex-grow: 0; + flex-shrink: 0; + font-size: 0; + height: 20px; + max-height: 20px; + max-width: 20px; + min-height: 20px; + min-width: 20px; + outline: none; + position: relative; + vertical-align: top; + width: 20px; } + .modal-close::before, .delete::before, .modal-close::after, .delete::after { + background-color: white; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + .modal-close::before, .delete::before { + height: 2px; + width: 50%; } + .modal-close::after, .delete::after { + height: 50%; + width: 2px; } + .modal-close:hover, .delete:hover, .modal-close:focus, .delete:focus { + background-color: rgba(10, 10, 10, 0.3); } + .modal-close:active, .delete:active { + background-color: rgba(10, 10, 10, 0.4); } + .is-small.modal-close, #documenter .docs-sidebar form.docs-search > input.modal-close, .is-small.delete, #documenter .docs-sidebar form.docs-search > input.delete { + height: 16px; + max-height: 16px; + max-width: 16px; + min-height: 16px; + min-width: 16px; + width: 16px; } + .is-medium.modal-close, .is-medium.delete { + height: 24px; + max-height: 24px; + max-width: 24px; + min-height: 24px; + min-width: 24px; + width: 24px; } + .is-large.modal-close, .is-large.delete { + height: 32px; + max-height: 32px; + max-width: 32px; + min-height: 32px; + min-width: 32px; + width: 32px; } + +.control.is-loading::after, .select.is-loading::after, .loader, .button.is-loading::after { + animation: spinAround 500ms infinite linear; + border: 2px solid #dbdbdb; + border-radius: 290486px; + border-right-color: transparent; + border-top-color: transparent; + content: ""; + display: block; + height: 1em; + position: relative; + width: 1em; } + +.hero-video, .modal-background, .modal, .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img, +.image.is-square .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img, +.image.is-1by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img, +.image.is-5by4 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img, +.image.is-4by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img, +.image.is-3by2 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img, +.image.is-5by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img, +.image.is-16by9 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img, +.image.is-2by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img, +.image.is-3by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img, +.image.is-4by5 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img, +.image.is-3by4 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img, +.image.is-2by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img, +.image.is-3by5 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img, +.image.is-9by16 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img, +.image.is-1by2 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img, +.image.is-1by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, .is-overlay { + bottom: 0; + left: 0; + position: absolute; + right: 0; + top: 0; } + +.pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis, .file-cta, +.file-name, .select select, .textarea, .input, #documenter .docs-sidebar form.docs-search > input, .button { + -moz-appearance: none; + -webkit-appearance: none; + align-items: center; + border: 1px solid transparent; + border-radius: 4px; + box-shadow: none; + display: inline-flex; + font-size: 1rem; + height: 2.25em; + justify-content: flex-start; + line-height: 1.5; + padding-bottom: calc(0.375em - 1px); + padding-left: calc(0.625em - 1px); + padding-right: calc(0.625em - 1px); + padding-top: calc(0.375em - 1px); + position: relative; + vertical-align: top; } + .pagination-previous:focus, + .pagination-next:focus, + .pagination-link:focus, + .pagination-ellipsis:focus, .file-cta:focus, + .file-name:focus, .select select:focus, .textarea:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .button:focus, .is-focused.pagination-previous, + .is-focused.pagination-next, + .is-focused.pagination-link, + .is-focused.pagination-ellipsis, .is-focused.file-cta, + .is-focused.file-name, .select select.is-focused, .is-focused.textarea, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-focused.button, .pagination-previous:active, + .pagination-next:active, + .pagination-link:active, + .pagination-ellipsis:active, .file-cta:active, + .file-name:active, .select select:active, .textarea:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .button:active, .is-active.pagination-previous, + .is-active.pagination-next, + .is-active.pagination-link, + .is-active.pagination-ellipsis, .is-active.file-cta, + .is-active.file-name, .select select.is-active, .is-active.textarea, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .is-active.button { + outline: none; } + .pagination-previous[disabled], + .pagination-next[disabled], + .pagination-link[disabled], + .pagination-ellipsis[disabled], .file-cta[disabled], + .file-name[disabled], .select select[disabled], .textarea[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], .button[disabled], fieldset[disabled] .pagination-previous, + fieldset[disabled] .pagination-next, + fieldset[disabled] .pagination-link, + fieldset[disabled] .pagination-ellipsis, fieldset[disabled] .file-cta, + fieldset[disabled] .file-name, fieldset[disabled] .select select, .select fieldset[disabled] select, fieldset[disabled] .textarea, fieldset[disabled] .input, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input, fieldset[disabled] .button { + cursor: not-allowed; } + +/*! minireset.css v0.0.4 | MIT License | github.com/jgthms/minireset.css */ +html, +body, +p, +ol, +ul, +li, +dl, +dt, +dd, +blockquote, +figure, +fieldset, +legend, +textarea, +pre, +iframe, +hr, +h1, +h2, +h3, +h4, +h5, +h6 { + margin: 0; + padding: 0; } + +h1, +h2, +h3, +h4, +h5, +h6 { + font-size: 100%; + font-weight: normal; } + +ul { + list-style: none; } + +button, +input, +select, +textarea { + margin: 0; } + +html { + box-sizing: border-box; } + +*, *::before, *::after { + box-sizing: inherit; } + +img, +embed, +iframe, +object, +video { + height: auto; + max-width: 100%; } + +audio { + max-width: 100%; } + +iframe { + border: 0; } + +table { + border-collapse: collapse; + border-spacing: 0; } + +td, +th { + padding: 0; } + td:not([align]), + th:not([align]) { + text-align: left; } + +html { + background-color: #fff; + font-size: 16px; + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + +article, +aside, +figure, +footer, +header, +hgroup, +section { + display: block; } + +body, +button, +input, +select, +textarea { + font-family: "Montserrat", sans-serif; } + +code, +pre { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; + font-family: "Source Code Pro", monospace; } + +body { + color: #202020; + font-size: 1em; + font-weight: 400; + line-height: 1.5; } + +a { + color: #149eaa; + cursor: pointer; + text-decoration: none; } + a strong { + color: currentColor; } + a:hover { + color: #107c85; } + +code { + background-color: #ebe8f4; + color: #000000; + font-size: 0.875em; + font-weight: normal; + padding: 0.1em; } + +hr { + background-color: whitesmoke; + border: none; + display: block; + height: 2px; + margin: 1.5rem 0; } + +img { + height: auto; + max-width: 100%; } + +input[type="checkbox"], +input[type="radio"] { + vertical-align: baseline; } + +small { + font-size: 0.875em; } + +span { + font-style: inherit; + font-weight: inherit; } + +strong { + color: #654ca3; + font-weight: 700; } + +fieldset { + border: none; } + +pre { + -webkit-overflow-scrolling: touch; + background-color: #ebe8f4; + color: #202020; + font-size: 0.875em; + overflow-x: auto; + padding: 1.25rem 1.5rem; 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} + .is-size-2-mobile { + font-size: 2.5rem !important; } + .is-size-3-mobile { + font-size: 2rem !important; } + .is-size-4-mobile { + font-size: 1.5rem !important; } + .is-size-5-mobile { + font-size: 1.25rem !important; } + .is-size-6-mobile { + font-size: 1rem !important; } + .is-size-7-mobile { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 769px), print { + .is-size-1-tablet { + font-size: 3rem !important; } + .is-size-2-tablet { + font-size: 2.5rem !important; } + .is-size-3-tablet { + font-size: 2rem !important; } + .is-size-4-tablet { + font-size: 1.5rem !important; } + .is-size-5-tablet { + font-size: 1.25rem !important; } + .is-size-6-tablet { + font-size: 1rem !important; } + .is-size-7-tablet { + font-size: 0.75rem !important; } } + +@media screen and (max-width: 1055px) { + .is-size-1-touch { + font-size: 3rem !important; } + .is-size-2-touch { + font-size: 2.5rem !important; } + .is-size-3-touch { + font-size: 2rem !important; } + .is-size-4-touch { + font-size: 1.5rem !important; 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} + .is-size-7-widescreen { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1408px) { + .is-size-1-fullhd { + font-size: 3rem !important; } + .is-size-2-fullhd { + font-size: 2.5rem !important; } + .is-size-3-fullhd { + font-size: 2rem !important; } + .is-size-4-fullhd { + font-size: 1.5rem !important; } + .is-size-5-fullhd { + font-size: 1.25rem !important; } + .is-size-6-fullhd { + font-size: 1rem !important; } + .is-size-7-fullhd { + font-size: 0.75rem !important; } } + +.has-text-centered { + text-align: center !important; } + +.has-text-justified { + text-align: justify !important; } + +.has-text-left { + text-align: left !important; } + +.has-text-right { + text-align: right !important; } + +@media screen and (max-width: 768px) { + .has-text-centered-mobile { + text-align: center !important; } } + +@media screen and (min-width: 769px), print { + .has-text-centered-tablet { + text-align: center !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-centered-tablet-only { + text-align: center !important; } } + +@media screen and (max-width: 1055px) { + .has-text-centered-touch { + text-align: center !important; } } + +@media screen and (min-width: 1056px) { + .has-text-centered-desktop { + text-align: center !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-centered-desktop-only { + text-align: center !important; } } + +@media screen and (min-width: 1216px) { + .has-text-centered-widescreen { + text-align: center !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-centered-widescreen-only { + text-align: center !important; } } + +@media screen and (min-width: 1408px) { + .has-text-centered-fullhd { + text-align: center !important; } } + +@media screen and (max-width: 768px) { + .has-text-justified-mobile { + text-align: justify !important; } } + +@media screen and (min-width: 769px), print { + .has-text-justified-tablet { + text-align: justify !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-justified-tablet-only { + text-align: justify !important; } } + +@media screen and (max-width: 1055px) { + .has-text-justified-touch { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) { + .has-text-justified-desktop { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-justified-desktop-only { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) { + .has-text-justified-widescreen { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-justified-widescreen-only { + text-align: justify !important; } } + +@media screen and (min-width: 1408px) { + .has-text-justified-fullhd { + text-align: justify !important; } } + +@media screen and (max-width: 768px) { + .has-text-left-mobile { + text-align: left !important; } } + +@media screen and (min-width: 769px), print { + .has-text-left-tablet { + text-align: left !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-left-tablet-only { + text-align: left !important; } } + +@media screen and (max-width: 1055px) { + .has-text-left-touch { + text-align: left !important; } } + +@media screen and (min-width: 1056px) { + .has-text-left-desktop { + text-align: left !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-left-desktop-only { + text-align: left !important; } } + +@media screen and (min-width: 1216px) { + .has-text-left-widescreen { + text-align: left !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-left-widescreen-only { + text-align: left !important; } } + +@media screen and (min-width: 1408px) { + .has-text-left-fullhd { + text-align: left !important; } } + +@media screen and (max-width: 768px) { + .has-text-right-mobile { + text-align: right !important; } } + +@media screen and (min-width: 769px), print { + .has-text-right-tablet { + text-align: right !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-right-tablet-only { + text-align: right !important; } } + +@media screen and (max-width: 1055px) { + .has-text-right-touch { + text-align: right !important; } } + +@media screen and (min-width: 1056px) { + .has-text-right-desktop { + text-align: right !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-right-desktop-only { + text-align: right !important; } } + +@media screen and (min-width: 1216px) { + .has-text-right-widescreen { + text-align: right !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-right-widescreen-only { + text-align: right !important; } } + +@media screen and (min-width: 1408px) { + .has-text-right-fullhd { + text-align: right !important; } } + +.is-capitalized { + text-transform: capitalize !important; } + +.is-lowercase { + text-transform: lowercase !important; } + +.is-uppercase { + text-transform: uppercase !important; } + +.is-italic { + font-style: italic !important; } + +.has-text-white { + color: white !important; } + +a.has-text-white:hover, a.has-text-white:focus { + color: #e6e6e6 !important; } + +.has-background-white { + background-color: white !important; } + +.has-text-black { + color: #0a0a0a !important; } + +a.has-text-black:hover, a.has-text-black:focus { + color: black !important; } + +.has-background-black { + background-color: #0a0a0a !important; } + +.has-text-light { + color: whitesmoke !important; } + +a.has-text-light:hover, a.has-text-light:focus { + color: #dbdbdb !important; } + +.has-background-light { + background-color: whitesmoke !important; } + +.has-text-dark { + color: #363636 !important; } + +a.has-text-dark:hover, a.has-text-dark:focus { + color: #1c1c1c !important; } + +.has-background-dark { + background-color: #363636 !important; } + +.has-text-primary { + color: #4eb5de !important; } + +a.has-text-primary:hover, a.has-text-primary:focus { + color: #27a1d2 !important; } + +.has-background-primary { + background-color: #4eb5de !important; } + +.has-text-link { + color: #149eaa !important; } + +a.has-text-link:hover, a.has-text-link:focus { + color: #0f747c !important; } + +.has-background-link { + background-color: #149eaa !important; } + +.has-text-info { + color: #209cee !important; } + +a.has-text-info:hover, a.has-text-info:focus { + color: #1081cb !important; } + +.has-background-info { + background-color: #209cee !important; } + +.has-text-success { + color: #22c35b !important; } + +a.has-text-success:hover, a.has-text-success:focus { + color: #1a9847 !important; } + +.has-background-success { + background-color: #22c35b !important; } + +.has-text-warning { + color: #ffdd57 !important; } + +a.has-text-warning:hover, a.has-text-warning:focus { + color: #ffd324 !important; } + +.has-background-warning { + background-color: #ffdd57 !important; } + +.has-text-danger { + color: #da0b00 !important; } + +a.has-text-danger:hover, a.has-text-danger:focus { + color: #a70800 !important; } + +.has-background-danger { + background-color: #da0b00 !important; } + +.has-text-black-bis { + color: #121212 !important; } + +.has-background-black-bis { + background-color: #121212 !important; } + +.has-text-black-ter { + color: #242424 !important; } + +.has-background-black-ter { + background-color: #242424 !important; } + +.has-text-grey-darker { + color: #363636 !important; } + +.has-background-grey-darker { + background-color: #363636 !important; } + +.has-text-grey-dark { + color: #4a4a4a !important; } + +.has-background-grey-dark { + background-color: #4a4a4a !important; } + +.has-text-grey { + color: #6b6b6b !important; } + +.has-background-grey { + background-color: #6b6b6b !important; } + +.has-text-grey-light { + color: #b5b5b5 !important; } + +.has-background-grey-light { + background-color: #b5b5b5 !important; } + +.has-text-grey-lighter { + color: #dbdbdb !important; } + +.has-background-grey-lighter { + background-color: #dbdbdb !important; } + +.has-text-white-ter { + color: whitesmoke !important; } + +.has-background-white-ter { + background-color: whitesmoke !important; } + +.has-text-white-bis { + color: #fafafa !important; } + +.has-background-white-bis { + background-color: #fafafa !important; } + +.has-text-weight-light { + font-weight: 300 !important; } + +.has-text-weight-normal { + font-weight: 400 !important; } + +.has-text-weight-medium { + font-weight: 500 !important; } + +.has-text-weight-semibold { + font-weight: 600 !important; } + +.has-text-weight-bold { + font-weight: 700 !important; } + +.is-family-primary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-secondary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-sans-serif { + font-family: "Montserrat", sans-serif !important; } + +.is-family-monospace { + font-family: "Source Code Pro", monospace !important; } + +.is-family-code { + font-family: "Source Code Pro", monospace !important; } + +.is-block { + display: block !important; } + +@media screen and (max-width: 768px) { + .is-block-mobile { + display: block !important; } } + +@media screen and (min-width: 769px), print { + .is-block-tablet { + display: block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-block-tablet-only { + display: block !important; } } + +@media screen and (max-width: 1055px) { + .is-block-touch { + display: block !important; } } + +@media screen and (min-width: 1056px) { + .is-block-desktop { + display: block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-block-desktop-only { + display: block !important; } } + +@media screen and (min-width: 1216px) { + .is-block-widescreen { + display: block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-block-widescreen-only { + display: block !important; } } + +@media screen and (min-width: 1408px) { + .is-block-fullhd { + display: block !important; } } + +.is-flex { + display: flex !important; } + +@media screen and (max-width: 768px) { + .is-flex-mobile { + display: flex !important; } } + +@media screen and (min-width: 769px), print { + .is-flex-tablet { + display: flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-flex-tablet-only { + display: flex !important; } } + +@media screen and (max-width: 1055px) { + .is-flex-touch { + display: flex !important; } } + +@media screen and (min-width: 1056px) { + .is-flex-desktop { + display: flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-flex-desktop-only { + display: flex !important; } } + +@media screen and (min-width: 1216px) { + .is-flex-widescreen { + display: flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-flex-widescreen-only { + display: flex !important; } } + +@media screen and (min-width: 1408px) { + .is-flex-fullhd { + display: flex !important; } } + +.is-inline { + display: inline !important; } + +@media screen and (max-width: 768px) { + .is-inline-mobile { + display: inline !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-tablet { + display: inline !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-tablet-only { + display: inline !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-touch { + display: inline !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-desktop { + display: inline !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-desktop-only { + display: inline !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-widescreen { + display: inline !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-widescreen-only { + display: inline !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-fullhd { + display: inline !important; } } + +.is-inline-block { + display: inline-block !important; } + +@media screen and (max-width: 768px) { + .is-inline-block-mobile { + display: inline-block !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-block-tablet { + display: inline-block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-block-tablet-only { + display: inline-block !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-block-touch { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-block-desktop { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-block-desktop-only { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-block-widescreen { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-block-widescreen-only { + display: inline-block !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-block-fullhd { + display: inline-block !important; } } + +.is-inline-flex { + display: inline-flex !important; } + +@media screen and (max-width: 768px) { + .is-inline-flex-mobile { + display: inline-flex !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-flex-tablet { + display: inline-flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-flex-tablet-only { + display: inline-flex !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-flex-touch { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-flex-desktop { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-flex-desktop-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-flex-widescreen { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-flex-widescreen-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-flex-fullhd { + display: inline-flex !important; } } + +.is-hidden { + display: none !important; } + +.is-sr-only { + border: none !important; + clip: rect(0, 0, 0, 0) !important; + height: 0.01em !important; + overflow: hidden !important; + padding: 0 !important; + position: absolute !important; + white-space: nowrap !important; + width: 0.01em !important; } + +@media screen and (max-width: 768px) { + .is-hidden-mobile { + display: none !important; } } + +@media screen and (min-width: 769px), print { + .is-hidden-tablet { + display: none !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-hidden-tablet-only { + display: none !important; } } + +@media screen and (max-width: 1055px) { + .is-hidden-touch { + display: none !important; } } + +@media screen and (min-width: 1056px) { + .is-hidden-desktop { + display: none !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-hidden-desktop-only { + display: none !important; } } + +@media screen and (min-width: 1216px) { + .is-hidden-widescreen { + display: none !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-hidden-widescreen-only { + display: none !important; } } + +@media screen and (min-width: 1408px) { + .is-hidden-fullhd { + display: none !important; } } + +.is-invisible { + visibility: hidden !important; } + +@media screen and (max-width: 768px) { + .is-invisible-mobile { + visibility: hidden !important; } } + +@media screen and (min-width: 769px), print { + .is-invisible-tablet { + visibility: hidden !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-invisible-tablet-only { + visibility: hidden !important; } } + +@media screen and (max-width: 1055px) { + .is-invisible-touch { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) { + .is-invisible-desktop { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-invisible-desktop-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) { + .is-invisible-widescreen { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-invisible-widescreen-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1408px) { + .is-invisible-fullhd { + visibility: hidden !important; } } + +.is-marginless { + margin: 0 !important; } + +.is-paddingless { + padding: 0 !important; } + +.is-radiusless { + border-radius: 0 !important; } + +.is-shadowless { + box-shadow: none !important; } + +.is-relative { + position: relative !important; } + +.box { + background-color: white; + border-radius: 6px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #202020; + display: block; + padding: 1.25rem; } + +a.box:hover, a.box:focus { + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #149eaa; } + +a.box:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #149eaa; } + +.button { + background-color: white; + border-color: #dbdbdb; + border-width: 1px; + color: #363636; + cursor: pointer; + justify-content: center; + padding-bottom: calc(0.375em - 1px); + padding-left: 0.75em; + padding-right: 0.75em; + padding-top: calc(0.375em - 1px); + text-align: center; + white-space: nowrap; } + .button strong { + color: inherit; } + .button .icon, .button .icon.is-small, .button #documenter .docs-sidebar form.docs-search > input.icon, #documenter .docs-sidebar .button form.docs-search > input.icon, .button .icon.is-medium, .button .icon.is-large { + height: 1.5em; + width: 1.5em; } + .button .icon:first-child:not(:last-child) { + margin-left: calc(-0.375em - 1px); + margin-right: 0.1875em; } + .button .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: calc(-0.375em - 1px); } + .button .icon:first-child:last-child { + margin-left: calc(-0.375em - 1px); + margin-right: calc(-0.375em - 1px); } + .button:hover, .button.is-hovered { + border-color: #b5b5b5; + color: #107c85; } + .button:focus, .button.is-focused { + border-color: #3c5dcd; + color: #363636; } + .button:focus:not(:active), .button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .button:active, .button.is-active { + border-color: #4a4a4a; + color: #363636; } + .button.is-text { + background-color: transparent; + border-color: transparent; + color: #202020; + text-decoration: underline; } + .button.is-text:hover, .button.is-text.is-hovered, .button.is-text:focus, .button.is-text.is-focused { + background-color: whitesmoke; + color: #654ca3; } + .button.is-text:active, .button.is-text.is-active { + background-color: #e8e8e8; + color: #654ca3; } + .button.is-text[disabled], fieldset[disabled] .button.is-text { + background-color: transparent; + border-color: transparent; + box-shadow: none; } + .button.is-white { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + .button.is-white:hover, .button.is-white.is-hovered { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + .button.is-white:focus, .button.is-white.is-focused { + border-color: transparent; + color: #0a0a0a; } + .button.is-white:focus:not(:active), .button.is-white.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .button.is-white:active, .button.is-white.is-active { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + .button.is-white[disabled], fieldset[disabled] .button.is-white { + background-color: white; + border-color: transparent; + box-shadow: none; } + .button.is-white.is-inverted { + background-color: #0a0a0a; + color: white; } + .button.is-white.is-inverted:hover, .button.is-white.is-inverted.is-hovered { + background-color: black; } + .button.is-white.is-inverted[disabled], fieldset[disabled] .button.is-white.is-inverted { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; + color: white; } + .button.is-white.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + .button.is-white.is-outlined:hover, .button.is-white.is-outlined.is-hovered, .button.is-white.is-outlined:focus, .button.is-white.is-outlined.is-focused { + background-color: white; + border-color: white; + color: #0a0a0a; } + .button.is-white.is-outlined.is-loading::after { + border-color: transparent transparent white white !important; } + .button.is-white.is-outlined.is-loading:hover::after, .button.is-white.is-outlined.is-loading.is-hovered::after, .button.is-white.is-outlined.is-loading:focus::after, .button.is-white.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-white.is-outlined[disabled], fieldset[disabled] .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + .button.is-white.is-inverted.is-outlined:hover, .button.is-white.is-inverted.is-outlined.is-hovered, .button.is-white.is-inverted.is-outlined:focus, .button.is-white.is-inverted.is-outlined.is-focused { + background-color: #0a0a0a; + color: white; } + .button.is-white.is-inverted.is-outlined.is-loading:hover::after, .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-white.is-inverted.is-outlined.is-loading:focus::after, .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + .button.is-white.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + .button.is-black:hover, .button.is-black.is-hovered { + background-color: #040404; + border-color: transparent; + color: white; } + .button.is-black:focus, .button.is-black.is-focused { + border-color: transparent; + color: white; } + .button.is-black:focus:not(:active), .button.is-black.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .button.is-black:active, .button.is-black.is-active { + background-color: black; + border-color: transparent; + color: white; } + .button.is-black[disabled], fieldset[disabled] .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; } + .button.is-black.is-inverted { + background-color: white; + color: #0a0a0a; } + .button.is-black.is-inverted:hover, .button.is-black.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-black.is-inverted[disabled], fieldset[disabled] .button.is-black.is-inverted { + background-color: white; + border-color: transparent; + box-shadow: none; + color: #0a0a0a; } + .button.is-black.is-loading::after { + border-color: transparent transparent white white !important; } + .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + .button.is-black.is-outlined:hover, .button.is-black.is-outlined.is-hovered, .button.is-black.is-outlined:focus, .button.is-black.is-outlined.is-focused { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .button.is-black.is-outlined.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-black.is-outlined.is-loading:hover::after, .button.is-black.is-outlined.is-loading.is-hovered::after, .button.is-black.is-outlined.is-loading:focus::after, .button.is-black.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + .button.is-black.is-outlined[disabled], fieldset[disabled] .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + .button.is-black.is-inverted.is-outlined:hover, .button.is-black.is-inverted.is-outlined.is-hovered, .button.is-black.is-inverted.is-outlined:focus, .button.is-black.is-inverted.is-outlined.is-focused { + background-color: white; + color: #0a0a0a; } + .button.is-black.is-inverted.is-outlined.is-loading:hover::after, .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-black.is-inverted.is-outlined.is-loading:focus::after, .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + .button.is-light { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + .button.is-light:hover, .button.is-light.is-hovered { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + .button.is-light:focus, .button.is-light.is-focused { + border-color: transparent; + color: #363636; } + .button.is-light:focus:not(:active), .button.is-light.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .button.is-light:active, .button.is-light.is-active { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + .button.is-light[disabled], fieldset[disabled] .button.is-light { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; } + .button.is-light.is-inverted { + background-color: #363636; + color: whitesmoke; } + .button.is-light.is-inverted:hover, .button.is-light.is-inverted.is-hovered { + background-color: #292929; } + .button.is-light.is-inverted[disabled], fieldset[disabled] .button.is-light.is-inverted { + background-color: #363636; + border-color: transparent; + box-shadow: none; + color: whitesmoke; } + .button.is-light.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + .button.is-light.is-outlined:hover, .button.is-light.is-outlined.is-hovered, .button.is-light.is-outlined:focus, .button.is-light.is-outlined.is-focused { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .button.is-light.is-outlined.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-light.is-outlined.is-loading:hover::after, .button.is-light.is-outlined.is-loading.is-hovered::after, .button.is-light.is-outlined.is-loading:focus::after, .button.is-light.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-light.is-outlined[disabled], fieldset[disabled] .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + .button.is-light.is-inverted.is-outlined:hover, .button.is-light.is-inverted.is-outlined.is-hovered, .button.is-light.is-inverted.is-outlined:focus, .button.is-light.is-inverted.is-outlined.is-focused { + background-color: #363636; + color: whitesmoke; } + .button.is-light.is-inverted.is-outlined.is-loading:hover::after, .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-light.is-inverted.is-outlined.is-loading:focus::after, .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + .button.is-dark, .content kbd.button { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + .button.is-dark:hover, .content kbd.button:hover, .button.is-dark.is-hovered, .content kbd.button.is-hovered { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + .button.is-dark:focus, .content kbd.button:focus, .button.is-dark.is-focused, .content kbd.button.is-focused { + border-color: transparent; + color: whitesmoke; } + .button.is-dark:focus:not(:active), .content kbd.button:focus:not(:active), .button.is-dark.is-focused:not(:active), .content kbd.button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .button.is-dark:active, .content kbd.button:active, .button.is-dark.is-active, .content kbd.button.is-active { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + .button.is-dark[disabled], .content kbd.button[disabled], fieldset[disabled] .button.is-dark, fieldset[disabled] .content kbd.button, .content fieldset[disabled] kbd.button { + background-color: #363636; + border-color: transparent; + box-shadow: none; } + .button.is-dark.is-inverted, .content kbd.button.is-inverted { + background-color: whitesmoke; + color: #363636; } + .button.is-dark.is-inverted:hover, .content kbd.button.is-inverted:hover, .button.is-dark.is-inverted.is-hovered, .content kbd.button.is-inverted.is-hovered { + background-color: #e8e8e8; } + .button.is-dark.is-inverted[disabled], .content kbd.button.is-inverted[disabled], fieldset[disabled] .button.is-dark.is-inverted, fieldset[disabled] .content kbd.button.is-inverted, .content fieldset[disabled] kbd.button.is-inverted { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; + color: #363636; } + .button.is-dark.is-loading::after, .content kbd.button.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-dark.is-outlined, .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + .button.is-dark.is-outlined:hover, .content kbd.button.is-outlined:hover, .button.is-dark.is-outlined.is-hovered, .content kbd.button.is-outlined.is-hovered, .button.is-dark.is-outlined:focus, .content kbd.button.is-outlined:focus, .button.is-dark.is-outlined.is-focused, .content kbd.button.is-outlined.is-focused { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .button.is-dark.is-outlined.is-loading::after, .content kbd.button.is-outlined.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-dark.is-outlined.is-loading:hover::after, .content kbd.button.is-outlined.is-loading:hover::after, .button.is-dark.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-outlined.is-loading:focus::after, .content kbd.button.is-outlined.is-loading:focus::after, .button.is-dark.is-outlined.is-loading.is-focused::after, .content kbd.button.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-dark.is-outlined[disabled], .content kbd.button.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-outlined, fieldset[disabled] .content kbd.button.is-outlined, .content fieldset[disabled] kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + .button.is-dark.is-inverted.is-outlined, .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + .button.is-dark.is-inverted.is-outlined:hover, .content kbd.button.is-inverted.is-outlined:hover, .button.is-dark.is-inverted.is-outlined.is-hovered, .content kbd.button.is-inverted.is-outlined.is-hovered, .button.is-dark.is-inverted.is-outlined:focus, .content kbd.button.is-inverted.is-outlined:focus, .button.is-dark.is-inverted.is-outlined.is-focused, .content kbd.button.is-inverted.is-outlined.is-focused { + background-color: whitesmoke; + color: #363636; } + .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-dark.is-inverted.is-outlined[disabled], .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-inverted.is-outlined, fieldset[disabled] .content kbd.button.is-inverted.is-outlined, .content fieldset[disabled] kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + .button.is-primary, .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + .button.is-primary:hover, .docstring > section > a.button.docs-sourcelink:hover, .button.is-primary.is-hovered, .docstring > section > a.button.is-hovered.docs-sourcelink { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + .button.is-primary:focus, .docstring > section > a.button.docs-sourcelink:focus, .button.is-primary.is-focused, .docstring > section > a.button.is-focused.docs-sourcelink { + border-color: transparent; + color: #fff; } + .button.is-primary:focus:not(:active), .docstring > section > a.button.docs-sourcelink:focus:not(:active), .button.is-primary.is-focused:not(:active), .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .button.is-primary:active, .docstring > section > a.button.docs-sourcelink:active, .button.is-primary.is-active, .docstring > section > a.button.is-active.docs-sourcelink { + background-color: #39acda; + border-color: transparent; + color: #fff; } + .button.is-primary[disabled], .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary, fieldset[disabled] .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + box-shadow: none; } + .button.is-primary.is-inverted, .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + .button.is-primary.is-inverted:hover, .docstring > section > a.button.is-inverted.docs-sourcelink:hover, .button.is-primary.is-inverted.is-hovered, .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { + background-color: #f2f2f2; } + .button.is-primary.is-inverted[disabled], .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted, fieldset[disabled] .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #4eb5de; } + .button.is-primary.is-loading::after, .docstring > section > a.button.is-loading.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-primary.is-outlined, .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + color: #4eb5de; } + .button.is-primary.is-outlined:hover, .docstring > section > a.button.is-outlined.docs-sourcelink:hover, .button.is-primary.is-outlined.is-hovered, .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-outlined:focus, .docstring > section > a.button.is-outlined.docs-sourcelink:focus, .button.is-primary.is-outlined.is-focused, .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + .button.is-primary.is-outlined.is-loading::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + .button.is-primary.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-primary.is-outlined[disabled], .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-outlined, fieldset[disabled] .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + box-shadow: none; + color: #4eb5de; } + .button.is-primary.is-inverted.is-outlined, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-primary.is-inverted.is-outlined:hover, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, .button.is-primary.is-inverted.is-outlined.is-hovered, .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-inverted.is-outlined:focus, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, .button.is-primary.is-inverted.is-outlined.is-focused, .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + .button.is-primary.is-inverted.is-outlined[disabled], .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted.is-outlined, fieldset[disabled] .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-link { + background-color: #149eaa; + border-color: transparent; + color: #fff; } + .button.is-link:hover, .button.is-link.is-hovered { + background-color: #13939f; + border-color: transparent; + color: #fff; } + .button.is-link:focus, .button.is-link.is-focused { + border-color: transparent; + color: #fff; } + .button.is-link:focus:not(:active), .button.is-link.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .button.is-link:active, .button.is-link.is-active { + background-color: #118993; + border-color: transparent; + color: #fff; } + .button.is-link[disabled], fieldset[disabled] .button.is-link { + background-color: #149eaa; + border-color: transparent; + box-shadow: none; } + .button.is-link.is-inverted { + background-color: #fff; + color: #149eaa; } + .button.is-link.is-inverted:hover, .button.is-link.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-link.is-inverted[disabled], fieldset[disabled] .button.is-link.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #149eaa; } + .button.is-link.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-link.is-outlined { + background-color: transparent; + border-color: #149eaa; + color: #149eaa; } + .button.is-link.is-outlined:hover, .button.is-link.is-outlined.is-hovered, .button.is-link.is-outlined:focus, .button.is-link.is-outlined.is-focused { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + .button.is-link.is-outlined.is-loading::after { + border-color: transparent transparent #149eaa #149eaa !important; } + .button.is-link.is-outlined.is-loading:hover::after, .button.is-link.is-outlined.is-loading.is-hovered::after, .button.is-link.is-outlined.is-loading:focus::after, .button.is-link.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-link.is-outlined[disabled], fieldset[disabled] .button.is-link.is-outlined { + background-color: transparent; + border-color: #149eaa; + box-shadow: none; + color: #149eaa; } + .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-link.is-inverted.is-outlined:hover, .button.is-link.is-inverted.is-outlined.is-hovered, .button.is-link.is-inverted.is-outlined:focus, .button.is-link.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #149eaa; } + .button.is-link.is-inverted.is-outlined.is-loading:hover::after, .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-link.is-inverted.is-outlined.is-loading:focus::after, .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #149eaa #149eaa !important; } + .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-info { + background-color: #209cee; + border-color: transparent; + color: #fff; } + .button.is-info:hover, .button.is-info.is-hovered { + background-color: #1497ed; + border-color: transparent; + color: #fff; } + .button.is-info:focus, .button.is-info.is-focused { + border-color: transparent; + color: #fff; } + .button.is-info:focus:not(:active), .button.is-info.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .button.is-info:active, .button.is-info.is-active { + background-color: #1190e3; + border-color: transparent; + color: #fff; } + .button.is-info[disabled], fieldset[disabled] .button.is-info { + background-color: #209cee; + border-color: transparent; + box-shadow: none; } + .button.is-info.is-inverted { + background-color: #fff; + color: #209cee; } + .button.is-info.is-inverted:hover, .button.is-info.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-info.is-inverted[disabled], fieldset[disabled] .button.is-info.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #209cee; } + .button.is-info.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-info.is-outlined { + background-color: transparent; + border-color: #209cee; + color: #209cee; } + .button.is-info.is-outlined:hover, .button.is-info.is-outlined.is-hovered, .button.is-info.is-outlined:focus, .button.is-info.is-outlined.is-focused { + background-color: #209cee; + border-color: #209cee; + color: #fff; } + .button.is-info.is-outlined.is-loading::after { + border-color: transparent transparent #209cee #209cee !important; } + .button.is-info.is-outlined.is-loading:hover::after, .button.is-info.is-outlined.is-loading.is-hovered::after, .button.is-info.is-outlined.is-loading:focus::after, .button.is-info.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-info.is-outlined[disabled], fieldset[disabled] .button.is-info.is-outlined { + background-color: transparent; + border-color: #209cee; + box-shadow: none; + color: #209cee; } + .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-info.is-inverted.is-outlined:hover, .button.is-info.is-inverted.is-outlined.is-hovered, .button.is-info.is-inverted.is-outlined:focus, .button.is-info.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #209cee; } + .button.is-info.is-inverted.is-outlined.is-loading:hover::after, .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-info.is-inverted.is-outlined.is-loading:focus::after, .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #209cee #209cee !important; } + .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-success { + background-color: #22c35b; + border-color: transparent; + color: #fff; } + .button.is-success:hover, .button.is-success.is-hovered { + background-color: #20b856; + border-color: transparent; + color: #fff; } + .button.is-success:focus, .button.is-success.is-focused { + border-color: transparent; + color: #fff; } + .button.is-success:focus:not(:active), .button.is-success.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .button.is-success:active, .button.is-success.is-active { + background-color: #1ead51; + border-color: transparent; + color: #fff; } + .button.is-success[disabled], fieldset[disabled] .button.is-success { + background-color: #22c35b; + border-color: transparent; + box-shadow: none; } + .button.is-success.is-inverted { + background-color: #fff; + color: #22c35b; } + .button.is-success.is-inverted:hover, .button.is-success.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-success.is-inverted[disabled], fieldset[disabled] .button.is-success.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #22c35b; } + .button.is-success.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-success.is-outlined { + background-color: transparent; + border-color: #22c35b; + color: #22c35b; } + .button.is-success.is-outlined:hover, .button.is-success.is-outlined.is-hovered, .button.is-success.is-outlined:focus, .button.is-success.is-outlined.is-focused { + background-color: #22c35b; + border-color: #22c35b; + color: #fff; } + .button.is-success.is-outlined.is-loading::after { + border-color: transparent transparent #22c35b #22c35b !important; } + .button.is-success.is-outlined.is-loading:hover::after, .button.is-success.is-outlined.is-loading.is-hovered::after, .button.is-success.is-outlined.is-loading:focus::after, .button.is-success.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-success.is-outlined[disabled], fieldset[disabled] .button.is-success.is-outlined { + background-color: transparent; + border-color: #22c35b; + box-shadow: none; + color: #22c35b; } + .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-success.is-inverted.is-outlined:hover, .button.is-success.is-inverted.is-outlined.is-hovered, .button.is-success.is-inverted.is-outlined:focus, .button.is-success.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #22c35b; } + .button.is-success.is-inverted.is-outlined.is-loading:hover::after, .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-success.is-inverted.is-outlined.is-loading:focus::after, .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #22c35b #22c35b !important; } + .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-warning { + background-color: #ffdd57; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:hover, .button.is-warning.is-hovered { + background-color: #ffda4a; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:focus, .button.is-warning.is-focused { + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:focus:not(:active), .button.is-warning.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .button.is-warning:active, .button.is-warning.is-active { + background-color: #ffd83e; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning[disabled], fieldset[disabled] .button.is-warning { + background-color: #ffdd57; + border-color: transparent; + box-shadow: none; } + .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .button.is-warning.is-inverted:hover, .button.is-warning.is-inverted.is-hovered { + background-color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-inverted[disabled], fieldset[disabled] .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + border-color: transparent; + box-shadow: none; + color: #ffdd57; } + .button.is-warning.is-loading::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + .button.is-warning.is-outlined { + background-color: transparent; + border-color: #ffdd57; + color: #ffdd57; } + .button.is-warning.is-outlined:hover, .button.is-warning.is-outlined.is-hovered, .button.is-warning.is-outlined:focus, .button.is-warning.is-outlined.is-focused { + background-color: #ffdd57; + border-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-outlined.is-loading::after { + border-color: transparent transparent #ffdd57 #ffdd57 !important; } + .button.is-warning.is-outlined.is-loading:hover::after, .button.is-warning.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-outlined.is-loading:focus::after, .button.is-warning.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + .button.is-warning.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-outlined { + background-color: transparent; + border-color: #ffdd57; + box-shadow: none; + color: #ffdd57; } + .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-inverted.is-outlined:hover, .button.is-warning.is-inverted.is-outlined.is-hovered, .button.is-warning.is-inverted.is-outlined:focus, .button.is-warning.is-inverted.is-outlined.is-focused { + background-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #ffdd57 #ffdd57 !important; } + .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + box-shadow: none; + color: rgba(0, 0, 0, 0.7); } + .button.is-danger { + background-color: #da0b00; + border-color: transparent; + color: #fff; } + .button.is-danger:hover, .button.is-danger.is-hovered { + background-color: #cd0a00; + border-color: transparent; + color: #fff; } + .button.is-danger:focus, .button.is-danger.is-focused { + border-color: transparent; + color: #fff; } + .button.is-danger:focus:not(:active), .button.is-danger.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .button.is-danger:active, .button.is-danger.is-active { + background-color: #c10a00; + border-color: transparent; + color: #fff; } + .button.is-danger[disabled], fieldset[disabled] .button.is-danger { + background-color: #da0b00; + border-color: transparent; + box-shadow: none; } + .button.is-danger.is-inverted { + background-color: #fff; + color: #da0b00; } + .button.is-danger.is-inverted:hover, .button.is-danger.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-danger.is-inverted[disabled], fieldset[disabled] .button.is-danger.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #da0b00; } + .button.is-danger.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-danger.is-outlined { + background-color: transparent; + border-color: #da0b00; + color: #da0b00; } + .button.is-danger.is-outlined:hover, .button.is-danger.is-outlined.is-hovered, .button.is-danger.is-outlined:focus, .button.is-danger.is-outlined.is-focused { + background-color: #da0b00; + border-color: #da0b00; + color: #fff; } + .button.is-danger.is-outlined.is-loading::after { + border-color: transparent transparent #da0b00 #da0b00 !important; } + .button.is-danger.is-outlined.is-loading:hover::after, .button.is-danger.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-outlined.is-loading:focus::after, .button.is-danger.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-danger.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-outlined { + background-color: transparent; + border-color: #da0b00; + box-shadow: none; + color: #da0b00; } + .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-danger.is-inverted.is-outlined:hover, .button.is-danger.is-inverted.is-outlined.is-hovered, .button.is-danger.is-inverted.is-outlined:focus, .button.is-danger.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #da0b00; } + .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #da0b00 #da0b00 !important; } + .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-small, #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 2px; + font-size: 0.75rem; } + .button.is-normal { + font-size: 1rem; } + .button.is-medium { + font-size: 1.25rem; } + .button.is-large { + font-size: 1.5rem; } + .button[disabled], fieldset[disabled] .button { + background-color: white; + border-color: #dbdbdb; + box-shadow: none; + opacity: 0.5; } + .button.is-fullwidth { + display: flex; + width: 100%; } + .button.is-loading { + color: transparent !important; + pointer-events: none; } + .button.is-loading::after { + position: absolute; + left: calc(50% - (1em / 2)); + top: calc(50% - (1em / 2)); + position: absolute !important; } + .button.is-static { + background-color: whitesmoke; + border-color: #dbdbdb; + color: #6b6b6b; + box-shadow: none; + pointer-events: none; } + .button.is-rounded, #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + +.buttons { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .buttons .button { + margin-bottom: 0.5rem; } + .buttons .button:not(:last-child):not(.is-fullwidth) { + margin-right: 0.5rem; } + .buttons:last-child { + margin-bottom: -0.5rem; } + .buttons:not(:last-child) { + margin-bottom: 1rem; } + .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { + border-radius: 2px; + font-size: 0.75rem; } + .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { + font-size: 1.25rem; } + .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { + font-size: 1.5rem; } + .buttons.has-addons .button:not(:first-child) { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .buttons.has-addons .button:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; + margin-right: -1px; } + .buttons.has-addons .button:last-child { + margin-right: 0; } + .buttons.has-addons .button:hover, .buttons.has-addons .button.is-hovered { + z-index: 2; } + .buttons.has-addons .button:focus, .buttons.has-addons .button.is-focused, .buttons.has-addons .button:active, .buttons.has-addons .button.is-active, .buttons.has-addons .button.is-selected { + z-index: 3; } + .buttons.has-addons .button:focus:hover, .buttons.has-addons .button.is-focused:hover, .buttons.has-addons .button:active:hover, .buttons.has-addons .button.is-active:hover, .buttons.has-addons .button.is-selected:hover { + z-index: 4; } + .buttons.has-addons .button.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .buttons.is-centered { + justify-content: center; } + .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + .buttons.is-right { + justify-content: flex-end; } + .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + +.container { + flex-grow: 1; + margin: 0 auto; + position: relative; + width: auto; } + @media screen and (min-width: 1056px) { + .container { + max-width: 992px; } + .container.is-fluid { + margin-left: 32px; + margin-right: 32px; + max-width: none; } } + @media screen and (max-width: 1215px) { + .container.is-widescreen { + max-width: 1152px; } } + @media screen and (max-width: 1407px) { + .container.is-fullhd { + max-width: 1344px; } } + @media screen and (min-width: 1216px) { + .container { + max-width: 1152px; } } + @media screen and (min-width: 1408px) { + .container { + max-width: 1344px; } } +.content li + li { + margin-top: 0.25em; } + +.content p:not(:last-child), +.content dl:not(:last-child), +.content ol:not(:last-child), +.content ul:not(:last-child), +.content blockquote:not(:last-child), +.content pre:not(:last-child), +.content table:not(:last-child) { + margin-bottom: 1em; } + +.content h1, +.content h2, +.content h3, +.content h4, +.content h5, +.content h6 { + color: #654ca3; + font-weight: 600; + line-height: 1.125; } + +.content h1 { + font-size: 2em; + margin-bottom: 0.5em; } + .content h1:not(:first-child) { + margin-top: 1em; } + +.content h2 { + font-size: 1.75em; + margin-bottom: 0.5714em; } + .content h2:not(:first-child) { + margin-top: 1.1428em; } + +.content h3 { + font-size: 1.5em; + margin-bottom: 0.6666em; } + .content h3:not(:first-child) { + margin-top: 1.3333em; } + +.content h4 { + font-size: 1.25em; + margin-bottom: 0.8em; } + +.content h5 { + font-size: 1.125em; + margin-bottom: 0.8888em; } + +.content h6 { + font-size: 1em; + margin-bottom: 1em; } + +.content blockquote { + background-color: whitesmoke; + border-left: 5px solid #dbdbdb; + padding: 1.25em 1.5em; } + +.content ol { + list-style-position: outside; + margin-left: 2em; + margin-top: 1em; } + .content ol:not([type]) { + list-style-type: decimal; } + .content ol.is-lower-alpha:not([type]) { + list-style-type: lower-alpha; } + .content ol.is-lower-roman:not([type]) { + list-style-type: lower-roman; } + .content ol.is-upper-alpha:not([type]) { + list-style-type: upper-alpha; } + .content ol.is-upper-roman:not([type]) { + list-style-type: upper-roman; } + +.content ul { + list-style: disc outside; + margin-left: 2em; + margin-top: 1em; } + .content ul ul { + list-style-type: circle; + margin-top: 0.5em; } + .content ul ul ul { + list-style-type: square; } + +.content dd { + margin-left: 2em; } + +.content figure { + margin-left: 2em; + margin-right: 2em; + text-align: center; } + .content figure:not(:first-child) { + margin-top: 2em; } + .content figure:not(:last-child) { + margin-bottom: 2em; } + .content figure img { + display: inline-block; } + .content figure figcaption { + font-style: italic; } + +.content pre { + -webkit-overflow-scrolling: touch; + overflow-x: auto; + padding: 0; + white-space: pre; + word-wrap: normal; } + +.content sup, +.content sub { + font-size: 75%; } + +.content table { + width: 100%; } + .content table td, + .content table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + .content table th { + color: #654ca3; } + .content table th:not([align]) { + text-align: left; } + .content table thead td, + .content table thead th { + border-width: 0 0 2px; + color: #654ca3; } + .content table tfoot td, + .content table tfoot th { + border-width: 2px 0 0; + color: #654ca3; } + .content table tbody tr:last-child td, + .content table tbody tr:last-child th { + border-bottom-width: 0; } + +.content .tabs li + li { + margin-top: 0; } + +.content.is-small, #documenter .docs-sidebar form.docs-search > input.content { + font-size: 0.75rem; } + +.content.is-medium { + font-size: 1.25rem; } + +.content.is-large { + font-size: 1.5rem; } + +.icon { + align-items: center; + display: inline-flex; + justify-content: center; + height: 1.5rem; + width: 1.5rem; } + .icon.is-small, #documenter .docs-sidebar form.docs-search > input.icon { + height: 1rem; + width: 1rem; } + .icon.is-medium { + height: 2rem; + width: 2rem; } + .icon.is-large { + height: 3rem; + width: 3rem; } + +.image, #documenter .docs-sidebar .docs-logo > img { + display: block; + position: relative; } + .image img, #documenter .docs-sidebar .docs-logo > img img { + display: block; + height: auto; + width: 100%; } + .image img.is-rounded, #documenter .docs-sidebar .docs-logo > img img.is-rounded { + border-radius: 290486px; } + .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img, + .image.is-square .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img, + .image.is-1by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img, + .image.is-5by4 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img, + .image.is-4by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img, + .image.is-3by2 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img, + .image.is-5by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img, + .image.is-16by9 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img, + .image.is-2by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img, + .image.is-3by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img, + .image.is-4by5 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img, + .image.is-3by4 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img, + .image.is-2by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img, + .image.is-3by5 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img, + .image.is-9by16 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img, + .image.is-1by2 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img, + .image.is-1by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { + height: 100%; + width: 100%; } + .image.is-square, #documenter .docs-sidebar .docs-logo > img.is-square, .image.is-1by1, #documenter .docs-sidebar .docs-logo > img.is-1by1 { + padding-top: 100%; } + .image.is-5by4, #documenter .docs-sidebar .docs-logo > img.is-5by4 { + padding-top: 80%; } + .image.is-4by3, #documenter .docs-sidebar .docs-logo > img.is-4by3 { + padding-top: 75%; } + .image.is-3by2, #documenter .docs-sidebar .docs-logo > img.is-3by2 { + padding-top: 66.6666%; } + .image.is-5by3, #documenter .docs-sidebar .docs-logo > img.is-5by3 { + padding-top: 60%; } + .image.is-16by9, #documenter .docs-sidebar .docs-logo > img.is-16by9 { + padding-top: 56.25%; } + .image.is-2by1, #documenter .docs-sidebar .docs-logo > img.is-2by1 { + padding-top: 50%; } + .image.is-3by1, #documenter .docs-sidebar .docs-logo > img.is-3by1 { + padding-top: 33.3333%; } + .image.is-4by5, #documenter .docs-sidebar .docs-logo > img.is-4by5 { + padding-top: 125%; } + .image.is-3by4, #documenter .docs-sidebar .docs-logo > img.is-3by4 { + padding-top: 133.3333%; } + .image.is-2by3, #documenter .docs-sidebar .docs-logo > img.is-2by3 { + padding-top: 150%; } + .image.is-3by5, #documenter .docs-sidebar .docs-logo > img.is-3by5 { + padding-top: 166.6666%; } + .image.is-9by16, #documenter .docs-sidebar .docs-logo > img.is-9by16 { + padding-top: 177.7777%; } + .image.is-1by2, #documenter .docs-sidebar .docs-logo > img.is-1by2 { + padding-top: 200%; } + .image.is-1by3, #documenter .docs-sidebar .docs-logo > img.is-1by3 { + padding-top: 300%; } + .image.is-16x16, #documenter .docs-sidebar .docs-logo > img.is-16x16 { + height: 16px; + width: 16px; } + .image.is-24x24, #documenter .docs-sidebar .docs-logo > img.is-24x24 { + height: 24px; + width: 24px; } + .image.is-32x32, #documenter .docs-sidebar .docs-logo > img.is-32x32 { + height: 32px; + width: 32px; } + .image.is-48x48, #documenter .docs-sidebar .docs-logo > img.is-48x48 { + height: 48px; + width: 48px; } + .image.is-64x64, #documenter .docs-sidebar .docs-logo > img.is-64x64 { + height: 64px; + width: 64px; } + .image.is-96x96, #documenter .docs-sidebar .docs-logo > img.is-96x96 { + height: 96px; + width: 96px; } + .image.is-128x128, #documenter .docs-sidebar .docs-logo > img.is-128x128 { + height: 128px; + width: 128px; } + +.notification { + background-color: whitesmoke; + border-radius: 4px; + padding: 1.25rem 2.5rem 1.25rem 1.5rem; + position: relative; } + .notification a:not(.button):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + .notification strong { + color: currentColor; } + .notification code, + .notification pre { + background: white; } + .notification pre code { + background: transparent; } + .notification > .delete { + position: absolute; + right: 0.5rem; + top: 0.5rem; } + .notification .title, + .notification .subtitle, + .notification .content { + color: currentColor; } + .notification.is-white { + background-color: white; + color: #0a0a0a; } + .notification.is-black { + background-color: #0a0a0a; + color: white; } + .notification.is-light { + background-color: whitesmoke; + color: #363636; } + .notification.is-dark, .content kbd.notification { + background-color: #363636; + color: whitesmoke; } + .notification.is-primary, .docstring > section > a.notification.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .notification.is-link { + background-color: #149eaa; + color: #fff; } + .notification.is-info { + background-color: #209cee; + color: #fff; } + .notification.is-success { + background-color: #22c35b; + color: #fff; } + .notification.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .notification.is-danger { + background-color: #da0b00; + color: #fff; } + +.progress { + -moz-appearance: none; + -webkit-appearance: none; + border: none; + border-radius: 290486px; + display: block; + height: 1rem; + overflow: hidden; + padding: 0; + width: 100%; } + .progress::-webkit-progress-bar { + background-color: #dbdbdb; } + .progress::-webkit-progress-value { + background-color: #202020; } + .progress::-moz-progress-bar { + background-color: #202020; } + .progress::-ms-fill { + background-color: #202020; + border: none; } + .progress.is-white::-webkit-progress-value { + background-color: white; } + .progress.is-white::-moz-progress-bar { + background-color: white; } + .progress.is-white::-ms-fill { + background-color: white; } + .progress.is-white:indeterminate { + background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); } + .progress.is-black::-webkit-progress-value { + background-color: #0a0a0a; } + .progress.is-black::-moz-progress-bar { + background-color: #0a0a0a; } + .progress.is-black::-ms-fill { + background-color: #0a0a0a; } + .progress.is-black:indeterminate { + background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); } + .progress.is-light::-webkit-progress-value { + background-color: whitesmoke; } + .progress.is-light::-moz-progress-bar { + background-color: whitesmoke; } + .progress.is-light::-ms-fill { + background-color: whitesmoke; } + .progress.is-light:indeterminate { + background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); } + .progress.is-dark::-webkit-progress-value, .content kbd.progress::-webkit-progress-value { + background-color: #363636; } + .progress.is-dark::-moz-progress-bar, .content kbd.progress::-moz-progress-bar { + background-color: #363636; } + .progress.is-dark::-ms-fill, .content kbd.progress::-ms-fill { + background-color: #363636; } + .progress.is-dark:indeterminate, .content kbd.progress:indeterminate { + background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); } + .progress.is-primary::-webkit-progress-value, .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { + background-color: #4eb5de; } + .progress.is-primary::-moz-progress-bar, .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { + background-color: #4eb5de; } + .progress.is-primary::-ms-fill, .docstring > section > a.progress.docs-sourcelink::-ms-fill { + background-color: #4eb5de; } + .progress.is-primary:indeterminate, .docstring > section > a.progress.docs-sourcelink:indeterminate { + background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); } + .progress.is-link::-webkit-progress-value { + background-color: #149eaa; } + .progress.is-link::-moz-progress-bar { + background-color: #149eaa; } + .progress.is-link::-ms-fill { + background-color: #149eaa; } + .progress.is-link:indeterminate { + background-image: linear-gradient(to right, #149eaa 30%, #dbdbdb 30%); } + .progress.is-info::-webkit-progress-value { + background-color: #209cee; } + .progress.is-info::-moz-progress-bar { + background-color: #209cee; } + .progress.is-info::-ms-fill { + background-color: #209cee; } + .progress.is-info:indeterminate { + background-image: linear-gradient(to right, #209cee 30%, #dbdbdb 30%); } + .progress.is-success::-webkit-progress-value { + background-color: #22c35b; } + .progress.is-success::-moz-progress-bar { + background-color: #22c35b; } + .progress.is-success::-ms-fill { + background-color: #22c35b; } + .progress.is-success:indeterminate { + background-image: linear-gradient(to right, #22c35b 30%, #dbdbdb 30%); } + .progress.is-warning::-webkit-progress-value { + background-color: #ffdd57; } + .progress.is-warning::-moz-progress-bar { + background-color: #ffdd57; } + .progress.is-warning::-ms-fill { + background-color: #ffdd57; } + .progress.is-warning:indeterminate { + background-image: linear-gradient(to right, #ffdd57 30%, #dbdbdb 30%); } + .progress.is-danger::-webkit-progress-value { + background-color: #da0b00; } + .progress.is-danger::-moz-progress-bar { + background-color: #da0b00; } + .progress.is-danger::-ms-fill { + background-color: #da0b00; } + .progress.is-danger:indeterminate { + background-image: linear-gradient(to right, #da0b00 30%, #dbdbdb 30%); } + .progress:indeterminate { + animation-duration: 1.5s; + animation-iteration-count: infinite; + animation-name: moveIndeterminate; + animation-timing-function: linear; + background-color: #dbdbdb; + background-image: linear-gradient(to right, #202020 30%, #dbdbdb 30%); + background-position: top left; + background-repeat: no-repeat; + background-size: 150% 150%; } + .progress:indeterminate::-webkit-progress-bar { + background-color: transparent; } + .progress:indeterminate::-moz-progress-bar { + background-color: transparent; } + .progress.is-small, #documenter .docs-sidebar form.docs-search > input.progress { + height: 0.75rem; } + .progress.is-medium { + height: 1.25rem; } + .progress.is-large { + height: 1.5rem; } + +@keyframes moveIndeterminate { + from { + background-position: 200% 0; } + to { + background-position: -200% 0; } } + +.table { + background-color: white; + color: #363636; } + .table td, + .table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + .table td.is-white, + .table th.is-white { + background-color: white; + border-color: white; + color: #0a0a0a; } + .table td.is-black, + .table th.is-black { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .table td.is-light, + .table th.is-light { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .table td.is-dark, + .table th.is-dark { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .table td.is-primary, + .table th.is-primary { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + .table td.is-link, + .table th.is-link { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + .table td.is-info, + .table th.is-info { + background-color: #209cee; + border-color: #209cee; + color: #fff; } + .table td.is-success, + .table th.is-success { + background-color: #22c35b; + border-color: #22c35b; + color: #fff; } + .table td.is-warning, + .table th.is-warning { + background-color: #ffdd57; + border-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .table td.is-danger, + .table th.is-danger { + background-color: #da0b00; + border-color: #da0b00; + color: #fff; } + .table td.is-narrow, + .table th.is-narrow { + white-space: nowrap; + width: 1%; } + .table td.is-selected, + .table th.is-selected { + background-color: #4eb5de; + color: #fff; } + .table td.is-selected a, + .table td.is-selected strong, + .table th.is-selected a, + .table th.is-selected strong { + color: currentColor; } + .table th { + color: #654ca3; } + .table th:not([align]) { + text-align: left; } + .table tr.is-selected { + background-color: #4eb5de; + color: #fff; } + .table tr.is-selected a, + .table tr.is-selected strong { + color: currentColor; } + .table tr.is-selected td, + .table tr.is-selected th { + border-color: #fff; + color: currentColor; } + .table thead { + background-color: transparent; } + .table thead td, + .table thead th { + border-width: 0 0 2px; + color: #654ca3; } + .table tfoot { + background-color: transparent; } + .table tfoot td, + .table tfoot th { + border-width: 2px 0 0; + color: #654ca3; } + .table tbody { + background-color: transparent; } + .table tbody tr:last-child td, + .table tbody tr:last-child th { + border-bottom-width: 0; } + .table.is-bordered td, + .table.is-bordered th { + border-width: 1px; } + .table.is-bordered tr:last-child td, + .table.is-bordered tr:last-child th { + border-bottom-width: 1px; } + .table.is-fullwidth { + width: 100%; } + .table.is-hoverable tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { + background-color: whitesmoke; } + .table.is-narrow td, + .table.is-narrow th { + padding: 0.25em 0.5em; } + .table.is-striped tbody tr:not(.is-selected):nth-child(even) { + background-color: #fafafa; } + +.table-container { + -webkit-overflow-scrolling: touch; + overflow: auto; + overflow-y: hidden; + max-width: 100%; } + +.tags { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .tags .tag, .tags .content kbd, .content .tags kbd, .tags .docstring > section > a.docs-sourcelink { + margin-bottom: 0.5rem; } + .tags .tag:not(:last-child), .tags .content kbd:not(:last-child), .content .tags kbd:not(:last-child), .tags .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0.5rem; } + .tags:last-child { + margin-bottom: -0.5rem; } + .tags:not(:last-child) { + margin-bottom: 1rem; } + .tags.are-medium .tag:not(.is-normal):not(.is-large), .tags.are-medium .content kbd:not(.is-normal):not(.is-large), .content .tags.are-medium kbd:not(.is-normal):not(.is-large), .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { + font-size: 1rem; } + .tags.are-large .tag:not(.is-normal):not(.is-medium), .tags.are-large .content kbd:not(.is-normal):not(.is-medium), .content .tags.are-large kbd:not(.is-normal):not(.is-medium), .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { + font-size: 1.25rem; } + .tags.is-centered { + justify-content: center; } + .tags.is-centered .tag, .tags.is-centered .content kbd, .content .tags.is-centered kbd, .tags.is-centered .docstring > section > a.docs-sourcelink { + margin-right: 0.25rem; + margin-left: 0.25rem; } + .tags.is-right { + justify-content: flex-end; } + .tags.is-right .tag:not(:first-child), .tags.is-right .content kbd:not(:first-child), .content .tags.is-right kbd:not(:first-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0.5rem; } + .tags.is-right .tag:not(:last-child), .tags.is-right .content kbd:not(:last-child), .content .tags.is-right kbd:not(:last-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0; } + .tags.has-addons .tag, .tags.has-addons .content kbd, .content .tags.has-addons kbd, .tags.has-addons .docstring > section > a.docs-sourcelink { + margin-right: 0; } + .tags.has-addons .tag:not(:first-child), .tags.has-addons .content kbd:not(:first-child), .content .tags.has-addons kbd:not(:first-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0; + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .tags.has-addons .tag:not(:last-child), .tags.has-addons .content kbd:not(:last-child), .content .tags.has-addons kbd:not(:last-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + +.tag:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink:not(body) { + align-items: center; + background-color: whitesmoke; + border-radius: 4px; + color: #202020; + display: inline-flex; + font-size: 0.75rem; + height: 2em; + justify-content: center; + line-height: 1.5; + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + .tag:not(body) .delete, .content kbd:not(body) .delete, .docstring > section > a.docs-sourcelink:not(body) .delete { + margin-left: 0.25rem; + margin-right: -0.375rem; } + .tag.is-white:not(body), .content kbd.is-white:not(body), .docstring > section > a.docs-sourcelink.is-white:not(body) { + background-color: white; + color: #0a0a0a; } + .tag.is-black:not(body), .content kbd.is-black:not(body), .docstring > section > a.docs-sourcelink.is-black:not(body) { + background-color: #0a0a0a; + color: white; } + .tag.is-light:not(body), .content kbd.is-light:not(body), .docstring > section > a.docs-sourcelink.is-light:not(body) { + background-color: whitesmoke; + color: #363636; } + .tag.is-dark:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink.is-dark:not(body), .content .docstring > section > kbd:not(body) { + background-color: #363636; + color: whitesmoke; } + .tag.is-primary:not(body), .content kbd.is-primary:not(body), .docstring > section > a.docs-sourcelink:not(body) { + background-color: #4eb5de; + color: #fff; } + .tag.is-link:not(body), .content kbd.is-link:not(body), .docstring > section > a.docs-sourcelink.is-link:not(body) { + background-color: #149eaa; + color: #fff; } + .tag.is-info:not(body), .content kbd.is-info:not(body), .docstring > section > a.docs-sourcelink.is-info:not(body) { + background-color: #209cee; + color: #fff; } + .tag.is-success:not(body), .content kbd.is-success:not(body), .docstring > section > a.docs-sourcelink.is-success:not(body) { + background-color: #22c35b; + color: #fff; } + .tag.is-warning:not(body), .content kbd.is-warning:not(body), .docstring > section > a.docs-sourcelink.is-warning:not(body) { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .tag.is-danger:not(body), .content kbd.is-danger:not(body), .docstring > section > a.docs-sourcelink.is-danger:not(body) { + background-color: #da0b00; + color: #fff; } + .tag.is-normal:not(body), .content kbd.is-normal:not(body), .docstring > section > a.docs-sourcelink.is-normal:not(body) { + font-size: 0.75rem; } + .tag.is-medium:not(body), .content kbd.is-medium:not(body), .docstring > section > a.docs-sourcelink.is-medium:not(body) { + font-size: 1rem; } + .tag.is-large:not(body), .content kbd.is-large:not(body), .docstring > section > a.docs-sourcelink.is-large:not(body) { + font-size: 1.25rem; } + .tag:not(body) .icon:first-child:not(:last-child), .content kbd:not(body) .icon:first-child:not(:last-child), .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { + margin-left: -0.375em; + margin-right: 0.1875em; } + .tag:not(body) .icon:last-child:not(:first-child), .content kbd:not(body) .icon:last-child:not(:first-child), .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: -0.375em; } + .tag:not(body) .icon:first-child:last-child, .content kbd:not(body) .icon:first-child:last-child, .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { + margin-left: -0.375em; + margin-right: -0.375em; } + .tag.is-delete:not(body), .content kbd.is-delete:not(body), .docstring > section > a.docs-sourcelink.is-delete:not(body) { + margin-left: 1px; + padding: 0; + position: relative; + width: 2em; } + .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + background-color: currentColor; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { + height: 1px; + width: 50%; } + .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + height: 50%; + width: 1px; } + .tag.is-delete:not(body):hover, .content kbd.is-delete:not(body):hover, .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, .tag.is-delete:not(body):focus, .content kbd.is-delete:not(body):focus, .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { + background-color: #e8e8e8; } + .tag.is-delete:not(body):active, .content kbd.is-delete:not(body):active, .docstring > section > a.docs-sourcelink.is-delete:not(body):active { + background-color: #dbdbdb; } + .tag.is-rounded:not(body), #documenter .docs-sidebar form.docs-search > input:not(body), .content kbd.is-rounded:not(body), #documenter .docs-sidebar .content form.docs-search > input:not(body), .docstring > section > a.docs-sourcelink.is-rounded:not(body) { + border-radius: 290486px; } + +a.tag:hover, .docstring > section > a.docs-sourcelink:hover { + text-decoration: underline; } + +.title, +.subtitle { + word-break: break-word; } + .title em, + .title span, + .subtitle em, + .subtitle span { + font-weight: inherit; } + .title sub, + .subtitle sub { + font-size: 0.75em; } + .title sup, + .subtitle sup { + font-size: 0.75em; } + .title .tag, .title .content kbd, .content .title kbd, .title .docstring > section > a.docs-sourcelink, + .subtitle .tag, + .subtitle .content kbd, + .content .subtitle kbd, + .subtitle .docstring > section > a.docs-sourcelink { + vertical-align: middle; } + +.title { + color: #363636; + font-size: 2rem; + font-weight: 600; + line-height: 1.125; } + .title strong { + color: inherit; + font-weight: inherit; } + .title + .highlight { + margin-top: -0.75rem; } + .title:not(.is-spaced) + .subtitle { + margin-top: -1.25rem; } + .title.is-1 { + font-size: 3rem; } + .title.is-2 { + font-size: 2.5rem; } + .title.is-3 { + font-size: 2rem; } + .title.is-4 { + font-size: 1.5rem; } + .title.is-5 { + font-size: 1.25rem; } + .title.is-6 { + font-size: 1rem; } + .title.is-7 { + font-size: 0.75rem; } + +.subtitle { + color: #4a4a4a; + font-size: 1.25rem; + font-weight: 400; + line-height: 1.25; } + .subtitle strong { + color: #363636; + font-weight: 600; } + .subtitle:not(.is-spaced) + .title { + margin-top: -1.25rem; } + .subtitle.is-1 { + font-size: 3rem; } + .subtitle.is-2 { + font-size: 2.5rem; } + .subtitle.is-3 { + font-size: 2rem; } + .subtitle.is-4 { + font-size: 1.5rem; } + .subtitle.is-5 { + font-size: 1.25rem; } + .subtitle.is-6 { + font-size: 1rem; } + .subtitle.is-7 { + font-size: 0.75rem; } + +.heading { + display: block; + font-size: 11px; + letter-spacing: 1px; + margin-bottom: 5px; + text-transform: uppercase; } + +.highlight { + font-weight: 400; + max-width: 100%; + overflow: hidden; + padding: 0; } + .highlight pre { + overflow: auto; + max-width: 100%; } + +.number { + align-items: center; + background-color: whitesmoke; + border-radius: 290486px; + display: inline-flex; + font-size: 1.25rem; + height: 2em; + justify-content: center; + margin-right: 1.5rem; + min-width: 2.5em; + padding: 0.25rem 0.5rem; + text-align: center; + vertical-align: top; } + +.select select, .textarea, .input, #documenter .docs-sidebar form.docs-search > input { + background-color: white; + border-color: #dbdbdb; + border-radius: 4px; + color: #363636; } + .select select::-moz-placeholder, .textarea::-moz-placeholder, .input::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select::-webkit-input-placeholder, .textarea::-webkit-input-placeholder, .input::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:-moz-placeholder, .textarea:-moz-placeholder, .input:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:-ms-input-placeholder, .textarea:-ms-input-placeholder, .input:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:hover, .textarea:hover, .input:hover, #documenter .docs-sidebar form.docs-search > input:hover, .select select.is-hovered, .is-hovered.textarea, .is-hovered.input, #documenter .docs-sidebar form.docs-search > input.is-hovered { + border-color: #149eaa; } + .select select:focus, .textarea:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .select select.is-focused, .is-focused.textarea, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .select select:active, .textarea:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .select select.is-active, .is-active.textarea, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + border-color: #fff; + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .select select[disabled], .textarea[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] .select select, .select fieldset[disabled] select, fieldset[disabled] .textarea, fieldset[disabled] .input, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input { + background-color: whitesmoke; + border-color: whitesmoke; + box-shadow: none; + color: #6b6b6b; } + .select select[disabled]::-moz-placeholder, .textarea[disabled]::-moz-placeholder, .input[disabled]::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] .select select::-moz-placeholder, .select fieldset[disabled] select::-moz-placeholder, fieldset[disabled] .textarea::-moz-placeholder, fieldset[disabled] .input::-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-moz-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]::-webkit-input-placeholder, .textarea[disabled]::-webkit-input-placeholder, .input[disabled]::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] .select select::-webkit-input-placeholder, .select fieldset[disabled] select::-webkit-input-placeholder, fieldset[disabled] .textarea::-webkit-input-placeholder, fieldset[disabled] .input::-webkit-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-webkit-input-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]:-moz-placeholder, .textarea[disabled]:-moz-placeholder, .input[disabled]:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] .select select:-moz-placeholder, .select fieldset[disabled] select:-moz-placeholder, fieldset[disabled] .textarea:-moz-placeholder, fieldset[disabled] .input:-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-moz-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]:-ms-input-placeholder, .textarea[disabled]:-ms-input-placeholder, .input[disabled]:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] .select select:-ms-input-placeholder, .select fieldset[disabled] select:-ms-input-placeholder, fieldset[disabled] .textarea:-ms-input-placeholder, fieldset[disabled] .input:-ms-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-ms-input-placeholder { + color: rgba(107, 107, 107, 0.3); } + +.textarea, .input, #documenter .docs-sidebar form.docs-search > input { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); + max-width: 100%; + width: 100%; } + .textarea[readonly], .input[readonly], #documenter .docs-sidebar form.docs-search > input[readonly] { + box-shadow: none; } + .is-white.textarea, .is-white.input, #documenter .docs-sidebar form.docs-search > input.is-white { + border-color: white; } + .is-white.textarea:focus, .is-white.input:focus, #documenter .docs-sidebar form.docs-search > input.is-white:focus, .is-white.is-focused.textarea, .is-white.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-white.textarea:active, .is-white.input:active, #documenter .docs-sidebar form.docs-search > input.is-white:active, .is-white.is-active.textarea, .is-white.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .is-black.textarea, .is-black.input, #documenter .docs-sidebar form.docs-search > input.is-black { + border-color: #0a0a0a; } + .is-black.textarea:focus, .is-black.input:focus, #documenter .docs-sidebar form.docs-search > input.is-black:focus, .is-black.is-focused.textarea, .is-black.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-black.textarea:active, .is-black.input:active, #documenter .docs-sidebar form.docs-search > input.is-black:active, .is-black.is-active.textarea, .is-black.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .is-light.textarea, .is-light.input, #documenter .docs-sidebar form.docs-search > input.is-light { + border-color: whitesmoke; } + .is-light.textarea:focus, .is-light.input:focus, #documenter .docs-sidebar form.docs-search > input.is-light:focus, .is-light.is-focused.textarea, .is-light.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-light.textarea:active, .is-light.input:active, #documenter .docs-sidebar form.docs-search > input.is-light:active, .is-light.is-active.textarea, .is-light.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .is-dark.textarea, .content kbd.textarea, .is-dark.input, #documenter .docs-sidebar form.docs-search > input.is-dark, .content kbd.input { + border-color: #363636; } + .is-dark.textarea:focus, .content kbd.textarea:focus, .is-dark.input:focus, #documenter .docs-sidebar form.docs-search > input.is-dark:focus, .content kbd.input:focus, .is-dark.is-focused.textarea, .content kbd.is-focused.textarea, .is-dark.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .content kbd.is-focused.input, #documenter .docs-sidebar .content form.docs-search > input.is-focused, .is-dark.textarea:active, .content kbd.textarea:active, .is-dark.input:active, #documenter .docs-sidebar form.docs-search > input.is-dark:active, .content kbd.input:active, .is-dark.is-active.textarea, .content kbd.is-active.textarea, .is-dark.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .content kbd.is-active.input, #documenter .docs-sidebar .content form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .is-primary.textarea, .docstring > section > a.textarea.docs-sourcelink, .is-primary.input, #documenter .docs-sidebar form.docs-search > input.is-primary, .docstring > section > a.input.docs-sourcelink { + border-color: #4eb5de; } + .is-primary.textarea:focus, .docstring > section > a.textarea.docs-sourcelink:focus, .is-primary.input:focus, #documenter .docs-sidebar form.docs-search > input.is-primary:focus, .docstring > section > a.input.docs-sourcelink:focus, .is-primary.is-focused.textarea, .docstring > section > a.is-focused.textarea.docs-sourcelink, .is-primary.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .docstring > section > a.is-focused.input.docs-sourcelink, .is-primary.textarea:active, .docstring > section > a.textarea.docs-sourcelink:active, .is-primary.input:active, #documenter .docs-sidebar form.docs-search > input.is-primary:active, .docstring > section > a.input.docs-sourcelink:active, .is-primary.is-active.textarea, .docstring > section > a.is-active.textarea.docs-sourcelink, .is-primary.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .docstring > section > a.is-active.input.docs-sourcelink { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .is-link.textarea, .is-link.input, #documenter .docs-sidebar form.docs-search > input.is-link { + border-color: #149eaa; } + .is-link.textarea:focus, .is-link.input:focus, #documenter .docs-sidebar form.docs-search > input.is-link:focus, .is-link.is-focused.textarea, .is-link.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-link.textarea:active, .is-link.input:active, #documenter .docs-sidebar form.docs-search > input.is-link:active, .is-link.is-active.textarea, .is-link.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .is-info.textarea, .is-info.input, #documenter .docs-sidebar form.docs-search > input.is-info { + border-color: #209cee; } + .is-info.textarea:focus, .is-info.input:focus, #documenter .docs-sidebar form.docs-search > input.is-info:focus, .is-info.is-focused.textarea, .is-info.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-info.textarea:active, .is-info.input:active, #documenter .docs-sidebar form.docs-search > input.is-info:active, .is-info.is-active.textarea, .is-info.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .is-success.textarea, .is-success.input, #documenter .docs-sidebar form.docs-search > input.is-success { + border-color: #22c35b; } + .is-success.textarea:focus, .is-success.input:focus, #documenter .docs-sidebar form.docs-search > input.is-success:focus, .is-success.is-focused.textarea, .is-success.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-success.textarea:active, .is-success.input:active, #documenter .docs-sidebar form.docs-search > input.is-success:active, .is-success.is-active.textarea, .is-success.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .is-warning.textarea, .is-warning.input, #documenter .docs-sidebar form.docs-search > input.is-warning { + border-color: #ffdd57; } + .is-warning.textarea:focus, .is-warning.input:focus, #documenter .docs-sidebar form.docs-search > input.is-warning:focus, .is-warning.is-focused.textarea, .is-warning.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-warning.textarea:active, .is-warning.input:active, #documenter .docs-sidebar form.docs-search > input.is-warning:active, .is-warning.is-active.textarea, .is-warning.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .is-danger.textarea, .is-danger.input, #documenter .docs-sidebar form.docs-search > input.is-danger { + border-color: #da0b00; } + .is-danger.textarea:focus, .is-danger.input:focus, #documenter .docs-sidebar form.docs-search > input.is-danger:focus, .is-danger.is-focused.textarea, .is-danger.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-danger.textarea:active, .is-danger.input:active, #documenter .docs-sidebar form.docs-search > input.is-danger:active, .is-danger.is-active.textarea, .is-danger.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .is-small.textarea, .is-small.input, #documenter .docs-sidebar form.docs-search > input { + border-radius: 2px; + font-size: 0.75rem; } + .is-medium.textarea, .is-medium.input, #documenter .docs-sidebar form.docs-search > input.is-medium { + font-size: 1.25rem; } + .is-large.textarea, .is-large.input, #documenter .docs-sidebar form.docs-search > input.is-large { + font-size: 1.5rem; } + .is-fullwidth.textarea, .is-fullwidth.input, #documenter .docs-sidebar form.docs-search > input.is-fullwidth { + display: block; + width: 100%; } + .is-inline.textarea, .is-inline.input, #documenter .docs-sidebar form.docs-search > input.is-inline { + display: inline; + width: auto; } + +.input.is-rounded, #documenter .docs-sidebar form.docs-search > input { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + +.input.is-static, #documenter .docs-sidebar form.docs-search > input.is-static { + background-color: transparent; + border-color: transparent; + box-shadow: none; + padding-left: 0; + padding-right: 0; } + +.textarea { + display: block; + max-width: 100%; + min-width: 100%; + padding: 0.625em; + resize: vertical; } + .textarea:not([rows]) { + max-height: 600px; + min-height: 120px; } + .textarea[rows] { + height: initial; } + .textarea.has-fixed-size { + resize: none; } + +.radio, .checkbox { + cursor: pointer; + display: inline-block; + line-height: 1.25; + position: relative; } + .radio input, .checkbox input { + cursor: pointer; } + .radio:hover, .checkbox:hover { + color: #363636; } + .radio[disabled], .checkbox[disabled], fieldset[disabled] .radio, fieldset[disabled] .checkbox { + color: #6b6b6b; + cursor: not-allowed; } + +.radio + .radio { + margin-left: 0.5em; } + +.select { + display: inline-block; + max-width: 100%; + position: relative; + vertical-align: top; } + .select:not(.is-multiple) { + height: 2.25em; } + .select:not(.is-multiple):not(.is-loading)::after { + border-color: #149eaa; + right: 1.125em; + z-index: 4; } + .select.is-rounded select, #documenter .docs-sidebar form.docs-search > input.select select { + border-radius: 290486px; + padding-left: 1em; } + .select select { + cursor: pointer; + display: block; + font-size: 1em; + max-width: 100%; + outline: none; } + .select select::-ms-expand { + display: none; } + .select select[disabled]:hover, fieldset[disabled] .select select:hover { + border-color: whitesmoke; } + .select select:not([multiple]) { + padding-right: 2.5em; } + .select select[multiple] { + height: auto; + padding: 0; } + .select select[multiple] option { + padding: 0.5em 1em; } + .select:not(.is-multiple):not(.is-loading):hover::after { + border-color: #363636; } + .select.is-white:not(:hover)::after { + border-color: white; } + .select.is-white select { + border-color: white; } + .select.is-white select:hover, .select.is-white select.is-hovered { + border-color: #f2f2f2; } + .select.is-white select:focus, .select.is-white select.is-focused, .select.is-white select:active, .select.is-white select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .select.is-black:not(:hover)::after { + border-color: #0a0a0a; } + .select.is-black select { + border-color: #0a0a0a; } + .select.is-black select:hover, .select.is-black select.is-hovered { + border-color: black; } + .select.is-black select:focus, .select.is-black select.is-focused, .select.is-black select:active, .select.is-black select.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .select.is-light:not(:hover)::after { + border-color: whitesmoke; } + .select.is-light select { + border-color: whitesmoke; } + .select.is-light select:hover, .select.is-light select.is-hovered { + border-color: #e8e8e8; } + .select.is-light select:focus, .select.is-light select.is-focused, .select.is-light select:active, .select.is-light select.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .select.is-dark:not(:hover)::after, .content kbd.select:not(:hover)::after { + border-color: #363636; } + .select.is-dark select, .content kbd.select select { + border-color: #363636; } + .select.is-dark select:hover, .content kbd.select select:hover, .select.is-dark select.is-hovered, .content kbd.select select.is-hovered { + border-color: #292929; } + .select.is-dark select:focus, .content kbd.select select:focus, .select.is-dark select.is-focused, .content kbd.select select.is-focused, .select.is-dark select:active, .content kbd.select select:active, .select.is-dark select.is-active, .content kbd.select select.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .select.is-primary:not(:hover)::after, .docstring > section > a.select.docs-sourcelink:not(:hover)::after { + border-color: #4eb5de; } + .select.is-primary select, .docstring > section > a.select.docs-sourcelink select { + border-color: #4eb5de; } + .select.is-primary select:hover, .docstring > section > a.select.docs-sourcelink select:hover, .select.is-primary select.is-hovered, .docstring > section > a.select.docs-sourcelink select.is-hovered { + border-color: #39acda; } + .select.is-primary select:focus, .docstring > section > a.select.docs-sourcelink select:focus, .select.is-primary select.is-focused, .docstring > section > a.select.docs-sourcelink select.is-focused, .select.is-primary select:active, .docstring > section > a.select.docs-sourcelink select:active, .select.is-primary select.is-active, .docstring > section > a.select.docs-sourcelink select.is-active { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .select.is-link:not(:hover)::after { + border-color: #149eaa; } + .select.is-link select { + border-color: #149eaa; } + .select.is-link select:hover, .select.is-link select.is-hovered { + border-color: #118993; } + .select.is-link select:focus, .select.is-link select.is-focused, .select.is-link select:active, .select.is-link select.is-active { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .select.is-info:not(:hover)::after { + border-color: #209cee; } + .select.is-info select { + border-color: #209cee; } + .select.is-info select:hover, .select.is-info select.is-hovered { + border-color: #1190e3; } + .select.is-info select:focus, .select.is-info select.is-focused, .select.is-info select:active, .select.is-info select.is-active { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .select.is-success:not(:hover)::after { + border-color: #22c35b; } + .select.is-success select { + border-color: #22c35b; } + .select.is-success select:hover, .select.is-success select.is-hovered { + border-color: #1ead51; } + .select.is-success select:focus, .select.is-success select.is-focused, .select.is-success select:active, .select.is-success select.is-active { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .select.is-warning:not(:hover)::after { + border-color: #ffdd57; } + .select.is-warning select { + border-color: #ffdd57; } + .select.is-warning select:hover, .select.is-warning select.is-hovered { + border-color: #ffd83e; } + .select.is-warning select:focus, .select.is-warning select.is-focused, .select.is-warning select:active, .select.is-warning select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .select.is-danger:not(:hover)::after { + border-color: #da0b00; } + .select.is-danger select { + border-color: #da0b00; } + .select.is-danger select:hover, .select.is-danger select.is-hovered { + border-color: #c10a00; } + .select.is-danger select:focus, .select.is-danger select.is-focused, .select.is-danger select:active, .select.is-danger select.is-active { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .select.is-small, #documenter .docs-sidebar form.docs-search > input.select { + border-radius: 2px; + font-size: 0.75rem; } + .select.is-medium { + font-size: 1.25rem; } + .select.is-large { + font-size: 1.5rem; } + .select.is-disabled::after { + border-color: #6b6b6b; } + .select.is-fullwidth { + width: 100%; } + .select.is-fullwidth select { + width: 100%; } + .select.is-loading::after { + margin-top: 0; + position: absolute; + right: 0.625em; + top: 0.625em; + transform: none; } + .select.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + .select.is-loading.is-medium:after { + font-size: 1.25rem; } + .select.is-loading.is-large:after { + font-size: 1.5rem; } + +.file { + align-items: stretch; + display: flex; + justify-content: flex-start; + position: relative; } + .file.is-white .file-cta { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + .file.is-white:hover .file-cta, .file.is-white.is-hovered .file-cta { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + .file.is-white:focus .file-cta, .file.is-white.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); + color: #0a0a0a; } + .file.is-white:active .file-cta, .file.is-white.is-active .file-cta { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + .file.is-black .file-cta { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + .file.is-black:hover .file-cta, .file.is-black.is-hovered .file-cta { + background-color: #040404; + border-color: transparent; + color: white; } + .file.is-black:focus .file-cta, .file.is-black.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); + color: white; } + .file.is-black:active .file-cta, .file.is-black.is-active .file-cta { + background-color: black; + border-color: transparent; + color: white; } + .file.is-light .file-cta { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + .file.is-light:hover .file-cta, .file.is-light.is-hovered .file-cta { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + .file.is-light:focus .file-cta, .file.is-light.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25); + color: #363636; } + .file.is-light:active .file-cta, .file.is-light.is-active .file-cta { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + .file.is-dark .file-cta, .content kbd.file .file-cta { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + .file.is-dark:hover .file-cta, .content kbd.file:hover .file-cta, .file.is-dark.is-hovered .file-cta, .content kbd.file.is-hovered .file-cta { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + .file.is-dark:focus .file-cta, .content kbd.file:focus .file-cta, .file.is-dark.is-focused .file-cta, .content kbd.file.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25); + color: whitesmoke; } + .file.is-dark:active .file-cta, .content kbd.file:active .file-cta, .file.is-dark.is-active .file-cta, .content kbd.file.is-active .file-cta { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + .file.is-primary .file-cta, .docstring > section > a.file.docs-sourcelink .file-cta { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + .file.is-primary:hover .file-cta, .docstring > section > a.file.docs-sourcelink:hover .file-cta, .file.is-primary.is-hovered .file-cta, .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + .file.is-primary:focus .file-cta, .docstring > section > a.file.docs-sourcelink:focus .file-cta, .file.is-primary.is-focused .file-cta, .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25); + color: #fff; } + .file.is-primary:active .file-cta, .docstring > section > a.file.docs-sourcelink:active .file-cta, .file.is-primary.is-active .file-cta, .docstring > section > a.file.is-active.docs-sourcelink .file-cta { + background-color: #39acda; + border-color: transparent; + color: #fff; } + .file.is-link .file-cta { + background-color: #149eaa; + border-color: transparent; + color: #fff; } + .file.is-link:hover .file-cta, .file.is-link.is-hovered .file-cta { + background-color: #13939f; + border-color: transparent; + color: #fff; } + .file.is-link:focus .file-cta, .file.is-link.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(20, 158, 170, 0.25); + color: #fff; } + .file.is-link:active .file-cta, .file.is-link.is-active .file-cta { + background-color: #118993; + border-color: transparent; + color: #fff; } + .file.is-info .file-cta { + background-color: #209cee; + border-color: transparent; + color: #fff; } + .file.is-info:hover .file-cta, .file.is-info.is-hovered .file-cta { + background-color: #1497ed; + border-color: transparent; + color: #fff; } + .file.is-info:focus .file-cta, .file.is-info.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(32, 156, 238, 0.25); + color: #fff; } + .file.is-info:active .file-cta, .file.is-info.is-active .file-cta { + background-color: #1190e3; + border-color: transparent; + color: #fff; } + .file.is-success .file-cta { + background-color: #22c35b; + border-color: transparent; + color: #fff; } + .file.is-success:hover .file-cta, .file.is-success.is-hovered .file-cta { + background-color: #20b856; + border-color: transparent; + color: #fff; } + .file.is-success:focus .file-cta, .file.is-success.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(34, 195, 91, 0.25); + color: #fff; } + .file.is-success:active .file-cta, .file.is-success.is-active .file-cta { + background-color: #1ead51; + border-color: transparent; + color: #fff; } + .file.is-warning .file-cta { + background-color: #ffdd57; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:hover .file-cta, .file.is-warning.is-hovered .file-cta { + background-color: #ffda4a; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:focus .file-cta, .file.is-warning.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 221, 87, 0.25); + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:active .file-cta, .file.is-warning.is-active .file-cta { + background-color: #ffd83e; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-danger .file-cta { + background-color: #da0b00; + border-color: transparent; + color: #fff; } + .file.is-danger:hover .file-cta, .file.is-danger.is-hovered .file-cta { + background-color: #cd0a00; + border-color: transparent; + color: #fff; } + .file.is-danger:focus .file-cta, .file.is-danger.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(218, 11, 0, 0.25); + color: #fff; } + .file.is-danger:active .file-cta, .file.is-danger.is-active .file-cta { + background-color: #c10a00; + border-color: transparent; + color: #fff; } + .file.is-small, #documenter .docs-sidebar form.docs-search > input.file { + font-size: 0.75rem; } + .file.is-medium { + font-size: 1.25rem; } + .file.is-medium .file-icon .fa { + font-size: 21px; } + .file.is-large { + font-size: 1.5rem; } + .file.is-large .file-icon .fa { + font-size: 28px; } + .file.has-name .file-cta { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + .file.has-name .file-name { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .file.has-name.is-empty .file-cta { + border-radius: 4px; } + .file.has-name.is-empty .file-name { + display: none; } + .file.is-boxed .file-label { + flex-direction: column; } + .file.is-boxed .file-cta { + flex-direction: column; + height: auto; + padding: 1em 3em; } + .file.is-boxed .file-name { + border-width: 0 1px 1px; } + .file.is-boxed .file-icon { + height: 1.5em; + width: 1.5em; } + .file.is-boxed .file-icon .fa { + font-size: 21px; } + .file.is-boxed.is-small .file-icon .fa, #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { + font-size: 14px; } + .file.is-boxed.is-medium .file-icon .fa { + font-size: 28px; } + .file.is-boxed.is-large .file-icon .fa { + font-size: 35px; } + .file.is-boxed.has-name .file-cta { + border-radius: 4px 4px 0 0; } + .file.is-boxed.has-name .file-name { + border-radius: 0 0 4px 4px; + border-width: 0 1px 1px; } + .file.is-centered { + justify-content: center; } + .file.is-fullwidth .file-label { + width: 100%; } + .file.is-fullwidth .file-name { + flex-grow: 1; + max-width: none; } + .file.is-right { + justify-content: flex-end; } + .file.is-right .file-cta { + border-radius: 0 4px 4px 0; } + .file.is-right .file-name { + border-radius: 4px 0 0 4px; + border-width: 1px 0 1px 1px; + order: -1; } + +.file-label { + align-items: stretch; + display: flex; + cursor: pointer; + justify-content: flex-start; + overflow: hidden; + position: relative; } + .file-label:hover .file-cta { + background-color: #eeeeee; + color: #363636; } + .file-label:hover .file-name { + border-color: #d5d5d5; } + .file-label:active .file-cta { + background-color: #e8e8e8; + color: #363636; } + .file-label:active .file-name { + border-color: #cfcfcf; } + +.file-input { + height: 100%; + left: 0; + opacity: 0; + outline: none; + position: absolute; + top: 0; + width: 100%; } + +.file-cta, +.file-name { + border-color: #dbdbdb; + border-radius: 4px; + font-size: 1em; + padding-left: 1em; + padding-right: 1em; + white-space: nowrap; } + +.file-cta { + background-color: whitesmoke; + color: #4a4a4a; } + +.file-name { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px 1px 1px 0; + display: block; + max-width: 16em; + overflow: hidden; + text-align: left; + text-overflow: ellipsis; } + +.file-icon { + align-items: center; + display: flex; + height: 1em; + justify-content: center; + margin-right: 0.5em; + width: 1em; } + .file-icon .fa { + font-size: 14px; } + +.label { + color: #363636; + display: block; + font-size: 1rem; + font-weight: 700; } + .label:not(:last-child) { + margin-bottom: 0.5em; } + .label.is-small, #documenter .docs-sidebar form.docs-search > input.label { + font-size: 0.75rem; } + .label.is-medium { + font-size: 1.25rem; } + .label.is-large { + font-size: 1.5rem; } + +.help { + display: block; + font-size: 0.75rem; + margin-top: 0.25rem; } + .help.is-white { + color: white; } + .help.is-black { + color: #0a0a0a; } + .help.is-light { + color: whitesmoke; } + .help.is-dark, .content kbd.help { + color: #363636; } + .help.is-primary, .docstring > section > a.help.docs-sourcelink { + color: #4eb5de; } + .help.is-link { + color: #149eaa; } + .help.is-info { + color: #209cee; } + .help.is-success { + color: #22c35b; } + .help.is-warning { + color: #ffdd57; } + .help.is-danger { + color: #da0b00; } + +.field:not(:last-child) { + margin-bottom: 0.75rem; } + +.field.has-addons { + display: flex; + justify-content: flex-start; } + .field.has-addons .control:not(:last-child) { + margin-right: -1px; } + .field.has-addons .control:not(:first-child):not(:last-child) .button, + .field.has-addons .control:not(:first-child):not(:last-child) .input, + .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, + .field.has-addons .control:not(:first-child):not(:last-child) .select select { + border-radius: 0; } + .field.has-addons .control:first-child:not(:only-child) .button, + .field.has-addons .control:first-child:not(:only-child) .input, + .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, + .field.has-addons .control:first-child:not(:only-child) .select select { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + .field.has-addons .control:last-child:not(:only-child) .button, + .field.has-addons .control:last-child:not(:only-child) .input, + .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, + .field.has-addons .control:last-child:not(:only-child) .select select { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .field.has-addons .control .button:not([disabled]):hover, .field.has-addons .control .button.is-hovered:not([disabled]), + .field.has-addons .control .input:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, + .field.has-addons .control .input.is-hovered:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), + .field.has-addons .control .select select:not([disabled]):hover, + .field.has-addons .control .select select.is-hovered:not([disabled]) { + z-index: 2; } + .field.has-addons .control .button:not([disabled]):focus, .field.has-addons .control .button.is-focused:not([disabled]), .field.has-addons .control .button:not([disabled]):active, .field.has-addons .control .button.is-active:not([disabled]), + .field.has-addons .control .input:not([disabled]):focus, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, + .field.has-addons .control .input.is-focused:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), + .field.has-addons .control .input:not([disabled]):active, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, + .field.has-addons .control .input.is-active:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), + .field.has-addons .control .select select:not([disabled]):focus, + .field.has-addons .control .select select.is-focused:not([disabled]), + .field.has-addons .control .select select:not([disabled]):active, + .field.has-addons .control .select select.is-active:not([disabled]) { + z-index: 3; } + .field.has-addons .control .button:not([disabled]):focus:hover, .field.has-addons .control .button.is-focused:not([disabled]):hover, .field.has-addons .control .button:not([disabled]):active:hover, .field.has-addons .control .button.is-active:not([disabled]):hover, + .field.has-addons .control .input:not([disabled]):focus:hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, + .field.has-addons .control .input.is-focused:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, + .field.has-addons .control .input:not([disabled]):active:hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, + .field.has-addons .control .input.is-active:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, + .field.has-addons .control .select select:not([disabled]):focus:hover, + .field.has-addons .control .select select.is-focused:not([disabled]):hover, + .field.has-addons .control .select select:not([disabled]):active:hover, + .field.has-addons .control .select select.is-active:not([disabled]):hover { + z-index: 4; } + .field.has-addons .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .field.has-addons.has-addons-centered { + justify-content: center; } + .field.has-addons.has-addons-right { + justify-content: flex-end; } + .field.has-addons.has-addons-fullwidth .control { + flex-grow: 1; + flex-shrink: 0; } + +.field.is-grouped { + display: flex; + justify-content: flex-start; } + .field.is-grouped > .control { + flex-shrink: 0; } + .field.is-grouped > .control:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + .field.is-grouped > .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .field.is-grouped.is-grouped-centered { + justify-content: center; } + .field.is-grouped.is-grouped-right { + justify-content: flex-end; } + .field.is-grouped.is-grouped-multiline { + flex-wrap: wrap; } + .field.is-grouped.is-grouped-multiline > .control:last-child, .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { + margin-bottom: 0.75rem; } + .field.is-grouped.is-grouped-multiline:last-child { + margin-bottom: -0.75rem; } + .field.is-grouped.is-grouped-multiline:not(:last-child) { + margin-bottom: 0; } + +@media screen and (min-width: 769px), print { + .field.is-horizontal { + display: flex; } } + +.field-label .label { + font-size: inherit; } + +@media screen and (max-width: 768px) { + .field-label { + margin-bottom: 0.5rem; } } + +@media screen and (min-width: 769px), print { + .field-label { + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + margin-right: 1.5rem; + text-align: right; } + .field-label.is-small, #documenter .docs-sidebar form.docs-search > input.field-label { + font-size: 0.75rem; + padding-top: 0.375em; } + .field-label.is-normal { + padding-top: 0.375em; } + .field-label.is-medium { + font-size: 1.25rem; + padding-top: 0.375em; } + .field-label.is-large { + font-size: 1.5rem; + padding-top: 0.375em; } } + +.field-body .field .field { + margin-bottom: 0; } + +@media screen and (min-width: 769px), print { + .field-body { + display: flex; + flex-basis: 0; + flex-grow: 5; + flex-shrink: 1; } + .field-body .field { + margin-bottom: 0; } + .field-body > .field { + flex-shrink: 1; } + .field-body > .field:not(.is-narrow) { + flex-grow: 1; } + .field-body > .field:not(:last-child) { + margin-right: 0.75rem; } } + +.control { + box-sizing: border-box; + clear: both; + font-size: 1rem; + position: relative; + text-align: left; } + .control.has-icons-left .input:focus ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, + .control.has-icons-left .select:focus ~ .icon, .control.has-icons-right .input:focus ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, + .control.has-icons-right .select:focus ~ .icon { + color: #6b6b6b; } + .control.has-icons-left .input.is-small ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, + .control.has-icons-left .select.is-small ~ .icon, .control.has-icons-right .input.is-small ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, + .control.has-icons-right .select.is-small ~ .icon { + font-size: 0.75rem; } + .control.has-icons-left .input.is-medium ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, + .control.has-icons-left .select.is-medium ~ .icon, .control.has-icons-right .input.is-medium ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, + .control.has-icons-right .select.is-medium ~ .icon { + font-size: 1.25rem; } + .control.has-icons-left .input.is-large ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, + .control.has-icons-left .select.is-large ~ .icon, .control.has-icons-right .input.is-large ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, + .control.has-icons-right .select.is-large ~ .icon { + font-size: 1.5rem; } + .control.has-icons-left .icon, .control.has-icons-right .icon { + color: #dbdbdb; + height: 2.25em; + pointer-events: none; + position: absolute; + top: 0; + width: 2.25em; + z-index: 4; } + .control.has-icons-left .input, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, + .control.has-icons-left .select select { + padding-left: 2.25em; } + .control.has-icons-left .icon.is-left { + left: 0; } + .control.has-icons-right .input, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, + .control.has-icons-right .select select { + padding-right: 2.25em; } + .control.has-icons-right .icon.is-right { + right: 0; } + .control.is-loading::after { + position: absolute !important; + right: 0.625em; + top: 0.625em; + z-index: 4; } + .control.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + .control.is-loading.is-medium:after { + font-size: 1.25rem; } + .control.is-loading.is-large:after { + font-size: 1.5rem; } + +.breadcrumb { + font-size: 1rem; + white-space: nowrap; } + .breadcrumb a { + align-items: center; + color: #149eaa; + display: flex; + justify-content: center; + padding: 0 0.75em; } + .breadcrumb a:hover { + color: #107c85; } + .breadcrumb li { + align-items: center; + display: flex; } + .breadcrumb li:first-child a { + padding-left: 0; } + .breadcrumb li.is-active a { + color: #654ca3; + cursor: default; + pointer-events: none; } + .breadcrumb li + li::before { + color: #b5b5b5; + content: "\0002f"; } + .breadcrumb ul, + .breadcrumb ol { + align-items: flex-start; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .breadcrumb .icon:first-child { + margin-right: 0.5em; } + .breadcrumb .icon:last-child { + margin-left: 0.5em; } + .breadcrumb.is-centered ol, + .breadcrumb.is-centered ul { + justify-content: center; } + .breadcrumb.is-right ol, + .breadcrumb.is-right ul { + justify-content: flex-end; } + .breadcrumb.is-small, #documenter .docs-sidebar form.docs-search > input.breadcrumb { + font-size: 0.75rem; } + .breadcrumb.is-medium { + font-size: 1.25rem; } + .breadcrumb.is-large { + font-size: 1.5rem; } + .breadcrumb.has-arrow-separator li + li::before { + content: "\02192"; } + .breadcrumb.has-bullet-separator li + li::before { + content: "\02022"; } + .breadcrumb.has-dot-separator li + li::before { + content: "\000b7"; } + .breadcrumb.has-succeeds-separator li + li::before { + content: "\0227B"; } + +.card { + background-color: white; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #202020; + max-width: 100%; + position: relative; } + +.card-header { + background-color: transparent; + align-items: stretch; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + display: flex; } + +.card-header-title { + align-items: center; + color: #654ca3; + display: flex; + flex-grow: 1; + font-weight: 700; + padding: 0.75rem; } + .card-header-title.is-centered { + justify-content: center; } + +.card-header-icon { + align-items: center; + cursor: pointer; + display: flex; + justify-content: center; + padding: 0.75rem; } + +.card-image { + display: block; + position: relative; } + +.card-content { + background-color: transparent; + padding: 1.5rem; } + +.card-footer { + background-color: transparent; + border-top: 1px solid #dbdbdb; + align-items: stretch; + display: flex; } + +.card-footer-item { + align-items: center; + display: flex; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + justify-content: center; + padding: 0.75rem; } + .card-footer-item:not(:last-child) { + border-right: 1px solid #dbdbdb; } + +.card .media:not(:last-child) { + margin-bottom: 1.5rem; } + +.dropdown { + display: inline-flex; + position: relative; + vertical-align: top; } + .dropdown.is-active .dropdown-menu, .dropdown.is-hoverable:hover .dropdown-menu { + display: block; } + .dropdown.is-right .dropdown-menu { + left: auto; + right: 0; } + .dropdown.is-up .dropdown-menu { + bottom: 100%; + padding-bottom: 4px; + padding-top: initial; + top: auto; } + +.dropdown-menu { + display: none; + left: 0; + min-width: 12rem; + padding-top: 4px; + position: absolute; + top: 100%; + z-index: 20; } + +.dropdown-content { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + +.dropdown-item { + color: #4a4a4a; + display: block; + font-size: 0.875rem; + line-height: 1.5; + padding: 0.375rem 1rem; + position: relative; } + +a.dropdown-item, +button.dropdown-item { + padding-right: 3rem; + text-align: left; + white-space: nowrap; + width: 100%; } + a.dropdown-item:hover, + button.dropdown-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + a.dropdown-item.is-active, + button.dropdown-item.is-active { + background-color: #149eaa; + color: #fff; } + +.dropdown-divider { + background-color: #dbdbdb; + border: none; + display: block; + height: 1px; + margin: 0.5rem 0; } + +.level { + align-items: center; + justify-content: space-between; } + .level code { + border-radius: 4px; } + .level img { + display: inline-block; + vertical-align: top; } + .level.is-mobile { + display: flex; } + .level.is-mobile .level-left, + .level.is-mobile .level-right { + display: flex; } + .level.is-mobile .level-left + .level-right { + margin-top: 0; } + .level.is-mobile .level-item:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + .level.is-mobile .level-item:not(.is-narrow) { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + .level { + display: flex; } + .level > .level-item:not(.is-narrow) { + flex-grow: 1; } } +.level-item { + align-items: center; + display: flex; + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; + justify-content: center; } + .level-item .title, + .level-item .subtitle { + margin-bottom: 0; } + @media screen and (max-width: 768px) { + .level-item:not(:last-child) { + margin-bottom: 0.75rem; } } +.level-left, +.level-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + .level-left .level-item.is-flexible, + .level-right .level-item.is-flexible { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + .level-left .level-item:not(:last-child), + .level-right .level-item:not(:last-child) { + margin-right: 0.75rem; } } +.level-left { + align-items: center; + justify-content: flex-start; } + @media screen and (max-width: 768px) { + .level-left + .level-right { + margin-top: 1.5rem; } } + @media screen and (min-width: 769px), print { + .level-left { + display: flex; } } +.level-right { + align-items: center; + justify-content: flex-end; } + @media screen and (min-width: 769px), print { + .level-right { + display: flex; } } +.list { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } + +.list-item { + display: block; + padding: 0.5em 1em; } + .list-item:not(a) { + color: #202020; } + .list-item:first-child { + border-top-left-radius: 4px; + border-top-right-radius: 4px; } + .list-item:last-child { + border-bottom-left-radius: 4px; + border-bottom-right-radius: 4px; } + .list-item:not(:last-child) { + border-bottom: 1px solid #dbdbdb; } + .list-item.is-active { + background-color: #149eaa; + color: #fff; } + +a.list-item { + background-color: whitesmoke; + cursor: pointer; } + +.media { + align-items: flex-start; + display: flex; + text-align: left; } + .media .content:not(:last-child) { + margin-bottom: 0.75rem; } + .media .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + display: flex; + padding-top: 0.75rem; } + .media .media .content:not(:last-child), + .media .media .control:not(:last-child) { + margin-bottom: 0.5rem; } + .media .media .media { + padding-top: 0.5rem; } + .media .media .media + .media { + margin-top: 0.5rem; } + .media + .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + margin-top: 1rem; + padding-top: 1rem; } + .media.is-large + .media { + margin-top: 1.5rem; + padding-top: 1.5rem; } + +.media-left, +.media-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + +.media-left { + margin-right: 1rem; } + +.media-right { + margin-left: 1rem; } + +.media-content { + flex-basis: auto; + flex-grow: 1; + flex-shrink: 1; + text-align: left; } + +@media screen and (max-width: 768px) { + .media-content { + overflow-x: auto; } } + +.menu { + font-size: 1rem; } + .menu.is-small, #documenter .docs-sidebar form.docs-search > input.menu { + font-size: 0.75rem; } + .menu.is-medium { + font-size: 1.25rem; } + .menu.is-large { + font-size: 1.5rem; } + +.menu-list { + line-height: 1.25; } + .menu-list a { + border-radius: 2px; + color: #202020; + display: block; + padding: 0.5em 0.75em; } + .menu-list a:hover { + background-color: whitesmoke; + color: #654ca3; } + .menu-list a.is-active { + background-color: #149eaa; + color: #fff; } + .menu-list li ul { + border-left: 1px solid #dbdbdb; + margin: 0.75em; + padding-left: 0.75em; } + +.menu-label { + color: #6b6b6b; + font-size: 0.75em; + letter-spacing: 0.1em; + text-transform: uppercase; } + .menu-label:not(:first-child) { + margin-top: 1em; } + .menu-label:not(:last-child) { + margin-bottom: 1em; } + +.message { + background-color: whitesmoke; + border-radius: 4px; + font-size: 1rem; } + .message strong { + color: currentColor; } + .message a:not(.button):not(.tag):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + .message.is-small, #documenter .docs-sidebar form.docs-search > input.message { + font-size: 0.75rem; } + .message.is-medium { + font-size: 1.25rem; } + .message.is-large { + font-size: 1.5rem; } + .message.is-white { + background-color: white; } + .message.is-white .message-header { + background-color: white; + color: #0a0a0a; } + .message.is-white .message-body { + border-color: white; + color: #4d4d4d; } + .message.is-black { + background-color: #fafafa; } + .message.is-black .message-header { + background-color: #0a0a0a; + color: white; } + .message.is-black .message-body { + border-color: #0a0a0a; + color: #090909; } + .message.is-light { + background-color: #fafafa; } + .message.is-light .message-header { + background-color: whitesmoke; + color: #363636; } + .message.is-light .message-body { + border-color: whitesmoke; + color: #505050; } + .message.is-dark, .content kbd.message { + background-color: #fafafa; } + .message.is-dark .message-header, .content kbd.message .message-header { + background-color: #363636; + color: whitesmoke; } + .message.is-dark .message-body, .content kbd.message .message-body { + border-color: #363636; + color: #2a2a2a; } + .message.is-primary, .docstring > section > a.message.docs-sourcelink { + background-color: #f6fbfd; } + .message.is-primary .message-header, .docstring > section > a.message.docs-sourcelink .message-header { + background-color: #4eb5de; + color: #fff; } + .message.is-primary .message-body, .docstring > section > a.message.docs-sourcelink .message-body { + border-color: #4eb5de; + color: #1f556a; } + .message.is-link { + background-color: #f6fdfe; } + .message.is-link .message-header { + background-color: #149eaa; + color: #fff; } + .message.is-link .message-body { + border-color: #149eaa; + color: #0b393d; } + .message.is-info { + background-color: #f6fbfe; } + .message.is-info .message-header { + background-color: #209cee; + color: #fff; } + .message.is-info .message-body { + border-color: #209cee; + color: #12537d; } + .message.is-success { + background-color: #f6fdf9; } + .message.is-success .message-header { + background-color: #22c35b; + color: #fff; } + .message.is-success .message-body { + border-color: #22c35b; + color: #0f361d; } + .message.is-warning { + background-color: #fffdf5; } + .message.is-warning .message-header { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .message.is-warning .message-body { + border-color: #ffdd57; + color: #3c3108; } + .message.is-danger { + background-color: #fff5f5; } + .message.is-danger .message-header { + background-color: #da0b00; + color: #fff; } + .message.is-danger .message-body { + border-color: #da0b00; + color: #9b0c04; } + +.message-header { + align-items: center; + background-color: #202020; + border-radius: 4px 4px 0 0; + color: #fff; + display: flex; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.75em 1em; + position: relative; } + .message-header .delete { + flex-grow: 0; + flex-shrink: 0; + margin-left: 0.75em; } + .message-header + .message-body { + border-width: 0; + border-top-left-radius: 0; + border-top-right-radius: 0; } + +.message-body { + border-color: #dbdbdb; + border-radius: 4px; + border-style: solid; + border-width: 0 0 0 4px; + color: #202020; + padding: 1.25em 1.5em; } + .message-body code, + .message-body pre { + background-color: white; } + .message-body pre code { + background-color: transparent; } + +.modal { + align-items: center; + display: none; + flex-direction: column; + justify-content: center; + overflow: hidden; + position: fixed; + z-index: 40; } + .modal.is-active { + display: flex; } + +.modal-background { + background-color: rgba(10, 10, 10, 0.86); } + +.modal-content, +.modal-card { + margin: 0 20px; + max-height: calc(100vh - 160px); + overflow: auto; + position: relative; + width: 100%; } + @media screen and (min-width: 769px), print { + .modal-content, + .modal-card { + margin: 0 auto; + max-height: calc(100vh - 40px); + width: 640px; } } +.modal-close { + background: none; + height: 40px; + position: fixed; + right: 20px; + top: 20px; + width: 40px; } + +.modal-card { + display: flex; + flex-direction: column; + max-height: calc(100vh - 40px); + overflow: hidden; + -ms-overflow-y: visible; } + +.modal-card-head, +.modal-card-foot { + align-items: center; + background-color: whitesmoke; + display: flex; + flex-shrink: 0; + justify-content: flex-start; + padding: 20px; + position: relative; } + +.modal-card-head { + border-bottom: 1px solid #dbdbdb; + border-top-left-radius: 6px; + border-top-right-radius: 6px; } + +.modal-card-title { + color: #654ca3; + flex-grow: 1; + flex-shrink: 0; + font-size: 1.5rem; + line-height: 1; } + +.modal-card-foot { + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 1px solid #dbdbdb; } + .modal-card-foot .button:not(:last-child) { + margin-right: 0.5em; } + +.modal-card-body { + -webkit-overflow-scrolling: touch; + background-color: white; + flex-grow: 1; + flex-shrink: 1; + overflow: auto; + padding: 20px; } + +.navbar { + background-color: white; + min-height: 3.25rem; + position: relative; + z-index: 30; } + .navbar.is-white { + background-color: white; + color: #0a0a0a; } + .navbar.is-white .navbar-brand > .navbar-item, + .navbar.is-white .navbar-brand .navbar-link { + color: #0a0a0a; } + .navbar.is-white .navbar-brand > a.navbar-item:focus, .navbar.is-white .navbar-brand > a.navbar-item:hover, .navbar.is-white .navbar-brand > a.navbar-item.is-active, + .navbar.is-white .navbar-brand .navbar-link:focus, + .navbar.is-white .navbar-brand .navbar-link:hover, + .navbar.is-white .navbar-brand .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-brand .navbar-link::after { + border-color: #0a0a0a; } + .navbar.is-white .navbar-burger { + color: #0a0a0a; } + @media screen and (min-width: 1056px) { + .navbar.is-white .navbar-start > .navbar-item, + .navbar.is-white .navbar-start .navbar-link, + .navbar.is-white .navbar-end > .navbar-item, + .navbar.is-white .navbar-end .navbar-link { + color: #0a0a0a; } + .navbar.is-white .navbar-start > a.navbar-item:focus, .navbar.is-white .navbar-start > a.navbar-item:hover, .navbar.is-white .navbar-start > a.navbar-item.is-active, + .navbar.is-white .navbar-start .navbar-link:focus, + .navbar.is-white .navbar-start .navbar-link:hover, + .navbar.is-white .navbar-start .navbar-link.is-active, + .navbar.is-white .navbar-end > a.navbar-item:focus, + .navbar.is-white .navbar-end > a.navbar-item:hover, + .navbar.is-white .navbar-end > a.navbar-item.is-active, + .navbar.is-white .navbar-end .navbar-link:focus, + .navbar.is-white .navbar-end .navbar-link:hover, + .navbar.is-white .navbar-end .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-start .navbar-link::after, + .navbar.is-white .navbar-end .navbar-link::after { + border-color: #0a0a0a; } + .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-dropdown a.navbar-item.is-active { + background-color: white; + color: #0a0a0a; } } + .navbar.is-black { + background-color: #0a0a0a; + color: white; } + .navbar.is-black .navbar-brand > .navbar-item, + .navbar.is-black .navbar-brand .navbar-link { + color: white; } + .navbar.is-black .navbar-brand > a.navbar-item:focus, .navbar.is-black .navbar-brand > a.navbar-item:hover, .navbar.is-black .navbar-brand > a.navbar-item.is-active, + .navbar.is-black .navbar-brand .navbar-link:focus, + .navbar.is-black .navbar-brand .navbar-link:hover, + .navbar.is-black .navbar-brand .navbar-link.is-active { + background-color: black; + color: white; } + .navbar.is-black .navbar-brand .navbar-link::after { + border-color: white; } + .navbar.is-black .navbar-burger { + color: white; } + @media screen and (min-width: 1056px) { + .navbar.is-black .navbar-start > .navbar-item, + .navbar.is-black .navbar-start .navbar-link, + .navbar.is-black .navbar-end > .navbar-item, + .navbar.is-black .navbar-end .navbar-link { + color: white; } + .navbar.is-black .navbar-start > a.navbar-item:focus, .navbar.is-black .navbar-start > a.navbar-item:hover, .navbar.is-black .navbar-start > a.navbar-item.is-active, + .navbar.is-black .navbar-start .navbar-link:focus, + .navbar.is-black .navbar-start .navbar-link:hover, + .navbar.is-black .navbar-start .navbar-link.is-active, + .navbar.is-black .navbar-end > a.navbar-item:focus, + .navbar.is-black .navbar-end > a.navbar-item:hover, + .navbar.is-black .navbar-end > a.navbar-item.is-active, + .navbar.is-black .navbar-end .navbar-link:focus, + .navbar.is-black .navbar-end .navbar-link:hover, + .navbar.is-black .navbar-end .navbar-link.is-active { + background-color: black; + color: white; } + .navbar.is-black .navbar-start .navbar-link::after, + .navbar.is-black .navbar-end .navbar-link::after { + border-color: white; } + .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { + background-color: black; + color: white; } + .navbar.is-black .navbar-dropdown a.navbar-item.is-active { + background-color: #0a0a0a; + color: white; } } + .navbar.is-light { + background-color: whitesmoke; + color: #363636; } + .navbar.is-light .navbar-brand > .navbar-item, + .navbar.is-light .navbar-brand .navbar-link { + color: #363636; } + .navbar.is-light .navbar-brand > a.navbar-item:focus, .navbar.is-light .navbar-brand > a.navbar-item:hover, .navbar.is-light .navbar-brand > a.navbar-item.is-active, + .navbar.is-light .navbar-brand .navbar-link:focus, + .navbar.is-light .navbar-brand .navbar-link:hover, + .navbar.is-light .navbar-brand .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-brand .navbar-link::after { + border-color: #363636; } + .navbar.is-light .navbar-burger { + color: #363636; } + @media screen and (min-width: 1056px) { + .navbar.is-light .navbar-start > .navbar-item, + .navbar.is-light .navbar-start .navbar-link, + .navbar.is-light .navbar-end > .navbar-item, + .navbar.is-light .navbar-end .navbar-link { + color: #363636; } + .navbar.is-light .navbar-start > a.navbar-item:focus, .navbar.is-light .navbar-start > a.navbar-item:hover, .navbar.is-light .navbar-start > a.navbar-item.is-active, + .navbar.is-light .navbar-start .navbar-link:focus, + .navbar.is-light .navbar-start .navbar-link:hover, + .navbar.is-light .navbar-start .navbar-link.is-active, + .navbar.is-light .navbar-end > a.navbar-item:focus, + .navbar.is-light .navbar-end > a.navbar-item:hover, + .navbar.is-light .navbar-end > a.navbar-item.is-active, + .navbar.is-light .navbar-end .navbar-link:focus, + .navbar.is-light .navbar-end .navbar-link:hover, + .navbar.is-light .navbar-end .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-start .navbar-link::after, + .navbar.is-light .navbar-end .navbar-link::after { + border-color: #363636; } + .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #363636; } } + .navbar.is-dark, .content kbd.navbar { + background-color: #363636; + color: whitesmoke; } + .navbar.is-dark .navbar-brand > .navbar-item, .content kbd.navbar .navbar-brand > .navbar-item, + .navbar.is-dark .navbar-brand .navbar-link, + .content kbd.navbar .navbar-brand .navbar-link { + color: whitesmoke; } + .navbar.is-dark .navbar-brand > a.navbar-item:focus, .content kbd.navbar .navbar-brand > a.navbar-item:focus, .navbar.is-dark .navbar-brand > a.navbar-item:hover, .content kbd.navbar .navbar-brand > a.navbar-item:hover, .navbar.is-dark .navbar-brand > a.navbar-item.is-active, .content kbd.navbar .navbar-brand > a.navbar-item.is-active, + .navbar.is-dark .navbar-brand .navbar-link:focus, + .content kbd.navbar .navbar-brand .navbar-link:focus, + .navbar.is-dark .navbar-brand .navbar-link:hover, + .content kbd.navbar .navbar-brand .navbar-link:hover, + .navbar.is-dark .navbar-brand .navbar-link.is-active, + .content kbd.navbar .navbar-brand .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-brand .navbar-link::after, .content kbd.navbar .navbar-brand .navbar-link::after { + border-color: whitesmoke; } + .navbar.is-dark .navbar-burger, .content kbd.navbar .navbar-burger { + color: whitesmoke; } + @media screen and (min-width: 1056px) { + .navbar.is-dark .navbar-start > .navbar-item, .content kbd.navbar .navbar-start > .navbar-item, + .navbar.is-dark .navbar-start .navbar-link, + .content kbd.navbar .navbar-start .navbar-link, + .navbar.is-dark .navbar-end > .navbar-item, + .content kbd.navbar .navbar-end > .navbar-item, + .navbar.is-dark .navbar-end .navbar-link, + .content kbd.navbar .navbar-end .navbar-link { + color: whitesmoke; } + .navbar.is-dark .navbar-start > a.navbar-item:focus, .content kbd.navbar .navbar-start > a.navbar-item:focus, .navbar.is-dark .navbar-start > a.navbar-item:hover, .content kbd.navbar .navbar-start > a.navbar-item:hover, .navbar.is-dark .navbar-start > a.navbar-item.is-active, .content kbd.navbar .navbar-start > a.navbar-item.is-active, + .navbar.is-dark .navbar-start .navbar-link:focus, + .content kbd.navbar .navbar-start .navbar-link:focus, + .navbar.is-dark .navbar-start .navbar-link:hover, + .content kbd.navbar .navbar-start .navbar-link:hover, + .navbar.is-dark .navbar-start .navbar-link.is-active, + .content kbd.navbar .navbar-start .navbar-link.is-active, + .navbar.is-dark .navbar-end > a.navbar-item:focus, + .content kbd.navbar .navbar-end > a.navbar-item:focus, + .navbar.is-dark .navbar-end > a.navbar-item:hover, + .content kbd.navbar .navbar-end > a.navbar-item:hover, + .navbar.is-dark .navbar-end > a.navbar-item.is-active, + .content kbd.navbar .navbar-end > a.navbar-item.is-active, + .navbar.is-dark .navbar-end .navbar-link:focus, + .content kbd.navbar .navbar-end .navbar-link:focus, + .navbar.is-dark .navbar-end .navbar-link:hover, + .content kbd.navbar .navbar-end .navbar-link:hover, + .navbar.is-dark .navbar-end .navbar-link.is-active, + .content kbd.navbar .navbar-end .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-start .navbar-link::after, .content kbd.navbar .navbar-start .navbar-link::after, + .navbar.is-dark .navbar-end .navbar-link::after, + .content kbd.navbar .navbar-end .navbar-link::after { + border-color: whitesmoke; } + .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, + .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, + .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { + background-color: #363636; + color: whitesmoke; } } + .navbar.is-primary, .docstring > section > a.navbar.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .navbar.is-primary .navbar-brand > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, + .navbar.is-primary .navbar-brand .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-primary .navbar-brand > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, .navbar.is-primary .navbar-brand > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, .navbar.is-primary .navbar-brand > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, + .navbar.is-primary .navbar-brand .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, + .navbar.is-primary .navbar-brand .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, + .navbar.is-primary .navbar-brand .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-brand .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-primary .navbar-burger, .docstring > section > a.navbar.docs-sourcelink .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-primary .navbar-start > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, + .navbar.is-primary .navbar-start .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, + .navbar.is-primary .navbar-end > .navbar-item, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, + .navbar.is-primary .navbar-end .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { + color: #fff; } + .navbar.is-primary .navbar-start > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, .navbar.is-primary .navbar-start > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, .navbar.is-primary .navbar-start > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, + .navbar.is-primary .navbar-start .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, + .navbar.is-primary .navbar-start .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, + .navbar.is-primary .navbar-start .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, + .navbar.is-primary .navbar-end > a.navbar-item:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, + .navbar.is-primary .navbar-end > a.navbar-item:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, + .navbar.is-primary .navbar-end > a.navbar-item.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, + .navbar.is-primary .navbar-end .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, + .navbar.is-primary .navbar-end .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, + .navbar.is-primary .navbar-end .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-start .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, + .navbar.is-primary .navbar-end .navbar-link::after, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { + background-color: #4eb5de; + color: #fff; } } + .navbar.is-link { + background-color: #149eaa; + color: #fff; } + .navbar.is-link .navbar-brand > .navbar-item, + .navbar.is-link .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-link .navbar-brand > a.navbar-item:focus, .navbar.is-link .navbar-brand > a.navbar-item:hover, .navbar.is-link .navbar-brand > a.navbar-item.is-active, + .navbar.is-link .navbar-brand .navbar-link:focus, + .navbar.is-link .navbar-brand .navbar-link:hover, + .navbar.is-link .navbar-brand .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-link .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-link .navbar-start > .navbar-item, + .navbar.is-link .navbar-start .navbar-link, + .navbar.is-link .navbar-end > .navbar-item, + .navbar.is-link .navbar-end .navbar-link { + color: #fff; } + .navbar.is-link .navbar-start > a.navbar-item:focus, .navbar.is-link .navbar-start > a.navbar-item:hover, .navbar.is-link .navbar-start > a.navbar-item.is-active, + .navbar.is-link .navbar-start .navbar-link:focus, + .navbar.is-link .navbar-start .navbar-link:hover, + .navbar.is-link .navbar-start .navbar-link.is-active, + .navbar.is-link .navbar-end > a.navbar-item:focus, + .navbar.is-link .navbar-end > a.navbar-item:hover, + .navbar.is-link .navbar-end > a.navbar-item.is-active, + .navbar.is-link .navbar-end .navbar-link:focus, + .navbar.is-link .navbar-end .navbar-link:hover, + .navbar.is-link .navbar-end .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-start .navbar-link::after, + .navbar.is-link .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-dropdown a.navbar-item.is-active { + background-color: #149eaa; + color: #fff; } } + .navbar.is-info { + background-color: #209cee; + color: #fff; } + .navbar.is-info .navbar-brand > .navbar-item, + .navbar.is-info .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-info .navbar-brand > a.navbar-item:focus, .navbar.is-info .navbar-brand > a.navbar-item:hover, .navbar.is-info .navbar-brand > a.navbar-item.is-active, + .navbar.is-info .navbar-brand .navbar-link:focus, + .navbar.is-info .navbar-brand .navbar-link:hover, + .navbar.is-info .navbar-brand .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-info .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-info .navbar-start > .navbar-item, + .navbar.is-info .navbar-start .navbar-link, + .navbar.is-info .navbar-end > .navbar-item, + .navbar.is-info .navbar-end .navbar-link { + color: #fff; } + .navbar.is-info .navbar-start > a.navbar-item:focus, .navbar.is-info .navbar-start > a.navbar-item:hover, .navbar.is-info .navbar-start > a.navbar-item.is-active, + .navbar.is-info .navbar-start .navbar-link:focus, + .navbar.is-info .navbar-start .navbar-link:hover, + .navbar.is-info .navbar-start .navbar-link.is-active, + .navbar.is-info .navbar-end > a.navbar-item:focus, + .navbar.is-info .navbar-end > a.navbar-item:hover, + .navbar.is-info .navbar-end > a.navbar-item.is-active, + .navbar.is-info .navbar-end .navbar-link:focus, + .navbar.is-info .navbar-end .navbar-link:hover, + .navbar.is-info .navbar-end .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-start .navbar-link::after, + .navbar.is-info .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-dropdown a.navbar-item.is-active { + background-color: #209cee; + color: #fff; } } + .navbar.is-success { + background-color: #22c35b; + color: #fff; } + .navbar.is-success .navbar-brand > .navbar-item, + .navbar.is-success .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-success .navbar-brand > a.navbar-item:focus, .navbar.is-success .navbar-brand > a.navbar-item:hover, .navbar.is-success .navbar-brand > a.navbar-item.is-active, + .navbar.is-success .navbar-brand .navbar-link:focus, + .navbar.is-success .navbar-brand .navbar-link:hover, + .navbar.is-success .navbar-brand .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-success .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-success .navbar-start > .navbar-item, + .navbar.is-success .navbar-start .navbar-link, + .navbar.is-success .navbar-end > .navbar-item, + .navbar.is-success .navbar-end .navbar-link { + color: #fff; } + .navbar.is-success .navbar-start > a.navbar-item:focus, .navbar.is-success .navbar-start > a.navbar-item:hover, .navbar.is-success .navbar-start > a.navbar-item.is-active, + .navbar.is-success .navbar-start .navbar-link:focus, + .navbar.is-success .navbar-start .navbar-link:hover, + .navbar.is-success .navbar-start .navbar-link.is-active, + .navbar.is-success .navbar-end > a.navbar-item:focus, + .navbar.is-success .navbar-end > a.navbar-item:hover, + .navbar.is-success .navbar-end > a.navbar-item.is-active, + .navbar.is-success .navbar-end .navbar-link:focus, + .navbar.is-success .navbar-end .navbar-link:hover, + .navbar.is-success .navbar-end .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-start .navbar-link::after, + .navbar.is-success .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-dropdown a.navbar-item.is-active { + background-color: #22c35b; + color: #fff; } } + .navbar.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand > .navbar-item, + .navbar.is-warning .navbar-brand .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand > a.navbar-item:focus, .navbar.is-warning .navbar-brand > a.navbar-item:hover, .navbar.is-warning .navbar-brand > a.navbar-item.is-active, + .navbar.is-warning .navbar-brand .navbar-link:focus, + .navbar.is-warning .navbar-brand .navbar-link:hover, + .navbar.is-warning .navbar-brand .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-burger { + color: rgba(0, 0, 0, 0.7); } + @media screen and (min-width: 1056px) { + .navbar.is-warning .navbar-start > .navbar-item, + .navbar.is-warning .navbar-start .navbar-link, + .navbar.is-warning .navbar-end > .navbar-item, + .navbar.is-warning .navbar-end .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-start > a.navbar-item:focus, .navbar.is-warning .navbar-start > a.navbar-item:hover, .navbar.is-warning .navbar-start > a.navbar-item.is-active, + .navbar.is-warning .navbar-start .navbar-link:focus, + .navbar.is-warning .navbar-start .navbar-link:hover, + .navbar.is-warning .navbar-start .navbar-link.is-active, + .navbar.is-warning .navbar-end > a.navbar-item:focus, + .navbar.is-warning .navbar-end > a.navbar-item:hover, + .navbar.is-warning .navbar-end > a.navbar-item.is-active, + .navbar.is-warning .navbar-end .navbar-link:focus, + .navbar.is-warning .navbar-end .navbar-link:hover, + .navbar.is-warning .navbar-end .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-start .navbar-link::after, + .navbar.is-warning .navbar-end .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } } + .navbar.is-danger { + background-color: #da0b00; + color: #fff; } + .navbar.is-danger .navbar-brand > .navbar-item, + .navbar.is-danger .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-danger .navbar-brand > a.navbar-item:focus, .navbar.is-danger .navbar-brand > a.navbar-item:hover, .navbar.is-danger .navbar-brand > a.navbar-item.is-active, + .navbar.is-danger .navbar-brand .navbar-link:focus, + .navbar.is-danger .navbar-brand .navbar-link:hover, + .navbar.is-danger .navbar-brand .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-danger .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-danger .navbar-start > .navbar-item, + .navbar.is-danger .navbar-start .navbar-link, + .navbar.is-danger .navbar-end > .navbar-item, + .navbar.is-danger .navbar-end .navbar-link { + color: #fff; } + .navbar.is-danger .navbar-start > a.navbar-item:focus, .navbar.is-danger .navbar-start > a.navbar-item:hover, .navbar.is-danger .navbar-start > a.navbar-item.is-active, + .navbar.is-danger .navbar-start .navbar-link:focus, + .navbar.is-danger .navbar-start .navbar-link:hover, + .navbar.is-danger .navbar-start .navbar-link.is-active, + .navbar.is-danger .navbar-end > a.navbar-item:focus, + .navbar.is-danger .navbar-end > a.navbar-item:hover, + .navbar.is-danger .navbar-end > a.navbar-item.is-active, + .navbar.is-danger .navbar-end .navbar-link:focus, + .navbar.is-danger .navbar-end .navbar-link:hover, + .navbar.is-danger .navbar-end .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-start .navbar-link::after, + .navbar.is-danger .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { + background-color: #da0b00; + color: #fff; } } + .navbar > .container { + align-items: stretch; + display: flex; + min-height: 3.25rem; + width: 100%; } + .navbar.has-shadow { + box-shadow: 0 2px 0 0 whitesmoke; } + .navbar.is-fixed-bottom, .navbar.is-fixed-top { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom { + bottom: 0; } + .navbar.is-fixed-bottom.has-shadow { + box-shadow: 0 -2px 0 0 whitesmoke; } + .navbar.is-fixed-top { + top: 0; } + +html.has-navbar-fixed-top, +body.has-navbar-fixed-top { + padding-top: 3.25rem; } + +html.has-navbar-fixed-bottom, +body.has-navbar-fixed-bottom { + padding-bottom: 3.25rem; } + +.navbar-brand, +.navbar-tabs { + align-items: stretch; + display: flex; + flex-shrink: 0; + min-height: 3.25rem; } + +.navbar-brand a.navbar-item:focus, .navbar-brand a.navbar-item:hover { + background-color: transparent; } + +.navbar-tabs { + -webkit-overflow-scrolling: touch; + max-width: 100vw; + overflow-x: auto; + overflow-y: hidden; } + +.navbar-burger { + color: #4a4a4a; + cursor: pointer; + display: block; + height: 3.25rem; + position: relative; + width: 3.25rem; + margin-left: auto; } + .navbar-burger span { + background-color: currentColor; + display: block; + height: 1px; + left: calc(50% - 8px); + position: absolute; + transform-origin: center; + transition-duration: 86ms; + transition-property: background-color, opacity, transform; + transition-timing-function: ease-out; + width: 16px; } + .navbar-burger span:nth-child(1) { + top: calc(50% - 6px); } + .navbar-burger span:nth-child(2) { + top: calc(50% - 1px); } + .navbar-burger span:nth-child(3) { + top: calc(50% + 4px); } + .navbar-burger:hover { + background-color: rgba(0, 0, 0, 0.05); } + .navbar-burger.is-active span:nth-child(1) { + transform: translateY(5px) rotate(45deg); } + .navbar-burger.is-active span:nth-child(2) { + opacity: 0; } + .navbar-burger.is-active span:nth-child(3) { + transform: translateY(-5px) rotate(-45deg); } + +.navbar-menu { + display: none; } + +.navbar-item, +.navbar-link { + color: #4a4a4a; + display: block; + line-height: 1.5; + padding: 0.5rem 0.75rem; + position: relative; } + .navbar-item .icon:only-child, + .navbar-link .icon:only-child { + margin-left: -0.25rem; + margin-right: -0.25rem; } + +a.navbar-item, +.navbar-link { + cursor: pointer; } + a.navbar-item:focus, a.navbar-item:focus-within, a.navbar-item:hover, a.navbar-item.is-active, + .navbar-link:focus, + .navbar-link:focus-within, + .navbar-link:hover, + .navbar-link.is-active { + background-color: #fafafa; + color: #149eaa; } + +.navbar-item { + display: block; + flex-grow: 0; + flex-shrink: 0; } + .navbar-item img { + max-height: 1.75rem; } + .navbar-item.has-dropdown { + padding: 0; } + .navbar-item.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .navbar-item.is-tab { + border-bottom: 1px solid transparent; + min-height: 3.25rem; + padding-bottom: calc(0.5rem - 1px); } + .navbar-item.is-tab:focus, .navbar-item.is-tab:hover { + background-color: transparent; + border-bottom-color: #149eaa; } + .navbar-item.is-tab.is-active { + background-color: transparent; + border-bottom-color: #149eaa; + border-bottom-style: solid; + border-bottom-width: 3px; + color: #149eaa; + padding-bottom: calc(0.5rem - 3px); } + +.navbar-content { + flex-grow: 1; + flex-shrink: 1; } + +.navbar-link:not(.is-arrowless) { + padding-right: 2.5em; } + .navbar-link:not(.is-arrowless)::after { + border-color: #149eaa; + margin-top: -0.375em; + right: 1.125em; } + +.navbar-dropdown { + font-size: 0.875rem; + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + .navbar-dropdown .navbar-item { + padding-left: 1.5rem; + padding-right: 1.5rem; } + +.navbar-divider { + background-color: whitesmoke; + border: none; + display: none; + height: 2px; + margin: 0.5rem 0; } + +@media screen and (max-width: 1055px) { + .navbar > .container { + display: block; } + .navbar-brand .navbar-item, + .navbar-tabs .navbar-item { + align-items: center; + display: flex; } + .navbar-link::after { + display: none; } + .navbar-menu { + background-color: white; + box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); + padding: 0.5rem 0; } + .navbar-menu.is-active { + display: block; } + .navbar.is-fixed-bottom-touch, .navbar.is-fixed-top-touch { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom-touch { + bottom: 0; } + .navbar.is-fixed-bottom-touch.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + .navbar.is-fixed-top-touch { + top: 0; } + .navbar.is-fixed-top .navbar-menu, .navbar.is-fixed-top-touch .navbar-menu { + -webkit-overflow-scrolling: touch; + max-height: calc(100vh - 3.25rem); + overflow: auto; } + html.has-navbar-fixed-top-touch, + body.has-navbar-fixed-top-touch { + padding-top: 3.25rem; } + html.has-navbar-fixed-bottom-touch, + body.has-navbar-fixed-bottom-touch { + padding-bottom: 3.25rem; } } + +@media screen and (min-width: 1056px) { + .navbar, + .navbar-menu, + .navbar-start, + .navbar-end { + align-items: stretch; + display: flex; } + .navbar { + min-height: 3.25rem; } + .navbar.is-spaced { + padding: 1rem 2rem; } + .navbar.is-spaced .navbar-start, + .navbar.is-spaced .navbar-end { + align-items: center; } + .navbar.is-spaced a.navbar-item, + .navbar.is-spaced .navbar-link { + border-radius: 4px; } + .navbar.is-transparent a.navbar-item:focus, .navbar.is-transparent a.navbar-item:hover, .navbar.is-transparent a.navbar-item.is-active, + .navbar.is-transparent .navbar-link:focus, + .navbar.is-transparent .navbar-link:hover, + .navbar.is-transparent .navbar-link.is-active { + background-color: transparent !important; } + .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { + background-color: transparent !important; } + .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #149eaa; } + .navbar-burger { + display: none; } + .navbar-item, + .navbar-link { + align-items: center; + display: flex; } + .navbar-item { + display: flex; } + .navbar-item.has-dropdown { + align-items: stretch; } + .navbar-item.has-dropdown-up .navbar-link::after { + transform: rotate(135deg) translate(0.25em, -0.25em); } + .navbar-item.has-dropdown-up .navbar-dropdown { + border-bottom: 2px solid #dbdbdb; + border-radius: 6px 6px 0 0; + border-top: none; + bottom: 100%; + box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); + top: auto; } + .navbar-item.is-active .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown { + display: block; } + .navbar.is-spaced .navbar-item.is-active .navbar-dropdown, .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:hover .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { + opacity: 1; + pointer-events: auto; + transform: translateY(0); } + .navbar-menu { + flex-grow: 1; + flex-shrink: 0; } + .navbar-start { + justify-content: flex-start; + margin-right: auto; } + .navbar-end { + justify-content: flex-end; + margin-left: auto; } + .navbar-dropdown { + background-color: white; + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 2px solid #dbdbdb; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); + display: none; + font-size: 0.875rem; + left: 0; + min-width: 100%; + position: absolute; + top: 100%; + z-index: 20; } + .navbar-dropdown .navbar-item { + padding: 0.375rem 1rem; + white-space: nowrap; } + .navbar-dropdown a.navbar-item { + padding-right: 3rem; } + .navbar-dropdown a.navbar-item:focus, .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #149eaa; } + .navbar.is-spaced .navbar-dropdown, .navbar-dropdown.is-boxed { + border-radius: 6px; + border-top: none; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + display: block; + opacity: 0; + pointer-events: none; + top: calc(100% + (-4px)); + transform: translateY(-5px); + transition-duration: 86ms; + transition-property: opacity, transform; } + .navbar-dropdown.is-right { + left: auto; + right: 0; } + .navbar-divider { + display: block; } + .navbar > .container .navbar-brand, + .container > .navbar .navbar-brand { + margin-left: -.75rem; } + .navbar > .container .navbar-menu, + .container > .navbar .navbar-menu { + margin-right: -.75rem; } + .navbar.is-fixed-bottom-desktop, .navbar.is-fixed-top-desktop { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom-desktop { + bottom: 0; } + .navbar.is-fixed-bottom-desktop.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + .navbar.is-fixed-top-desktop { + top: 0; } + html.has-navbar-fixed-top-desktop, + body.has-navbar-fixed-top-desktop { + padding-top: 3.25rem; } + html.has-navbar-fixed-bottom-desktop, + body.has-navbar-fixed-bottom-desktop { + padding-bottom: 3.25rem; } + html.has-spaced-navbar-fixed-top, + body.has-spaced-navbar-fixed-top { + padding-top: 5.25rem; } + html.has-spaced-navbar-fixed-bottom, + body.has-spaced-navbar-fixed-bottom { + padding-bottom: 5.25rem; } + a.navbar-item.is-active, + .navbar-link.is-active { + color: #0a0a0a; } + a.navbar-item.is-active:not(:focus):not(:hover), + .navbar-link.is-active:not(:focus):not(:hover) { + background-color: transparent; } + .navbar-item.has-dropdown:focus .navbar-link, .navbar-item.has-dropdown:hover .navbar-link, .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #fafafa; } } + +.hero.is-fullheight-with-navbar { + min-height: calc(100vh - 3.25rem); } + +.pagination { + font-size: 1rem; + margin: -0.25rem; } + .pagination.is-small, #documenter .docs-sidebar form.docs-search > input.pagination { + font-size: 0.75rem; } + .pagination.is-medium { + font-size: 1.25rem; } + .pagination.is-large { + font-size: 1.5rem; } + .pagination.is-rounded .pagination-previous, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, + .pagination.is-rounded .pagination-next, + #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { + padding-left: 1em; + padding-right: 1em; + border-radius: 290486px; } + .pagination.is-rounded .pagination-link, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { + border-radius: 290486px; } + +.pagination, +.pagination-list { + align-items: center; + display: flex; + justify-content: center; + text-align: center; } + +.pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis { + font-size: 1em; + justify-content: center; + margin: 0.25rem; + padding-left: 0.5em; + padding-right: 0.5em; + text-align: center; } + +.pagination-previous, +.pagination-next, +.pagination-link { + border-color: #dbdbdb; + color: #363636; + min-width: 2.25em; } + .pagination-previous:hover, + .pagination-next:hover, + .pagination-link:hover { + border-color: #b5b5b5; + color: #107c85; } + .pagination-previous:focus, + .pagination-next:focus, + .pagination-link:focus { + border-color: #3c5dcd; } + .pagination-previous:active, + .pagination-next:active, + .pagination-link:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } + .pagination-previous[disabled], + .pagination-next[disabled], + .pagination-link[disabled] { + background-color: #dbdbdb; + border-color: #dbdbdb; + box-shadow: none; + color: #6b6b6b; + opacity: 0.5; } + +.pagination-previous, +.pagination-next { + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + +.pagination-link.is-current { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + +.pagination-ellipsis { + color: #b5b5b5; + pointer-events: none; } + +.pagination-list { + flex-wrap: wrap; } + +@media screen and (max-width: 768px) { + .pagination { + flex-wrap: wrap; } + .pagination-previous, + .pagination-next { + flex-grow: 1; + flex-shrink: 1; } + .pagination-list li { + flex-grow: 1; + flex-shrink: 1; } } + +@media screen and (min-width: 769px), print { + .pagination-list { + flex-grow: 1; + flex-shrink: 1; + justify-content: flex-start; + order: 1; } + .pagination-previous { + order: 2; } + .pagination-next { + order: 3; } + .pagination { + justify-content: space-between; } + .pagination.is-centered .pagination-previous { + order: 1; } + .pagination.is-centered .pagination-list { + justify-content: center; + order: 2; } + .pagination.is-centered .pagination-next { + order: 3; } + .pagination.is-right .pagination-previous { + order: 1; } + .pagination.is-right .pagination-next { + order: 2; } + .pagination.is-right .pagination-list { + justify-content: flex-end; + order: 3; } } + +.panel { + font-size: 1rem; } + .panel:not(:last-child) { + margin-bottom: 1.5rem; } + +.panel-heading, +.panel-tabs, +.panel-block { + border-bottom: 1px solid #dbdbdb; + border-left: 1px solid #dbdbdb; + border-right: 1px solid #dbdbdb; } + .panel-heading:first-child, + .panel-tabs:first-child, + .panel-block:first-child { + border-top: 1px solid #dbdbdb; } + +.panel-heading { + background-color: whitesmoke; + border-radius: 4px 4px 0 0; + color: #654ca3; + font-size: 1.25em; + font-weight: 300; + line-height: 1.25; + padding: 0.5em 0.75em; } + +.panel-tabs { + align-items: flex-end; + display: flex; + font-size: 0.875em; + justify-content: center; } + .panel-tabs a { + border-bottom: 1px solid #dbdbdb; + margin-bottom: -1px; + padding: 0.5em; } + .panel-tabs a.is-active { + border-bottom-color: #4a4a4a; + color: #363636; } + +.panel-list a { + color: #202020; } + .panel-list a:hover { + color: #149eaa; } + +.panel-block { + align-items: center; + color: #654ca3; + display: flex; + justify-content: flex-start; + padding: 0.5em 0.75em; } + .panel-block input[type="checkbox"] { + margin-right: 0.75em; } + .panel-block > .control { + flex-grow: 1; + flex-shrink: 1; + width: 100%; } + .panel-block.is-wrapped { + flex-wrap: wrap; } + .panel-block.is-active { + border-left-color: #149eaa; + color: #363636; } + .panel-block.is-active .panel-icon { + color: #149eaa; } + +a.panel-block, +label.panel-block { + cursor: pointer; } + a.panel-block:hover, + label.panel-block:hover { + background-color: whitesmoke; } + +.panel-icon { + display: inline-block; + font-size: 14px; + height: 1em; + line-height: 1em; + text-align: center; + vertical-align: top; + width: 1em; + color: #6b6b6b; + margin-right: 0.75em; } + .panel-icon .fa { + font-size: inherit; + line-height: inherit; } + +.tabs { + -webkit-overflow-scrolling: touch; + align-items: stretch; + display: flex; + font-size: 1rem; + justify-content: space-between; + overflow: hidden; + overflow-x: auto; + white-space: nowrap; } + .tabs a { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + color: #202020; + display: flex; + justify-content: center; + margin-bottom: -1px; + padding: 0.5em 1em; + vertical-align: top; } + .tabs a:hover { + border-bottom-color: #654ca3; + color: #654ca3; } + .tabs li { + display: block; } + .tabs li.is-active a { + border-bottom-color: #149eaa; + color: #149eaa; } + .tabs ul { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + display: flex; + flex-grow: 1; + flex-shrink: 0; + justify-content: flex-start; } + .tabs ul.is-left { + padding-right: 0.75em; } + .tabs ul.is-center { + flex: none; + justify-content: center; + padding-left: 0.75em; + padding-right: 0.75em; } + .tabs ul.is-right { + justify-content: flex-end; + padding-left: 0.75em; } + .tabs .icon:first-child { + margin-right: 0.5em; } + .tabs .icon:last-child { + margin-left: 0.5em; } + .tabs.is-centered ul { + justify-content: center; } + .tabs.is-right ul { + justify-content: flex-end; } + .tabs.is-boxed a { + border: 1px solid transparent; + border-radius: 4px 4px 0 0; } + .tabs.is-boxed a:hover { + background-color: whitesmoke; + border-bottom-color: #dbdbdb; } + .tabs.is-boxed li.is-active a { + background-color: white; + border-color: #dbdbdb; + border-bottom-color: transparent !important; } + .tabs.is-fullwidth li { + flex-grow: 1; + flex-shrink: 0; } + .tabs.is-toggle a { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px; + margin-bottom: 0; + position: relative; } + .tabs.is-toggle a:hover { + background-color: whitesmoke; + border-color: #b5b5b5; + z-index: 2; } + .tabs.is-toggle li + li { + margin-left: -1px; } + .tabs.is-toggle li:first-child a { + border-radius: 4px 0 0 4px; } + .tabs.is-toggle li:last-child a { + border-radius: 0 4px 4px 0; } + .tabs.is-toggle li.is-active a { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; + z-index: 1; } + .tabs.is-toggle ul { + border-bottom: none; } + .tabs.is-toggle.is-toggle-rounded li:first-child a { + border-bottom-left-radius: 290486px; + border-top-left-radius: 290486px; + padding-left: 1.25em; } + .tabs.is-toggle.is-toggle-rounded li:last-child a { + border-bottom-right-radius: 290486px; + border-top-right-radius: 290486px; + padding-right: 1.25em; } + .tabs.is-small, #documenter .docs-sidebar form.docs-search > input.tabs { + font-size: 0.75rem; } + .tabs.is-medium { + font-size: 1.25rem; } + .tabs.is-large { + font-size: 1.5rem; } + +.column { + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + padding: 0.75rem; } + .columns.is-mobile > .column.is-narrow { + flex: none; } + .columns.is-mobile > .column.is-full { + flex: none; + width: 100%; } + .columns.is-mobile > .column.is-three-quarters { + flex: none; + width: 75%; } + .columns.is-mobile > .column.is-two-thirds { + flex: none; + width: 66.6666%; } + .columns.is-mobile > .column.is-half { + flex: none; + width: 50%; } + .columns.is-mobile > .column.is-one-third { + flex: none; + width: 33.3333%; } + .columns.is-mobile > .column.is-one-quarter { + flex: none; + width: 25%; } + .columns.is-mobile > .column.is-one-fifth { + flex: none; + width: 20%; } + .columns.is-mobile > .column.is-two-fifths { + flex: none; + width: 40%; } + .columns.is-mobile > .column.is-three-fifths { + flex: none; + width: 60%; } + .columns.is-mobile > .column.is-four-fifths { + flex: none; + width: 80%; } + .columns.is-mobile > .column.is-offset-three-quarters { + margin-left: 75%; } + .columns.is-mobile > .column.is-offset-two-thirds { + margin-left: 66.6666%; } + .columns.is-mobile > .column.is-offset-half { + margin-left: 50%; } + .columns.is-mobile > .column.is-offset-one-third { + margin-left: 33.3333%; } + .columns.is-mobile > .column.is-offset-one-quarter { + margin-left: 25%; } + .columns.is-mobile > .column.is-offset-one-fifth { + margin-left: 20%; } + .columns.is-mobile > .column.is-offset-two-fifths { + margin-left: 40%; } + .columns.is-mobile > .column.is-offset-three-fifths { + margin-left: 60%; } + .columns.is-mobile > .column.is-offset-four-fifths { + margin-left: 80%; } + .columns.is-mobile > .column.is-0 { + flex: none; + width: 0%; } + .columns.is-mobile > .column.is-offset-0 { + margin-left: 0%; } + .columns.is-mobile > .column.is-1 { + flex: none; + width: 8.3333333333%; } + .columns.is-mobile > .column.is-offset-1 { + margin-left: 8.3333333333%; } + .columns.is-mobile > .column.is-2 { + flex: none; + width: 16.6666666667%; } + .columns.is-mobile > .column.is-offset-2 { + margin-left: 16.6666666667%; } + .columns.is-mobile > .column.is-3 { + flex: none; + width: 25%; } + .columns.is-mobile > .column.is-offset-3 { + margin-left: 25%; } + .columns.is-mobile > .column.is-4 { + flex: none; + width: 33.3333333333%; } + .columns.is-mobile > .column.is-offset-4 { + margin-left: 33.3333333333%; } + .columns.is-mobile > .column.is-5 { + flex: none; + width: 41.6666666667%; } + .columns.is-mobile > .column.is-offset-5 { + margin-left: 41.6666666667%; } + .columns.is-mobile > .column.is-6 { + flex: none; + width: 50%; } + .columns.is-mobile > .column.is-offset-6 { + margin-left: 50%; } + .columns.is-mobile > .column.is-7 { + flex: none; + width: 58.3333333333%; } + .columns.is-mobile > .column.is-offset-7 { + margin-left: 58.3333333333%; } + .columns.is-mobile > .column.is-8 { + flex: none; + width: 66.6666666667%; } + .columns.is-mobile > .column.is-offset-8 { + margin-left: 66.6666666667%; } + .columns.is-mobile > .column.is-9 { + flex: none; + width: 75%; } + .columns.is-mobile > .column.is-offset-9 { + margin-left: 75%; } + .columns.is-mobile > .column.is-10 { + flex: none; + width: 83.3333333333%; } + .columns.is-mobile > .column.is-offset-10 { + margin-left: 83.3333333333%; } + .columns.is-mobile > .column.is-11 { + flex: none; + width: 91.6666666667%; } + .columns.is-mobile > .column.is-offset-11 { + margin-left: 91.6666666667%; } + .columns.is-mobile > .column.is-12 { + flex: none; + width: 100%; } + .columns.is-mobile > .column.is-offset-12 { + margin-left: 100%; } + @media screen and (max-width: 768px) { + .column.is-narrow-mobile { + flex: none; } + .column.is-full-mobile { + flex: none; + width: 100%; } + .column.is-three-quarters-mobile { + flex: none; + width: 75%; } + .column.is-two-thirds-mobile { + flex: none; + width: 66.6666%; } + .column.is-half-mobile { + flex: none; + width: 50%; } + .column.is-one-third-mobile { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-mobile { + flex: none; + width: 25%; } + .column.is-one-fifth-mobile { + flex: none; + width: 20%; } + .column.is-two-fifths-mobile { + flex: none; + width: 40%; } + .column.is-three-fifths-mobile { + flex: none; + width: 60%; } + .column.is-four-fifths-mobile { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-mobile { + margin-left: 75%; } + .column.is-offset-two-thirds-mobile { + margin-left: 66.6666%; } + .column.is-offset-half-mobile { + margin-left: 50%; } + .column.is-offset-one-third-mobile { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-mobile { + margin-left: 25%; } + .column.is-offset-one-fifth-mobile { + margin-left: 20%; } + .column.is-offset-two-fifths-mobile { + margin-left: 40%; } + .column.is-offset-three-fifths-mobile { + margin-left: 60%; } + .column.is-offset-four-fifths-mobile { + margin-left: 80%; } + .column.is-0-mobile { + flex: none; + width: 0%; } + .column.is-offset-0-mobile { + margin-left: 0%; } + .column.is-1-mobile { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-mobile { + margin-left: 8.3333333333%; } + .column.is-2-mobile { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-mobile { + margin-left: 16.6666666667%; } + .column.is-3-mobile { + flex: none; + width: 25%; } + .column.is-offset-3-mobile { + margin-left: 25%; } + .column.is-4-mobile { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-mobile { + margin-left: 33.3333333333%; } + .column.is-5-mobile { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-mobile { + margin-left: 41.6666666667%; } + .column.is-6-mobile { + flex: none; + width: 50%; } + .column.is-offset-6-mobile { + margin-left: 50%; } + .column.is-7-mobile { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-mobile { + margin-left: 58.3333333333%; } + .column.is-8-mobile { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-mobile { + margin-left: 66.6666666667%; } + .column.is-9-mobile { + flex: none; + width: 75%; } + .column.is-offset-9-mobile { + margin-left: 75%; } + .column.is-10-mobile { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-mobile { + margin-left: 83.3333333333%; } + .column.is-11-mobile { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-mobile { + margin-left: 91.6666666667%; } + .column.is-12-mobile { + flex: none; + width: 100%; } + .column.is-offset-12-mobile { + margin-left: 100%; } } + @media screen and (min-width: 769px), print { + .column.is-narrow, .column.is-narrow-tablet { + flex: none; } + .column.is-full, .column.is-full-tablet { + flex: none; + width: 100%; } + .column.is-three-quarters, .column.is-three-quarters-tablet { + flex: none; + width: 75%; } + .column.is-two-thirds, .column.is-two-thirds-tablet { + flex: none; + width: 66.6666%; } + .column.is-half, .column.is-half-tablet { + flex: none; + width: 50%; } + .column.is-one-third, .column.is-one-third-tablet { + flex: none; + width: 33.3333%; } + .column.is-one-quarter, .column.is-one-quarter-tablet { + flex: none; + width: 25%; } + .column.is-one-fifth, .column.is-one-fifth-tablet { + flex: none; + width: 20%; } + .column.is-two-fifths, .column.is-two-fifths-tablet { + flex: none; + width: 40%; } + .column.is-three-fifths, .column.is-three-fifths-tablet { + flex: none; + width: 60%; } + .column.is-four-fifths, .column.is-four-fifths-tablet { + flex: none; + width: 80%; } + .column.is-offset-three-quarters, .column.is-offset-three-quarters-tablet { + margin-left: 75%; } + .column.is-offset-two-thirds, .column.is-offset-two-thirds-tablet { + margin-left: 66.6666%; } + .column.is-offset-half, .column.is-offset-half-tablet { + margin-left: 50%; } + .column.is-offset-one-third, .column.is-offset-one-third-tablet { + margin-left: 33.3333%; } + .column.is-offset-one-quarter, .column.is-offset-one-quarter-tablet { + margin-left: 25%; } + .column.is-offset-one-fifth, .column.is-offset-one-fifth-tablet { + margin-left: 20%; } + .column.is-offset-two-fifths, .column.is-offset-two-fifths-tablet { + margin-left: 40%; } + .column.is-offset-three-fifths, .column.is-offset-three-fifths-tablet { + margin-left: 60%; } + .column.is-offset-four-fifths, .column.is-offset-four-fifths-tablet { + margin-left: 80%; } + .column.is-0, .column.is-0-tablet { + flex: none; + width: 0%; } + .column.is-offset-0, .column.is-offset-0-tablet { + margin-left: 0%; } + .column.is-1, .column.is-1-tablet { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1, .column.is-offset-1-tablet { + margin-left: 8.3333333333%; } + .column.is-2, .column.is-2-tablet { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2, .column.is-offset-2-tablet { + margin-left: 16.6666666667%; } + .column.is-3, .column.is-3-tablet { + flex: none; + width: 25%; } + .column.is-offset-3, .column.is-offset-3-tablet { + margin-left: 25%; } + .column.is-4, .column.is-4-tablet { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4, .column.is-offset-4-tablet { + margin-left: 33.3333333333%; } + .column.is-5, .column.is-5-tablet { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5, .column.is-offset-5-tablet { + margin-left: 41.6666666667%; } + .column.is-6, .column.is-6-tablet { + flex: none; + width: 50%; } + .column.is-offset-6, .column.is-offset-6-tablet { + margin-left: 50%; } + .column.is-7, .column.is-7-tablet { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7, .column.is-offset-7-tablet { + margin-left: 58.3333333333%; } + .column.is-8, .column.is-8-tablet { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8, .column.is-offset-8-tablet { + margin-left: 66.6666666667%; } + .column.is-9, .column.is-9-tablet { + flex: none; + width: 75%; } + .column.is-offset-9, .column.is-offset-9-tablet { + margin-left: 75%; } + .column.is-10, .column.is-10-tablet { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10, .column.is-offset-10-tablet { + margin-left: 83.3333333333%; } + .column.is-11, .column.is-11-tablet { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11, .column.is-offset-11-tablet { + margin-left: 91.6666666667%; } + .column.is-12, .column.is-12-tablet { + flex: none; + width: 100%; } + .column.is-offset-12, .column.is-offset-12-tablet { + margin-left: 100%; } } + @media screen and (max-width: 1055px) { + .column.is-narrow-touch { + flex: none; } + .column.is-full-touch { + flex: none; + width: 100%; } + .column.is-three-quarters-touch { + flex: none; + width: 75%; } + .column.is-two-thirds-touch { + flex: none; + width: 66.6666%; } + .column.is-half-touch { + flex: none; + width: 50%; } + .column.is-one-third-touch { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-touch { + flex: none; + width: 25%; } + .column.is-one-fifth-touch { + flex: none; + width: 20%; } + .column.is-two-fifths-touch { + flex: none; + width: 40%; } + .column.is-three-fifths-touch { + flex: none; + width: 60%; } + .column.is-four-fifths-touch { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-touch { + margin-left: 75%; } + .column.is-offset-two-thirds-touch { + margin-left: 66.6666%; } + .column.is-offset-half-touch { + margin-left: 50%; } + .column.is-offset-one-third-touch { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-touch { + margin-left: 25%; } + .column.is-offset-one-fifth-touch { + margin-left: 20%; } + .column.is-offset-two-fifths-touch { + margin-left: 40%; } + .column.is-offset-three-fifths-touch { + margin-left: 60%; } + .column.is-offset-four-fifths-touch { + margin-left: 80%; } + .column.is-0-touch { + flex: none; + width: 0%; } + .column.is-offset-0-touch { + margin-left: 0%; } + .column.is-1-touch { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-touch { + margin-left: 8.3333333333%; } + .column.is-2-touch { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-touch { + margin-left: 16.6666666667%; } + .column.is-3-touch { + flex: none; + width: 25%; } + .column.is-offset-3-touch { + margin-left: 25%; } + .column.is-4-touch { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-touch { + margin-left: 33.3333333333%; } + .column.is-5-touch { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-touch { + margin-left: 41.6666666667%; } + .column.is-6-touch { + flex: none; + width: 50%; } + .column.is-offset-6-touch { + margin-left: 50%; } + .column.is-7-touch { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-touch { + margin-left: 58.3333333333%; } + .column.is-8-touch { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-touch { + margin-left: 66.6666666667%; } + .column.is-9-touch { + flex: none; + width: 75%; } + .column.is-offset-9-touch { + margin-left: 75%; } + .column.is-10-touch { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-touch { + margin-left: 83.3333333333%; } + .column.is-11-touch { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-touch { + margin-left: 91.6666666667%; } + .column.is-12-touch { + flex: none; + width: 100%; } + .column.is-offset-12-touch { + margin-left: 100%; } } + @media screen and (min-width: 1056px) { + .column.is-narrow-desktop { + flex: none; } + .column.is-full-desktop { + flex: none; + width: 100%; } + .column.is-three-quarters-desktop { + flex: none; + width: 75%; } + .column.is-two-thirds-desktop { + flex: none; + width: 66.6666%; } + .column.is-half-desktop { + flex: none; + width: 50%; } + .column.is-one-third-desktop { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-desktop { + flex: none; + width: 25%; } + .column.is-one-fifth-desktop { + flex: none; + width: 20%; } + .column.is-two-fifths-desktop { + flex: none; + width: 40%; } + .column.is-three-fifths-desktop { + flex: none; + width: 60%; } + .column.is-four-fifths-desktop { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-desktop { + margin-left: 75%; } + .column.is-offset-two-thirds-desktop { + margin-left: 66.6666%; } + .column.is-offset-half-desktop { + margin-left: 50%; } + .column.is-offset-one-third-desktop { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-desktop { + margin-left: 25%; } + .column.is-offset-one-fifth-desktop { + margin-left: 20%; } + .column.is-offset-two-fifths-desktop { + margin-left: 40%; } + .column.is-offset-three-fifths-desktop { + margin-left: 60%; } + .column.is-offset-four-fifths-desktop { + margin-left: 80%; } + .column.is-0-desktop { + flex: none; + width: 0%; } + .column.is-offset-0-desktop { + margin-left: 0%; } + .column.is-1-desktop { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-desktop { + margin-left: 8.3333333333%; } + .column.is-2-desktop { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-desktop { + margin-left: 16.6666666667%; } + .column.is-3-desktop { + flex: none; + width: 25%; } + .column.is-offset-3-desktop { + margin-left: 25%; } + .column.is-4-desktop { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-desktop { + margin-left: 33.3333333333%; } + .column.is-5-desktop { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-desktop { + margin-left: 41.6666666667%; } + .column.is-6-desktop { + flex: none; + width: 50%; } + .column.is-offset-6-desktop { + margin-left: 50%; } + .column.is-7-desktop { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-desktop { + margin-left: 58.3333333333%; } + .column.is-8-desktop { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-desktop { + margin-left: 66.6666666667%; } + .column.is-9-desktop { + flex: none; + width: 75%; } + .column.is-offset-9-desktop { + margin-left: 75%; } + .column.is-10-desktop { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-desktop { + margin-left: 83.3333333333%; } + .column.is-11-desktop { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-desktop { + margin-left: 91.6666666667%; } + .column.is-12-desktop { + flex: none; + width: 100%; } + .column.is-offset-12-desktop { + margin-left: 100%; } } + @media screen and (min-width: 1216px) { + .column.is-narrow-widescreen { + flex: none; } + .column.is-full-widescreen { + flex: none; + width: 100%; } + .column.is-three-quarters-widescreen { + flex: none; + width: 75%; } + .column.is-two-thirds-widescreen { + flex: none; + width: 66.6666%; } + .column.is-half-widescreen { + flex: none; + width: 50%; } + .column.is-one-third-widescreen { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-widescreen { + flex: none; + width: 25%; } + .column.is-one-fifth-widescreen { + flex: none; + width: 20%; } + .column.is-two-fifths-widescreen { + flex: none; + width: 40%; } + .column.is-three-fifths-widescreen { + flex: none; + width: 60%; } + .column.is-four-fifths-widescreen { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-widescreen { + margin-left: 75%; } + .column.is-offset-two-thirds-widescreen { + margin-left: 66.6666%; } + .column.is-offset-half-widescreen { + margin-left: 50%; } + .column.is-offset-one-third-widescreen { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-widescreen { + margin-left: 25%; } + .column.is-offset-one-fifth-widescreen { + margin-left: 20%; } + .column.is-offset-two-fifths-widescreen { + margin-left: 40%; } + .column.is-offset-three-fifths-widescreen { + margin-left: 60%; } + .column.is-offset-four-fifths-widescreen { + margin-left: 80%; } + .column.is-0-widescreen { + flex: none; + width: 0%; } + .column.is-offset-0-widescreen { + margin-left: 0%; } + .column.is-1-widescreen { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-widescreen { + margin-left: 8.3333333333%; } + .column.is-2-widescreen { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-widescreen { + margin-left: 16.6666666667%; } + .column.is-3-widescreen { + flex: none; + width: 25%; } + .column.is-offset-3-widescreen { + margin-left: 25%; } + .column.is-4-widescreen { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-widescreen { + margin-left: 33.3333333333%; } + .column.is-5-widescreen { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-widescreen { + margin-left: 41.6666666667%; } + .column.is-6-widescreen { + flex: none; + width: 50%; } + .column.is-offset-6-widescreen { + margin-left: 50%; } + .column.is-7-widescreen { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-widescreen { + margin-left: 58.3333333333%; } + .column.is-8-widescreen { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-widescreen { + margin-left: 66.6666666667%; } + .column.is-9-widescreen { + flex: none; + width: 75%; } + .column.is-offset-9-widescreen { + margin-left: 75%; } + .column.is-10-widescreen { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-widescreen { + margin-left: 83.3333333333%; } + .column.is-11-widescreen { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-widescreen { + margin-left: 91.6666666667%; } + .column.is-12-widescreen { + flex: none; + width: 100%; } + .column.is-offset-12-widescreen { + margin-left: 100%; } } + @media screen and (min-width: 1408px) { + .column.is-narrow-fullhd { + flex: none; } + .column.is-full-fullhd { + flex: none; + width: 100%; } + .column.is-three-quarters-fullhd { + flex: none; + width: 75%; } + .column.is-two-thirds-fullhd { + flex: none; + width: 66.6666%; } + .column.is-half-fullhd { + flex: none; + width: 50%; } + .column.is-one-third-fullhd { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-fullhd { + flex: none; + width: 25%; } + .column.is-one-fifth-fullhd { + flex: none; + width: 20%; } + .column.is-two-fifths-fullhd { + flex: none; + width: 40%; } + .column.is-three-fifths-fullhd { + flex: none; + width: 60%; } + .column.is-four-fifths-fullhd { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-fullhd { + margin-left: 75%; } + .column.is-offset-two-thirds-fullhd { + margin-left: 66.6666%; } + .column.is-offset-half-fullhd { + margin-left: 50%; } + .column.is-offset-one-third-fullhd { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-fullhd { + margin-left: 25%; } + .column.is-offset-one-fifth-fullhd { + margin-left: 20%; } + .column.is-offset-two-fifths-fullhd { + margin-left: 40%; } + .column.is-offset-three-fifths-fullhd { + margin-left: 60%; } + .column.is-offset-four-fifths-fullhd { + margin-left: 80%; } + .column.is-0-fullhd { + flex: none; + width: 0%; } + .column.is-offset-0-fullhd { + margin-left: 0%; } + .column.is-1-fullhd { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-fullhd { + margin-left: 8.3333333333%; } + .column.is-2-fullhd { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-fullhd { + margin-left: 16.6666666667%; } + .column.is-3-fullhd { + flex: none; + width: 25%; } + .column.is-offset-3-fullhd { + margin-left: 25%; } + .column.is-4-fullhd { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-fullhd { + margin-left: 33.3333333333%; } + .column.is-5-fullhd { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-fullhd { + margin-left: 41.6666666667%; } + .column.is-6-fullhd { + flex: none; + width: 50%; } + .column.is-offset-6-fullhd { + margin-left: 50%; } + .column.is-7-fullhd { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-fullhd { + margin-left: 58.3333333333%; } + .column.is-8-fullhd { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-fullhd { + margin-left: 66.6666666667%; } + .column.is-9-fullhd { + flex: none; + width: 75%; } + .column.is-offset-9-fullhd { + margin-left: 75%; } + .column.is-10-fullhd { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-fullhd { + margin-left: 83.3333333333%; } + .column.is-11-fullhd { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-fullhd { + margin-left: 91.6666666667%; } + .column.is-12-fullhd { + flex: none; + width: 100%; } + .column.is-offset-12-fullhd { + margin-left: 100%; } } +.columns { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + .columns:last-child { + margin-bottom: -0.75rem; } + .columns:not(:last-child) { + margin-bottom: calc(1.5rem - 0.75rem); } + .columns.is-centered { + justify-content: center; } + .columns.is-gapless { + margin-left: 0; + margin-right: 0; + margin-top: 0; } + .columns.is-gapless > .column { + margin: 0; + padding: 0 !important; } + .columns.is-gapless:not(:last-child) { + margin-bottom: 1.5rem; } + .columns.is-gapless:last-child { + margin-bottom: 0; } + .columns.is-mobile { + display: flex; } + .columns.is-multiline { + flex-wrap: wrap; } + .columns.is-vcentered { + align-items: center; } + @media screen and (min-width: 769px), print { + .columns:not(.is-desktop) { + display: flex; } } + @media screen and (min-width: 1056px) { + .columns.is-desktop { + display: flex; } } +.columns.is-variable { + --columnGap: 0.75rem; + margin-left: calc(-1 * var(--columnGap)); + margin-right: calc(-1 * var(--columnGap)); } + .columns.is-variable .column { + padding-left: var(--columnGap); + padding-right: var(--columnGap); } + .columns.is-variable.is-0 { + --columnGap: 0rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-0-mobile { + --columnGap: 0rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-0-tablet { + --columnGap: 0rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-0-tablet-only { + --columnGap: 0rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-0-touch { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-0-desktop { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-0-desktop-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-0-widescreen { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-0-widescreen-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-0-fullhd { + --columnGap: 0rem; } } + .columns.is-variable.is-1 { + --columnGap: 0.25rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-1-mobile { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-1-tablet { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-1-tablet-only { + --columnGap: 0.25rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-1-touch { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-1-desktop { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-1-desktop-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-1-widescreen { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-1-widescreen-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-1-fullhd { + --columnGap: 0.25rem; } } + .columns.is-variable.is-2 { + --columnGap: 0.5rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-2-mobile { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-2-tablet { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-2-tablet-only { + --columnGap: 0.5rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-2-touch { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-2-desktop { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-2-desktop-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-2-widescreen { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-2-widescreen-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-2-fullhd { + --columnGap: 0.5rem; } } + .columns.is-variable.is-3 { + --columnGap: 0.75rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-3-mobile { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-3-tablet { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-3-tablet-only { + --columnGap: 0.75rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-3-touch { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-3-desktop { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-3-desktop-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-3-widescreen { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-3-widescreen-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-3-fullhd { + --columnGap: 0.75rem; } } + .columns.is-variable.is-4 { + --columnGap: 1rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-4-mobile { + --columnGap: 1rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-4-tablet { + --columnGap: 1rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-4-tablet-only { + --columnGap: 1rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-4-touch { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-4-desktop { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-4-desktop-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-4-widescreen { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-4-widescreen-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-4-fullhd { + --columnGap: 1rem; } } + .columns.is-variable.is-5 { + --columnGap: 1.25rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-5-mobile { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-5-tablet { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-5-tablet-only { + --columnGap: 1.25rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-5-touch { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-5-desktop { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-5-desktop-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-5-widescreen { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-5-widescreen-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-5-fullhd { + --columnGap: 1.25rem; } } + .columns.is-variable.is-6 { + --columnGap: 1.5rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-6-mobile { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-6-tablet { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-6-tablet-only { + --columnGap: 1.5rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-6-touch { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-6-desktop { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-6-desktop-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-6-widescreen { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-6-widescreen-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-6-fullhd { + --columnGap: 1.5rem; } } + .columns.is-variable.is-7 { + --columnGap: 1.75rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-7-mobile { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-7-tablet { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-7-tablet-only { + --columnGap: 1.75rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-7-touch { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-7-desktop { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-7-desktop-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-7-widescreen { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-7-widescreen-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-7-fullhd { + --columnGap: 1.75rem; } } + .columns.is-variable.is-8 { + --columnGap: 2rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-8-mobile { + --columnGap: 2rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-8-tablet { + --columnGap: 2rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-8-tablet-only { + --columnGap: 2rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-8-touch { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-8-desktop { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-8-desktop-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-8-widescreen { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-8-widescreen-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-8-fullhd { + --columnGap: 2rem; } } +.tile { + align-items: stretch; + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + min-height: min-content; } + .tile.is-ancestor { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + .tile.is-ancestor:last-child { + margin-bottom: -0.75rem; } + .tile.is-ancestor:not(:last-child) { + margin-bottom: 0.75rem; } + .tile.is-child { + margin: 0 !important; } + .tile.is-parent { + padding: 0.75rem; } + .tile.is-vertical { + flex-direction: column; } + .tile.is-vertical > .tile.is-child:not(:last-child) { + margin-bottom: 1.5rem !important; } + @media screen and (min-width: 769px), print { + .tile:not(.is-child) { + display: flex; } + .tile.is-1 { + flex: none; + width: 8.3333333333%; } + .tile.is-2 { + flex: none; + width: 16.6666666667%; } + .tile.is-3 { + flex: none; + width: 25%; } + .tile.is-4 { + flex: none; + width: 33.3333333333%; } + .tile.is-5 { + flex: none; + width: 41.6666666667%; } + .tile.is-6 { + flex: none; + width: 50%; } + .tile.is-7 { + flex: none; + width: 58.3333333333%; } + .tile.is-8 { + flex: none; + width: 66.6666666667%; } + .tile.is-9 { + flex: none; + width: 75%; } + .tile.is-10 { + flex: none; + width: 83.3333333333%; } + .tile.is-11 { + flex: none; + width: 91.6666666667%; } + .tile.is-12 { + flex: none; + width: 100%; } } +.hero { + align-items: stretch; + display: flex; + flex-direction: column; + justify-content: space-between; } + .hero .navbar { + background: none; } + .hero .tabs ul { + border-bottom: none; } + .hero.is-white { + background-color: white; + color: #0a0a0a; } + .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-white strong { + color: inherit; } + .hero.is-white .title { + color: #0a0a0a; } + .hero.is-white .subtitle { + color: rgba(10, 10, 10, 0.9); } + .hero.is-white .subtitle a:not(.button), + .hero.is-white .subtitle strong { + color: #0a0a0a; } + @media screen and (max-width: 1055px) { + .hero.is-white .navbar-menu { + background-color: white; } } + .hero.is-white .navbar-item, + .hero.is-white .navbar-link { + color: rgba(10, 10, 10, 0.7); } + .hero.is-white a.navbar-item:hover, .hero.is-white a.navbar-item.is-active, + .hero.is-white .navbar-link:hover, + .hero.is-white .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .hero.is-white .tabs a { + color: #0a0a0a; + opacity: 0.9; } + .hero.is-white .tabs a:hover { + opacity: 1; } + .hero.is-white .tabs li.is-active a { + opacity: 1; } + .hero.is-white .tabs.is-boxed a, .hero.is-white .tabs.is-toggle a { + color: #0a0a0a; } + .hero.is-white .tabs.is-boxed a:hover, .hero.is-white .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-white .tabs.is-boxed li.is-active a, .hero.is-white .tabs.is-boxed li.is-active a:hover, .hero.is-white .tabs.is-toggle li.is-active a, .hero.is-white .tabs.is-toggle li.is-active a:hover { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .hero.is-white.is-bold { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } + @media screen and (max-width: 768px) { + .hero.is-white.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } + .hero.is-black { + background-color: #0a0a0a; + color: white; } + .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-black strong { + color: inherit; } + .hero.is-black .title { + color: white; } + .hero.is-black .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-black .subtitle a:not(.button), + .hero.is-black .subtitle strong { + color: white; } + @media screen and (max-width: 1055px) { + .hero.is-black .navbar-menu { + background-color: #0a0a0a; } } + .hero.is-black .navbar-item, + .hero.is-black .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-black a.navbar-item:hover, .hero.is-black a.navbar-item.is-active, + .hero.is-black .navbar-link:hover, + .hero.is-black .navbar-link.is-active { + background-color: black; + color: white; } + .hero.is-black .tabs a { + color: white; + opacity: 0.9; } + .hero.is-black .tabs a:hover { + opacity: 1; } + .hero.is-black .tabs li.is-active a { + opacity: 1; } + .hero.is-black .tabs.is-boxed a, .hero.is-black .tabs.is-toggle a { + color: white; } + .hero.is-black .tabs.is-boxed a:hover, .hero.is-black .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-black .tabs.is-boxed li.is-active a, .hero.is-black .tabs.is-boxed li.is-active a:hover, .hero.is-black .tabs.is-toggle li.is-active a, .hero.is-black .tabs.is-toggle li.is-active a:hover { + background-color: white; + border-color: white; + color: #0a0a0a; } + .hero.is-black.is-bold { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } + @media screen and (max-width: 768px) { + .hero.is-black.is-bold .navbar-menu { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } + .hero.is-light { + background-color: whitesmoke; + color: #363636; } + .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-light strong { + color: inherit; } + .hero.is-light .title { + color: #363636; } + .hero.is-light .subtitle { + color: rgba(54, 54, 54, 0.9); } + .hero.is-light .subtitle a:not(.button), + .hero.is-light .subtitle strong { + color: #363636; } + @media screen and (max-width: 1055px) { + .hero.is-light .navbar-menu { + background-color: whitesmoke; } } + .hero.is-light .navbar-item, + .hero.is-light .navbar-link { + color: rgba(54, 54, 54, 0.7); } + .hero.is-light a.navbar-item:hover, .hero.is-light a.navbar-item.is-active, + .hero.is-light .navbar-link:hover, + .hero.is-light .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .hero.is-light .tabs a { + color: #363636; + opacity: 0.9; } + .hero.is-light .tabs a:hover { + opacity: 1; } + .hero.is-light .tabs li.is-active a { + opacity: 1; } + .hero.is-light .tabs.is-boxed a, .hero.is-light .tabs.is-toggle a { + color: #363636; } + .hero.is-light .tabs.is-boxed a:hover, .hero.is-light .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-light .tabs.is-boxed li.is-active a, .hero.is-light .tabs.is-boxed li.is-active a:hover, .hero.is-light .tabs.is-toggle li.is-active a, .hero.is-light .tabs.is-toggle li.is-active a:hover { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .hero.is-light.is-bold { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } + @media screen and (max-width: 768px) { + .hero.is-light.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } } + .hero.is-dark, .content kbd.hero { + background-color: #363636; + color: whitesmoke; } + .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-dark strong, + .content kbd.hero strong { + color: inherit; } + .hero.is-dark .title, .content kbd.hero .title { + color: whitesmoke; } + .hero.is-dark .subtitle, .content kbd.hero .subtitle { + color: rgba(245, 245, 245, 0.9); } + .hero.is-dark .subtitle a:not(.button), .content kbd.hero .subtitle a:not(.button), + .hero.is-dark .subtitle strong, + .content kbd.hero .subtitle strong { + color: whitesmoke; } + @media screen and (max-width: 1055px) { + .hero.is-dark .navbar-menu, .content kbd.hero .navbar-menu { + background-color: #363636; } } + .hero.is-dark .navbar-item, .content kbd.hero .navbar-item, + .hero.is-dark .navbar-link, + .content kbd.hero .navbar-link { + color: rgba(245, 245, 245, 0.7); } + .hero.is-dark a.navbar-item:hover, .content kbd.hero a.navbar-item:hover, .hero.is-dark a.navbar-item.is-active, .content kbd.hero a.navbar-item.is-active, + .hero.is-dark .navbar-link:hover, + .content kbd.hero .navbar-link:hover, + .hero.is-dark .navbar-link.is-active, + .content kbd.hero .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .hero.is-dark .tabs a, .content kbd.hero .tabs a { + color: whitesmoke; + opacity: 0.9; } + .hero.is-dark .tabs a:hover, .content kbd.hero .tabs a:hover { + opacity: 1; } + .hero.is-dark .tabs li.is-active a, .content kbd.hero .tabs li.is-active a { + opacity: 1; } + .hero.is-dark .tabs.is-boxed a, .content kbd.hero .tabs.is-boxed a, .hero.is-dark .tabs.is-toggle a, .content kbd.hero .tabs.is-toggle a { + color: whitesmoke; } + .hero.is-dark .tabs.is-boxed a:hover, .content kbd.hero .tabs.is-boxed a:hover, .hero.is-dark .tabs.is-toggle a:hover, .content kbd.hero .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-dark .tabs.is-boxed li.is-active a, .content kbd.hero .tabs.is-boxed li.is-active a, .hero.is-dark .tabs.is-boxed li.is-active a:hover, .hero.is-dark .tabs.is-toggle li.is-active a, .content kbd.hero .tabs.is-toggle li.is-active a, .hero.is-dark .tabs.is-toggle li.is-active a:hover { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .hero.is-dark.is-bold, .content kbd.hero.is-bold { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } + @media screen and (max-width: 768px) { + .hero.is-dark.is-bold .navbar-menu, .content kbd.hero.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } } + .hero.is-primary, .docstring > section > a.hero.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-primary strong, + .docstring > section > a.hero.docs-sourcelink strong { + color: inherit; } + .hero.is-primary .title, .docstring > section > a.hero.docs-sourcelink .title { + color: #fff; } + .hero.is-primary .subtitle, .docstring > section > a.hero.docs-sourcelink .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-primary .subtitle a:not(.button), .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), + .hero.is-primary .subtitle strong, + .docstring > section > a.hero.docs-sourcelink .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-primary .navbar-menu, .docstring > section > a.hero.docs-sourcelink .navbar-menu { + background-color: #4eb5de; } } + .hero.is-primary .navbar-item, .docstring > section > a.hero.docs-sourcelink .navbar-item, + .hero.is-primary .navbar-link, + .docstring > section > a.hero.docs-sourcelink .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-primary a.navbar-item:hover, .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, .hero.is-primary a.navbar-item.is-active, .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, + .hero.is-primary .navbar-link:hover, + .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, + .hero.is-primary .navbar-link.is-active, + .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .hero.is-primary .tabs a, .docstring > section > a.hero.docs-sourcelink .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-primary .tabs a:hover, .docstring > section > a.hero.docs-sourcelink .tabs a:hover { + opacity: 1; } + .hero.is-primary .tabs li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { + opacity: 1; } + .hero.is-primary .tabs.is-boxed a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, .hero.is-primary .tabs.is-toggle a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { + color: #fff; } + .hero.is-primary .tabs.is-boxed a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, .hero.is-primary .tabs.is-toggle a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-primary .tabs.is-boxed li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, .hero.is-primary .tabs.is-boxed li.is-active a:hover, .hero.is-primary .tabs.is-toggle li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, .hero.is-primary .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #4eb5de; } + .hero.is-primary.is-bold, .docstring > section > a.hero.is-bold.docs-sourcelink { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } + @media screen and (max-width: 768px) { + .hero.is-primary.is-bold .navbar-menu, .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } } + .hero.is-link { + background-color: #149eaa; + color: #fff; } + .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-link strong { + color: inherit; } + .hero.is-link .title { + color: #fff; } + .hero.is-link .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-link .subtitle a:not(.button), + .hero.is-link .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-link .navbar-menu { + background-color: #149eaa; } } + .hero.is-link .navbar-item, + .hero.is-link .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-link a.navbar-item:hover, .hero.is-link a.navbar-item.is-active, + .hero.is-link .navbar-link:hover, + .hero.is-link .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .hero.is-link .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-link .tabs a:hover { + opacity: 1; } + .hero.is-link .tabs li.is-active a { + opacity: 1; } + .hero.is-link .tabs.is-boxed a, .hero.is-link .tabs.is-toggle a { + color: #fff; } + .hero.is-link .tabs.is-boxed a:hover, .hero.is-link .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-link .tabs.is-boxed li.is-active a, .hero.is-link .tabs.is-boxed li.is-active a:hover, .hero.is-link .tabs.is-toggle li.is-active a, .hero.is-link .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #149eaa; } + .hero.is-link.is-bold { + background-image: linear-gradient(141deg, #088379 0%, #149eaa 71%, #119ac6 100%); } + @media screen and (max-width: 768px) { + .hero.is-link.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #088379 0%, #149eaa 71%, #119ac6 100%); } } + .hero.is-info { + background-color: #209cee; + color: #fff; } + .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-info strong { + color: inherit; } + .hero.is-info .title { + color: #fff; } + .hero.is-info .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-info .subtitle a:not(.button), + .hero.is-info .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-info .navbar-menu { + background-color: #209cee; } } + .hero.is-info .navbar-item, + .hero.is-info .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-info a.navbar-item:hover, .hero.is-info a.navbar-item.is-active, + .hero.is-info .navbar-link:hover, + .hero.is-info .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .hero.is-info .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-info .tabs a:hover { + opacity: 1; } + .hero.is-info .tabs li.is-active a { + opacity: 1; } + .hero.is-info .tabs.is-boxed a, .hero.is-info .tabs.is-toggle a { + color: #fff; } + .hero.is-info .tabs.is-boxed a:hover, .hero.is-info .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-info .tabs.is-boxed li.is-active a, .hero.is-info .tabs.is-boxed li.is-active a:hover, .hero.is-info .tabs.is-toggle li.is-active a, .hero.is-info .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #209cee; } + .hero.is-info.is-bold { + background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } + @media screen and (max-width: 768px) { + .hero.is-info.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } } + .hero.is-success { + background-color: #22c35b; + color: #fff; } + .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-success strong { + color: inherit; } + .hero.is-success .title { + color: #fff; } + .hero.is-success .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-success .subtitle a:not(.button), + .hero.is-success .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-success .navbar-menu { + background-color: #22c35b; } } + .hero.is-success .navbar-item, + .hero.is-success .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-success a.navbar-item:hover, .hero.is-success a.navbar-item.is-active, + .hero.is-success .navbar-link:hover, + .hero.is-success .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .hero.is-success .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-success .tabs a:hover { + opacity: 1; } + .hero.is-success .tabs li.is-active a { + opacity: 1; } + .hero.is-success .tabs.is-boxed a, .hero.is-success .tabs.is-toggle a { + color: #fff; } + .hero.is-success .tabs.is-boxed a:hover, .hero.is-success .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-success .tabs.is-boxed li.is-active a, .hero.is-success .tabs.is-boxed li.is-active a:hover, .hero.is-success .tabs.is-toggle li.is-active a, .hero.is-success .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #22c35b; } + .hero.is-success.is-bold { + background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } + @media screen and (max-width: 768px) { + .hero.is-success.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } } + .hero.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-warning strong { + color: inherit; } + .hero.is-warning .title { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .subtitle { + color: rgba(0, 0, 0, 0.9); } + .hero.is-warning .subtitle a:not(.button), + .hero.is-warning .subtitle strong { + color: rgba(0, 0, 0, 0.7); } + @media screen and (max-width: 1055px) { + .hero.is-warning .navbar-menu { + background-color: #ffdd57; } } + .hero.is-warning .navbar-item, + .hero.is-warning .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning a.navbar-item:hover, .hero.is-warning a.navbar-item.is-active, + .hero.is-warning .navbar-link:hover, + .hero.is-warning .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .tabs a { + color: rgba(0, 0, 0, 0.7); + opacity: 0.9; } + .hero.is-warning .tabs a:hover { + opacity: 1; } + .hero.is-warning .tabs li.is-active a { + opacity: 1; } + .hero.is-warning .tabs.is-boxed a, .hero.is-warning .tabs.is-toggle a { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .tabs.is-boxed a:hover, .hero.is-warning .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-warning .tabs.is-boxed li.is-active a, .hero.is-warning .tabs.is-boxed li.is-active a:hover, .hero.is-warning .tabs.is-toggle li.is-active a, .hero.is-warning .tabs.is-toggle li.is-active a:hover { + background-color: rgba(0, 0, 0, 0.7); + border-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .hero.is-warning.is-bold { + background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } + @media screen and (max-width: 768px) { + .hero.is-warning.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } } + .hero.is-danger { + background-color: #da0b00; + color: #fff; } + .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-danger strong { + color: inherit; } + .hero.is-danger .title { + color: #fff; } + .hero.is-danger .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-danger .subtitle a:not(.button), + .hero.is-danger .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-danger .navbar-menu { + background-color: #da0b00; } } + .hero.is-danger .navbar-item, + .hero.is-danger .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-danger a.navbar-item:hover, .hero.is-danger a.navbar-item.is-active, + .hero.is-danger .navbar-link:hover, + .hero.is-danger .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .hero.is-danger .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-danger .tabs a:hover { + opacity: 1; } + .hero.is-danger .tabs li.is-active a { + opacity: 1; } + .hero.is-danger .tabs.is-boxed a, .hero.is-danger .tabs.is-toggle a { + color: #fff; } + .hero.is-danger .tabs.is-boxed a:hover, .hero.is-danger .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-danger .tabs.is-boxed li.is-active a, .hero.is-danger .tabs.is-boxed li.is-active a:hover, .hero.is-danger .tabs.is-toggle li.is-active a, .hero.is-danger .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #da0b00; } + .hero.is-danger.is-bold { + background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } + @media screen and (max-width: 768px) { + .hero.is-danger.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } } + .hero.is-small .hero-body, #documenter .docs-sidebar form.docs-search > input.hero .hero-body { + padding-bottom: 1.5rem; + padding-top: 1.5rem; } + @media screen and (min-width: 769px), print { + .hero.is-medium .hero-body { + padding-bottom: 9rem; + padding-top: 9rem; } } + @media screen and (min-width: 769px), print { + .hero.is-large .hero-body { + padding-bottom: 18rem; + padding-top: 18rem; } } + .hero.is-halfheight .hero-body, .hero.is-fullheight .hero-body, .hero.is-fullheight-with-navbar .hero-body { + align-items: center; + display: flex; } + .hero.is-halfheight .hero-body > .container, .hero.is-fullheight .hero-body > .container, .hero.is-fullheight-with-navbar .hero-body > .container { + flex-grow: 1; + flex-shrink: 1; } + .hero.is-halfheight { + min-height: 50vh; } + .hero.is-fullheight { + min-height: 100vh; } + +.hero-video { + overflow: hidden; } + .hero-video video { + left: 50%; + min-height: 100%; + min-width: 100%; + position: absolute; + top: 50%; + transform: translate3d(-50%, -50%, 0); } + .hero-video.is-transparent { + opacity: 0.3; } + @media screen and (max-width: 768px) { + .hero-video { + display: none; } } +.hero-buttons { + margin-top: 1.5rem; } + @media screen and (max-width: 768px) { + .hero-buttons .button { + display: flex; } + .hero-buttons .button:not(:last-child) { + margin-bottom: 0.75rem; } } + @media screen and (min-width: 769px), print { + .hero-buttons { + display: flex; + justify-content: center; } + .hero-buttons .button:not(:last-child) { + margin-right: 1.5rem; } } +.hero-head, +.hero-foot { + flex-grow: 0; + flex-shrink: 0; } + +.hero-body { + flex-grow: 1; + flex-shrink: 0; + padding: 3rem 1.5rem; } + +.section { + padding: 3rem 1.5rem; } + @media screen and (min-width: 1056px) { + .section.is-medium { + padding: 9rem 1.5rem; } + .section.is-large { + padding: 18rem 1.5rem; } } +.footer { + background-color: #fafafa; + padding: 3rem 1.5rem 6rem; } + +h1 .docs-heading-anchor, h1 .docs-heading-anchor:hover, h1 .docs-heading-anchor:visited, h2 .docs-heading-anchor, h2 .docs-heading-anchor:hover, h2 .docs-heading-anchor:visited, h3 .docs-heading-anchor, h3 .docs-heading-anchor:hover, h3 .docs-heading-anchor:visited, h4 .docs-heading-anchor, h4 .docs-heading-anchor:hover, h4 .docs-heading-anchor:visited, h5 .docs-heading-anchor, h5 .docs-heading-anchor:hover, h5 .docs-heading-anchor:visited, h6 .docs-heading-anchor, h6 .docs-heading-anchor:hover, h6 .docs-heading-anchor:visited { + color: #654ca3; } + +h1 .docs-heading-anchor-permalink, h2 .docs-heading-anchor-permalink, h3 .docs-heading-anchor-permalink, h4 .docs-heading-anchor-permalink, h5 .docs-heading-anchor-permalink, h6 .docs-heading-anchor-permalink { + visibility: hidden; + vertical-align: middle; + margin-left: 0.5em; + font-size: 0.7rem; } + h1 .docs-heading-anchor-permalink::before, h2 .docs-heading-anchor-permalink::before, h3 .docs-heading-anchor-permalink::before, h4 .docs-heading-anchor-permalink::before, h5 .docs-heading-anchor-permalink::before, h6 .docs-heading-anchor-permalink::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f0c1"; } + +h1:hover .docs-heading-anchor-permalink, h2:hover .docs-heading-anchor-permalink, h3:hover .docs-heading-anchor-permalink, h4:hover .docs-heading-anchor-permalink, h5:hover .docs-heading-anchor-permalink, h6:hover .docs-heading-anchor-permalink { + visibility: visible; } + +.docs-dark-only { + display: none !important; } + +pre { + position: relative; + overflow: hidden; } + pre code, pre code.hljs { + padding: 0 0.75rem !important; + overflow: auto; + display: block; } + pre code:first-of-type, pre code.hljs:first-of-type { + padding-top: 0.5rem !important; } + pre code:last-of-type, pre code.hljs:last-of-type { + padding-bottom: 0.5rem !important; } + pre .copy-button { + opacity: 0.2; + transition: opacity 0.2s; + position: absolute; + right: 0em; + top: 0em; + padding: 0.5em; + width: 2.5em; + height: 2.5em; + background: transparent; + border: none; + font-family: "Font Awesome 5 Free"; + color: #202020; + cursor: pointer; + text-align: center; } + pre .copy-button:focus, pre .copy-button:hover { + opacity: 1; + background: rgba(32, 32, 32, 0.1); + color: #149eaa; } + pre .copy-button.success { + color: #259a12; + opacity: 1; } + pre .copy-button.error { + color: #cb3c33; + opacity: 1; } + pre:hover .copy-button { + opacity: 1; } + +.admonition { + background-color: #b5b5b5; + border-style: solid; + border-width: 1px; + border-color: #363636; + border-radius: 4px; + font-size: 1rem; } + .admonition strong { + color: currentColor; } + .admonition.is-small, #documenter .docs-sidebar form.docs-search > input.admonition { + font-size: 0.75rem; } + .admonition.is-medium { + font-size: 1.25rem; } + .admonition.is-large { + font-size: 1.5rem; } + .admonition.is-default { + background-color: #b5b5b5; + border-color: #363636; } + .admonition.is-default > .admonition-header { + background-color: #363636; + color: #fff; } + .admonition.is-default > .admonition-body { + color: #fff; } + .admonition.is-info { + background-color: #def0fc; + border-color: #209cee; } + .admonition.is-info > .admonition-header { + background-color: #209cee; + color: #fff; } + .admonition.is-info > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-success { + background-color: #bdf4d1; + border-color: #22c35b; } + .admonition.is-success > .admonition-header { + background-color: #22c35b; + color: #fff; } + .admonition.is-success > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-warning { + background-color: #fff3c5; + border-color: #ffdd57; } + .admonition.is-warning > .admonition-header { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .admonition.is-warning > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-danger { + background-color: #ffaba7; + border-color: #da0b00; } + .admonition.is-danger > .admonition-header { + background-color: #da0b00; + color: #fff; } + .admonition.is-danger > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-compat { + background-color: #bdeff5; + border-color: #1db5c9; } + .admonition.is-compat > .admonition-header { + background-color: #1db5c9; + color: #fff; } + .admonition.is-compat > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + +.admonition-header { + color: #fff; + background-color: #363636; + align-items: center; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.5rem 0.75rem; + position: relative; } + .admonition-header:before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + margin-right: 0.75rem; + content: "\f06a"; } + +.admonition-body { + color: #202020; + padding: 0.5rem 0.75rem; } + .admonition-body pre { + background-color: #ebe8f4; } + .admonition-body code { + background-color: #ebe8f4; } + +.docstring { + margin-bottom: 1em; + background-color: transparent; + border: 1px solid #dbdbdb; + box-shadow: 2px 2px 3px rgba(10, 10, 10, 0.1); + max-width: 100%; } + .docstring > header { + display: flex; + flex-grow: 1; + align-items: stretch; + padding: 0.5rem 0.75rem; + background-color: #f7f7f7; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + box-shadow: none; + border-bottom: 1px solid #dbdbdb; } + .docstring > header code { + background-color: transparent; } + .docstring > header .docstring-binding { + margin-right: 0.3em; } + .docstring > header .docstring-category { + margin-left: 0.3em; } + .docstring > section { + position: relative; + padding: 0.75rem 0.75rem; + border-bottom: 1px solid #dbdbdb; } + .docstring > section:last-child { + border-bottom: none; } + .docstring > section > a.docs-sourcelink { + transition: opacity 0.3s; + opacity: 0; + position: absolute; + right: 0.375rem; + bottom: 0.375rem; } + .docstring > section > a.docs-sourcelink:focus { + opacity: 1 !important; } + .docstring:hover > section > a.docs-sourcelink { + opacity: 0.2; } + .docstring:focus-within > section > a.docs-sourcelink { + opacity: 0.2; } + .docstring > section:hover a.docs-sourcelink { + opacity: 1; } + +.documenter-example-output { + background-color: #fff; } + +.outdated-warning-overlay { + position: fixed; + top: 0; + left: 0; + right: 0; + box-shadow: 0 0 10px rgba(0, 0, 0, 0.3); + z-index: 999; + background-color: #ffaba7; + color: rgba(0, 0, 0, 0.7); + border-bottom: 3px solid #da0b00; + padding: 10px 35px; + text-align: center; + font-size: 15px; } + .outdated-warning-overlay .outdated-warning-closer { + position: absolute; + top: calc(50% - 10px); + right: 18px; + cursor: pointer; + width: 12px; } + .outdated-warning-overlay a { + color: #149eaa; } + .outdated-warning-overlay a:hover { + color: #107c85; } + +.content pre { + border: 1px solid #dbdbdb; } + +.content code { + font-weight: inherit; } + +.content a code { + color: #149eaa; } + +.content h1 code, .content h2 code, .content h3 code, .content h4 code, .content h5 code, .content h6 code { + color: #654ca3; } + +.content table { + display: block; + width: initial; + max-width: 100%; + overflow-x: auto; } + +.content blockquote > ul:first-child, .content blockquote > ol:first-child, .content .admonition-body > ul:first-child, .content .admonition-body > ol:first-child { + margin-top: 0; } + +pre, code { + font-variant-ligatures: no-contextual; } + +.breadcrumb a.is-disabled { + cursor: default; + pointer-events: none; } + .breadcrumb a.is-disabled, .breadcrumb a.is-disabled:hover { + color: #654ca3; } + +.hljs { + background: initial !important; } + +.katex .katex-mathml { + top: 0; + right: 0; } + +.katex-display, mjx-container, .MathJax_Display { + margin: 0.5em 0 !important; } + +html { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; } + +li.no-marker { + list-style: none; } + +/* This file contain the overall layout. + * + * The main container is
      that is identified by id #documenter. + */ +#documenter .docs-main > article { + overflow-wrap: break-word; } + #documenter .docs-main > article .math-container { + overflow-x: auto; + overflow-y: hidden; } + +@media screen and (min-width: 1056px) { + #documenter .docs-main { + max-width: 52rem; + margin-left: 20rem; + padding-right: 1rem; } } + +@media screen and (max-width: 1055px) { + #documenter .docs-main { + width: 100%; } + #documenter .docs-main > article { + max-width: 52rem; + margin-left: auto; + margin-right: auto; + margin-bottom: 1rem; + padding: 0 1rem; } + #documenter .docs-main > header, #documenter .docs-main > nav { + max-width: 100%; + width: 100%; + margin: 0; } } + +#documenter .docs-main header.docs-navbar { + background-color: #fff; + border-bottom: 1px solid #dbdbdb; + z-index: 2; + min-height: 4rem; + margin-bottom: 1rem; + display: flex; } + #documenter .docs-main header.docs-navbar .breadcrumb { + flex-grow: 1; } + #documenter .docs-main header.docs-navbar .docs-right { + display: flex; + white-space: nowrap; } + #documenter .docs-main header.docs-navbar .docs-right .docs-icon, #documenter .docs-main header.docs-navbar .docs-right .docs-label, #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + display: inline-block; } + #documenter .docs-main header.docs-navbar .docs-right .docs-label { + padding: 0; + margin-left: 0.3em; } + #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button { + margin: auto 0 auto 1rem; } + #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + font-size: 1.5rem; + margin: auto 0 auto 1rem; } + #documenter .docs-main header.docs-navbar > * { + margin: auto 0; } + @media screen and (max-width: 1055px) { + #documenter .docs-main header.docs-navbar { + position: sticky; + top: 0; + padding: 0 1rem; + /* For Headroom.js */ + transition-property: top, box-shadow; + -webkit-transition-property: top, box-shadow; + /* Safari */ + transition-duration: 0.3s; + -webkit-transition-duration: 0.3s; + /* Safari */ } + #documenter .docs-main header.docs-navbar.headroom--not-top { + box-shadow: 0.2rem 0rem 0.4rem #bbb; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } + #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { + top: -4.5rem; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } } +#documenter .docs-main section.footnotes { + border-top: 1px solid #dbdbdb; } + #documenter .docs-main section.footnotes li .tag:first-child, #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, #documenter .docs-main section.footnotes li .content kbd:first-child, .content #documenter .docs-main section.footnotes li kbd:first-child { + margin-right: 1em; + margin-bottom: 0.4em; } + +#documenter .docs-main .docs-footer { + display: flex; + flex-wrap: wrap; + margin-left: 0; + margin-right: 0; + border-top: 1px solid #dbdbdb; + padding-top: 1rem; + padding-bottom: 1rem; } + @media screen and (max-width: 1055px) { + #documenter .docs-main .docs-footer { + padding-left: 1rem; + padding-right: 1rem; } } + #documenter .docs-main .docs-footer .docs-footer-nextpage, #documenter .docs-main .docs-footer .docs-footer-prevpage { + flex-grow: 1; } + #documenter .docs-main .docs-footer .docs-footer-nextpage { + text-align: right; } + #documenter .docs-main .docs-footer .flexbox-break { + flex-basis: 100%; + height: 0; } + #documenter .docs-main .docs-footer .footer-message { + font-size: 0.8em; + margin: 0.5em auto 0 auto; + text-align: center; } + +#documenter .docs-sidebar { + display: flex; + flex-direction: column; + color: #fff; + background-color: #654ca3; + border-right: 1px solid #dbdbdb; + padding: 0; + flex: 0 0 18rem; + z-index: 5; + font-size: 1em; + position: fixed; + left: -18rem; + width: 18rem; + height: 100%; + transition: left 0.3s; + /* Setting up a nicer theme style for the scrollbar */ } + #documenter .docs-sidebar.visible { + left: 0; + box-shadow: 0.4rem 0rem 0.8rem #bbb; } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar.visible { + box-shadow: none; } } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar { + left: 0; + top: 0; } } + #documenter .docs-sidebar .docs-logo { + margin-top: 1rem; + padding: 0 1rem; } + #documenter .docs-sidebar .docs-logo > img { + max-height: 6rem; + margin: auto; } + #documenter .docs-sidebar .docs-package-name { + flex-shrink: 0; + font-size: 1.5rem; + font-weight: 700; + text-align: center; + white-space: nowrap; + overflow: hidden; + padding: 0.5rem 0; } + #documenter .docs-sidebar .docs-package-name .docs-autofit { + max-width: 16.2rem; } + #documenter .docs-sidebar .docs-package-name a, #documenter .docs-sidebar .docs-package-name a:hover { + color: #fff; } + #documenter .docs-sidebar .docs-version-selector { + border-top: 1px solid #dbdbdb; + display: none; + padding: 0.5rem; } + #documenter .docs-sidebar .docs-version-selector.visible { + display: flex; } + #documenter .docs-sidebar ul.docs-menu { + flex-grow: 1; + user-select: none; + border-top: 1px solid #dbdbdb; + padding-bottom: 1.5rem; + /* Managing collapsible submenus */ } + #documenter .docs-sidebar ul.docs-menu > li > .tocitem { + font-weight: bold; } + #documenter .docs-sidebar ul.docs-menu > li li { + font-size: 0.95em; + margin-left: 1em; + border-left: 1px solid #dbdbdb; } + #documenter .docs-sidebar ul.docs-menu input.collapse-toggle { + display: none; } + #documenter .docs-sidebar ul.docs-menu ul.collapsed { + display: none; } + #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed { + display: block; } + #documenter .docs-sidebar ul.docs-menu label.tocitem { + display: flex; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label { + flex-grow: 2; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron { + display: inline-block; + font-style: normal; + font-variant: normal; + text-rendering: auto; + line-height: 1; + font-size: 0.75em; + margin-left: 1rem; + margin-top: auto; + margin-bottom: auto; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f054"; } + #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before { + content: "\f078"; } + #documenter .docs-sidebar ul.docs-menu .tocitem { + display: block; + padding: 0.5rem 0.5rem; } + #documenter .docs-sidebar ul.docs-menu .tocitem, #documenter .docs-sidebar ul.docs-menu .tocitem:hover { + color: #fff; + background: #654ca3; } + #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, #documenter .docs-sidebar ul.docs-menu label.tocitem:hover { + color: #fff; + background-color: #4b3979; } + #documenter .docs-sidebar ul.docs-menu li.is-active { + border-top: 1px solid #dbdbdb; + border-bottom: 1px solid #dbdbdb; + background-color: #fff; } + #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover { + background-color: #fff; + color: #202020; } + #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover { + background-color: #ddd7ec; + color: #202020; } + #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child { + border-top: none; } + #documenter .docs-sidebar ul.docs-menu ul.internal { + margin: 0 0.5rem 0.5rem; + border-top: 1px solid #dbdbdb; } + #documenter .docs-sidebar ul.docs-menu ul.internal li { + font-size: 0.85em; + border-left: none; + margin-left: 0; + margin-top: 0.5rem; } + #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem { + width: 100%; + padding: 0; } + #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before { + content: "⚬"; + margin-right: 0.4em; } + #documenter .docs-sidebar form.docs-search { + margin: auto; + margin-top: 0.5rem; + margin-bottom: 0.5rem; } + #documenter .docs-sidebar form.docs-search > input { + width: 14.4rem; } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar ul.docs-menu { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar { + width: .3rem; + background: none; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #543f87; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover { + background: #43326b; } } + @media screen and (max-width: 1055px) { + #documenter .docs-sidebar { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + #documenter .docs-sidebar::-webkit-scrollbar { + width: .3rem; + background: none; } + #documenter .docs-sidebar::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #543f87; } + #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover { + background: #43326b; } } +#documenter .docs-main #documenter-search-info { + margin-bottom: 1rem; } + +#documenter .docs-main #documenter-search-results { + list-style-type: circle; + list-style-position: outside; } + #documenter .docs-main #documenter-search-results li { + margin-left: 2rem; } + #documenter .docs-main #documenter-search-results .docs-highlight { + background-color: yellow; } + +.ansi span.sgr1 { + font-weight: bolder; } + +.ansi span.sgr2 { + font-weight: lighter; } + +.ansi span.sgr3 { + font-style: italic; } + +.ansi span.sgr4 { + text-decoration: underline; } + +.ansi span.sgr7 { + color: #fff; + background-color: #202020; } + +.ansi span.sgr8 { + color: transparent; } + .ansi span.sgr8 span { + color: transparent; } + +.ansi span.sgr9 { + text-decoration: line-through; } + +.ansi span.sgr30 { + color: #242424; } + +.ansi span.sgr31 { + color: #a7201f; } + +.ansi span.sgr32 { + color: #066f00; } + +.ansi span.sgr33 { + color: #856b00; } + +.ansi span.sgr34 { + color: #2149b0; } + +.ansi span.sgr35 { + color: #7d4498; } + +.ansi span.sgr36 { + color: #007989; } + +.ansi span.sgr37 { + color: gray; } + +.ansi span.sgr40 { + background-color: #242424; } + +.ansi span.sgr41 { + background-color: #a7201f; } + +.ansi span.sgr42 { + background-color: #066f00; } + +.ansi span.sgr43 { + background-color: #856b00; } + +.ansi span.sgr44 { + background-color: #2149b0; } + +.ansi span.sgr45 { + background-color: #7d4498; } + +.ansi span.sgr46 { + background-color: #007989; } + +.ansi span.sgr47 { + background-color: gray; } + +.ansi span.sgr90 { + color: #616161; } + +.ansi span.sgr91 { + color: #cb3c33; } + +.ansi span.sgr92 { + color: #0e8300; } + +.ansi span.sgr93 { + color: #a98800; } + +.ansi span.sgr94 { + color: #3c5dcd; } + +.ansi span.sgr95 { + color: #9256af; } + +.ansi span.sgr96 { + color: #008fa3; } + +.ansi span.sgr97 { + color: whitesmoke; } + +.ansi span.sgr100 { + background-color: #616161; } + +.ansi span.sgr101 { + background-color: #cb3c33; } + +.ansi span.sgr102 { + background-color: #0e8300; } + +.ansi span.sgr103 { + background-color: #a98800; } + +.ansi span.sgr104 { + background-color: #3c5dcd; } + +.ansi span.sgr105 { + background-color: #9256af; } + +.ansi span.sgr106 { + background-color: #008fa3; } + +.ansi span.sgr107 { + background-color: whitesmoke; } + +code.language-julia-repl > span.hljs-meta { + color: #066f00; + font-weight: bolder; } + +/*! + Theme: Default + Description: Original highlight.js style + Author: (c) Ivan Sagalaev + Maintainer: @highlightjs/core-team + Website: https://highlightjs.org/ + License: see project LICENSE + Touched: 2021 +*/ +/* +This is left on purpose making default.css the single file that can be lifted +as-is from the repository directly without the need for a build step + +Typically this "required" baseline CSS is added by `makestuff.js` during build. +*/ +pre code.hljs { + display: block; + overflow-x: auto; } + +code.hljs { + padding: 3px 5px; } + +/* end baseline CSS */ +.hljs { + background: #F0F0F0; + color: #444; } + +/* Base color: saturation 0; */ +.hljs-subst { + /* default */ } + +/* purposely ignored */ +.hljs-comment { + color: #888888; } + +.hljs-tag, +.hljs-punctuation { + color: #444a; } + +.hljs-tag .hljs-name, +.hljs-tag .hljs-attr { + color: #444; } + +.hljs-keyword, +.hljs-attribute, +.hljs-selector-tag, +.hljs-meta .hljs-keyword, +.hljs-doctag, +.hljs-name { + font-weight: bold; } + +/* User color: hue: 0 */ +.hljs-type, +.hljs-string, +.hljs-number, +.hljs-selector-id, +.hljs-selector-class, +.hljs-quote, +.hljs-template-tag, +.hljs-deletion { + color: #880000; } + +.hljs-title, +.hljs-section { + color: #880000; + font-weight: bold; } + +.hljs-regexp, +.hljs-symbol, +.hljs-variable, +.hljs-template-variable, +.hljs-link, +.hljs-selector-attr, +.hljs-operator, +.hljs-selector-pseudo { + color: #BC6060; } + +/* Language color: hue: 90; */ +.hljs-literal { + color: #78A960; } + +.hljs-built_in, +.hljs-bullet, +.hljs-code, +.hljs-addition { + color: #397300; } + +/* Meta color: hue: 200 */ +.hljs-meta { + color: #1f7199; } + +.hljs-meta .hljs-string { + color: #4d99bf; } + +/* Misc effects */ +.hljs-emphasis { + font-style: italic; } + +.hljs-strong { + font-weight: bold; } + +#documenter .docs-sidebar { + border-right: none; + box-shadow: 0.24rem 0rem 0.4rem #bbb; } + #documenter .docs-sidebar form.docs-search > input { + color: #fff; + background-color: #543f87; + border-color: #43326b; + margin-top: 1.0rem; + margin-bottom: 1.0rem; } + #documenter .docs-sidebar form.docs-search > input::placeholder { + color: #fff; } diff --git a/previews/PR18/assets/themeswap.js b/previews/PR18/assets/themeswap.js new file mode 100644 index 00000000..c58e993e --- /dev/null +++ b/previews/PR18/assets/themeswap.js @@ -0,0 +1,66 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Intialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if(window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the browser supports user color preference + var darkPreference = false; + // Check if the users preference is for dark color scheme + if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { + darkPreference = true; + } + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; var disabled = []; var darkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if(themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); + // Check if the theme is primary dark theme + var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null); + // If ss is for dark theme then set the value of darkTheme to the name of the theme + if(isDarkTheme) darkTheme = themename; + // If we find a matching theme (and it's not the default), we'll set active to non-null + if(themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if(themename !== theme) disabled.push(ss); + } + if(active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + theme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + else if(darkTheme !== null && darkPreference === true) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + darkTheme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + if (ss.ownerNode.getAttribute("data-theme-name") !== darkTheme) { + ss.disabled = true; + } + }); + } +} +set_theme_from_local_storage(); diff --git a/previews/PR18/assets/warner.js b/previews/PR18/assets/warner.js new file mode 100644 index 00000000..5531c885 --- /dev/null +++ b/previews/PR18/assets/warner.js @@ -0,0 +1,49 @@ +function maybeAddWarning () { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return + }; + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return + }; + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return + }; + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement('meta'); + meta.name = 'robots'; + meta.content = 'noindex'; + + document.getElementsByTagName('head')[0].appendChild(meta); + }; + + const div = document.createElement('div'); + div.classList.add('outdated-warning-overlay'); + const closer = document.createElement('button'); + closer.classList.add('outdated-warning-closer', 'delete'); + closer.addEventListener('click', function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + '/../' + window.DOCUMENTER_STABLE; + div.innerHTML = 'This documentation is not for the latest stable release, but for either the development version or an older release.
      Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/previews/PR18/index.html b/previews/PR18/index.html new file mode 100644 index 00000000..8ce0c027 --- /dev/null +++ b/previews/PR18/index.html @@ -0,0 +1,34 @@ + +TransitionIndicators.jl · TransitionIndicators.jl
      Edit on GitHub

      TransitionIndicators.jl

      TransitionIndicators — Module

      TransitionIndicators.jl

      CI codecov Package Downloads

      A Julia package that can estimates indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime Shift Identifiers / Change Point Detectors, or however else you want to call them!

      To install it, run import Pkg; Pkg.add("TransitionIndicators").

      All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

      source

      Example

      using TransitionIndicators
+using Statistics: mean, var
+
+n = 1001
+t = collect(1.0:n)
+x = copy(t)
+p = init_metaanalysis_params(n_surrogates = 100)
+res = analyze_indicators(t, x, [mean, var], ridge_slope, p)
+
+# The trend of mean(windowview) is the stride for x=t
+meantrend_ground_truth = fill(p.wv_indicator_stride, length(res.t_evolution))
+# The trend of var(windowview) is 0 for x any affine function of t.
+vartrend_ground_truth = fill(0.0, length(res.t_evolution))
      201-element Vector{Float64}:
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ ⋮
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0
+ 0.0

      API

      TransitionIndicators.analyze_indicators — Function
      analyze_indicators(t, x, indicators, evolution_metrics, p)

      Compute the indicators and their evolution_metrics for a timeseries t, x and its surrogates. If t is not provided, it is simply assumed to be 1:length(x). This meta-analysis is performed based on p::MetaAnalysisParameters.

      source
      diff --git a/previews/PR18/search/index.html b/previews/PR18/search/index.html new file mode 100644 index 00000000..c1959f26 --- /dev/null +++ b/previews/PR18/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionIndicators.jl

      Loading search...

        diff --git a/previews/PR18/search_index.js b/previews/PR18/search_index.js new file mode 100644 index 00000000..8c550da1 --- /dev/null +++ b/previews/PR18/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"#TransitionIndicators.jl","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"TransitionIndicators","category":"page"},{"location":"#TransitionIndicators","page":"TransitionIndicators.jl","title":"TransitionIndicators","text":"TransitionIndicators.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimates indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime Shift Identifiers / Change Point Detectors, or however else you want to call them!\n\nTo install it, run import Pkg; Pkg.add(\"TransitionIndicators\").\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"#Example","page":"TransitionIndicators.jl","title":"Example","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"using TransitionIndicators\nusing Statistics: mean, var\n\nn = 1001\nt = collect(1.0:n)\nx = copy(t)\np = init_metaanalysis_params(n_surrogates = 100)\nres = analyze_indicators(t, x, [mean, var], ridge_slope, p)\n\n# The trend of mean(windowview) is the stride for x=t\nmeantrend_ground_truth = fill(p.wv_indicator_stride, length(res.t_evolution))\n# The trend of var(windowview) is 0 for x any affine function of t.\nvartrend_ground_truth = fill(0.0, length(res.t_evolution))","category":"page"},{"location":"#API","page":"TransitionIndicators.jl","title":"API","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"analyze_indicators","category":"page"},{"location":"#TransitionIndicators.analyze_indicators","page":"TransitionIndicators.jl","title":"TransitionIndicators.analyze_indicators","text":"analyze_indicators(t, x, indicators, evolution_metrics, p)\n\nCompute the indicators and their evolution_metrics for a timeseries t, x and its surrogates. If t is not provided, it is simply assumed to be 1:length(x). This meta-analysis is performed based on p::MetaAnalysisParameters.\n\n\n\n\n\n","category":"function"}] +} diff --git a/previews/PR18/siteinfo.js b/previews/PR18/siteinfo.js new file mode 100644 index 00000000..6e902683 --- /dev/null +++ b/previews/PR18/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR18"; diff --git a/previews/PR19/api/index.html b/previews/PR19/api/index.html new file mode 100644 index 00000000..01ae6f91 --- /dev/null +++ b/previews/PR19/api/index.html @@ -0,0 +1,15 @@ + +API · TransitionIndicators.jl
        Edit on GitHub

        API

        Load data

        Indicators analysis

        TransitionIndicators.IndicatorsConfig — Type
        IndicatorsConfig(indicators...; window_kwargs...)

        A configuration for computing indicators from timeseries. Indicators are standard Julia functions that input an AbstractVector and output a real number. Any number of indicators can be given. Indicators typically used in the literature are listed in the documentation section Indicators.

        Keywords are propagated into WindowViewer to create a sliding window for estimating the indicators.

        Along with SignificanceConfig it is given to indicators_analysis.

        source
        TransitionIndicators.SignificanceConfig — Type
        SignificanceConfig(change_metrics...; kwargs...)

        A configuration for estimating a significant change of indicators computed from timeseries. Along with IndicatorsConfig it is given to indicators_analysis.

        change_metrics can be a single Julia function, in which case the same metric is applied over all indicators in IndicatorsConfig. change_metrics can also be many functions, each one for each indicator.

        Keyword arguments

        • n_surrogates::Int = 10_000: how many surrogates to create.
        • surrogate_method::S = RandomFourier(): what method to use to create the surrogates. Any Surrogate subtype from TimeseriesSurrogates.jl is valid.
        • rng::AbstractRNG = Random.default_rng()`: a random number generator for the surrogates. See the Julia manual for more.
        • wv_indicator_width::Int = 100,
        • wv_indicator_stride::Int = 5,
        • width, stride = 20, 1: width and stride given to the WindowViewer of the indicator timeseries. Notice that here the default values are different.
        source
        TransitionIndicators.indicators_analysis — Function
        indicators_analysis(x, indicators::IndicatorsConfig, significance::SignificanceConfig)

        Perform an analysis of transition indicators for input timeseries x by specifying which indicators to use and with what sliding window (IndicatorsConfig), as well as how to measure significant changes in the indicators (SignificanceConfig).

        Return the output as IndicatorsResults.

        This function performs the analysis described in the documentation Example sections. It computes various indicators over sliding windows of x, and then computes change metrics of over sliding windows of the indicators. In parallel it does exactly the same computations for surrogates of x. The returned output contains all these computed timeseries and can be given to indicators_significance.

        source

        Indicators significance

        TransitionIndicators.indicators_significance — Function
        indicators_significance(res::IndicatorsResults, q::SignificanceTest) → out

        Given the output of indicators_analysis, estimate when the computed indicators have a statistically significant change, with "significant" defined by q, which is a subtype of SignificanceTest.

        The output is returned as an n×m matrix with n the length of the time vector of the change metric timeseries, and m the number of change metrics (which is the same as the number of indicators). The values of the matrix are Booleans (true for significant).

        You can use prod(out; dim = 2) for logical & product across indicators.

        source
        Missing docstring.

        Missing docstring for SignificanceTest. Check Documenter's build log for details.

        Missing docstring.

        Missing docstring for Quantile. Check Documenter's build log for details.

        Missing docstring.

        Missing docstring for Sigma. Check Documenter's build log for details.

        Missing docstring.

        Missing docstring for significant. Check Documenter's build log for details.

        Indicators

        TransitionIndicators.ar1_whitenoise — Function
        ar1_whitenoise(x) → ̂θ

        Estimate the AR1 regression coefficient θ of a vector time series x. Computation based on the analytic solution of the least-square parameter estimation:

        \[ \hat{\theta} = \dfrac{\sum_{i=2}^{n} x_i \, x_{i-1}}{\sum_{i=2}^{n} x_{i-1}^2}\]

        source
        Statistics.mean — Method
        mean(itr)

        Compute the mean of all elements in a collection.

        Note

        If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

        Examples

        julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
        Statistics.var — Method
        var(itr; corrected::Bool=true, mean=nothing[, dims])

        Compute the sample variance of collection itr.

        The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1)). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

        If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

        A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

        Note

        If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

        StatsBase.skewness — Function
        skewness(v, [wv::AbstractWeights], m=mean(v))

        Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

        StatsBase.kurtosis — Function
        kurtosis(v, [wv::AbstractWeights], m=mean(v))

        Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

        Change metrics

        TransitionIndicators.RidgeRegression — Type
        RidgeRegression(t, width; lambda = 0.0) → rr

        Initialize a ridge regression for a time vector t, a sliding-window width and an optional regularizeation term lambda. The output rr can then be used as a function to perform the regression and extract the slope! If lambda = 0, linear regression is recovered (default case). For more information, visit: https://en.wikipedia.org/wiki/Ridge_regression.

        Examples

        julia> t = 0.0:1.0:100;
+julia> x = 2.3 .* t .+ 1.2;
+julia> rr = RidgeRegression(t);
+julia> rr(x)
+2.299999999999999
        source

        Surrogates

        For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

        Significance metrics

        Missing docstring.

        Missing docstring for threshold_indicators. Check Documenter's build log for details.

        Missing docstring.

        Missing docstring for measure_significance. Check Documenter's build log for details.

        Missing docstring.

        Missing docstring for confidence_interval. Check Documenter's build log for details.

        Missing docstring.

        Missing docstring for normalized_percentile. Check Documenter's build log for details.

        Sliding windows

        TransitionIndicators.WindowViewer — Type
        WindowViewer(x; width, stride)

        Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

        If not given, the keywords width, stride as taken as length(x)÷100 and 1.

        source
        TransitionIndicators.windowmap — Function
        windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

        A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

        source
        diff --git a/previews/PR19/assets/documenter.js b/previews/PR19/assets/documenter.js new file mode 100644 index 00000000..6adfbbbf --- /dev/null +++ b/previews/PR19/assets/documenter.js @@ -0,0 +1,331 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fas", "fa-copy"); 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+ + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); 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+ } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR19/assets/search.js b/previews/PR19/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR19/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
      • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR19/assets/themes/documenter-dark.css b/previews/PR19/assets/themes/documenter-dark.css new file mode 100644 index 00000000..aedf20e6 --- /dev/null +++ b/previews/PR19/assets/themes/documenter-dark.css @@ -0,0 +1,7396 @@ +@charset "UTF-8"; +/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */ +@keyframes spinAround { + from { + transform: rotate(0deg); } + to { + transform: rotate(359deg); } } + +html.theme--documenter-dark .tabs, html.theme--documenter-dark .pagination-previous, +html.theme--documenter-dark .pagination-next, +html.theme--documenter-dark .pagination-link, +html.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .breadcrumb, html.theme--documenter-dark .file, html.theme--documenter-dark .button, .is-unselectable, html.theme--documenter-dark .modal-close, html.theme--documenter-dark .delete { + -webkit-touch-callout: none; + -webkit-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; } + +html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after, html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after { + border: 3px solid transparent; + border-radius: 2px; + border-right: 0; + border-top: 0; + content: " "; + display: block; + height: 0.625em; + margin-top: -0.4375em; + pointer-events: none; + position: absolute; + top: 50%; + transform: rotate(-45deg); + transform-origin: center; + width: 0.625em; } + +html.theme--documenter-dark .admonition:not(:last-child), html.theme--documenter-dark .tabs:not(:last-child), html.theme--documenter-dark .message:not(:last-child), html.theme--documenter-dark .list:not(:last-child), html.theme--documenter-dark .level:not(:last-child), html.theme--documenter-dark .breadcrumb:not(:last-child), html.theme--documenter-dark .highlight:not(:last-child), html.theme--documenter-dark .block:not(:last-child), html.theme--documenter-dark .title:not(:last-child), +html.theme--documenter-dark .subtitle:not(:last-child), html.theme--documenter-dark .table-container:not(:last-child), html.theme--documenter-dark .table:not(:last-child), html.theme--documenter-dark .progress:not(:last-child), html.theme--documenter-dark .notification:not(:last-child), html.theme--documenter-dark .content:not(:last-child), html.theme--documenter-dark .box:not(:last-child) { + margin-bottom: 1.5rem; } + +html.theme--documenter-dark .modal-close, html.theme--documenter-dark .delete { + -moz-appearance: none; + -webkit-appearance: none; + background-color: rgba(10, 10, 10, 0.2); + border: none; + border-radius: 290486px; + cursor: pointer; + pointer-events: auto; + display: inline-block; + flex-grow: 0; + flex-shrink: 0; + font-size: 0; + height: 20px; + max-height: 20px; + max-width: 20px; + min-height: 20px; + min-width: 20px; + outline: none; + position: relative; + vertical-align: top; + width: 20px; } + html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::before, html.theme--documenter-dark .modal-close::after, html.theme--documenter-dark .delete::after { + background-color: white; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::before { + height: 2px; + width: 50%; } + html.theme--documenter-dark .modal-close::after, html.theme--documenter-dark .delete::after { + height: 50%; + width: 2px; } + html.theme--documenter-dark .modal-close:hover, html.theme--documenter-dark .delete:hover, html.theme--documenter-dark .modal-close:focus, html.theme--documenter-dark .delete:focus { + background-color: rgba(10, 10, 10, 0.3); } + html.theme--documenter-dark .modal-close:active, html.theme--documenter-dark .delete:active { + background-color: rgba(10, 10, 10, 0.4); } + html.theme--documenter-dark .is-small.modal-close, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.modal-close, html.theme--documenter-dark .is-small.delete, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.delete { + height: 16px; + max-height: 16px; + max-width: 16px; + min-height: 16px; + min-width: 16px; + width: 16px; } + html.theme--documenter-dark .is-medium.modal-close, html.theme--documenter-dark .is-medium.delete { + height: 24px; + max-height: 24px; + max-width: 24px; + min-height: 24px; + min-width: 24px; + width: 24px; } + html.theme--documenter-dark .is-large.modal-close, html.theme--documenter-dark .is-large.delete { + height: 32px; + max-height: 32px; + max-width: 32px; + min-height: 32px; + min-width: 32px; + width: 32px; } + +html.theme--documenter-dark .control.is-loading::after, html.theme--documenter-dark .select.is-loading::after, html.theme--documenter-dark .loader, html.theme--documenter-dark .button.is-loading::after { + animation: spinAround 500ms infinite linear; + border: 2px solid #dbdbdb; + border-radius: 290486px; + border-right-color: transparent; + border-top-color: transparent; + content: ""; + display: block; + height: 1em; + position: relative; + width: 1em; } + +html.theme--documenter-dark .hero-video, html.theme--documenter-dark .modal-background, html.theme--documenter-dark .modal, html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img, +html.theme--documenter-dark .image.is-square .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img, +html.theme--documenter-dark .image.is-1by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img, +html.theme--documenter-dark .image.is-5by4 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img, +html.theme--documenter-dark .image.is-4by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img, +html.theme--documenter-dark .image.is-3by2 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img, +html.theme--documenter-dark .image.is-5by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img, +html.theme--documenter-dark .image.is-16by9 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img, +html.theme--documenter-dark .image.is-2by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img, +html.theme--documenter-dark .image.is-3by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img, +html.theme--documenter-dark .image.is-4by5 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img, +html.theme--documenter-dark .image.is-3by4 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img, +html.theme--documenter-dark .image.is-2by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img, +html.theme--documenter-dark .image.is-3by5 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img, +html.theme--documenter-dark .image.is-9by16 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img, +html.theme--documenter-dark .image.is-1by2 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img, +html.theme--documenter-dark .image.is-1by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, .is-overlay { + bottom: 0; + left: 0; + position: absolute; + right: 0; + top: 0; } + +html.theme--documenter-dark .pagination-previous, +html.theme--documenter-dark .pagination-next, +html.theme--documenter-dark .pagination-link, +html.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .file-cta, +html.theme--documenter-dark .file-name, html.theme--documenter-dark .select select, html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .button { + -moz-appearance: none; + -webkit-appearance: none; + align-items: center; + border: 1px solid transparent; + border-radius: 4px; + box-shadow: none; + display: inline-flex; + font-size: 1rem; + height: 2.25em; + justify-content: flex-start; + line-height: 1.5; + padding-bottom: calc(0.375em - 1px); + padding-left: calc(0.625em - 1px); + padding-right: calc(0.625em - 1px); + padding-top: calc(0.375em - 1px); + position: relative; + vertical-align: top; } + html.theme--documenter-dark .pagination-previous:focus, + html.theme--documenter-dark .pagination-next:focus, + html.theme--documenter-dark .pagination-link:focus, + html.theme--documenter-dark .pagination-ellipsis:focus, html.theme--documenter-dark .file-cta:focus, + html.theme--documenter-dark .file-name:focus, html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .button:focus, html.theme--documenter-dark .is-focused.pagination-previous, + html.theme--documenter-dark .is-focused.pagination-next, + html.theme--documenter-dark .is-focused.pagination-link, + html.theme--documenter-dark .is-focused.pagination-ellipsis, html.theme--documenter-dark .is-focused.file-cta, + html.theme--documenter-dark .is-focused.file-name, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-focused.button, html.theme--documenter-dark .pagination-previous:active, + html.theme--documenter-dark .pagination-next:active, + html.theme--documenter-dark .pagination-link:active, + html.theme--documenter-dark .pagination-ellipsis:active, html.theme--documenter-dark .file-cta:active, + html.theme--documenter-dark .file-name:active, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .button:active, html.theme--documenter-dark .is-active.pagination-previous, + html.theme--documenter-dark .is-active.pagination-next, + html.theme--documenter-dark .is-active.pagination-link, + html.theme--documenter-dark .is-active.pagination-ellipsis, html.theme--documenter-dark .is-active.file-cta, + html.theme--documenter-dark .is-active.file-name, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .is-active.button { + outline: none; } + html.theme--documenter-dark .pagination-previous[disabled], + html.theme--documenter-dark .pagination-next[disabled], + html.theme--documenter-dark .pagination-link[disabled], + html.theme--documenter-dark .pagination-ellipsis[disabled], html.theme--documenter-dark .file-cta[disabled], + html.theme--documenter-dark .file-name[disabled], html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], html.theme--documenter-dark .button[disabled], fieldset[disabled] html.theme--documenter-dark .pagination-previous, html.theme--documenter-dark fieldset[disabled] .pagination-previous, + 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+ box-sizing: inherit; } + +img, +embed, +iframe, +object, +video { + height: auto; + max-width: 100%; } + +audio { + max-width: 100%; } + +iframe { + border: 0; } + +table { + border-collapse: collapse; + border-spacing: 0; } + +td, +th { + padding: 0; } + td:not([align]), + th:not([align]) { + text-align: left; } + +.is-clearfix::after { + clear: both; + content: " "; + display: table; } + +.is-pulled-left { + float: left !important; } + +.is-pulled-right { + float: right !important; } + +.is-clipped { + overflow: hidden !important; } + +.is-size-1 { + font-size: 3rem !important; } + +.is-size-2 { + font-size: 2.5rem !important; } + +.is-size-3 { + font-size: 2rem !important; } + +.is-size-4 { + font-size: 1.5rem !important; } + +.is-size-5 { + font-size: 1.25rem !important; } + +.is-size-6 { + font-size: 1rem !important; } + +.is-size-7, html.theme--documenter-dark .docstring > section > a.docs-sourcelink { + font-size: 0.75rem !important; } + +@media screen and (max-width: 768px) { 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(max-width: 1055px) { + .is-inline-flex-touch { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-flex-desktop { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-flex-desktop-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-flex-widescreen { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-flex-widescreen-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-flex-fullhd { + display: inline-flex !important; } } + +.is-hidden { + display: none !important; } + +.is-sr-only { + border: none !important; + clip: rect(0, 0, 0, 0) !important; + height: 0.01em !important; + overflow: hidden !important; + padding: 0 !important; + position: absolute !important; + white-space: nowrap !important; + width: 0.01em !important; } + +@media screen and (max-width: 768px) { + .is-hidden-mobile { + display: none !important; } } + +@media screen and (min-width: 769px), print { + .is-hidden-tablet { + display: none !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-hidden-tablet-only { + display: none !important; } } + +@media screen and (max-width: 1055px) { + .is-hidden-touch { + display: none !important; } } + +@media screen and (min-width: 1056px) { + .is-hidden-desktop { + display: none !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-hidden-desktop-only { + display: none !important; } } + +@media screen and (min-width: 1216px) { + .is-hidden-widescreen { + display: none !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-hidden-widescreen-only { + display: none !important; } } + +@media screen and (min-width: 1408px) { + .is-hidden-fullhd { + display: none !important; } } + +.is-invisible { + visibility: hidden !important; } + +@media screen and (max-width: 768px) { + .is-invisible-mobile { + visibility: hidden !important; } } + +@media screen and (min-width: 769px), print { + .is-invisible-tablet { + visibility: hidden !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-invisible-tablet-only { + visibility: hidden !important; } } + +@media screen and (max-width: 1055px) { + .is-invisible-touch { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) { + .is-invisible-desktop { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-invisible-desktop-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) { + .is-invisible-widescreen { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-invisible-widescreen-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1408px) { + .is-invisible-fullhd { + visibility: hidden !important; } } + +.is-marginless { + margin: 0 !important; } + +.is-paddingless { + padding: 0 !important; } + +.is-radiusless { + border-radius: 0 !important; } + +.is-shadowless { + box-shadow: none !important; } + +.is-relative { + position: relative !important; } + +html.theme--documenter-dark { + /* This file contain the overall layout. + * + * The main container is
        that is identified by id #documenter. + */ + /*! + Theme: a11y-dark + Author: @ericwbailey + Maintainer: @ericwbailey + + Based on the Tomorrow Night Eighties theme: https://github.com/isagalaev/highlight.js/blob/master/src/styles/tomorrow-night-eighties.css +*/ + /* Comment */ + /* Red */ + /* Orange */ + /* Yellow */ + /* Green */ + /* Blue */ + /* Purple */ } + html.theme--documenter-dark html { + background-color: #1e1e20; + font-size: 16px; + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + html.theme--documenter-dark article, + html.theme--documenter-dark aside, + html.theme--documenter-dark figure, + html.theme--documenter-dark footer, + html.theme--documenter-dark header, + html.theme--documenter-dark hgroup, + html.theme--documenter-dark section { + display: block; } + html.theme--documenter-dark body, + html.theme--documenter-dark button, + html.theme--documenter-dark input, + html.theme--documenter-dark select, + html.theme--documenter-dark textarea { + font-family: "Montserrat", sans-serif; } + html.theme--documenter-dark code, + html.theme--documenter-dark pre { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; + font-family: "Source Code Pro", monospace; } + html.theme--documenter-dark body { + color: #fbfbfb; + font-size: 1em; + font-weight: 400; + line-height: 1.5; } + html.theme--documenter-dark a { + color: #2ad7e6; + cursor: pointer; + text-decoration: none; } + html.theme--documenter-dark a strong { + color: currentColor; } + html.theme--documenter-dark a:hover { + color: #97ebf3; } + html.theme--documenter-dark code { + background-color: #312550; + color: #fff; + font-size: 0.875em; + font-weight: normal; + padding: 0.1em; } + html.theme--documenter-dark hr { + background-color: whitesmoke; + border: none; + display: block; + height: 2px; + margin: 1.5rem 0; } + html.theme--documenter-dark img { + height: auto; + max-width: 100%; } + html.theme--documenter-dark input[type="checkbox"], + html.theme--documenter-dark input[type="radio"] { + vertical-align: baseline; } + html.theme--documenter-dark small { + font-size: 0.875em; } + html.theme--documenter-dark span { + font-style: inherit; + font-weight: inherit; } + html.theme--documenter-dark strong { + color: #cdc3e3; + font-weight: 700; } + html.theme--documenter-dark fieldset { + border: none; } + html.theme--documenter-dark pre { + -webkit-overflow-scrolling: touch; + background-color: #312550; + color: #fbfbfb; + font-size: 0.875em; + overflow-x: auto; + padding: 1.25rem 1.5rem; + white-space: pre; + word-wrap: normal; } + html.theme--documenter-dark pre code { + background-color: transparent; + color: currentColor; + font-size: 1em; + padding: 0; } + html.theme--documenter-dark table td, + html.theme--documenter-dark table th { + vertical-align: top; } + html.theme--documenter-dark table td:not([align]), + html.theme--documenter-dark table th:not([align]) { + text-align: left; } + html.theme--documenter-dark table th { + color: #cdc3e3; } + html.theme--documenter-dark .box { + background-color: white; + border-radius: 6px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #fbfbfb; + display: block; + padding: 1.25rem; } + html.theme--documenter-dark a.box:hover, html.theme--documenter-dark a.box:focus { + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #2ad7e6; } + html.theme--documenter-dark a.box:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #2ad7e6; } + html.theme--documenter-dark .button { + background-color: white; + border-color: #dbdbdb; + border-width: 1px; + color: #363636; + cursor: pointer; + justify-content: center; + padding-bottom: calc(0.375em - 1px); + padding-left: 0.75em; + padding-right: 0.75em; + padding-top: calc(0.375em - 1px); + text-align: center; + white-space: nowrap; } + html.theme--documenter-dark .button strong { + color: inherit; } + html.theme--documenter-dark .button .icon, html.theme--documenter-dark .button .icon.is-small, html.theme--documenter-dark .button #documenter .docs-sidebar form.docs-search > input.icon, html.theme--documenter-dark #documenter .docs-sidebar .button form.docs-search > input.icon, html.theme--documenter-dark .button .icon.is-medium, html.theme--documenter-dark .button .icon.is-large { + height: 1.5em; + width: 1.5em; } + html.theme--documenter-dark .button .icon:first-child:not(:last-child) { + margin-left: calc(-0.375em - 1px); + margin-right: 0.1875em; } + html.theme--documenter-dark .button .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: calc(-0.375em - 1px); } + html.theme--documenter-dark .button .icon:first-child:last-child { + margin-left: calc(-0.375em - 1px); + margin-right: calc(-0.375em - 1px); } + html.theme--documenter-dark .button:hover, html.theme--documenter-dark .button.is-hovered { + border-color: #b5b5b5; + color: #97ebf3; } + html.theme--documenter-dark .button:focus, html.theme--documenter-dark .button.is-focused { + border-color: #3c5dcd; + color: #363636; } + html.theme--documenter-dark .button:focus:not(:active), html.theme--documenter-dark .button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .button:active, html.theme--documenter-dark .button.is-active { + border-color: #4a4a4a; + color: #363636; } + html.theme--documenter-dark .button.is-text { + background-color: transparent; + border-color: transparent; + color: #fbfbfb; + text-decoration: underline; } + html.theme--documenter-dark .button.is-text:hover, html.theme--documenter-dark .button.is-text.is-hovered, html.theme--documenter-dark .button.is-text:focus, html.theme--documenter-dark .button.is-text.is-focused { + background-color: whitesmoke; + color: #cdc3e3; } + html.theme--documenter-dark .button.is-text:active, html.theme--documenter-dark .button.is-text.is-active { + background-color: #e8e8e8; + color: #cdc3e3; } + html.theme--documenter-dark .button.is-text[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-text { + background-color: transparent; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-white { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:hover, html.theme--documenter-dark .button.is-white.is-hovered { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:focus, html.theme--documenter-dark .button.is-white.is-focused { + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:focus:not(:active), html.theme--documenter-dark .button.is-white.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .button.is-white:active, html.theme--documenter-dark .button.is-white.is-active { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white { + background-color: white; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-white.is-inverted { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-hovered { + background-color: black; } + html.theme--documenter-dark .button.is-white.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-white.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + html.theme--documenter-dark .button.is-white.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-outlined.is-focused { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-white.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:hover, html.theme--documenter-dark .button.is-black.is-hovered { + background-color: #040404; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:focus, html.theme--documenter-dark .button.is-black.is-focused { + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:focus:not(:active), html.theme--documenter-dark .button.is-black.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .button.is-black:active, html.theme--documenter-dark .button.is-black.is-active { + background-color: black; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-black.is-inverted { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-black.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted { + background-color: white; + border-color: transparent; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-loading::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-outlined.is-focused { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-black.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-light { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:hover, html.theme--documenter-dark .button.is-light.is-hovered { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:focus, html.theme--documenter-dark .button.is-light.is-focused { + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:focus:not(:active), html.theme--documenter-dark .button.is-light.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .button.is-light:active, html.theme--documenter-dark .button.is-light.is-active { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-light.is-inverted { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-hovered { + background-color: #292929; } + html.theme--documenter-dark .button.is-light.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted { + background-color: #363636; + border-color: transparent; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-outlined.is-focused { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-light.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark, html.theme--documenter-dark .content kbd.button { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:hover, html.theme--documenter-dark .content kbd.button:hover, html.theme--documenter-dark .button.is-dark.is-hovered, html.theme--documenter-dark .content kbd.button.is-hovered { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:focus, html.theme--documenter-dark .content kbd.button:focus, html.theme--documenter-dark .button.is-dark.is-focused, html.theme--documenter-dark .content kbd.button.is-focused { + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:focus:not(:active), html.theme--documenter-dark .content kbd.button:focus:not(:active), html.theme--documenter-dark .button.is-dark.is-focused:not(:active), html.theme--documenter-dark .content kbd.button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .button.is-dark:active, html.theme--documenter-dark .content kbd.button:active, html.theme--documenter-dark .button.is-dark.is-active, html.theme--documenter-dark .content kbd.button.is-active { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark[disabled], html.theme--documenter-dark .content kbd.button[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark, fieldset[disabled] html.theme--documenter-dark .content kbd.button { + background-color: #363636; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-dark.is-inverted, html.theme--documenter-dark .content kbd.button.is-inverted { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted:hover, html.theme--documenter-dark .content kbd.button.is-inverted:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered { + background-color: #e8e8e8; } + html.theme--documenter-dark .button.is-dark.is-inverted[disabled], html.theme--documenter-dark .content kbd.button.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-loading::after, html.theme--documenter-dark .content kbd.button.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-dark.is-outlined, html.theme--documenter-dark .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-outlined.is-focused { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-dark.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-primary, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:hover, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-hovered.docs-sourcelink { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:focus, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:focus:not(:active), html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus:not(:active), html.theme--documenter-dark .button.is-primary.is-focused:not(:active), html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .button.is-primary:active, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:active, html.theme--documenter-dark .button.is-primary.is-active, html.theme--documenter-dark .docstring > section > a.button.is-active.docs-sourcelink { + background-color: #39acda; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary[disabled], html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-primary.is-inverted, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-primary.is-inverted[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-loading.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-primary.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-primary.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + box-shadow: none; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-link { + background-color: #2ad7e6; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:hover, html.theme--documenter-dark .button.is-link.is-hovered { + background-color: #1ed5e5; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:focus, html.theme--documenter-dark .button.is-link.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:focus:not(:active), html.theme--documenter-dark .button.is-link.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .button.is-link:active, html.theme--documenter-dark .button.is-link.is-active { + background-color: #1acddc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link { + background-color: #2ad7e6; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-link.is-inverted { + background-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-link.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-link.is-outlined { + background-color: transparent; + border-color: #2ad7e6; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-outlined.is-focused { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after { + border-color: transparent transparent #2ad7e6 #2ad7e6 !important; } + html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-link.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined { + background-color: transparent; + border-color: #2ad7e6; + box-shadow: none; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #2ad7e6 #2ad7e6 !important; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-info { + background-color: #3489da; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:hover, html.theme--documenter-dark .button.is-info.is-hovered { + background-color: #2983d8; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:focus, html.theme--documenter-dark .button.is-info.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:focus:not(:active), html.theme--documenter-dark .button.is-info.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .button.is-info:active, html.theme--documenter-dark .button.is-info.is-active { + background-color: #267ccf; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info { + background-color: #3489da; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-info.is-inverted { + background-color: #fff; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-info.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-info.is-outlined { + background-color: transparent; + border-color: #3489da; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-outlined.is-focused { + background-color: #3489da; + border-color: #3489da; + color: #fff; } + html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after { + border-color: transparent transparent #3489da #3489da !important; } + html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-info.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined { + background-color: transparent; + border-color: #3489da; + box-shadow: none; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #3489da #3489da !important; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-success { + background-color: #259a12; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:hover, html.theme--documenter-dark .button.is-success.is-hovered { + background-color: #228f11; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:focus, html.theme--documenter-dark .button.is-success.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:focus:not(:active), html.theme--documenter-dark .button.is-success.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .button.is-success:active, html.theme--documenter-dark .button.is-success.is-active { + background-color: #20830f; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success { + background-color: #259a12; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-success.is-inverted { + background-color: #fff; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-success.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-success.is-outlined { + background-color: transparent; + border-color: #259a12; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-outlined.is-focused { + background-color: #259a12; + border-color: #259a12; + color: #fff; } + html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after { + border-color: transparent transparent #259a12 #259a12 !important; } + html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-success.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined { + background-color: transparent; + border-color: #259a12; + box-shadow: none; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #259a12 #259a12 !important; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-warning { + background-color: #f4c72f; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:hover, html.theme--documenter-dark .button.is-warning.is-hovered { + background-color: #f3c423; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:focus, html.theme--documenter-dark .button.is-warning.is-focused { + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:focus:not(:active), html.theme--documenter-dark .button.is-warning.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .button.is-warning:active, html.theme--documenter-dark .button.is-warning.is-active { + background-color: #f3c017; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning { + background-color: #f4c72f; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered { + background-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + border-color: transparent; + box-shadow: none; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-loading::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + html.theme--documenter-dark .button.is-warning.is-outlined { + background-color: transparent; + border-color: #f4c72f; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-outlined.is-focused { + background-color: #f4c72f; + border-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after { + border-color: transparent transparent #f4c72f #f4c72f !important; } + html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + html.theme--documenter-dark .button.is-warning.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined { + background-color: transparent; + border-color: #f4c72f; + box-shadow: none; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused { + background-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #f4c72f #f4c72f !important; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + box-shadow: none; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-danger { + background-color: #cb3c33; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:hover, html.theme--documenter-dark .button.is-danger.is-hovered { + background-color: #c13930; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:focus, html.theme--documenter-dark .button.is-danger.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:focus:not(:active), html.theme--documenter-dark .button.is-danger.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .button.is-danger:active, html.theme--documenter-dark .button.is-danger.is-active { + background-color: #b7362e; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger { + background-color: #cb3c33; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-danger.is-inverted { + background-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-danger.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-danger.is-outlined { + background-color: transparent; + border-color: #cb3c33; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-outlined.is-focused { + background-color: #cb3c33; + border-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after { + border-color: transparent transparent #cb3c33 #cb3c33 !important; } + html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-danger.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined { + background-color: transparent; + border-color: #cb3c33; + box-shadow: none; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #cb3c33 #cb3c33 !important; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .button.is-normal { + font-size: 1rem; } + html.theme--documenter-dark .button.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .button.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .button[disabled], fieldset[disabled] html.theme--documenter-dark .button { + background-color: white; + border-color: #dbdbdb; + box-shadow: none; + opacity: 0.5; } + html.theme--documenter-dark .button.is-fullwidth { + display: flex; + width: 100%; } + html.theme--documenter-dark .button.is-loading { + color: transparent !important; + pointer-events: none; } + html.theme--documenter-dark .button.is-loading::after { + position: absolute; + left: calc(50% - (1em / 2)); + top: calc(50% - (1em / 2)); + position: absolute !important; } + html.theme--documenter-dark .button.is-static { + background-color: whitesmoke; + border-color: #dbdbdb; + color: #7a7a7a; + box-shadow: none; + pointer-events: none; } + html.theme--documenter-dark .button.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + html.theme--documenter-dark .buttons { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .buttons .button { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth) { + margin-right: 0.5rem; } + html.theme--documenter-dark .buttons:last-child { + margin-bottom: -0.5rem; } + html.theme--documenter-dark .buttons:not(:last-child) { + margin-bottom: 1rem; } + html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { + font-size: 1.25rem; } + html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { + font-size: 1.5rem; } + html.theme--documenter-dark .buttons.has-addons .button:not(:first-child) { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .buttons.has-addons .button:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; + margin-right: -1px; } + html.theme--documenter-dark .buttons.has-addons .button:last-child { + margin-right: 0; } + html.theme--documenter-dark .buttons.has-addons .button:hover, html.theme--documenter-dark .buttons.has-addons .button.is-hovered { + z-index: 2; } + html.theme--documenter-dark .buttons.has-addons .button:focus, html.theme--documenter-dark .buttons.has-addons .button.is-focused, html.theme--documenter-dark .buttons.has-addons .button:active, html.theme--documenter-dark .buttons.has-addons .button.is-active, html.theme--documenter-dark .buttons.has-addons .button.is-selected { + z-index: 3; } + html.theme--documenter-dark .buttons.has-addons .button:focus:hover, html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover, html.theme--documenter-dark .buttons.has-addons .button:active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover { + z-index: 4; } + html.theme--documenter-dark .buttons.has-addons .button.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .buttons.is-centered { + justify-content: center; } + html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + html.theme--documenter-dark .buttons.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + html.theme--documenter-dark .container { + flex-grow: 1; + margin: 0 auto; + position: relative; + width: auto; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .container { + max-width: 992px; } + html.theme--documenter-dark .container.is-fluid { + margin-left: 32px; + margin-right: 32px; + max-width: none; } } + @media screen and (max-width: 1215px) { + html.theme--documenter-dark .container.is-widescreen { + max-width: 1152px; } } + @media screen and (max-width: 1407px) { + html.theme--documenter-dark .container.is-fullhd { + max-width: 1344px; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .container { + max-width: 1152px; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .container { + max-width: 1344px; } } + html.theme--documenter-dark .content li + li { + margin-top: 0.25em; } + html.theme--documenter-dark .content p:not(:last-child), + html.theme--documenter-dark .content dl:not(:last-child), + html.theme--documenter-dark .content ol:not(:last-child), + html.theme--documenter-dark .content ul:not(:last-child), + html.theme--documenter-dark .content blockquote:not(:last-child), + html.theme--documenter-dark .content pre:not(:last-child), + html.theme--documenter-dark .content table:not(:last-child) { + margin-bottom: 1em; } + html.theme--documenter-dark .content h1, + html.theme--documenter-dark .content h2, + html.theme--documenter-dark .content h3, + html.theme--documenter-dark .content h4, + html.theme--documenter-dark .content h5, + html.theme--documenter-dark .content h6 { + color: #cdc3e3; + font-weight: 600; + line-height: 1.125; } + html.theme--documenter-dark .content h1 { + font-size: 2em; + margin-bottom: 0.5em; } + html.theme--documenter-dark .content h1:not(:first-child) { + margin-top: 1em; } + html.theme--documenter-dark .content h2 { + font-size: 1.75em; + margin-bottom: 0.5714em; } + html.theme--documenter-dark .content h2:not(:first-child) { + margin-top: 1.1428em; } + html.theme--documenter-dark .content h3 { + font-size: 1.5em; + margin-bottom: 0.6666em; } + html.theme--documenter-dark .content h3:not(:first-child) { + margin-top: 1.3333em; } + html.theme--documenter-dark .content h4 { + font-size: 1.25em; + margin-bottom: 0.8em; } + html.theme--documenter-dark .content h5 { + font-size: 1.125em; + margin-bottom: 0.8888em; } + html.theme--documenter-dark .content h6 { + font-size: 1em; + margin-bottom: 1em; } + html.theme--documenter-dark .content blockquote { + background-color: whitesmoke; + border-left: 5px solid #dbdbdb; + padding: 1.25em 1.5em; } + html.theme--documenter-dark .content ol { + list-style-position: outside; + margin-left: 2em; + margin-top: 1em; } + html.theme--documenter-dark .content ol:not([type]) { + list-style-type: decimal; } + html.theme--documenter-dark .content ol.is-lower-alpha:not([type]) { + list-style-type: lower-alpha; } + html.theme--documenter-dark .content ol.is-lower-roman:not([type]) { + list-style-type: lower-roman; } + html.theme--documenter-dark .content ol.is-upper-alpha:not([type]) { + list-style-type: upper-alpha; } + html.theme--documenter-dark .content ol.is-upper-roman:not([type]) { + list-style-type: upper-roman; } + html.theme--documenter-dark .content ul { + list-style: disc outside; + margin-left: 2em; + margin-top: 1em; } + html.theme--documenter-dark .content ul ul { + list-style-type: circle; + margin-top: 0.5em; } + html.theme--documenter-dark .content ul ul ul { + list-style-type: square; } + html.theme--documenter-dark .content dd { + margin-left: 2em; } + html.theme--documenter-dark .content figure { + margin-left: 2em; + margin-right: 2em; + text-align: center; } + html.theme--documenter-dark .content figure:not(:first-child) { + margin-top: 2em; } + html.theme--documenter-dark .content figure:not(:last-child) { + margin-bottom: 2em; } + html.theme--documenter-dark .content figure img { + display: inline-block; } + html.theme--documenter-dark .content figure figcaption { + font-style: italic; } + html.theme--documenter-dark .content pre { + -webkit-overflow-scrolling: touch; + overflow-x: auto; + padding: 0; + white-space: pre; + word-wrap: normal; } + html.theme--documenter-dark .content sup, + html.theme--documenter-dark .content sub { + font-size: 75%; } + html.theme--documenter-dark .content table { + width: 100%; } + html.theme--documenter-dark .content table td, + html.theme--documenter-dark .content table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + html.theme--documenter-dark .content table th { + color: #cdc3e3; } + html.theme--documenter-dark .content table th:not([align]) { + text-align: left; } + html.theme--documenter-dark .content table thead td, + html.theme--documenter-dark .content table thead th { + border-width: 0 0 2px; + color: #cdc3e3; } + html.theme--documenter-dark .content table tfoot td, + html.theme--documenter-dark .content table tfoot th { + border-width: 2px 0 0; + color: #cdc3e3; } + html.theme--documenter-dark .content table tbody tr:last-child td, + html.theme--documenter-dark .content table tbody tr:last-child th { + border-bottom-width: 0; } + html.theme--documenter-dark .content .tabs li + li { + margin-top: 0; } + html.theme--documenter-dark .content.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.content { + font-size: 0.75rem; } + html.theme--documenter-dark .content.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .content.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .icon { + align-items: center; + display: inline-flex; + justify-content: center; + height: 1.5rem; + width: 1.5rem; } + html.theme--documenter-dark .icon.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.icon { + height: 1rem; + width: 1rem; } + html.theme--documenter-dark .icon.is-medium { + height: 2rem; + width: 2rem; } + html.theme--documenter-dark .icon.is-large { + height: 3rem; + width: 3rem; } + html.theme--documenter-dark .image, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { + display: block; + position: relative; } + html.theme--documenter-dark .image img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img { + display: block; + height: auto; + width: 100%; } + html.theme--documenter-dark .image img.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img.is-rounded { + border-radius: 290486px; } + html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img, + html.theme--documenter-dark .image.is-square .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img, + html.theme--documenter-dark .image.is-1by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img, + html.theme--documenter-dark .image.is-5by4 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img, + html.theme--documenter-dark .image.is-4by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img, + html.theme--documenter-dark .image.is-3by2 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img, + html.theme--documenter-dark .image.is-5by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img, + html.theme--documenter-dark .image.is-16by9 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img, + html.theme--documenter-dark .image.is-2by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img, + html.theme--documenter-dark .image.is-3by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img, + html.theme--documenter-dark .image.is-4by5 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img, + html.theme--documenter-dark .image.is-3by4 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img, + html.theme--documenter-dark .image.is-2by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img, + html.theme--documenter-dark .image.is-3by5 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img, + html.theme--documenter-dark .image.is-9by16 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img, + html.theme--documenter-dark .image.is-1by2 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img, + html.theme--documenter-dark .image.is-1by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { + height: 100%; + width: 100%; } + html.theme--documenter-dark .image.is-square, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square, html.theme--documenter-dark .image.is-1by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 { + padding-top: 100%; } + html.theme--documenter-dark .image.is-5by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 { + padding-top: 80%; } + html.theme--documenter-dark .image.is-4by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 { + padding-top: 75%; } + html.theme--documenter-dark .image.is-3by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 { + padding-top: 66.6666%; } + html.theme--documenter-dark .image.is-5by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 { + padding-top: 60%; } + html.theme--documenter-dark .image.is-16by9, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 { + padding-top: 56.25%; } + html.theme--documenter-dark .image.is-2by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 { + padding-top: 50%; } + html.theme--documenter-dark .image.is-3by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 { + padding-top: 33.3333%; } + html.theme--documenter-dark .image.is-4by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 { + padding-top: 125%; } + html.theme--documenter-dark .image.is-3by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 { + padding-top: 133.3333%; } + html.theme--documenter-dark .image.is-2by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 { + padding-top: 150%; } + html.theme--documenter-dark .image.is-3by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 { + padding-top: 166.6666%; } + html.theme--documenter-dark .image.is-9by16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 { + padding-top: 177.7777%; } + html.theme--documenter-dark .image.is-1by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 { + padding-top: 200%; } + html.theme--documenter-dark .image.is-1by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 { + padding-top: 300%; } + html.theme--documenter-dark .image.is-16x16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16x16 { + height: 16px; + width: 16px; } + html.theme--documenter-dark .image.is-24x24, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-24x24 { + height: 24px; + width: 24px; } + html.theme--documenter-dark .image.is-32x32, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-32x32 { + height: 32px; + width: 32px; } + html.theme--documenter-dark .image.is-48x48, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-48x48 { + height: 48px; + width: 48px; } + html.theme--documenter-dark .image.is-64x64, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-64x64 { + height: 64px; + width: 64px; } + html.theme--documenter-dark .image.is-96x96, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-96x96 { + height: 96px; + width: 96px; } + html.theme--documenter-dark .image.is-128x128, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-128x128 { + height: 128px; + width: 128px; } + html.theme--documenter-dark .notification { + background-color: whitesmoke; + border-radius: 4px; + padding: 1.25rem 2.5rem 1.25rem 1.5rem; + position: relative; } + html.theme--documenter-dark .notification a:not(.button):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + html.theme--documenter-dark .notification strong { + color: currentColor; } + html.theme--documenter-dark .notification code, + html.theme--documenter-dark .notification pre { + background: white; } + html.theme--documenter-dark .notification pre code { + background: transparent; } + html.theme--documenter-dark .notification > .delete { + position: absolute; + right: 0.5rem; + top: 0.5rem; } + html.theme--documenter-dark .notification .title, + html.theme--documenter-dark .notification .subtitle, + html.theme--documenter-dark .notification .content { + color: currentColor; } + html.theme--documenter-dark .notification.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .notification.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .notification.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .notification.is-dark, html.theme--documenter-dark .content kbd.notification { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .notification.is-primary, html.theme--documenter-dark .docstring > section > a.notification.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .notification.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .notification.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .notification.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .notification.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .notification.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .progress { + -moz-appearance: none; + -webkit-appearance: none; + border: none; + border-radius: 290486px; + display: block; + height: 1rem; + overflow: hidden; + padding: 0; + width: 100%; } + html.theme--documenter-dark .progress::-webkit-progress-bar { + background-color: #dbdbdb; } + html.theme--documenter-dark .progress::-webkit-progress-value { + background-color: #fbfbfb; } + html.theme--documenter-dark .progress::-moz-progress-bar { + background-color: #fbfbfb; } + html.theme--documenter-dark .progress::-ms-fill { + background-color: #fbfbfb; + border: none; } + html.theme--documenter-dark .progress.is-white::-webkit-progress-value { + background-color: white; } + html.theme--documenter-dark .progress.is-white::-moz-progress-bar { + background-color: white; } + html.theme--documenter-dark .progress.is-white::-ms-fill { + background-color: white; } + html.theme--documenter-dark .progress.is-white:indeterminate { + background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-black::-webkit-progress-value { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black::-moz-progress-bar { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black::-ms-fill { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black:indeterminate { + background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-light::-webkit-progress-value { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light::-moz-progress-bar { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light::-ms-fill { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light:indeterminate { + background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-dark::-webkit-progress-value, html.theme--documenter-dark .content kbd.progress::-webkit-progress-value { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark::-moz-progress-bar, html.theme--documenter-dark .content kbd.progress::-moz-progress-bar { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark::-ms-fill, html.theme--documenter-dark .content kbd.progress::-ms-fill { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark:indeterminate, html.theme--documenter-dark .content kbd.progress:indeterminate { + background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-primary::-webkit-progress-value, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary::-moz-progress-bar, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary::-ms-fill, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-ms-fill { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary:indeterminate, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink:indeterminate { + background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-link::-webkit-progress-value { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link::-moz-progress-bar { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link::-ms-fill { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link:indeterminate { + background-image: linear-gradient(to right, #2ad7e6 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-info::-webkit-progress-value { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info::-moz-progress-bar { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info::-ms-fill { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info:indeterminate { + background-image: linear-gradient(to right, #3489da 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-success::-webkit-progress-value { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success::-moz-progress-bar { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success::-ms-fill { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success:indeterminate { + background-image: linear-gradient(to right, #259a12 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-warning::-webkit-progress-value { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning::-moz-progress-bar { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning::-ms-fill { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning:indeterminate { + background-image: linear-gradient(to right, #f4c72f 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-danger::-webkit-progress-value { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger::-moz-progress-bar { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger::-ms-fill { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger:indeterminate { + background-image: linear-gradient(to right, #cb3c33 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress:indeterminate { + animation-duration: 1.5s; + animation-iteration-count: infinite; + animation-name: moveIndeterminate; + animation-timing-function: linear; + background-color: #dbdbdb; + background-image: linear-gradient(to right, #fbfbfb 30%, #dbdbdb 30%); + background-position: top left; + background-repeat: no-repeat; + background-size: 150% 150%; } + html.theme--documenter-dark .progress:indeterminate::-webkit-progress-bar { + background-color: transparent; } + html.theme--documenter-dark .progress:indeterminate::-moz-progress-bar { + background-color: transparent; } + html.theme--documenter-dark .progress.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.progress { + height: 0.75rem; } + html.theme--documenter-dark .progress.is-medium { + height: 1.25rem; } + html.theme--documenter-dark .progress.is-large { + height: 1.5rem; } + +@keyframes moveIndeterminate { + from { + background-position: 200% 0; } + to { + background-position: -200% 0; } } + html.theme--documenter-dark .table { + background-color: white; + color: #363636; } + html.theme--documenter-dark .table td, + html.theme--documenter-dark .table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + html.theme--documenter-dark .table td.is-white, + html.theme--documenter-dark .table th.is-white { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .table td.is-black, + html.theme--documenter-dark .table th.is-black { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .table td.is-light, + html.theme--documenter-dark .table th.is-light { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .table td.is-dark, + html.theme--documenter-dark .table th.is-dark { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .table td.is-primary, + html.theme--documenter-dark .table th.is-primary { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table td.is-link, + html.theme--documenter-dark .table th.is-link { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .table td.is-info, + html.theme--documenter-dark .table th.is-info { + background-color: #3489da; + border-color: #3489da; + color: #fff; } + html.theme--documenter-dark .table td.is-success, + html.theme--documenter-dark .table th.is-success { + background-color: #259a12; + border-color: #259a12; + color: #fff; } + html.theme--documenter-dark .table td.is-warning, + html.theme--documenter-dark .table th.is-warning { + background-color: #f4c72f; + border-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .table td.is-danger, + html.theme--documenter-dark .table th.is-danger { + background-color: #cb3c33; + border-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .table td.is-narrow, + html.theme--documenter-dark .table th.is-narrow { + white-space: nowrap; + width: 1%; } + html.theme--documenter-dark .table td.is-selected, + html.theme--documenter-dark .table th.is-selected { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table td.is-selected a, + html.theme--documenter-dark .table td.is-selected strong, + html.theme--documenter-dark .table th.is-selected a, + html.theme--documenter-dark .table th.is-selected strong { + color: currentColor; } + html.theme--documenter-dark .table th { + color: #cdc3e3; } + html.theme--documenter-dark .table th:not([align]) { + text-align: left; } + html.theme--documenter-dark .table tr.is-selected { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table tr.is-selected a, + html.theme--documenter-dark .table tr.is-selected strong { + color: currentColor; } + html.theme--documenter-dark .table tr.is-selected td, + html.theme--documenter-dark .table tr.is-selected th { + border-color: #fff; + color: currentColor; } + html.theme--documenter-dark .table thead { + background-color: transparent; } + html.theme--documenter-dark .table thead td, + html.theme--documenter-dark .table thead th { + border-width: 0 0 2px; + color: #cdc3e3; } + html.theme--documenter-dark .table tfoot { + background-color: transparent; } + html.theme--documenter-dark .table tfoot td, + html.theme--documenter-dark .table tfoot th { + border-width: 2px 0 0; + color: #cdc3e3; } + html.theme--documenter-dark .table tbody { + background-color: transparent; } + html.theme--documenter-dark .table tbody tr:last-child td, + html.theme--documenter-dark .table tbody tr:last-child th { + border-bottom-width: 0; } + html.theme--documenter-dark .table.is-bordered td, + html.theme--documenter-dark .table.is-bordered th { + border-width: 1px; } + html.theme--documenter-dark .table.is-bordered tr:last-child td, + html.theme--documenter-dark .table.is-bordered tr:last-child th { + border-bottom-width: 1px; } + html.theme--documenter-dark .table.is-fullwidth { + width: 100%; } + html.theme--documenter-dark .table.is-hoverable tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { + background-color: whitesmoke; } + html.theme--documenter-dark .table.is-narrow td, + html.theme--documenter-dark .table.is-narrow th { + padding: 0.25em 0.5em; } + html.theme--documenter-dark .table.is-striped tbody tr:not(.is-selected):nth-child(even) { + background-color: #fafafa; } + html.theme--documenter-dark .table-container { + -webkit-overflow-scrolling: touch; + overflow: auto; + overflow-y: hidden; + max-width: 100%; } + html.theme--documenter-dark .tags { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .tags .tag, html.theme--documenter-dark .tags .content kbd, html.theme--documenter-dark .content .tags kbd, html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .tags .tag:not(:last-child), html.theme--documenter-dark .tags .content kbd:not(:last-child), html.theme--documenter-dark .content .tags kbd:not(:last-child), html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0.5rem; } + html.theme--documenter-dark .tags:last-child { + margin-bottom: -0.5rem; } + html.theme--documenter-dark .tags:not(:last-child) { + margin-bottom: 1rem; } + html.theme--documenter-dark .tags.are-medium .tag:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .content kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .content .tags.are-medium kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { + font-size: 1rem; } + html.theme--documenter-dark .tags.are-large .tag:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .content kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .content .tags.are-large kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { + font-size: 1.25rem; } + html.theme--documenter-dark .tags.is-centered { + justify-content: center; } + html.theme--documenter-dark .tags.is-centered .tag, html.theme--documenter-dark .tags.is-centered .content kbd, html.theme--documenter-dark .content .tags.is-centered kbd, html.theme--documenter-dark .tags.is-centered .docstring > section > a.docs-sourcelink { + margin-right: 0.25rem; + margin-left: 0.25rem; } + html.theme--documenter-dark .tags.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .tags.is-right .tag:not(:first-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:first-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0.5rem; } + html.theme--documenter-dark .tags.is-right .tag:not(:last-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:last-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0; } + html.theme--documenter-dark .tags.has-addons .tag, html.theme--documenter-dark .tags.has-addons .content kbd, html.theme--documenter-dark .content .tags.has-addons kbd, html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink { + margin-right: 0; } + html.theme--documenter-dark .tags.has-addons .tag:not(:first-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:first-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0; + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .tags.has-addons .tag:not(:last-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:last-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .tag:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { + align-items: center; + background-color: whitesmoke; + border-radius: 4px; + color: #fbfbfb; + display: inline-flex; + font-size: 0.75rem; + height: 2em; + justify-content: center; + line-height: 1.5; + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + html.theme--documenter-dark .tag:not(body) .delete, html.theme--documenter-dark .content kbd:not(body) .delete, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .delete { + margin-left: 0.25rem; + margin-right: -0.375rem; } + html.theme--documenter-dark .tag.is-white:not(body), html.theme--documenter-dark .content kbd.is-white:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-white:not(body) { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .tag.is-black:not(body), html.theme--documenter-dark .content kbd.is-black:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-black:not(body) { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .tag.is-light:not(body), html.theme--documenter-dark .content kbd.is-light:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-light:not(body) { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .tag.is-dark:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-dark:not(body), html.theme--documenter-dark .content .docstring > section > kbd:not(body) { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .tag.is-primary:not(body), html.theme--documenter-dark .content kbd.is-primary:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .tag.is-link:not(body), html.theme--documenter-dark .content kbd.is-link:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-link:not(body) { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .tag.is-info:not(body), html.theme--documenter-dark .content kbd.is-info:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-info:not(body) { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .tag.is-success:not(body), html.theme--documenter-dark .content kbd.is-success:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-success:not(body) { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .tag.is-warning:not(body), html.theme--documenter-dark .content kbd.is-warning:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-warning:not(body) { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .tag.is-danger:not(body), html.theme--documenter-dark .content kbd.is-danger:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-danger:not(body) { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .tag.is-normal:not(body), html.theme--documenter-dark .content kbd.is-normal:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-normal:not(body) { + font-size: 0.75rem; } + html.theme--documenter-dark .tag.is-medium:not(body), html.theme--documenter-dark .content kbd.is-medium:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-medium:not(body) { + font-size: 1rem; } + html.theme--documenter-dark .tag.is-large:not(body), html.theme--documenter-dark .content kbd.is-large:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-large:not(body) { + font-size: 1.25rem; } + html.theme--documenter-dark .tag:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .content kbd:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { + margin-left: -0.375em; + margin-right: 0.1875em; } + html.theme--documenter-dark .tag:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .content kbd:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: -0.375em; } + html.theme--documenter-dark .tag:not(body) .icon:first-child:last-child, html.theme--documenter-dark .content kbd:not(body) .icon:first-child:last-child, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { + margin-left: -0.375em; + margin-right: -0.375em; } + html.theme--documenter-dark .tag.is-delete:not(body), html.theme--documenter-dark .content kbd.is-delete:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body) { + margin-left: 1px; + padding: 0; + position: relative; + width: 2em; } + html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + background-color: currentColor; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { + height: 1px; + width: 50%; } + html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + height: 50%; + width: 1px; } + html.theme--documenter-dark .tag.is-delete:not(body):hover, html.theme--documenter-dark .content kbd.is-delete:not(body):hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, html.theme--documenter-dark .tag.is-delete:not(body):focus, html.theme--documenter-dark .content kbd.is-delete:not(body):focus, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { + background-color: #e8e8e8; } + html.theme--documenter-dark .tag.is-delete:not(body):active, html.theme--documenter-dark .content kbd.is-delete:not(body):active, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):active { + background-color: #dbdbdb; } + html.theme--documenter-dark .tag.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:not(body), html.theme--documenter-dark .content kbd.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-rounded:not(body) { + border-radius: 290486px; } + html.theme--documenter-dark a.tag:hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:hover { + text-decoration: underline; } + html.theme--documenter-dark .title, + html.theme--documenter-dark .subtitle { + word-break: break-word; } + html.theme--documenter-dark .title em, + html.theme--documenter-dark .title span, + html.theme--documenter-dark .subtitle em, + html.theme--documenter-dark .subtitle span { + font-weight: inherit; } + html.theme--documenter-dark .title sub, + html.theme--documenter-dark .subtitle sub { + font-size: 0.75em; } + html.theme--documenter-dark .title sup, + html.theme--documenter-dark .subtitle sup { + font-size: 0.75em; } + html.theme--documenter-dark .title .tag, html.theme--documenter-dark .title .content kbd, html.theme--documenter-dark .content .title kbd, html.theme--documenter-dark .title .docstring > section > a.docs-sourcelink, + html.theme--documenter-dark .subtitle .tag, + html.theme--documenter-dark .subtitle .content kbd, + html.theme--documenter-dark .content .subtitle kbd, + html.theme--documenter-dark .subtitle .docstring > section > a.docs-sourcelink { + vertical-align: middle; } + html.theme--documenter-dark .title { + color: #363636; + font-size: 2rem; + font-weight: 600; + line-height: 1.125; } + html.theme--documenter-dark .title strong { + color: inherit; + font-weight: inherit; } + html.theme--documenter-dark .title + .highlight { + margin-top: -0.75rem; } + html.theme--documenter-dark .title:not(.is-spaced) + .subtitle { + margin-top: -1.25rem; } + html.theme--documenter-dark .title.is-1 { + font-size: 3rem; } + html.theme--documenter-dark .title.is-2 { + font-size: 2.5rem; } + html.theme--documenter-dark .title.is-3 { + font-size: 2rem; } + html.theme--documenter-dark .title.is-4 { + font-size: 1.5rem; } + html.theme--documenter-dark .title.is-5 { + font-size: 1.25rem; } + html.theme--documenter-dark .title.is-6 { + font-size: 1rem; } + html.theme--documenter-dark .title.is-7 { + font-size: 0.75rem; } + html.theme--documenter-dark .subtitle { + color: #4a4a4a; + font-size: 1.25rem; + font-weight: 400; + line-height: 1.25; } + html.theme--documenter-dark .subtitle strong { + color: #363636; + font-weight: 600; } + html.theme--documenter-dark .subtitle:not(.is-spaced) + .title { + margin-top: -1.25rem; } + html.theme--documenter-dark .subtitle.is-1 { + font-size: 3rem; } + html.theme--documenter-dark .subtitle.is-2 { + font-size: 2.5rem; } + html.theme--documenter-dark .subtitle.is-3 { + font-size: 2rem; } + html.theme--documenter-dark .subtitle.is-4 { + font-size: 1.5rem; } + html.theme--documenter-dark .subtitle.is-5 { + font-size: 1.25rem; } + html.theme--documenter-dark .subtitle.is-6 { + font-size: 1rem; } + html.theme--documenter-dark .subtitle.is-7 { + font-size: 0.75rem; } + html.theme--documenter-dark .heading { + display: block; + font-size: 11px; + letter-spacing: 1px; + margin-bottom: 5px; + text-transform: uppercase; } + html.theme--documenter-dark .highlight { + font-weight: 400; + max-width: 100%; + overflow: hidden; + padding: 0; } + html.theme--documenter-dark .highlight pre { + overflow: auto; + max-width: 100%; } + html.theme--documenter-dark .number { + align-items: center; + background-color: whitesmoke; + border-radius: 290486px; + display: inline-flex; + font-size: 1.25rem; + height: 2em; + justify-content: center; + margin-right: 1.5rem; + min-width: 2.5em; + padding: 0.25rem 0.5rem; + text-align: center; + vertical-align: top; } + html.theme--documenter-dark .select select, html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + background-color: white; + border-color: #dbdbdb; + border-radius: 4px; + color: #363636; } + html.theme--documenter-dark .select select::-moz-placeholder, html.theme--documenter-dark .textarea::-moz-placeholder, html.theme--documenter-dark .input::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select::-webkit-input-placeholder, html.theme--documenter-dark .textarea::-webkit-input-placeholder, html.theme--documenter-dark .input::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:-moz-placeholder, html.theme--documenter-dark .textarea:-moz-placeholder, html.theme--documenter-dark .input:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:-ms-input-placeholder, html.theme--documenter-dark .textarea:-ms-input-placeholder, html.theme--documenter-dark .input:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:hover, html.theme--documenter-dark .textarea:hover, html.theme--documenter-dark .input:hover, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:hover, html.theme--documenter-dark .select select.is-hovered, html.theme--documenter-dark .is-hovered.textarea, html.theme--documenter-dark .is-hovered.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-hovered { + border-color: #149eaa; } + html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + border-color: #fff; + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] html.theme--documenter-dark .select select, fieldset[disabled] html.theme--documenter-dark .textarea, fieldset[disabled] html.theme--documenter-dark .input, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + background-color: whitesmoke; + border-color: whitesmoke; + box-shadow: none; + color: #7a7a7a; } + html.theme--documenter-dark .select select[disabled]::-moz-placeholder, html.theme--documenter-dark .textarea[disabled]::-moz-placeholder, html.theme--documenter-dark .input[disabled]::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .textarea[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .input[disabled]::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]:-moz-placeholder, html.theme--documenter-dark .textarea[disabled]:-moz-placeholder, html.theme--documenter-dark .input[disabled]:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]:-ms-input-placeholder, html.theme--documenter-dark .textarea[disabled]:-ms-input-placeholder, html.theme--documenter-dark .input[disabled]:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); + max-width: 100%; + width: 100%; } + html.theme--documenter-dark .textarea[readonly], html.theme--documenter-dark .input[readonly], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[readonly] { + box-shadow: none; } + html.theme--documenter-dark .is-white.textarea, html.theme--documenter-dark .is-white.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white { + border-color: white; } + html.theme--documenter-dark .is-white.textarea:focus, html.theme--documenter-dark .is-white.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:focus, html.theme--documenter-dark .is-white.is-focused.textarea, html.theme--documenter-dark .is-white.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-white.textarea:active, html.theme--documenter-dark .is-white.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:active, html.theme--documenter-dark .is-white.is-active.textarea, html.theme--documenter-dark .is-white.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .is-black.textarea, html.theme--documenter-dark .is-black.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black { + border-color: #0a0a0a; } + html.theme--documenter-dark .is-black.textarea:focus, html.theme--documenter-dark .is-black.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:focus, html.theme--documenter-dark .is-black.is-focused.textarea, html.theme--documenter-dark .is-black.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-black.textarea:active, html.theme--documenter-dark .is-black.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:active, html.theme--documenter-dark .is-black.is-active.textarea, html.theme--documenter-dark .is-black.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .is-light.textarea, html.theme--documenter-dark .is-light.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light { + border-color: whitesmoke; } + html.theme--documenter-dark .is-light.textarea:focus, html.theme--documenter-dark .is-light.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:focus, html.theme--documenter-dark .is-light.is-focused.textarea, html.theme--documenter-dark .is-light.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-light.textarea:active, html.theme--documenter-dark .is-light.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:active, html.theme--documenter-dark .is-light.is-active.textarea, html.theme--documenter-dark .is-light.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .is-dark.textarea, html.theme--documenter-dark .content kbd.textarea, html.theme--documenter-dark .is-dark.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark, html.theme--documenter-dark .content kbd.input { + border-color: #363636; } + html.theme--documenter-dark .is-dark.textarea:focus, html.theme--documenter-dark .content kbd.textarea:focus, html.theme--documenter-dark .is-dark.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:focus, html.theme--documenter-dark .content kbd.input:focus, html.theme--documenter-dark .is-dark.is-focused.textarea, html.theme--documenter-dark .content kbd.is-focused.textarea, html.theme--documenter-dark .is-dark.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .content kbd.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-focused, html.theme--documenter-dark .is-dark.textarea:active, html.theme--documenter-dark .content kbd.textarea:active, html.theme--documenter-dark .is-dark.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:active, html.theme--documenter-dark .content kbd.input:active, html.theme--documenter-dark .is-dark.is-active.textarea, html.theme--documenter-dark .content kbd.is-active.textarea, html.theme--documenter-dark .is-dark.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .content kbd.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .is-primary.textarea, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink { + border-color: #4eb5de; } + html.theme--documenter-dark .is-primary.textarea:focus, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:focus, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.is-focused.textarea, html.theme--documenter-dark .docstring > section > a.is-focused.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .docstring > section > a.is-focused.input.docs-sourcelink, html.theme--documenter-dark .is-primary.textarea:active, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:active, html.theme--documenter-dark .is-primary.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:active, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:active, html.theme--documenter-dark .is-primary.is-active.textarea, html.theme--documenter-dark .docstring > section > a.is-active.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .docstring > section > a.is-active.input.docs-sourcelink { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .is-link.textarea, html.theme--documenter-dark .is-link.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link { + border-color: #2ad7e6; } + html.theme--documenter-dark .is-link.textarea:focus, html.theme--documenter-dark .is-link.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:focus, html.theme--documenter-dark .is-link.is-focused.textarea, html.theme--documenter-dark .is-link.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-link.textarea:active, html.theme--documenter-dark .is-link.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:active, html.theme--documenter-dark .is-link.is-active.textarea, html.theme--documenter-dark .is-link.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .is-info.textarea, html.theme--documenter-dark .is-info.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info { + border-color: #3489da; } + html.theme--documenter-dark .is-info.textarea:focus, html.theme--documenter-dark .is-info.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:focus, html.theme--documenter-dark .is-info.is-focused.textarea, html.theme--documenter-dark .is-info.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-info.textarea:active, html.theme--documenter-dark .is-info.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:active, html.theme--documenter-dark .is-info.is-active.textarea, html.theme--documenter-dark .is-info.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .is-success.textarea, html.theme--documenter-dark .is-success.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success { + border-color: #259a12; } + html.theme--documenter-dark .is-success.textarea:focus, html.theme--documenter-dark .is-success.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:focus, html.theme--documenter-dark .is-success.is-focused.textarea, html.theme--documenter-dark .is-success.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-success.textarea:active, html.theme--documenter-dark .is-success.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:active, html.theme--documenter-dark .is-success.is-active.textarea, html.theme--documenter-dark .is-success.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .is-warning.textarea, html.theme--documenter-dark .is-warning.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning { + border-color: #f4c72f; } + html.theme--documenter-dark .is-warning.textarea:focus, html.theme--documenter-dark .is-warning.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:focus, html.theme--documenter-dark .is-warning.is-focused.textarea, html.theme--documenter-dark .is-warning.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-warning.textarea:active, html.theme--documenter-dark .is-warning.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:active, html.theme--documenter-dark .is-warning.is-active.textarea, html.theme--documenter-dark .is-warning.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .is-danger.textarea, html.theme--documenter-dark .is-danger.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger { + border-color: #cb3c33; } + html.theme--documenter-dark .is-danger.textarea:focus, html.theme--documenter-dark .is-danger.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:focus, html.theme--documenter-dark .is-danger.is-focused.textarea, html.theme--documenter-dark .is-danger.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-danger.textarea:active, html.theme--documenter-dark .is-danger.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:active, html.theme--documenter-dark .is-danger.is-active.textarea, html.theme--documenter-dark .is-danger.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .is-small.textarea, html.theme--documenter-dark .is-small.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .is-medium.textarea, html.theme--documenter-dark .is-medium.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .is-large.textarea, html.theme--documenter-dark .is-large.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .is-fullwidth.textarea, html.theme--documenter-dark .is-fullwidth.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-fullwidth { + display: block; + width: 100%; } + html.theme--documenter-dark .is-inline.textarea, html.theme--documenter-dark .is-inline.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-inline { + display: inline; + width: auto; } + html.theme--documenter-dark .input.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + html.theme--documenter-dark .input.is-static, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-static { + background-color: transparent; + border-color: transparent; + box-shadow: none; + padding-left: 0; + padding-right: 0; } + html.theme--documenter-dark .textarea { + display: block; + max-width: 100%; + min-width: 100%; + padding: 0.625em; + resize: vertical; } + html.theme--documenter-dark .textarea:not([rows]) { + max-height: 600px; + min-height: 120px; } + html.theme--documenter-dark .textarea[rows] { + height: initial; } + html.theme--documenter-dark .textarea.has-fixed-size { + resize: none; } + html.theme--documenter-dark .radio, html.theme--documenter-dark .checkbox { + cursor: pointer; + display: inline-block; + line-height: 1.25; + position: relative; } + html.theme--documenter-dark .radio input, html.theme--documenter-dark .checkbox input { + cursor: pointer; } + html.theme--documenter-dark .radio:hover, html.theme--documenter-dark .checkbox:hover { + color: #363636; } + html.theme--documenter-dark .radio[disabled], html.theme--documenter-dark .checkbox[disabled], fieldset[disabled] html.theme--documenter-dark .radio, fieldset[disabled] html.theme--documenter-dark .checkbox { + color: #7a7a7a; + cursor: not-allowed; } + html.theme--documenter-dark .radio + .radio { + margin-left: 0.5em; } + html.theme--documenter-dark .select { + display: inline-block; + max-width: 100%; + position: relative; + vertical-align: top; } + html.theme--documenter-dark .select:not(.is-multiple) { + height: 2.25em; } + html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after { + border-color: #2ad7e6; + right: 1.125em; + z-index: 4; } + html.theme--documenter-dark .select.is-rounded select, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select select { + border-radius: 290486px; + padding-left: 1em; } + html.theme--documenter-dark .select select { + cursor: pointer; + display: block; + font-size: 1em; + max-width: 100%; + outline: none; } + html.theme--documenter-dark .select select::-ms-expand { + display: none; } + html.theme--documenter-dark .select select[disabled]:hover, fieldset[disabled] html.theme--documenter-dark .select select:hover { + border-color: whitesmoke; } + html.theme--documenter-dark .select select:not([multiple]) { + padding-right: 2.5em; } + html.theme--documenter-dark .select select[multiple] { + height: auto; + padding: 0; } + html.theme--documenter-dark .select select[multiple] option { + padding: 0.5em 1em; } + html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading):hover::after { + border-color: #363636; } + html.theme--documenter-dark .select.is-white:not(:hover)::after { + border-color: white; } + html.theme--documenter-dark .select.is-white select { + border-color: white; } + html.theme--documenter-dark .select.is-white select:hover, html.theme--documenter-dark .select.is-white select.is-hovered { + border-color: #f2f2f2; } + html.theme--documenter-dark .select.is-white select:focus, html.theme--documenter-dark .select.is-white select.is-focused, html.theme--documenter-dark .select.is-white select:active, html.theme--documenter-dark .select.is-white select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .select.is-black:not(:hover)::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .select.is-black select { + border-color: #0a0a0a; } + html.theme--documenter-dark .select.is-black select:hover, html.theme--documenter-dark .select.is-black select.is-hovered { + border-color: black; } + html.theme--documenter-dark .select.is-black select:focus, html.theme--documenter-dark .select.is-black select.is-focused, html.theme--documenter-dark .select.is-black select:active, html.theme--documenter-dark .select.is-black select.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .select.is-light:not(:hover)::after { + border-color: whitesmoke; } + html.theme--documenter-dark .select.is-light select { + border-color: whitesmoke; } + html.theme--documenter-dark .select.is-light select:hover, html.theme--documenter-dark .select.is-light select.is-hovered { + border-color: #e8e8e8; } + html.theme--documenter-dark .select.is-light select:focus, html.theme--documenter-dark .select.is-light select.is-focused, html.theme--documenter-dark .select.is-light select:active, html.theme--documenter-dark .select.is-light select.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .select.is-dark:not(:hover)::after, html.theme--documenter-dark .content kbd.select:not(:hover)::after { + border-color: #363636; } + html.theme--documenter-dark .select.is-dark select, html.theme--documenter-dark .content kbd.select select { + border-color: #363636; } + html.theme--documenter-dark .select.is-dark select:hover, html.theme--documenter-dark .content kbd.select select:hover, html.theme--documenter-dark .select.is-dark select.is-hovered, html.theme--documenter-dark .content kbd.select select.is-hovered { + border-color: #292929; } + html.theme--documenter-dark .select.is-dark select:focus, html.theme--documenter-dark .content kbd.select select:focus, html.theme--documenter-dark .select.is-dark select.is-focused, html.theme--documenter-dark .content kbd.select select.is-focused, html.theme--documenter-dark .select.is-dark select:active, html.theme--documenter-dark .content kbd.select select:active, html.theme--documenter-dark .select.is-dark select.is-active, html.theme--documenter-dark .content kbd.select select.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .select.is-primary:not(:hover)::after, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink:not(:hover)::after { + border-color: #4eb5de; } + html.theme--documenter-dark .select.is-primary select, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select { + border-color: #4eb5de; } + html.theme--documenter-dark .select.is-primary select:hover, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:hover, html.theme--documenter-dark .select.is-primary select.is-hovered, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-hovered { + border-color: #39acda; } + html.theme--documenter-dark .select.is-primary select:focus, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:focus, html.theme--documenter-dark .select.is-primary select.is-focused, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-focused, html.theme--documenter-dark .select.is-primary select:active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:active, html.theme--documenter-dark .select.is-primary select.is-active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-active { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .select.is-link:not(:hover)::after { + border-color: #2ad7e6; } + html.theme--documenter-dark .select.is-link select { + border-color: #2ad7e6; } + html.theme--documenter-dark .select.is-link select:hover, html.theme--documenter-dark .select.is-link select.is-hovered { + border-color: #1acddc; } + html.theme--documenter-dark .select.is-link select:focus, html.theme--documenter-dark .select.is-link select.is-focused, html.theme--documenter-dark .select.is-link select:active, html.theme--documenter-dark .select.is-link select.is-active { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .select.is-info:not(:hover)::after { + border-color: #3489da; } + html.theme--documenter-dark .select.is-info select { + border-color: #3489da; } + html.theme--documenter-dark .select.is-info select:hover, html.theme--documenter-dark .select.is-info select.is-hovered { + border-color: #267ccf; } + html.theme--documenter-dark .select.is-info select:focus, html.theme--documenter-dark .select.is-info select.is-focused, html.theme--documenter-dark .select.is-info select:active, html.theme--documenter-dark .select.is-info select.is-active { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .select.is-success:not(:hover)::after { + border-color: #259a12; } + html.theme--documenter-dark .select.is-success select { + border-color: #259a12; } + html.theme--documenter-dark .select.is-success select:hover, html.theme--documenter-dark .select.is-success select.is-hovered { + border-color: #20830f; } + html.theme--documenter-dark .select.is-success select:focus, html.theme--documenter-dark .select.is-success select.is-focused, html.theme--documenter-dark .select.is-success select:active, html.theme--documenter-dark .select.is-success select.is-active { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .select.is-warning:not(:hover)::after { + border-color: #f4c72f; } + html.theme--documenter-dark .select.is-warning select { + border-color: #f4c72f; } + html.theme--documenter-dark .select.is-warning select:hover, html.theme--documenter-dark .select.is-warning select.is-hovered { + border-color: #f3c017; } + html.theme--documenter-dark .select.is-warning select:focus, html.theme--documenter-dark .select.is-warning select.is-focused, html.theme--documenter-dark .select.is-warning select:active, html.theme--documenter-dark .select.is-warning select.is-active { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .select.is-danger:not(:hover)::after { + border-color: #cb3c33; } + html.theme--documenter-dark .select.is-danger select { + border-color: #cb3c33; } + html.theme--documenter-dark .select.is-danger select:hover, html.theme--documenter-dark .select.is-danger select.is-hovered { + border-color: #b7362e; } + html.theme--documenter-dark .select.is-danger select:focus, html.theme--documenter-dark .select.is-danger select.is-focused, html.theme--documenter-dark .select.is-danger select:active, html.theme--documenter-dark .select.is-danger select.is-active { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .select.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .select.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .select.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .select.is-disabled::after { + border-color: #7a7a7a; } + html.theme--documenter-dark .select.is-fullwidth { + width: 100%; } + html.theme--documenter-dark .select.is-fullwidth select { + width: 100%; } + html.theme--documenter-dark .select.is-loading::after { + margin-top: 0; + position: absolute; + right: 0.625em; + top: 0.625em; + transform: none; } + html.theme--documenter-dark .select.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + html.theme--documenter-dark .select.is-loading.is-medium:after { + font-size: 1.25rem; } + html.theme--documenter-dark .select.is-loading.is-large:after { + font-size: 1.5rem; } + html.theme--documenter-dark .file { + align-items: stretch; + display: flex; + justify-content: flex-start; + position: relative; } + html.theme--documenter-dark .file.is-white .file-cta { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:hover .file-cta, html.theme--documenter-dark .file.is-white.is-hovered .file-cta { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:focus .file-cta, html.theme--documenter-dark .file.is-white.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:active .file-cta, html.theme--documenter-dark .file.is-white.is-active .file-cta { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-black .file-cta { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-black:hover .file-cta, html.theme--documenter-dark .file.is-black.is-hovered .file-cta { + background-color: #040404; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-black:focus .file-cta, html.theme--documenter-dark .file.is-black.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); + color: white; } + html.theme--documenter-dark .file.is-black:active .file-cta, html.theme--documenter-dark .file.is-black.is-active .file-cta { + background-color: black; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-light .file-cta { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-light:hover .file-cta, html.theme--documenter-dark .file.is-light.is-hovered .file-cta { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-light:focus .file-cta, html.theme--documenter-dark .file.is-light.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25); + color: #363636; } + html.theme--documenter-dark .file.is-light:active .file-cta, html.theme--documenter-dark .file.is-light.is-active .file-cta { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-dark .file-cta, html.theme--documenter-dark .content kbd.file .file-cta { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:hover .file-cta, html.theme--documenter-dark .content kbd.file:hover .file-cta, html.theme--documenter-dark .file.is-dark.is-hovered .file-cta, html.theme--documenter-dark .content kbd.file.is-hovered .file-cta { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:focus .file-cta, html.theme--documenter-dark .content kbd.file:focus .file-cta, html.theme--documenter-dark .file.is-dark.is-focused .file-cta, html.theme--documenter-dark .content kbd.file.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25); + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:active .file-cta, html.theme--documenter-dark .content kbd.file:active .file-cta, html.theme--documenter-dark .file.is-dark.is-active .file-cta, html.theme--documenter-dark .content kbd.file.is-active .file-cta { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-primary .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink .file-cta { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-primary:hover .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:hover .file-cta, html.theme--documenter-dark .file.is-primary.is-hovered .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-primary:focus .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:focus .file-cta, html.theme--documenter-dark .file.is-primary.is-focused .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-primary:active .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:active .file-cta, html.theme--documenter-dark .file.is-primary.is-active .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-active.docs-sourcelink .file-cta { + background-color: #39acda; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link .file-cta { + background-color: #2ad7e6; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link:hover .file-cta, html.theme--documenter-dark .file.is-link.is-hovered .file-cta { + background-color: #1ed5e5; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link:focus .file-cta, html.theme--documenter-dark .file.is-link.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(42, 215, 230, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-link:active .file-cta, html.theme--documenter-dark .file.is-link.is-active .file-cta { + background-color: #1acddc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info .file-cta { + background-color: #3489da; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info:hover .file-cta, html.theme--documenter-dark .file.is-info.is-hovered .file-cta { + background-color: #2983d8; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info:focus .file-cta, html.theme--documenter-dark .file.is-info.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(52, 137, 218, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-info:active .file-cta, html.theme--documenter-dark .file.is-info.is-active .file-cta { + background-color: #267ccf; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success .file-cta { + background-color: #259a12; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success:hover .file-cta, html.theme--documenter-dark .file.is-success.is-hovered .file-cta { + background-color: #228f11; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success:focus .file-cta, html.theme--documenter-dark .file.is-success.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(37, 154, 18, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-success:active .file-cta, html.theme--documenter-dark .file.is-success.is-active .file-cta { + background-color: #20830f; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-warning .file-cta { + background-color: #f4c72f; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:hover .file-cta, html.theme--documenter-dark .file.is-warning.is-hovered .file-cta { + background-color: #f3c423; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:focus .file-cta, html.theme--documenter-dark .file.is-warning.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(244, 199, 47, 0.25); + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:active .file-cta, html.theme--documenter-dark .file.is-warning.is-active .file-cta { + background-color: #f3c017; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-danger .file-cta { + background-color: #cb3c33; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-danger:hover .file-cta, html.theme--documenter-dark .file.is-danger.is-hovered .file-cta { + background-color: #c13930; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-danger:focus .file-cta, html.theme--documenter-dark .file.is-danger.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(203, 60, 51, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-danger:active .file-cta, html.theme--documenter-dark .file.is-danger.is-active .file-cta { + background-color: #b7362e; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.file { + font-size: 0.75rem; } + html.theme--documenter-dark .file.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .file.is-medium .file-icon .fa { + font-size: 21px; } + html.theme--documenter-dark .file.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .file.is-large .file-icon .fa { + font-size: 28px; } + html.theme--documenter-dark .file.has-name .file-cta { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .file.has-name .file-name { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .file.has-name.is-empty .file-cta { + border-radius: 4px; } + html.theme--documenter-dark .file.has-name.is-empty .file-name { + display: none; } + html.theme--documenter-dark .file.is-boxed .file-label { + flex-direction: column; } + html.theme--documenter-dark .file.is-boxed .file-cta { + flex-direction: column; + height: auto; + padding: 1em 3em; } + html.theme--documenter-dark .file.is-boxed .file-name { + border-width: 0 1px 1px; } + html.theme--documenter-dark .file.is-boxed .file-icon { + height: 1.5em; + width: 1.5em; } + html.theme--documenter-dark .file.is-boxed .file-icon .fa { + font-size: 21px; } + html.theme--documenter-dark .file.is-boxed.is-small .file-icon .fa, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { + font-size: 14px; } + html.theme--documenter-dark .file.is-boxed.is-medium .file-icon .fa { + font-size: 28px; } + html.theme--documenter-dark .file.is-boxed.is-large .file-icon .fa { + font-size: 35px; } + html.theme--documenter-dark .file.is-boxed.has-name .file-cta { + border-radius: 4px 4px 0 0; } + html.theme--documenter-dark .file.is-boxed.has-name .file-name { + border-radius: 0 0 4px 4px; + border-width: 0 1px 1px; } + html.theme--documenter-dark .file.is-centered { + justify-content: center; } + html.theme--documenter-dark .file.is-fullwidth .file-label { + width: 100%; } + html.theme--documenter-dark .file.is-fullwidth .file-name { + flex-grow: 1; + max-width: none; } + html.theme--documenter-dark .file.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .file.is-right .file-cta { + border-radius: 0 4px 4px 0; } + html.theme--documenter-dark .file.is-right .file-name { + border-radius: 4px 0 0 4px; + border-width: 1px 0 1px 1px; + order: -1; } + html.theme--documenter-dark .file-label { + align-items: stretch; + display: flex; + cursor: pointer; + justify-content: flex-start; + overflow: hidden; + position: relative; } + html.theme--documenter-dark .file-label:hover .file-cta { + background-color: #eeeeee; + color: #363636; } + html.theme--documenter-dark .file-label:hover .file-name { + border-color: #d5d5d5; } + html.theme--documenter-dark .file-label:active .file-cta { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .file-label:active .file-name { + border-color: #cfcfcf; } + html.theme--documenter-dark .file-input { + height: 100%; + left: 0; + opacity: 0; + outline: none; + position: absolute; + top: 0; + width: 100%; } + html.theme--documenter-dark .file-cta, + html.theme--documenter-dark .file-name { + border-color: #dbdbdb; + border-radius: 4px; + font-size: 1em; + padding-left: 1em; + padding-right: 1em; + white-space: nowrap; } + html.theme--documenter-dark .file-cta { + background-color: whitesmoke; + color: #4a4a4a; } + html.theme--documenter-dark .file-name { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px 1px 1px 0; + display: block; + max-width: 16em; + overflow: hidden; + text-align: left; + text-overflow: ellipsis; } + html.theme--documenter-dark .file-icon { + align-items: center; + display: flex; + height: 1em; + justify-content: center; + margin-right: 0.5em; + width: 1em; } + html.theme--documenter-dark .file-icon .fa { + font-size: 14px; } + html.theme--documenter-dark .label { + color: #363636; + display: block; + font-size: 1rem; + font-weight: 700; } + html.theme--documenter-dark .label:not(:last-child) { + margin-bottom: 0.5em; } + html.theme--documenter-dark .label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.label { + font-size: 0.75rem; } + html.theme--documenter-dark .label.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .label.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .help { + display: block; + font-size: 0.75rem; + margin-top: 0.25rem; } + html.theme--documenter-dark .help.is-white { + color: white; } + html.theme--documenter-dark .help.is-black { + color: #0a0a0a; } + html.theme--documenter-dark .help.is-light { + color: whitesmoke; } + html.theme--documenter-dark .help.is-dark, html.theme--documenter-dark .content kbd.help { + color: #363636; } + html.theme--documenter-dark .help.is-primary, html.theme--documenter-dark .docstring > section > a.help.docs-sourcelink { + color: #4eb5de; } + html.theme--documenter-dark .help.is-link { + color: #2ad7e6; } + html.theme--documenter-dark .help.is-info { + color: #3489da; } + html.theme--documenter-dark .help.is-success { + color: #259a12; } + html.theme--documenter-dark .help.is-warning { + color: #f4c72f; } + html.theme--documenter-dark .help.is-danger { + color: #cb3c33; } + html.theme--documenter-dark .field:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .field.has-addons { + display: flex; + justify-content: flex-start; } + html.theme--documenter-dark .field.has-addons .control:not(:last-child) { + margin-right: -1px; } + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .button, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .input, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .select select { + border-radius: 0; } + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .button, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .input, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .select select { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .button, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .input, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .select select { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-hovered:not([disabled]) { + z-index: 2; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]), html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]) { + z-index: 3; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus:hover, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active:hover, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]):hover { + z-index: 4; } + html.theme--documenter-dark .field.has-addons .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .field.has-addons.has-addons-centered { + justify-content: center; } + html.theme--documenter-dark .field.has-addons.has-addons-right { + justify-content: flex-end; } + html.theme--documenter-dark .field.has-addons.has-addons-fullwidth .control { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .field.is-grouped { + display: flex; + justify-content: flex-start; } + html.theme--documenter-dark .field.is-grouped > .control { + flex-shrink: 0; } + html.theme--documenter-dark .field.is-grouped > .control:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + html.theme--documenter-dark .field.is-grouped > .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .field.is-grouped.is-grouped-centered { + justify-content: center; } + html.theme--documenter-dark .field.is-grouped.is-grouped-right { + justify-content: flex-end; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline { + flex-wrap: wrap; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:last-child, html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:not(:last-child) { + margin-bottom: 0; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field.is-horizontal { + display: flex; } } + html.theme--documenter-dark .field-label .label { + font-size: inherit; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .field-label { + margin-bottom: 0.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field-label { + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + margin-right: 1.5rem; + text-align: right; } + html.theme--documenter-dark .field-label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.field-label { + font-size: 0.75rem; + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-normal { + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-medium { + font-size: 1.25rem; + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-large { + font-size: 1.5rem; + padding-top: 0.375em; } } + html.theme--documenter-dark .field-body .field .field { + margin-bottom: 0; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field-body { + display: flex; + flex-basis: 0; + flex-grow: 5; + flex-shrink: 1; } + html.theme--documenter-dark .field-body .field { + margin-bottom: 0; } + html.theme--documenter-dark .field-body > .field { + flex-shrink: 1; } + html.theme--documenter-dark .field-body > .field:not(.is-narrow) { + flex-grow: 1; } + html.theme--documenter-dark .field-body > .field:not(:last-child) { + margin-right: 0.75rem; } } + html.theme--documenter-dark .control { + box-sizing: border-box; + clear: both; + font-size: 1rem; + position: relative; + text-align: left; } + html.theme--documenter-dark .control.has-icons-left .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select:focus ~ .icon { + color: #7a7a7a; } + html.theme--documenter-dark .control.has-icons-left .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-small ~ .icon { + font-size: 0.75rem; } + html.theme--documenter-dark .control.has-icons-left .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-medium ~ .icon { + font-size: 1.25rem; } + html.theme--documenter-dark .control.has-icons-left .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-large ~ .icon { + font-size: 1.5rem; } + html.theme--documenter-dark .control.has-icons-left .icon, html.theme--documenter-dark .control.has-icons-right .icon { + color: #dbdbdb; + height: 2.25em; + pointer-events: none; + position: absolute; + top: 0; + width: 2.25em; + z-index: 4; } + html.theme--documenter-dark .control.has-icons-left .input, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, + html.theme--documenter-dark .control.has-icons-left .select select { + padding-left: 2.25em; } + html.theme--documenter-dark .control.has-icons-left .icon.is-left { + left: 0; } + html.theme--documenter-dark .control.has-icons-right .input, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, + html.theme--documenter-dark .control.has-icons-right .select select { + padding-right: 2.25em; } + html.theme--documenter-dark .control.has-icons-right .icon.is-right { + right: 0; } + html.theme--documenter-dark .control.is-loading::after { + position: absolute !important; + right: 0.625em; + top: 0.625em; + z-index: 4; } + html.theme--documenter-dark .control.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + html.theme--documenter-dark .control.is-loading.is-medium:after { + font-size: 1.25rem; } + html.theme--documenter-dark .control.is-loading.is-large:after { + font-size: 1.5rem; } + html.theme--documenter-dark .breadcrumb { + font-size: 1rem; + white-space: nowrap; } + html.theme--documenter-dark .breadcrumb a { + align-items: center; + color: #2ad7e6; + display: flex; + justify-content: center; + padding: 0 0.75em; } + html.theme--documenter-dark .breadcrumb a:hover { + color: #97ebf3; } + html.theme--documenter-dark .breadcrumb li { + align-items: center; + display: flex; } + html.theme--documenter-dark .breadcrumb li:first-child a { + padding-left: 0; } + html.theme--documenter-dark .breadcrumb li.is-active a { + color: #cdc3e3; + cursor: default; + pointer-events: none; } + html.theme--documenter-dark .breadcrumb li + li::before { + color: #b5b5b5; + content: "\0002f"; } + html.theme--documenter-dark .breadcrumb ul, + html.theme--documenter-dark .breadcrumb ol { + align-items: flex-start; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .breadcrumb .icon:first-child { + margin-right: 0.5em; } + html.theme--documenter-dark .breadcrumb .icon:last-child { + margin-left: 0.5em; } + html.theme--documenter-dark .breadcrumb.is-centered ol, + html.theme--documenter-dark .breadcrumb.is-centered ul { + justify-content: center; } + html.theme--documenter-dark .breadcrumb.is-right ol, + html.theme--documenter-dark .breadcrumb.is-right ul { + justify-content: flex-end; } + html.theme--documenter-dark .breadcrumb.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.breadcrumb { + font-size: 0.75rem; } + html.theme--documenter-dark .breadcrumb.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .breadcrumb.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .breadcrumb.has-arrow-separator li + li::before { + content: "\02192"; } + html.theme--documenter-dark .breadcrumb.has-bullet-separator li + li::before { + content: "\02022"; } + html.theme--documenter-dark .breadcrumb.has-dot-separator li + li::before { + content: "\000b7"; } + html.theme--documenter-dark .breadcrumb.has-succeeds-separator li + li::before { + content: "\0227B"; } + html.theme--documenter-dark .card { + background-color: white; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #fbfbfb; + max-width: 100%; + position: relative; } + html.theme--documenter-dark .card-header { + background-color: transparent; + align-items: stretch; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + display: flex; } + html.theme--documenter-dark .card-header-title { + align-items: center; + color: #cdc3e3; + display: flex; + flex-grow: 1; + font-weight: 700; + padding: 0.75rem; } + html.theme--documenter-dark .card-header-title.is-centered { + justify-content: center; } + html.theme--documenter-dark .card-header-icon { + align-items: center; + cursor: pointer; + display: flex; + justify-content: center; + padding: 0.75rem; } + html.theme--documenter-dark .card-image { + display: block; + position: relative; } + html.theme--documenter-dark .card-content { + background-color: transparent; + padding: 1.5rem; } + html.theme--documenter-dark .card-footer { + background-color: transparent; + border-top: 1px solid #dbdbdb; + align-items: stretch; + display: flex; } + html.theme--documenter-dark .card-footer-item { + align-items: center; + display: flex; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + justify-content: center; + padding: 0.75rem; } + html.theme--documenter-dark .card-footer-item:not(:last-child) { + border-right: 1px solid #dbdbdb; } + html.theme--documenter-dark .card .media:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .dropdown { + display: inline-flex; + position: relative; + vertical-align: top; } + html.theme--documenter-dark .dropdown.is-active .dropdown-menu, html.theme--documenter-dark .dropdown.is-hoverable:hover .dropdown-menu { + display: block; } + html.theme--documenter-dark .dropdown.is-right .dropdown-menu { + left: auto; + right: 0; } + html.theme--documenter-dark .dropdown.is-up .dropdown-menu { + bottom: 100%; + padding-bottom: 4px; + padding-top: initial; + top: auto; } + html.theme--documenter-dark .dropdown-menu { + display: none; + left: 0; + min-width: 12rem; + padding-top: 4px; + position: absolute; + top: 100%; + z-index: 20; } + html.theme--documenter-dark .dropdown-content { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + html.theme--documenter-dark .dropdown-item { + color: #4a4a4a; + display: block; + font-size: 0.875rem; + line-height: 1.5; + padding: 0.375rem 1rem; + position: relative; } + html.theme--documenter-dark a.dropdown-item, + html.theme--documenter-dark button.dropdown-item { + padding-right: 3rem; + text-align: left; + white-space: nowrap; + width: 100%; } + html.theme--documenter-dark a.dropdown-item:hover, + html.theme--documenter-dark button.dropdown-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark a.dropdown-item.is-active, + html.theme--documenter-dark button.dropdown-item.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .dropdown-divider { + background-color: #dbdbdb; + border: none; + display: block; + height: 1px; + margin: 0.5rem 0; } + html.theme--documenter-dark .level { + align-items: center; + justify-content: space-between; } + html.theme--documenter-dark .level code { + border-radius: 4px; } + html.theme--documenter-dark .level img { + display: inline-block; + vertical-align: top; } + html.theme--documenter-dark .level.is-mobile { + display: flex; } + html.theme--documenter-dark .level.is-mobile .level-left, + html.theme--documenter-dark .level.is-mobile .level-right { + display: flex; } + html.theme--documenter-dark .level.is-mobile .level-left + .level-right { + margin-top: 0; } + html.theme--documenter-dark .level.is-mobile .level-item:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + html.theme--documenter-dark .level.is-mobile .level-item:not(.is-narrow) { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level { + display: flex; } + html.theme--documenter-dark .level > .level-item:not(.is-narrow) { + flex-grow: 1; } } + html.theme--documenter-dark .level-item { + align-items: center; + display: flex; + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; + justify-content: center; } + html.theme--documenter-dark .level-item .title, + html.theme--documenter-dark .level-item .subtitle { + margin-bottom: 0; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .level-item:not(:last-child) { + margin-bottom: 0.75rem; } } + html.theme--documenter-dark .level-left, + html.theme--documenter-dark .level-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .level-left .level-item.is-flexible, + html.theme--documenter-dark .level-right .level-item.is-flexible { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-left .level-item:not(:last-child), + html.theme--documenter-dark .level-right .level-item:not(:last-child) { + margin-right: 0.75rem; } } + html.theme--documenter-dark .level-left { + align-items: center; + justify-content: flex-start; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .level-left + .level-right { + margin-top: 1.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-left { + display: flex; } } + html.theme--documenter-dark .level-right { + align-items: center; + justify-content: flex-end; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-right { + display: flex; } } + html.theme--documenter-dark .list { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .list-item { + display: block; + padding: 0.5em 1em; } + html.theme--documenter-dark .list-item:not(a) { + color: #fbfbfb; } + html.theme--documenter-dark .list-item:first-child { + border-top-left-radius: 4px; + border-top-right-radius: 4px; } + html.theme--documenter-dark .list-item:last-child { + border-bottom-left-radius: 4px; + border-bottom-right-radius: 4px; } + html.theme--documenter-dark .list-item:not(:last-child) { + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .list-item.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark a.list-item { + background-color: whitesmoke; + cursor: pointer; } + html.theme--documenter-dark .media { + align-items: flex-start; + display: flex; + text-align: left; } + html.theme--documenter-dark .media .content:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .media .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + display: flex; + padding-top: 0.75rem; } + html.theme--documenter-dark .media .media .content:not(:last-child), + html.theme--documenter-dark .media .media .control:not(:last-child) { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .media .media .media { + padding-top: 0.5rem; } + html.theme--documenter-dark .media .media .media + .media { + margin-top: 0.5rem; } + html.theme--documenter-dark .media + .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + margin-top: 1rem; + padding-top: 1rem; } + html.theme--documenter-dark .media.is-large + .media { + margin-top: 1.5rem; + padding-top: 1.5rem; } + html.theme--documenter-dark .media-left, + html.theme--documenter-dark .media-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .media-left { + margin-right: 1rem; } + html.theme--documenter-dark .media-right { + margin-left: 1rem; } + html.theme--documenter-dark .media-content { + flex-basis: auto; + flex-grow: 1; + flex-shrink: 1; + text-align: left; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .media-content { + overflow-x: auto; } } + html.theme--documenter-dark .menu { + font-size: 1rem; } + html.theme--documenter-dark .menu.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.menu { + font-size: 0.75rem; } + html.theme--documenter-dark .menu.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .menu.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .menu-list { + line-height: 1.25; } + html.theme--documenter-dark .menu-list a { + border-radius: 2px; + color: #fbfbfb; + display: block; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .menu-list a:hover { + background-color: whitesmoke; + color: #cdc3e3; } + html.theme--documenter-dark .menu-list a.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .menu-list li ul { + border-left: 1px solid #dbdbdb; + margin: 0.75em; + padding-left: 0.75em; } + html.theme--documenter-dark .menu-label { + color: #7a7a7a; + font-size: 0.75em; + letter-spacing: 0.1em; + text-transform: uppercase; } + html.theme--documenter-dark .menu-label:not(:first-child) { + margin-top: 1em; } + html.theme--documenter-dark .menu-label:not(:last-child) { + margin-bottom: 1em; } + html.theme--documenter-dark .message { + background-color: whitesmoke; + border-radius: 4px; + font-size: 1rem; } + html.theme--documenter-dark .message strong { + color: currentColor; } + html.theme--documenter-dark .message a:not(.button):not(.tag):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + html.theme--documenter-dark .message.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.message { + font-size: 0.75rem; } + html.theme--documenter-dark .message.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .message.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .message.is-white { + background-color: white; } + html.theme--documenter-dark .message.is-white .message-header { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .message.is-white .message-body { + border-color: white; + color: #4d4d4d; } + html.theme--documenter-dark .message.is-black { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-black .message-header { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .message.is-black .message-body { + border-color: #0a0a0a; + color: #090909; } + html.theme--documenter-dark .message.is-light { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-light .message-header { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .message.is-light .message-body { + border-color: whitesmoke; + color: #505050; } + html.theme--documenter-dark .message.is-dark, html.theme--documenter-dark .content kbd.message { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-dark .message-header, html.theme--documenter-dark .content kbd.message .message-header { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .message.is-dark .message-body, html.theme--documenter-dark .content kbd.message .message-body { + border-color: #363636; + color: #2a2a2a; } + html.theme--documenter-dark .message.is-primary, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink { + background-color: #f6fbfd; } + html.theme--documenter-dark .message.is-primary .message-header, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-header { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .message.is-primary .message-body, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-body { + border-color: #4eb5de; + color: #1f556a; } + html.theme--documenter-dark .message.is-link { + background-color: #f6fdfe; } + html.theme--documenter-dark .message.is-link .message-header { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .message.is-link .message-body { + border-color: #2ad7e6; + color: #0c2f32; } + html.theme--documenter-dark .message.is-info { + background-color: #f6fafd; } + html.theme--documenter-dark .message.is-info .message-header { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .message.is-info .message-body { + border-color: #3489da; + color: #215485; } + html.theme--documenter-dark .message.is-success { + background-color: #f7fef6; } + html.theme--documenter-dark .message.is-success .message-header { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .message.is-success .message-body { + border-color: #259a12; + color: #113b0a; } + html.theme--documenter-dark .message.is-warning { + background-color: #fefcf5; } + html.theme--documenter-dark .message.is-warning .message-header { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .message.is-warning .message-body { + border-color: #f4c72f; + color: #332909; } + html.theme--documenter-dark .message.is-danger { + background-color: #fdf7f7; } + html.theme--documenter-dark .message.is-danger .message-header { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .message.is-danger .message-body { + border-color: #cb3c33; + color: #8d302a; } + html.theme--documenter-dark .message-header { + align-items: center; + background-color: #fbfbfb; + border-radius: 4px 4px 0 0; + color: rgba(0, 0, 0, 0.7); + display: flex; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.75em 1em; + position: relative; } + html.theme--documenter-dark .message-header .delete { + flex-grow: 0; + flex-shrink: 0; + margin-left: 0.75em; } + html.theme--documenter-dark .message-header + .message-body { + border-width: 0; + border-top-left-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .message-body { + border-color: #dbdbdb; + border-radius: 4px; + border-style: solid; + border-width: 0 0 0 4px; + color: #fbfbfb; + padding: 1.25em 1.5em; } + html.theme--documenter-dark .message-body code, + html.theme--documenter-dark .message-body pre { + background-color: white; } + html.theme--documenter-dark .message-body pre code { + background-color: transparent; } + html.theme--documenter-dark .modal { + align-items: center; + display: none; + flex-direction: column; + justify-content: center; + overflow: hidden; + position: fixed; + z-index: 40; } + html.theme--documenter-dark .modal.is-active { + display: flex; } + html.theme--documenter-dark .modal-background { + background-color: rgba(10, 10, 10, 0.86); } + html.theme--documenter-dark .modal-content, + html.theme--documenter-dark .modal-card { + margin: 0 20px; + max-height: calc(100vh - 160px); + overflow: auto; + position: relative; + width: 100%; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .modal-content, + html.theme--documenter-dark .modal-card { + margin: 0 auto; + max-height: calc(100vh - 40px); + width: 640px; } } + html.theme--documenter-dark .modal-close { + background: none; + height: 40px; + position: fixed; + right: 20px; + top: 20px; + width: 40px; } + html.theme--documenter-dark .modal-card { + display: flex; + flex-direction: column; + max-height: calc(100vh - 40px); + overflow: hidden; + -ms-overflow-y: visible; } + html.theme--documenter-dark .modal-card-head, + html.theme--documenter-dark .modal-card-foot { + align-items: center; + background-color: whitesmoke; + display: flex; + flex-shrink: 0; + justify-content: flex-start; + padding: 20px; + position: relative; } + html.theme--documenter-dark .modal-card-head { + border-bottom: 1px solid #dbdbdb; + border-top-left-radius: 6px; + border-top-right-radius: 6px; } + html.theme--documenter-dark .modal-card-title { + color: #cdc3e3; + flex-grow: 1; + flex-shrink: 0; + font-size: 1.5rem; + line-height: 1; } + html.theme--documenter-dark .modal-card-foot { + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark .modal-card-foot .button:not(:last-child) { + margin-right: 0.5em; } + html.theme--documenter-dark .modal-card-body { + -webkit-overflow-scrolling: touch; + background-color: white; + flex-grow: 1; + flex-shrink: 1; + overflow: auto; + padding: 20px; } + html.theme--documenter-dark .navbar { + background-color: white; + min-height: 3.25rem; + position: relative; + z-index: 30; } + html.theme--documenter-dark .navbar.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link { + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-burger { + color: #0a0a0a; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-white .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link { + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-dropdown a.navbar-item.is-active { + background-color: white; + color: #0a0a0a; } } + html.theme--documenter-dark .navbar.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link { + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link::after { + border-color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-burger { + color: white; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-black .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link { + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link::after { + border-color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-dropdown a.navbar-item.is-active { + background-color: #0a0a0a; + color: white; } } + html.theme--documenter-dark .navbar.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link { + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link::after { + border-color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-burger { + color: #363636; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-light .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link { + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link::after { + border-color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #363636; } } + html.theme--documenter-dark .navbar.is-dark, html.theme--documenter-dark .content kbd.navbar { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link { + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link::after { + border-color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-burger, html.theme--documenter-dark .content kbd.navbar .navbar-burger { + color: whitesmoke; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-dark .navbar-start > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-end > .navbar-item, + html.theme--documenter-dark .content kbd.navbar .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link { + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link::after, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link::after { + border-color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { + background-color: #363636; + color: whitesmoke; } } + html.theme--documenter-dark .navbar.is-primary, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-burger, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-primary .navbar-start > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-end > .navbar-item, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link::after, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { + background-color: #4eb5de; + color: #fff; } } + html.theme--documenter-dark .navbar.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-link .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-dropdown a.navbar-item.is-active { + background-color: #2ad7e6; + color: #fff; } } + html.theme--documenter-dark .navbar.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-info .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-dropdown a.navbar-item.is-active { + background-color: #3489da; + color: #fff; } } + html.theme--documenter-dark .navbar.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-success .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-dropdown a.navbar-item.is-active { + background-color: #259a12; + color: #fff; } } + html.theme--documenter-dark .navbar.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-burger { + color: rgba(0, 0, 0, 0.7); } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-warning .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } } + html.theme--documenter-dark .navbar.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-danger .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { + background-color: #cb3c33; + color: #fff; } } + html.theme--documenter-dark .navbar > .container { + align-items: stretch; + display: flex; + min-height: 3.25rem; + width: 100%; } + html.theme--documenter-dark .navbar.has-shadow { + box-shadow: 0 2px 0 0 whitesmoke; } + html.theme--documenter-dark .navbar.is-fixed-bottom, html.theme--documenter-dark .navbar.is-fixed-top { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom.has-shadow { + box-shadow: 0 -2px 0 0 whitesmoke; } + html.theme--documenter-dark .navbar.is-fixed-top { + top: 0; } + html.theme--documenter-dark html.has-navbar-fixed-top, + html.theme--documenter-dark body.has-navbar-fixed-top { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom, + html.theme--documenter-dark body.has-navbar-fixed-bottom { + padding-bottom: 3.25rem; } + html.theme--documenter-dark .navbar-brand, + html.theme--documenter-dark .navbar-tabs { + align-items: stretch; + display: flex; + flex-shrink: 0; + min-height: 3.25rem; } + html.theme--documenter-dark .navbar-brand a.navbar-item:focus, html.theme--documenter-dark .navbar-brand a.navbar-item:hover { + background-color: transparent; } + html.theme--documenter-dark .navbar-tabs { + -webkit-overflow-scrolling: touch; + max-width: 100vw; + overflow-x: auto; + overflow-y: hidden; } + html.theme--documenter-dark .navbar-burger { + color: #4a4a4a; + cursor: pointer; + display: block; + height: 3.25rem; + position: relative; + width: 3.25rem; + margin-left: auto; } + html.theme--documenter-dark .navbar-burger span { + background-color: currentColor; + display: block; + height: 1px; + left: calc(50% - 8px); + position: absolute; + transform-origin: center; + transition-duration: 86ms; + transition-property: background-color, opacity, transform; + transition-timing-function: ease-out; + width: 16px; } + html.theme--documenter-dark .navbar-burger span:nth-child(1) { + top: calc(50% - 6px); } + html.theme--documenter-dark .navbar-burger span:nth-child(2) { + top: calc(50% - 1px); } + html.theme--documenter-dark .navbar-burger span:nth-child(3) { + top: calc(50% + 4px); } + html.theme--documenter-dark .navbar-burger:hover { + background-color: rgba(0, 0, 0, 0.05); } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(1) { + transform: translateY(5px) rotate(45deg); } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(2) { + opacity: 0; } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(3) { + transform: translateY(-5px) rotate(-45deg); } + html.theme--documenter-dark .navbar-menu { + display: none; } + html.theme--documenter-dark .navbar-item, + html.theme--documenter-dark .navbar-link { + color: #4a4a4a; + display: block; + line-height: 1.5; + padding: 0.5rem 0.75rem; + position: relative; } + html.theme--documenter-dark .navbar-item .icon:only-child, + html.theme--documenter-dark .navbar-link .icon:only-child { + margin-left: -0.25rem; + margin-right: -0.25rem; } + html.theme--documenter-dark a.navbar-item, + html.theme--documenter-dark .navbar-link { + cursor: pointer; } + html.theme--documenter-dark a.navbar-item:focus, html.theme--documenter-dark a.navbar-item:focus-within, html.theme--documenter-dark a.navbar-item:hover, html.theme--documenter-dark a.navbar-item.is-active, + html.theme--documenter-dark .navbar-link:focus, + html.theme--documenter-dark .navbar-link:focus-within, + html.theme--documenter-dark .navbar-link:hover, + html.theme--documenter-dark .navbar-link.is-active { + background-color: #fafafa; + color: #2ad7e6; } + html.theme--documenter-dark .navbar-item { + display: block; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .navbar-item img { + max-height: 1.75rem; } + html.theme--documenter-dark .navbar-item.has-dropdown { + padding: 0; } + html.theme--documenter-dark .navbar-item.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .navbar-item.is-tab { + border-bottom: 1px solid transparent; + min-height: 3.25rem; + padding-bottom: calc(0.5rem - 1px); } + html.theme--documenter-dark .navbar-item.is-tab:focus, html.theme--documenter-dark .navbar-item.is-tab:hover { + background-color: transparent; + border-bottom-color: #2ad7e6; } + html.theme--documenter-dark .navbar-item.is-tab.is-active { + background-color: transparent; + border-bottom-color: #2ad7e6; + border-bottom-style: solid; + border-bottom-width: 3px; + color: #2ad7e6; + padding-bottom: calc(0.5rem - 3px); } + html.theme--documenter-dark .navbar-content { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .navbar-link:not(.is-arrowless) { + padding-right: 2.5em; } + html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after { + border-color: #2ad7e6; + margin-top: -0.375em; + right: 1.125em; } + html.theme--documenter-dark .navbar-dropdown { + font-size: 0.875rem; + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + html.theme--documenter-dark .navbar-dropdown .navbar-item { + padding-left: 1.5rem; + padding-right: 1.5rem; } + html.theme--documenter-dark .navbar-divider { + background-color: whitesmoke; + border: none; + display: none; + height: 2px; + margin: 0.5rem 0; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .navbar > .container { + display: block; } + html.theme--documenter-dark .navbar-brand .navbar-item, + html.theme--documenter-dark .navbar-tabs .navbar-item { + align-items: center; + display: flex; } + html.theme--documenter-dark .navbar-link::after { + display: none; } + html.theme--documenter-dark .navbar-menu { + background-color: white; + box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); + padding: 0.5rem 0; } + html.theme--documenter-dark .navbar-menu.is-active { + display: block; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch, html.theme--documenter-dark .navbar.is-fixed-top-touch { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .navbar.is-fixed-top-touch { + top: 0; } + html.theme--documenter-dark .navbar.is-fixed-top .navbar-menu, html.theme--documenter-dark .navbar.is-fixed-top-touch .navbar-menu { + -webkit-overflow-scrolling: touch; + max-height: calc(100vh - 3.25rem); + overflow: auto; } + html.theme--documenter-dark html.has-navbar-fixed-top-touch, + html.theme--documenter-dark body.has-navbar-fixed-top-touch { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom-touch, + html.theme--documenter-dark body.has-navbar-fixed-bottom-touch { + padding-bottom: 3.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar, + html.theme--documenter-dark .navbar-menu, + html.theme--documenter-dark .navbar-start, + html.theme--documenter-dark .navbar-end { + align-items: stretch; + display: flex; } + html.theme--documenter-dark .navbar { + min-height: 3.25rem; } + html.theme--documenter-dark .navbar.is-spaced { + padding: 1rem 2rem; } + html.theme--documenter-dark .navbar.is-spaced .navbar-start, + html.theme--documenter-dark .navbar.is-spaced .navbar-end { + align-items: center; } + html.theme--documenter-dark .navbar.is-spaced a.navbar-item, + html.theme--documenter-dark .navbar.is-spaced .navbar-link { + border-radius: 4px; } + html.theme--documenter-dark .navbar.is-transparent a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent a.navbar-item:hover, html.theme--documenter-dark .navbar.is-transparent a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-transparent .navbar-link:focus, + html.theme--documenter-dark .navbar.is-transparent .navbar-link:hover, + html.theme--documenter-dark .navbar.is-transparent .navbar-link.is-active { + background-color: transparent !important; } + html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { + background-color: transparent !important; } + html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #2ad7e6; } + html.theme--documenter-dark .navbar-burger { + display: none; } + html.theme--documenter-dark .navbar-item, + html.theme--documenter-dark .navbar-link { + align-items: center; + display: flex; } + html.theme--documenter-dark .navbar-item { + display: flex; } + html.theme--documenter-dark .navbar-item.has-dropdown { + align-items: stretch; } + html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-link::after { + transform: rotate(135deg) translate(0.25em, -0.25em); } + html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-dropdown { + border-bottom: 2px solid #dbdbdb; + border-radius: 6px 6px 0 0; + border-top: none; + bottom: 100%; + box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); + top: auto; } + html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown { + display: block; } + .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { + opacity: 1; + pointer-events: auto; + transform: translateY(0); } + html.theme--documenter-dark .navbar-menu { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .navbar-start { + justify-content: flex-start; + margin-right: auto; } + html.theme--documenter-dark .navbar-end { + justify-content: flex-end; + margin-left: auto; } + html.theme--documenter-dark .navbar-dropdown { + background-color: white; + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 2px solid #dbdbdb; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); + display: none; + font-size: 0.875rem; + left: 0; + min-width: 100%; + position: absolute; + top: 100%; + z-index: 20; } + html.theme--documenter-dark .navbar-dropdown .navbar-item { + padding: 0.375rem 1rem; + white-space: nowrap; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item { + padding-right: 3rem; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #2ad7e6; } + .navbar.is-spaced html.theme--documenter-dark .navbar-dropdown, html.theme--documenter-dark .navbar-dropdown.is-boxed { + border-radius: 6px; + border-top: none; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + display: block; + opacity: 0; + pointer-events: none; + top: calc(100% + (-4px)); + transform: translateY(-5px); + transition-duration: 86ms; + transition-property: opacity, transform; } + html.theme--documenter-dark .navbar-dropdown.is-right { + left: auto; + right: 0; } + html.theme--documenter-dark .navbar-divider { + display: block; } + html.theme--documenter-dark .navbar > .container .navbar-brand, + html.theme--documenter-dark .container > .navbar .navbar-brand { + margin-left: -.75rem; } + html.theme--documenter-dark .navbar > .container .navbar-menu, + html.theme--documenter-dark .container > .navbar .navbar-menu { + margin-right: -.75rem; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop, html.theme--documenter-dark .navbar.is-fixed-top-desktop { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .navbar.is-fixed-top-desktop { + top: 0; } + html.theme--documenter-dark html.has-navbar-fixed-top-desktop, + html.theme--documenter-dark body.has-navbar-fixed-top-desktop { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop, + html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop { + padding-bottom: 3.25rem; } + html.theme--documenter-dark html.has-spaced-navbar-fixed-top, + html.theme--documenter-dark body.has-spaced-navbar-fixed-top { + padding-top: 5.25rem; } + html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom, + html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom { + padding-bottom: 5.25rem; } + html.theme--documenter-dark a.navbar-item.is-active, + html.theme--documenter-dark .navbar-link.is-active { + color: #0a0a0a; } + html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover), + html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover) { + background-color: transparent; } + html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #fafafa; } } + html.theme--documenter-dark .hero.is-fullheight-with-navbar { + min-height: calc(100vh - 3.25rem); } + html.theme--documenter-dark .pagination { + font-size: 1rem; + margin: -0.25rem; } + html.theme--documenter-dark .pagination.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination { + font-size: 0.75rem; } + html.theme--documenter-dark .pagination.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .pagination.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .pagination.is-rounded .pagination-previous, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, + html.theme--documenter-dark .pagination.is-rounded .pagination-next, + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { + padding-left: 1em; + padding-right: 1em; + border-radius: 290486px; } + html.theme--documenter-dark .pagination.is-rounded .pagination-link, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { + border-radius: 290486px; } + html.theme--documenter-dark .pagination, + html.theme--documenter-dark .pagination-list { + align-items: center; + display: flex; + justify-content: center; + text-align: center; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark .pagination-link, + html.theme--documenter-dark .pagination-ellipsis { + font-size: 1em; + justify-content: center; + margin: 0.25rem; + padding-left: 0.5em; + padding-right: 0.5em; + text-align: center; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark .pagination-link { + border-color: #dbdbdb; + color: #363636; + min-width: 2.25em; } + html.theme--documenter-dark .pagination-previous:hover, + html.theme--documenter-dark .pagination-next:hover, + html.theme--documenter-dark .pagination-link:hover { + border-color: #b5b5b5; + color: #97ebf3; } + html.theme--documenter-dark .pagination-previous:focus, + html.theme--documenter-dark .pagination-next:focus, + html.theme--documenter-dark .pagination-link:focus { + border-color: #3c5dcd; } + html.theme--documenter-dark .pagination-previous:active, + html.theme--documenter-dark .pagination-next:active, + html.theme--documenter-dark .pagination-link:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } + html.theme--documenter-dark .pagination-previous[disabled], + html.theme--documenter-dark .pagination-next[disabled], + html.theme--documenter-dark .pagination-link[disabled] { + background-color: #dbdbdb; + border-color: #dbdbdb; + box-shadow: none; + color: #7a7a7a; + opacity: 0.5; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next { + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + html.theme--documenter-dark .pagination-link.is-current { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .pagination-ellipsis { + color: #b5b5b5; + pointer-events: none; } + html.theme--documenter-dark .pagination-list { + flex-wrap: wrap; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .pagination { + flex-wrap: wrap; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .pagination-list li { + flex-grow: 1; + flex-shrink: 1; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .pagination-list { + flex-grow: 1; + flex-shrink: 1; + justify-content: flex-start; + order: 1; } + html.theme--documenter-dark .pagination-previous { + order: 2; } + html.theme--documenter-dark .pagination-next { + order: 3; } + html.theme--documenter-dark .pagination { + justify-content: space-between; } + html.theme--documenter-dark .pagination.is-centered .pagination-previous { + order: 1; } + html.theme--documenter-dark .pagination.is-centered .pagination-list { + justify-content: center; + order: 2; } + html.theme--documenter-dark .pagination.is-centered .pagination-next { + order: 3; } + html.theme--documenter-dark .pagination.is-right .pagination-previous { + order: 1; } + html.theme--documenter-dark .pagination.is-right .pagination-next { + order: 2; } + html.theme--documenter-dark .pagination.is-right .pagination-list { + justify-content: flex-end; + order: 3; } } + html.theme--documenter-dark .panel { + font-size: 1rem; } + html.theme--documenter-dark .panel:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .panel-heading, + html.theme--documenter-dark .panel-tabs, + html.theme--documenter-dark .panel-block { + border-bottom: 1px solid #dbdbdb; + border-left: 1px solid #dbdbdb; + border-right: 1px solid #dbdbdb; } + html.theme--documenter-dark .panel-heading:first-child, + html.theme--documenter-dark .panel-tabs:first-child, + html.theme--documenter-dark .panel-block:first-child { + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark .panel-heading { + background-color: whitesmoke; + border-radius: 4px 4px 0 0; + color: #cdc3e3; + font-size: 1.25em; + font-weight: 300; + line-height: 1.25; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .panel-tabs { + align-items: flex-end; + display: flex; + font-size: 0.875em; + justify-content: center; } + html.theme--documenter-dark .panel-tabs a { + border-bottom: 1px solid #dbdbdb; + margin-bottom: -1px; + padding: 0.5em; } + html.theme--documenter-dark .panel-tabs a.is-active { + border-bottom-color: #4a4a4a; + color: #363636; } + html.theme--documenter-dark .panel-list a { + color: #fbfbfb; } + html.theme--documenter-dark .panel-list a:hover { + color: #2ad7e6; } + html.theme--documenter-dark .panel-block { + align-items: center; + color: #cdc3e3; + display: flex; + justify-content: flex-start; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .panel-block input[type="checkbox"] { + margin-right: 0.75em; } + html.theme--documenter-dark .panel-block > .control { + flex-grow: 1; + flex-shrink: 1; + width: 100%; } + html.theme--documenter-dark .panel-block.is-wrapped { + flex-wrap: wrap; } + html.theme--documenter-dark .panel-block.is-active { + border-left-color: #2ad7e6; + color: #363636; } + html.theme--documenter-dark .panel-block.is-active .panel-icon { + color: #2ad7e6; } + html.theme--documenter-dark a.panel-block, + html.theme--documenter-dark label.panel-block { + cursor: pointer; } + html.theme--documenter-dark a.panel-block:hover, + html.theme--documenter-dark label.panel-block:hover { + background-color: whitesmoke; } + html.theme--documenter-dark .panel-icon { + display: inline-block; + font-size: 14px; + height: 1em; + line-height: 1em; + text-align: center; + vertical-align: top; + width: 1em; + color: #7a7a7a; + margin-right: 0.75em; } + html.theme--documenter-dark .panel-icon .fa { + font-size: inherit; + line-height: inherit; } + html.theme--documenter-dark .tabs { + -webkit-overflow-scrolling: touch; + align-items: stretch; + display: flex; + font-size: 1rem; + justify-content: space-between; + overflow: hidden; + overflow-x: auto; + white-space: nowrap; } + html.theme--documenter-dark .tabs a { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + color: #fbfbfb; + display: flex; + justify-content: center; + margin-bottom: -1px; + padding: 0.5em 1em; + vertical-align: top; } + html.theme--documenter-dark .tabs a:hover { + border-bottom-color: #cdc3e3; + color: #cdc3e3; } + html.theme--documenter-dark .tabs li { + display: block; } + html.theme--documenter-dark .tabs li.is-active a { + border-bottom-color: #2ad7e6; + color: #2ad7e6; } + html.theme--documenter-dark .tabs ul { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + display: flex; + flex-grow: 1; + flex-shrink: 0; + justify-content: flex-start; } + html.theme--documenter-dark .tabs ul.is-left { + padding-right: 0.75em; } + html.theme--documenter-dark .tabs ul.is-center { + flex: none; + justify-content: center; + padding-left: 0.75em; + padding-right: 0.75em; } + html.theme--documenter-dark .tabs ul.is-right { + justify-content: flex-end; + padding-left: 0.75em; } + html.theme--documenter-dark .tabs .icon:first-child { + margin-right: 0.5em; } + html.theme--documenter-dark .tabs .icon:last-child { + margin-left: 0.5em; } + html.theme--documenter-dark .tabs.is-centered ul { + justify-content: center; } + html.theme--documenter-dark .tabs.is-right ul { + justify-content: flex-end; } + html.theme--documenter-dark .tabs.is-boxed a { + border: 1px solid transparent; + border-radius: 4px 4px 0 0; } + html.theme--documenter-dark .tabs.is-boxed a:hover { + background-color: whitesmoke; + border-bottom-color: #dbdbdb; } + html.theme--documenter-dark .tabs.is-boxed li.is-active a { + background-color: white; + border-color: #dbdbdb; + border-bottom-color: transparent !important; } + html.theme--documenter-dark .tabs.is-fullwidth li { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .tabs.is-toggle a { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px; + margin-bottom: 0; + position: relative; } + html.theme--documenter-dark .tabs.is-toggle a:hover { + background-color: whitesmoke; + border-color: #b5b5b5; + z-index: 2; } + html.theme--documenter-dark .tabs.is-toggle li + li { + margin-left: -1px; } + html.theme--documenter-dark .tabs.is-toggle li:first-child a { + border-radius: 4px 0 0 4px; } + html.theme--documenter-dark .tabs.is-toggle li:last-child a { + border-radius: 0 4px 4px 0; } + html.theme--documenter-dark .tabs.is-toggle li.is-active a { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; + z-index: 1; } + html.theme--documenter-dark .tabs.is-toggle ul { + border-bottom: none; } + html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:first-child a { + border-bottom-left-radius: 290486px; + border-top-left-radius: 290486px; + padding-left: 1.25em; } + html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:last-child a { + border-bottom-right-radius: 290486px; + border-top-right-radius: 290486px; + padding-right: 1.25em; } + html.theme--documenter-dark .tabs.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.tabs { + font-size: 0.75rem; } + html.theme--documenter-dark .tabs.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .tabs.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .column { + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + padding: 0.75rem; } + .columns.is-mobile > html.theme--documenter-dark .column.is-narrow { + flex: none; } + .columns.is-mobile > html.theme--documenter-dark .column.is-full { + flex: none; + width: 100%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-three-quarters { + flex: none; + width: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-two-thirds { + flex: none; + width: 66.6666%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-half { + flex: none; + width: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-third { + flex: none; + width: 33.3333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-quarter { + flex: none; + width: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-fifth { + flex: none; + width: 20%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-two-fifths { + flex: none; + width: 40%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-three-fifths { + flex: none; + width: 60%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-four-fifths { + flex: none; + width: 80%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-quarters { + margin-left: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-thirds { + margin-left: 66.6666%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-half { + margin-left: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-third { + margin-left: 33.3333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-quarter { + margin-left: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-fifth { + margin-left: 20%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-fifths { + margin-left: 40%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-fifths { + margin-left: 60%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-four-fifths { + margin-left: 80%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-0 { + flex: none; + width: 0%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-0 { + margin-left: 0%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-1 { + flex: none; + width: 8.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-1 { + margin-left: 8.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-2 { + flex: none; + width: 16.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-2 { + margin-left: 16.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-3 { + flex: none; + width: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-3 { + margin-left: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-4 { + flex: none; + width: 33.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-4 { + margin-left: 33.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-5 { + flex: none; + width: 41.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-5 { + margin-left: 41.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-6 { + flex: none; + width: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-6 { + margin-left: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-7 { + flex: none; + width: 58.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-7 { + margin-left: 58.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-8 { + flex: none; + width: 66.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-8 { + margin-left: 66.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-9 { + flex: none; + width: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-9 { + margin-left: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-10 { + flex: none; + width: 83.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-10 { + margin-left: 83.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-11 { + flex: none; + width: 91.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-11 { + margin-left: 91.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-12 { + flex: none; + width: 100%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-12 { + margin-left: 100%; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .column.is-narrow-mobile { + flex: none; } + html.theme--documenter-dark .column.is-full-mobile { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-mobile { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-mobile { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-mobile { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-mobile { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-mobile { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-mobile { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-mobile { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-mobile { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-mobile { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-mobile { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-mobile { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-mobile { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-mobile { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-mobile { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-mobile { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-mobile { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-mobile { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-mobile { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-mobile { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-mobile { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-mobile { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-mobile { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-mobile { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-mobile { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-mobile { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-mobile { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-mobile { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-mobile { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-mobile { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-mobile { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-mobile { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-mobile { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-mobile { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-mobile { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-mobile { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-mobile { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-mobile { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-mobile { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-mobile { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-mobile { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-mobile { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-mobile { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-mobile { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-mobile { + margin-left: 100%; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .column.is-narrow, html.theme--documenter-dark .column.is-narrow-tablet { + flex: none; } + html.theme--documenter-dark .column.is-full, html.theme--documenter-dark .column.is-full-tablet { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters, html.theme--documenter-dark .column.is-three-quarters-tablet { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds, html.theme--documenter-dark .column.is-two-thirds-tablet { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half, html.theme--documenter-dark .column.is-half-tablet { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third, html.theme--documenter-dark .column.is-one-third-tablet { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter, html.theme--documenter-dark .column.is-one-quarter-tablet { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth, html.theme--documenter-dark .column.is-one-fifth-tablet { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths, html.theme--documenter-dark .column.is-two-fifths-tablet { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths, html.theme--documenter-dark .column.is-three-fifths-tablet { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths, html.theme--documenter-dark .column.is-four-fifths-tablet { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters, html.theme--documenter-dark .column.is-offset-three-quarters-tablet { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds, html.theme--documenter-dark .column.is-offset-two-thirds-tablet { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half, html.theme--documenter-dark .column.is-offset-half-tablet { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third, html.theme--documenter-dark .column.is-offset-one-third-tablet { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter, html.theme--documenter-dark .column.is-offset-one-quarter-tablet { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth, html.theme--documenter-dark .column.is-offset-one-fifth-tablet { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths, html.theme--documenter-dark .column.is-offset-two-fifths-tablet { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths, html.theme--documenter-dark .column.is-offset-three-fifths-tablet { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths, html.theme--documenter-dark .column.is-offset-four-fifths-tablet { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0, html.theme--documenter-dark .column.is-0-tablet { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0, html.theme--documenter-dark .column.is-offset-0-tablet { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1, html.theme--documenter-dark .column.is-1-tablet { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1, html.theme--documenter-dark .column.is-offset-1-tablet { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2, html.theme--documenter-dark .column.is-2-tablet { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2, html.theme--documenter-dark .column.is-offset-2-tablet { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3, html.theme--documenter-dark .column.is-3-tablet { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3, html.theme--documenter-dark .column.is-offset-3-tablet { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4, html.theme--documenter-dark .column.is-4-tablet { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4, html.theme--documenter-dark .column.is-offset-4-tablet { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5, html.theme--documenter-dark .column.is-5-tablet { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5, html.theme--documenter-dark .column.is-offset-5-tablet { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6, html.theme--documenter-dark .column.is-6-tablet { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6, html.theme--documenter-dark .column.is-offset-6-tablet { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7, html.theme--documenter-dark .column.is-7-tablet { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7, html.theme--documenter-dark .column.is-offset-7-tablet { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8, html.theme--documenter-dark .column.is-8-tablet { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8, html.theme--documenter-dark .column.is-offset-8-tablet { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9, html.theme--documenter-dark .column.is-9-tablet { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9, html.theme--documenter-dark .column.is-offset-9-tablet { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10, html.theme--documenter-dark .column.is-10-tablet { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10, html.theme--documenter-dark .column.is-offset-10-tablet { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11, html.theme--documenter-dark .column.is-11-tablet { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11, html.theme--documenter-dark .column.is-offset-11-tablet { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12, html.theme--documenter-dark .column.is-12-tablet { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12, html.theme--documenter-dark .column.is-offset-12-tablet { + margin-left: 100%; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .column.is-narrow-touch { + flex: none; } + html.theme--documenter-dark .column.is-full-touch { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-touch { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-touch { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-touch { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-touch { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-touch { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-touch { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-touch { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-touch { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-touch { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-touch { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-touch { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-touch { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-touch { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-touch { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-touch { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-touch { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-touch { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-touch { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-touch { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-touch { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-touch { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-touch { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-touch { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-touch { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-touch { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-touch { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-touch { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-touch { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-touch { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-touch { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-touch { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-touch { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-touch { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-touch { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-touch { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-touch { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-touch { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-touch { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-touch { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-touch { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-touch { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-touch { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-touch { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-touch { + margin-left: 100%; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .column.is-narrow-desktop { + flex: none; } + html.theme--documenter-dark .column.is-full-desktop { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-desktop { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-desktop { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-desktop { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-desktop { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-desktop { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-desktop { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-desktop { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-desktop { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-desktop { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-desktop { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-desktop { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-desktop { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-desktop { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-desktop { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-desktop { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-desktop { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-desktop { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-desktop { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-desktop { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-desktop { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-desktop { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-desktop { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-desktop { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-desktop { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-desktop { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-desktop { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-desktop { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-desktop { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-desktop { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-desktop { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-desktop { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-desktop { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-desktop { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-desktop { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-desktop { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-desktop { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-desktop { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-desktop { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-desktop { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-desktop { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-desktop { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-desktop { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-desktop { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-desktop { + margin-left: 100%; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .column.is-narrow-widescreen { + flex: none; } + html.theme--documenter-dark .column.is-full-widescreen { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-widescreen { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-widescreen { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-widescreen { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-widescreen { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-widescreen { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-widescreen { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-widescreen { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-widescreen { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-widescreen { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-widescreen { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-widescreen { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-widescreen { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-widescreen { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-widescreen { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-widescreen { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-widescreen { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-widescreen { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-widescreen { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-widescreen { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-widescreen { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-widescreen { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-widescreen { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-widescreen { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-widescreen { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-widescreen { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-widescreen { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-widescreen { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-widescreen { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-widescreen { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-widescreen { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-widescreen { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-widescreen { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-widescreen { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-widescreen { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-widescreen { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-widescreen { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-widescreen { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-widescreen { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-widescreen { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-widescreen { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-widescreen { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-widescreen { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-widescreen { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-widescreen { + margin-left: 100%; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .column.is-narrow-fullhd { + flex: none; } + html.theme--documenter-dark .column.is-full-fullhd { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-fullhd { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-fullhd { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-fullhd { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-fullhd { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-fullhd { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-fullhd { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-fullhd { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-fullhd { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-fullhd { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-fullhd { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-fullhd { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-fullhd { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-fullhd { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-fullhd { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-fullhd { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-fullhd { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-fullhd { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-fullhd { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-fullhd { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-fullhd { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-fullhd { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-fullhd { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-fullhd { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-fullhd { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-fullhd { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-fullhd { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-fullhd { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-fullhd { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-fullhd { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-fullhd { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-fullhd { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-fullhd { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-fullhd { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-fullhd { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-fullhd { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-fullhd { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-fullhd { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-fullhd { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-fullhd { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-fullhd { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-fullhd { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-fullhd { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-fullhd { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-fullhd { + margin-left: 100%; } } + html.theme--documenter-dark .columns { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + html.theme--documenter-dark .columns:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .columns:not(:last-child) { + margin-bottom: calc(1.5rem - 0.75rem); } + html.theme--documenter-dark .columns.is-centered { + justify-content: center; } + html.theme--documenter-dark .columns.is-gapless { + margin-left: 0; + margin-right: 0; + margin-top: 0; } + html.theme--documenter-dark .columns.is-gapless > .column { + margin: 0; + padding: 0 !important; } + html.theme--documenter-dark .columns.is-gapless:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .columns.is-gapless:last-child { + margin-bottom: 0; } + html.theme--documenter-dark .columns.is-mobile { + display: flex; } + html.theme--documenter-dark .columns.is-multiline { + flex-wrap: wrap; } + html.theme--documenter-dark .columns.is-vcentered { + align-items: center; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns:not(.is-desktop) { + display: flex; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-desktop { + display: flex; } } + html.theme--documenter-dark .columns.is-variable { + --columnGap: 0.75rem; + margin-left: calc(-1 * var(--columnGap)); + margin-right: calc(-1 * var(--columnGap)); } + html.theme--documenter-dark .columns.is-variable .column { + padding-left: var(--columnGap); + padding-right: var(--columnGap); } + html.theme--documenter-dark .columns.is-variable.is-0 { + --columnGap: 0rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-0-mobile { + --columnGap: 0rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-0-tablet { + --columnGap: 0rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-0-tablet-only { + --columnGap: 0rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-0-touch { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-0-desktop { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-0-desktop-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-0-widescreen { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-0-widescreen-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-0-fullhd { + --columnGap: 0rem; } } + html.theme--documenter-dark .columns.is-variable.is-1 { + --columnGap: 0.25rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-1-mobile { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-1-tablet { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-1-tablet-only { + --columnGap: 0.25rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-1-touch { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-1-desktop { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-1-desktop-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-1-widescreen { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-1-widescreen-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-1-fullhd { + --columnGap: 0.25rem; } } + html.theme--documenter-dark .columns.is-variable.is-2 { + --columnGap: 0.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-2-mobile { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-2-tablet { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-2-tablet-only { + --columnGap: 0.5rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-2-touch { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-2-desktop { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-2-desktop-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-2-widescreen { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-2-widescreen-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-2-fullhd { + --columnGap: 0.5rem; } } + html.theme--documenter-dark .columns.is-variable.is-3 { + --columnGap: 0.75rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-3-mobile { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-3-tablet { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-3-tablet-only { + --columnGap: 0.75rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-3-touch { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-3-desktop { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-3-desktop-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-3-widescreen { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-3-widescreen-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-3-fullhd { + --columnGap: 0.75rem; } } + html.theme--documenter-dark .columns.is-variable.is-4 { + --columnGap: 1rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-4-mobile { + --columnGap: 1rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-4-tablet { + --columnGap: 1rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-4-tablet-only { + --columnGap: 1rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-4-touch { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-4-desktop { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-4-desktop-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-4-widescreen { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-4-widescreen-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-4-fullhd { + --columnGap: 1rem; } } + html.theme--documenter-dark .columns.is-variable.is-5 { + --columnGap: 1.25rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-5-mobile { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-5-tablet { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-5-tablet-only { + --columnGap: 1.25rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-5-touch { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-5-desktop { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-5-desktop-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-5-widescreen { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-5-widescreen-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-5-fullhd { + --columnGap: 1.25rem; } } + html.theme--documenter-dark .columns.is-variable.is-6 { + --columnGap: 1.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-6-mobile { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-6-tablet { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-6-tablet-only { + --columnGap: 1.5rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-6-touch { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-6-desktop { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-6-desktop-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-6-widescreen { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-6-widescreen-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-6-fullhd { + --columnGap: 1.5rem; } } + html.theme--documenter-dark .columns.is-variable.is-7 { + --columnGap: 1.75rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-7-mobile { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-7-tablet { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-7-tablet-only { + --columnGap: 1.75rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-7-touch { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-7-desktop { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-7-desktop-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-7-widescreen { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-7-fullhd { + --columnGap: 1.75rem; } } + html.theme--documenter-dark .columns.is-variable.is-8 { + --columnGap: 2rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-8-mobile { + --columnGap: 2rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-8-tablet { + --columnGap: 2rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-8-tablet-only { + --columnGap: 2rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-8-touch { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-8-desktop { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-8-desktop-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-8-widescreen { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-8-widescreen-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-8-fullhd { + --columnGap: 2rem; } } + html.theme--documenter-dark .tile { + align-items: stretch; + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + min-height: min-content; } + html.theme--documenter-dark .tile.is-ancestor { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + html.theme--documenter-dark .tile.is-ancestor:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .tile.is-ancestor:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .tile.is-child { + margin: 0 !important; } + html.theme--documenter-dark .tile.is-parent { + padding: 0.75rem; } + html.theme--documenter-dark .tile.is-vertical { + flex-direction: column; } + html.theme--documenter-dark .tile.is-vertical > .tile.is-child:not(:last-child) { + margin-bottom: 1.5rem !important; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .tile:not(.is-child) { + display: flex; } + html.theme--documenter-dark .tile.is-1 { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .tile.is-2 { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .tile.is-3 { + flex: none; + width: 25%; } + html.theme--documenter-dark .tile.is-4 { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .tile.is-5 { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .tile.is-6 { + flex: none; + width: 50%; } + html.theme--documenter-dark .tile.is-7 { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .tile.is-8 { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .tile.is-9 { + flex: none; + width: 75%; } + html.theme--documenter-dark .tile.is-10 { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .tile.is-11 { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .tile.is-12 { + flex: none; + width: 100%; } } + html.theme--documenter-dark .hero { + align-items: stretch; + display: flex; + flex-direction: column; + justify-content: space-between; } + html.theme--documenter-dark .hero .navbar { + background: none; } + html.theme--documenter-dark .hero .tabs ul { + border-bottom: none; } + html.theme--documenter-dark .hero.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-white strong { + color: inherit; } + html.theme--documenter-dark .hero.is-white .title { + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .subtitle { + color: rgba(10, 10, 10, 0.9); } + html.theme--documenter-dark .hero.is-white .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-white .subtitle strong { + color: #0a0a0a; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-white .navbar-menu { + background-color: white; } } + html.theme--documenter-dark .hero.is-white .navbar-item, + html.theme--documenter-dark .hero.is-white .navbar-link { + color: rgba(10, 10, 10, 0.7); } + html.theme--documenter-dark .hero.is-white a.navbar-item:hover, html.theme--documenter-dark .hero.is-white a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-white .navbar-link:hover, + html.theme--documenter-dark .hero.is-white .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .tabs a { + color: #0a0a0a; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-white .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-white .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a { + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a:hover { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .hero.is-white.is-bold { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-white.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } + html.theme--documenter-dark .hero.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-black strong { + color: inherit; } + html.theme--documenter-dark .hero.is-black .title { + color: white; } + html.theme--documenter-dark .hero.is-black .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-black .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-black .subtitle strong { + color: white; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-black .navbar-menu { + background-color: #0a0a0a; } } + html.theme--documenter-dark .hero.is-black .navbar-item, + html.theme--documenter-dark .hero.is-black .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-black a.navbar-item:hover, html.theme--documenter-dark .hero.is-black a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-black .navbar-link:hover, + html.theme--documenter-dark .hero.is-black .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .hero.is-black .tabs a { + color: white; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-black .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-black .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a { + color: white; } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a:hover { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-black.is-bold { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-black.is-bold .navbar-menu { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } + html.theme--documenter-dark .hero.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-light strong { + color: inherit; } + html.theme--documenter-dark .hero.is-light .title { + color: #363636; } + html.theme--documenter-dark .hero.is-light .subtitle { + color: rgba(54, 54, 54, 0.9); } + html.theme--documenter-dark .hero.is-light .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-light .subtitle strong { + color: #363636; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-light .navbar-menu { + background-color: whitesmoke; } } + html.theme--documenter-dark .hero.is-light .navbar-item, + html.theme--documenter-dark .hero.is-light .navbar-link { + color: rgba(54, 54, 54, 0.7); } + html.theme--documenter-dark .hero.is-light a.navbar-item:hover, html.theme--documenter-dark .hero.is-light a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-light .navbar-link:hover, + html.theme--documenter-dark .hero.is-light .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .hero.is-light .tabs a { + color: #363636; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-light .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-light .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a { + color: #363636; } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a:hover { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-light.is-bold { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-light.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } } + html.theme--documenter-dark .hero.is-dark, html.theme--documenter-dark .content kbd.hero { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-dark strong, + html.theme--documenter-dark .content kbd.hero strong { + color: inherit; } + html.theme--documenter-dark .hero.is-dark .title, html.theme--documenter-dark .content kbd.hero .title { + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .subtitle, html.theme--documenter-dark .content kbd.hero .subtitle { + color: rgba(245, 245, 245, 0.9); } + html.theme--documenter-dark .hero.is-dark .subtitle a:not(.button), html.theme--documenter-dark .content kbd.hero .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-dark .subtitle strong, + html.theme--documenter-dark .content kbd.hero .subtitle strong { + color: whitesmoke; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-dark .navbar-menu, html.theme--documenter-dark .content kbd.hero .navbar-menu { + background-color: #363636; } } + html.theme--documenter-dark .hero.is-dark .navbar-item, html.theme--documenter-dark .content kbd.hero .navbar-item, + html.theme--documenter-dark .hero.is-dark .navbar-link, + html.theme--documenter-dark .content kbd.hero .navbar-link { + color: rgba(245, 245, 245, 0.7); } + html.theme--documenter-dark .hero.is-dark a.navbar-item:hover, html.theme--documenter-dark .content kbd.hero a.navbar-item:hover, html.theme--documenter-dark .hero.is-dark a.navbar-item.is-active, html.theme--documenter-dark .content kbd.hero a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-dark .navbar-link:hover, + html.theme--documenter-dark .content kbd.hero .navbar-link:hover, + html.theme--documenter-dark .hero.is-dark .navbar-link.is-active, + html.theme--documenter-dark .content kbd.hero .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .tabs a, html.theme--documenter-dark .content kbd.hero .tabs a { + color: whitesmoke; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-dark .tabs a:hover, html.theme--documenter-dark .content kbd.hero .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-dark .tabs li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a { + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a:hover { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .hero.is-dark.is-bold, html.theme--documenter-dark .content kbd.hero.is-bold { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-dark.is-bold .navbar-menu, html.theme--documenter-dark .content kbd.hero.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } } + html.theme--documenter-dark .hero.is-primary, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-primary strong, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink strong { + color: inherit; } + html.theme--documenter-dark .hero.is-primary .title, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .title { + color: #fff; } + html.theme--documenter-dark .hero.is-primary .subtitle, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-primary .subtitle a:not(.button), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-primary .subtitle strong, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-primary .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-menu { + background-color: #4eb5de; } } + html.theme--documenter-dark .hero.is-primary .navbar-item, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-item, + html.theme--documenter-dark .hero.is-primary .navbar-link, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-primary a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, html.theme--documenter-dark .hero.is-primary a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-primary .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, + html.theme--documenter-dark .hero.is-primary .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .hero.is-primary .tabs a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-primary .tabs a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-primary .tabs li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .hero.is-primary.is-bold, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-primary.is-bold .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } } + html.theme--documenter-dark .hero.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-link strong { + color: inherit; } + html.theme--documenter-dark .hero.is-link .title { + color: #fff; } + html.theme--documenter-dark .hero.is-link .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-link .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-link .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-link .navbar-menu { + background-color: #2ad7e6; } } + html.theme--documenter-dark .hero.is-link .navbar-item, + html.theme--documenter-dark .hero.is-link .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-link a.navbar-item:hover, html.theme--documenter-dark .hero.is-link a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-link .navbar-link:hover, + html.theme--documenter-dark .hero.is-link .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .hero.is-link .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-link .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-link .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .hero.is-link.is-bold { + background-image: linear-gradient(141deg, #0cd0bf 0%, #2ad7e6 71%, #3bc2ee 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-link.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #0cd0bf 0%, #2ad7e6 71%, #3bc2ee 100%); } } + html.theme--documenter-dark .hero.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-info strong { + color: inherit; } + html.theme--documenter-dark .hero.is-info .title { + color: #fff; } + html.theme--documenter-dark .hero.is-info .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-info .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-info .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-info .navbar-menu { + background-color: #3489da; } } + html.theme--documenter-dark .hero.is-info .navbar-item, + html.theme--documenter-dark .hero.is-info .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-info a.navbar-item:hover, html.theme--documenter-dark .hero.is-info a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-info .navbar-link:hover, + html.theme--documenter-dark .hero.is-info .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .hero.is-info .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-info .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-info .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #3489da; } + html.theme--documenter-dark .hero.is-info.is-bold { + background-image: linear-gradient(141deg, #178cc4 0%, #3489da 71%, #447be3 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-info.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #178cc4 0%, #3489da 71%, #447be3 100%); } } + html.theme--documenter-dark .hero.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-success strong { + color: inherit; } + html.theme--documenter-dark .hero.is-success .title { + color: #fff; } + html.theme--documenter-dark .hero.is-success .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-success .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-success .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-success .navbar-menu { + background-color: #259a12; } } + html.theme--documenter-dark .hero.is-success .navbar-item, + html.theme--documenter-dark .hero.is-success .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-success a.navbar-item:hover, html.theme--documenter-dark .hero.is-success a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-success .navbar-link:hover, + html.theme--documenter-dark .hero.is-success .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .hero.is-success .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-success .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-success .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #259a12; } + html.theme--documenter-dark .hero.is-success.is-bold { + background-image: linear-gradient(141deg, #287207 0%, #259a12 71%, #10b614 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-success.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #287207 0%, #259a12 71%, #10b614 100%); } } + html.theme--documenter-dark .hero.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-warning strong { + color: inherit; } + html.theme--documenter-dark .hero.is-warning .title { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .subtitle { + color: rgba(0, 0, 0, 0.9); } + html.theme--documenter-dark .hero.is-warning .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-warning .subtitle strong { + color: rgba(0, 0, 0, 0.7); } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-warning .navbar-menu { + background-color: #f4c72f; } } + html.theme--documenter-dark .hero.is-warning .navbar-item, + html.theme--documenter-dark .hero.is-warning .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning a.navbar-item:hover, html.theme--documenter-dark .hero.is-warning a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-warning .navbar-link:hover, + html.theme--documenter-dark .hero.is-warning .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .tabs a { + color: rgba(0, 0, 0, 0.7); + opacity: 0.9; } + html.theme--documenter-dark .hero.is-warning .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-warning .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a:hover { + background-color: rgba(0, 0, 0, 0.7); + border-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .hero.is-warning.is-bold { + background-image: linear-gradient(141deg, #f09100 0%, #f4c72f 71%, #faef42 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-warning.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #f09100 0%, #f4c72f 71%, #faef42 100%); } } + html.theme--documenter-dark .hero.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-danger strong { + color: inherit; } + html.theme--documenter-dark .hero.is-danger .title { + color: #fff; } + html.theme--documenter-dark .hero.is-danger .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-danger .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-danger .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-danger .navbar-menu { + background-color: #cb3c33; } } + html.theme--documenter-dark .hero.is-danger .navbar-item, + html.theme--documenter-dark .hero.is-danger .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-danger a.navbar-item:hover, html.theme--documenter-dark .hero.is-danger a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-danger .navbar-link:hover, + html.theme--documenter-dark .hero.is-danger .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .hero.is-danger .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-danger .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-danger .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .hero.is-danger.is-bold { + background-image: linear-gradient(141deg, #ac1f2e 0%, #cb3c33 71%, #d66341 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-danger.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #ac1f2e 0%, #cb3c33 71%, #d66341 100%); } } + html.theme--documenter-dark .hero.is-small .hero-body, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.hero .hero-body { + padding-bottom: 1.5rem; + padding-top: 1.5rem; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero.is-medium .hero-body { + padding-bottom: 9rem; + padding-top: 9rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero.is-large .hero-body { + padding-bottom: 18rem; + padding-top: 18rem; } } + html.theme--documenter-dark .hero.is-halfheight .hero-body, html.theme--documenter-dark .hero.is-fullheight .hero-body, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body { + align-items: center; + display: flex; } + html.theme--documenter-dark .hero.is-halfheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body > .container { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .hero.is-halfheight { + min-height: 50vh; } + html.theme--documenter-dark .hero.is-fullheight { + min-height: 100vh; } + html.theme--documenter-dark .hero-video { + overflow: hidden; } + html.theme--documenter-dark .hero-video video { + left: 50%; + min-height: 100%; + min-width: 100%; + position: absolute; + top: 50%; + transform: translate3d(-50%, -50%, 0); } + html.theme--documenter-dark .hero-video.is-transparent { + opacity: 0.3; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero-video { + display: none; } } + html.theme--documenter-dark .hero-buttons { + margin-top: 1.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero-buttons .button { + display: flex; } + html.theme--documenter-dark .hero-buttons .button:not(:last-child) { + margin-bottom: 0.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero-buttons { + display: flex; + justify-content: center; } + html.theme--documenter-dark .hero-buttons .button:not(:last-child) { + margin-right: 1.5rem; } } + html.theme--documenter-dark .hero-head, + html.theme--documenter-dark .hero-foot { + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .hero-body { + flex-grow: 1; + flex-shrink: 0; + padding: 3rem 1.5rem; } + html.theme--documenter-dark .section { + padding: 3rem 1.5rem; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .section.is-medium { + padding: 9rem 1.5rem; } + html.theme--documenter-dark .section.is-large { + padding: 18rem 1.5rem; } } + html.theme--documenter-dark .footer { + background-color: #fafafa; + padding: 3rem 1.5rem 6rem; } + html.theme--documenter-dark h1 .docs-heading-anchor, html.theme--documenter-dark h1 .docs-heading-anchor:hover, html.theme--documenter-dark h1 .docs-heading-anchor:visited, html.theme--documenter-dark h2 .docs-heading-anchor, html.theme--documenter-dark h2 .docs-heading-anchor:hover, html.theme--documenter-dark h2 .docs-heading-anchor:visited, html.theme--documenter-dark h3 .docs-heading-anchor, html.theme--documenter-dark h3 .docs-heading-anchor:hover, html.theme--documenter-dark h3 .docs-heading-anchor:visited, html.theme--documenter-dark h4 .docs-heading-anchor, html.theme--documenter-dark h4 .docs-heading-anchor:hover, html.theme--documenter-dark h4 .docs-heading-anchor:visited, html.theme--documenter-dark h5 .docs-heading-anchor, html.theme--documenter-dark h5 .docs-heading-anchor:hover, html.theme--documenter-dark h5 .docs-heading-anchor:visited, html.theme--documenter-dark h6 .docs-heading-anchor, html.theme--documenter-dark h6 .docs-heading-anchor:hover, html.theme--documenter-dark h6 .docs-heading-anchor:visited { + color: #cdc3e3; } + html.theme--documenter-dark h1 .docs-heading-anchor-permalink, html.theme--documenter-dark h2 .docs-heading-anchor-permalink, html.theme--documenter-dark h3 .docs-heading-anchor-permalink, html.theme--documenter-dark h4 .docs-heading-anchor-permalink, html.theme--documenter-dark h5 .docs-heading-anchor-permalink, html.theme--documenter-dark h6 .docs-heading-anchor-permalink { + visibility: hidden; + vertical-align: middle; + margin-left: 0.5em; + font-size: 0.7rem; } + html.theme--documenter-dark h1 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h2 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h3 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h4 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h5 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h6 .docs-heading-anchor-permalink::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f0c1"; } + html.theme--documenter-dark h1:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h2:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h3:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h4:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h5:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h6:hover .docs-heading-anchor-permalink { + visibility: visible; } + html.theme--documenter-dark .docs-light-only { + display: none !important; } + html.theme--documenter-dark pre { + position: relative; + overflow: hidden; } + html.theme--documenter-dark pre code, html.theme--documenter-dark pre code.hljs { + padding: 0 0.75rem !important; + overflow: auto; + display: block; } + html.theme--documenter-dark pre code:first-of-type, html.theme--documenter-dark pre code.hljs:first-of-type { + padding-top: 0.5rem !important; } + html.theme--documenter-dark pre code:last-of-type, html.theme--documenter-dark pre code.hljs:last-of-type { + padding-bottom: 0.5rem !important; } + html.theme--documenter-dark pre .copy-button { + opacity: 0.2; + transition: opacity 0.2s; + position: absolute; + right: 0em; + top: 0em; + padding: 0.5em; + width: 2.5em; + height: 2.5em; + background: transparent; + border: none; + font-family: "Font Awesome 5 Free"; + color: #fbfbfb; + cursor: pointer; + text-align: center; } + html.theme--documenter-dark pre .copy-button:focus, html.theme--documenter-dark pre .copy-button:hover { + opacity: 1; + background: rgba(251, 251, 251, 0.1); + color: #2ad7e6; } + html.theme--documenter-dark pre .copy-button.success { + color: #259a12; + opacity: 1; } + html.theme--documenter-dark pre .copy-button.error { + color: #cb3c33; + opacity: 1; } + html.theme--documenter-dark pre:hover .copy-button { + opacity: 1; } + html.theme--documenter-dark .admonition { + background-color: #28282b; + border-style: solid; + border-width: 1px; + border-color: #ba3f1f; + border-radius: 4px; + font-size: 1rem; } + html.theme--documenter-dark .admonition strong { + color: currentColor; } + html.theme--documenter-dark .admonition.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.admonition { + font-size: 0.75rem; } + html.theme--documenter-dark .admonition.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .admonition.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .admonition.is-default { + background-color: #28282b; + border-color: #ba3f1f; } + html.theme--documenter-dark .admonition.is-default > .admonition-header { + background-color: #ba3f1f; } + html.theme--documenter-dark .admonition.is-info { + background-color: #28282b; + border-color: #28c; } + html.theme--documenter-dark .admonition.is-info > .admonition-header { + background-color: #28c; } + html.theme--documenter-dark .admonition.is-success { + background-color: #28282b; + border-color: #42ac68; } + html.theme--documenter-dark .admonition.is-success > .admonition-header { + background-color: #42ac68; } + html.theme--documenter-dark .admonition.is-warning { + background-color: #28282b; + border-color: #a88b17; } + html.theme--documenter-dark .admonition.is-warning > .admonition-header { + background-color: #a88b17; } + html.theme--documenter-dark .admonition.is-danger { + background-color: #28282b; + border-color: #c7524c; } + html.theme--documenter-dark .admonition.is-danger > .admonition-header { + background-color: #c7524c; } + html.theme--documenter-dark .admonition.is-compat { + background-color: #28282b; + border-color: #00a1b7; } + html.theme--documenter-dark .admonition.is-compat > .admonition-header { + background-color: #00a1b7; } + html.theme--documenter-dark .admonition-header { + background-color: #ba3f1f; + align-items: center; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.5rem 0.75rem; + position: relative; } + html.theme--documenter-dark .admonition-header:before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + margin-right: 0.75rem; + content: "\f06a"; } + html.theme--documenter-dark .admonition-body { + color: #fbfbfb; + padding: 0.5rem 0.75rem; } + html.theme--documenter-dark .admonition-body pre { + background-color: #312550; } + html.theme--documenter-dark .admonition-body code { + background-color: #312550; } + html.theme--documenter-dark .docstring { + margin-bottom: 1em; + background-color: transparent; + border: 1px solid #dbdbdb; + box-shadow: 3px 3px 4px #444444; + max-width: 100%; } + html.theme--documenter-dark .docstring > header { + display: flex; + flex-grow: 1; + align-items: stretch; + padding: 0.5rem 0.75rem; + background-color: #28282b; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + box-shadow: none; + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .docstring > header code { + background-color: transparent; } + html.theme--documenter-dark .docstring > header .docstring-binding { + margin-right: 0.3em; } + html.theme--documenter-dark .docstring > header .docstring-category { + margin-left: 0.3em; } + html.theme--documenter-dark .docstring > section { + position: relative; + padding: 0.75rem 0.75rem; + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .docstring > section:last-child { + border-bottom: none; } + html.theme--documenter-dark .docstring > section > a.docs-sourcelink { + transition: opacity 0.3s; + opacity: 0; + position: absolute; + right: 0.375rem; + bottom: 0.375rem; } + html.theme--documenter-dark .docstring > section > a.docs-sourcelink:focus { + opacity: 1 !important; } + html.theme--documenter-dark .docstring:hover > section > a.docs-sourcelink { + opacity: 0.2; } + html.theme--documenter-dark .docstring:focus-within > section > a.docs-sourcelink { + opacity: 0.2; } + html.theme--documenter-dark .docstring > section:hover a.docs-sourcelink { + opacity: 1; } + html.theme--documenter-dark .documenter-example-output { + background-color: #1e1e20; } + html.theme--documenter-dark .outdated-warning-overlay { + position: fixed; + top: 0; + left: 0; + right: 0; + box-shadow: 0 0 10px rgba(0, 0, 0, 0.3); + z-index: 999; + background-color: #28282b; + border-bottom: 3px solid #c7524c; + padding: 10px 35px; + text-align: center; + font-size: 15px; } + html.theme--documenter-dark .outdated-warning-overlay .outdated-warning-closer { + position: absolute; + top: calc(50% - 10px); + right: 18px; + cursor: pointer; + width: 12px; } + html.theme--documenter-dark .outdated-warning-overlay a { + color: #2ad7e6; } + html.theme--documenter-dark .outdated-warning-overlay a:hover { + color: #97ebf3; } + html.theme--documenter-dark .content pre { + border: 1px solid #dbdbdb; } + html.theme--documenter-dark .content code { + font-weight: inherit; } + html.theme--documenter-dark .content a code { + color: #2ad7e6; } + html.theme--documenter-dark .content h1 code, html.theme--documenter-dark .content h2 code, html.theme--documenter-dark .content h3 code, html.theme--documenter-dark .content h4 code, html.theme--documenter-dark .content h5 code, html.theme--documenter-dark .content h6 code { + color: #cdc3e3; } + html.theme--documenter-dark .content table { + display: block; + width: initial; + max-width: 100%; + overflow-x: auto; } + html.theme--documenter-dark .content blockquote > ul:first-child, html.theme--documenter-dark .content blockquote > ol:first-child, html.theme--documenter-dark .content .admonition-body > ul:first-child, html.theme--documenter-dark .content .admonition-body > ol:first-child { + margin-top: 0; } + html.theme--documenter-dark pre, html.theme--documenter-dark code { + font-variant-ligatures: no-contextual; } + html.theme--documenter-dark .breadcrumb a.is-disabled { + cursor: default; + pointer-events: none; } + html.theme--documenter-dark .breadcrumb a.is-disabled, html.theme--documenter-dark .breadcrumb a.is-disabled:hover { + color: #cdc3e3; } + html.theme--documenter-dark .hljs { + background: initial !important; } + html.theme--documenter-dark .katex .katex-mathml { + top: 0; + right: 0; } + html.theme--documenter-dark .katex-display, html.theme--documenter-dark mjx-container, html.theme--documenter-dark .MathJax_Display { + margin: 0.5em 0 !important; } + html.theme--documenter-dark html { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; } + html.theme--documenter-dark li.no-marker { + list-style: none; } + html.theme--documenter-dark #documenter .docs-main > article { + overflow-wrap: break-word; } + html.theme--documenter-dark #documenter .docs-main > article .math-container { + overflow-x: auto; + overflow-y: hidden; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-main { + max-width: 52rem; + margin-left: 20rem; + padding-right: 1rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main { + width: 100%; } + html.theme--documenter-dark #documenter .docs-main > article { + max-width: 52rem; + margin-left: auto; + margin-right: auto; + margin-bottom: 1rem; + padding: 0 1rem; } + html.theme--documenter-dark #documenter .docs-main > header, html.theme--documenter-dark #documenter .docs-main > nav { + max-width: 100%; + width: 100%; + margin: 0; } } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar { + background-color: #1e1e20; + border-bottom: 1px solid #dbdbdb; + z-index: 2; + min-height: 4rem; + margin-bottom: 1rem; + display: flex; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .breadcrumb { + flex-grow: 1; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right { + display: flex; + white-space: nowrap; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-icon, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + display: inline-block; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label { + padding: 0; + margin-left: 0.3em; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button { + margin: auto 0 auto 1rem; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + font-size: 1.5rem; + margin: auto 0 auto 1rem; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar > * { + margin: auto 0; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main header.docs-navbar { + position: sticky; + top: 0; + padding: 0 1rem; + /* For Headroom.js */ + transition-property: top, box-shadow; + -webkit-transition-property: top, box-shadow; + /* Safari */ + transition-duration: 0.3s; + -webkit-transition-duration: 0.3s; + /* Safari */ } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--not-top { + box-shadow: 0.2rem 0rem 0.4rem #bbb; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { + top: -4.5rem; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } } + html.theme--documenter-dark #documenter .docs-main section.footnotes { + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-main section.footnotes li .tag:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .content kbd:first-child, html.theme--documenter-dark .content #documenter .docs-main section.footnotes li kbd:first-child { + margin-right: 1em; + margin-bottom: 0.4em; } + html.theme--documenter-dark #documenter .docs-main .docs-footer { + display: flex; + flex-wrap: wrap; + margin-left: 0; + margin-right: 0; + border-top: 1px solid #dbdbdb; + padding-top: 1rem; + padding-bottom: 1rem; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main .docs-footer { + padding-left: 1rem; + padding-right: 1rem; } } + html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage, html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-prevpage { + flex-grow: 1; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage { + text-align: right; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .flexbox-break { + flex-basis: 100%; + height: 0; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .footer-message { + font-size: 0.8em; + margin: 0.5em auto 0 auto; + text-align: center; } + html.theme--documenter-dark #documenter .docs-sidebar { + display: flex; + flex-direction: column; + color: #fbfbfb; + background-color: #503c82; + border-right: 1px solid #dbdbdb; + padding: 0; + flex: 0 0 18rem; + z-index: 5; + font-size: 1rem; + position: fixed; + left: -18rem; + width: 18rem; + height: 100%; + transition: left 0.3s; + /* Setting up a nicer theme style for the scrollbar */ } + html.theme--documenter-dark #documenter .docs-sidebar.visible { + left: 0; + box-shadow: 0.4rem 0rem 0.8rem #bbb; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar.visible { + box-shadow: none; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar { + left: 0; + top: 0; } } + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo { + margin-top: 1rem; + padding: 0 1rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { + max-height: 6rem; + margin: auto; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name { + flex-shrink: 0; + font-size: 1.5rem; + font-weight: 700; + text-align: center; + white-space: nowrap; + overflow: hidden; + padding: 0.5rem 0; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name .docs-autofit { + max-width: 16.2rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a, html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a:hover { + color: #fbfbfb; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector { + border-top: 1px solid #dbdbdb; + display: none; + padding: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector.visible { + display: flex; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { + flex-grow: 1; + user-select: none; + border-top: 1px solid #dbdbdb; + padding-bottom: 1.5rem; + /* Managing collapsible submenus */ } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li > .tocitem { + font-weight: bold; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li li { + font-size: 0.95rem; + margin-left: 1em; + border-left: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input.collapse-toggle { + display: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.collapsed { + display: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed { + display: block; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem { + display: flex; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label { + flex-grow: 2; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron { + display: inline-block; + font-style: normal; + font-variant: normal; + text-rendering: auto; + line-height: 1; + font-size: 0.75rem; + margin-left: 1rem; + margin-top: auto; + margin-bottom: auto; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f054"; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before { + content: "\f078"; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem { + display: block; + padding: 0.5rem 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem:hover { + color: #fbfbfb; + background: #503c82; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem:hover { + color: #fbfbfb; + background-color: #3c2d60; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active { + border-top: 1px solid #dbdbdb; + border-bottom: 1px solid #dbdbdb; + background-color: #1e1e20; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover { + background-color: #1e1e20; + color: #fff; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover { + background-color: #3f2f66; + color: #fff; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child { + border-top: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal { + margin: 0 0.5rem 0.5rem; + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal li { + font-size: 0.85rem; + border-left: none; + margin-left: 0; + margin-top: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem { + width: 100%; + padding: 0; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before { + content: "⚬"; + margin-right: 0.4em; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search { + margin: auto; + margin-top: 0.5rem; + margin-bottom: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + width: 14.4rem; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar { + width: .3rem; + background: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #3f2f66; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover { + background: #2e224a; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-sidebar { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar { + width: .3rem; + background: none; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #3f2f66; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover { + background: #2e224a; } } + html.theme--documenter-dark #documenter .docs-main #documenter-search-info { + margin-bottom: 1rem; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results { + list-style-type: circle; + list-style-position: outside; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results li { + margin-left: 2rem; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results .docs-highlight { + background-color: yellow; } + html.theme--documenter-dark { + background-color: #1e1e20; + font-size: 16px; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + html.theme--documenter-dark #documenter .docs-sidebar { + border-right: none; + box-shadow: 0.24rem 0rem 0.4rem #444444; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + color: #fff; + background-color: #3f2f66; + border-color: #2e224a; + margin-top: 1.0rem; + margin-bottom: 1.0rem; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::placeholder { + color: #fff; } + html.theme--documenter-dark .hljs { + background: #2b2b2b; + color: #f8f8f2; } + html.theme--documenter-dark .hljs-comment, + html.theme--documenter-dark .hljs-quote { + color: #d4d0ab; } + html.theme--documenter-dark .hljs-variable, + html.theme--documenter-dark .hljs-template-variable, + html.theme--documenter-dark .hljs-tag, + html.theme--documenter-dark .hljs-name, + html.theme--documenter-dark .hljs-selector-id, + html.theme--documenter-dark .hljs-selector-class, + html.theme--documenter-dark .hljs-regexp, + html.theme--documenter-dark .hljs-deletion { + color: #ffa07a; } + html.theme--documenter-dark .hljs-number, + html.theme--documenter-dark .hljs-built_in, + html.theme--documenter-dark .hljs-literal, + html.theme--documenter-dark .hljs-type, + html.theme--documenter-dark .hljs-params, + html.theme--documenter-dark .hljs-meta, + html.theme--documenter-dark .hljs-link { + color: #f5ab35; } + html.theme--documenter-dark .hljs-attribute { + color: #ffd700; } + html.theme--documenter-dark .hljs-string, + html.theme--documenter-dark .hljs-symbol, + html.theme--documenter-dark .hljs-bullet, + html.theme--documenter-dark .hljs-addition { + color: #abe338; } + html.theme--documenter-dark .hljs-title, + html.theme--documenter-dark .hljs-section { + color: #00e0e0; } + html.theme--documenter-dark .hljs-keyword, + html.theme--documenter-dark .hljs-selector-tag { + color: #dcc6e0; } + html.theme--documenter-dark .hljs-emphasis { + font-style: italic; } + html.theme--documenter-dark .hljs-strong { + font-weight: bold; } + @media screen and (-ms-high-contrast: active) { + html.theme--documenter-dark .hljs-addition, + html.theme--documenter-dark .hljs-attribute, + html.theme--documenter-dark .hljs-built_in, + html.theme--documenter-dark .hljs-bullet, + html.theme--documenter-dark .hljs-comment, + html.theme--documenter-dark .hljs-link, + html.theme--documenter-dark .hljs-literal, + html.theme--documenter-dark .hljs-meta, + html.theme--documenter-dark .hljs-number, + html.theme--documenter-dark .hljs-params, + html.theme--documenter-dark .hljs-string, + html.theme--documenter-dark .hljs-symbol, + html.theme--documenter-dark .hljs-type, + html.theme--documenter-dark .hljs-quote { + color: highlight; } + html.theme--documenter-dark .hljs-keyword, + html.theme--documenter-dark .hljs-selector-tag { + font-weight: bold; } } + html.theme--documenter-dark .hljs-subst { + color: #f8f8f2; } diff --git a/previews/PR19/assets/themes/documenter-light.css b/previews/PR19/assets/themes/documenter-light.css new file mode 100644 index 00000000..e2c74638 --- /dev/null +++ b/previews/PR19/assets/themes/documenter-light.css @@ -0,0 +1,7750 @@ +@charset "UTF-8"; +/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */ +@keyframes spinAround { + from { + transform: rotate(0deg); } + to { + transform: rotate(359deg); } } + +.tabs, .pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis, .breadcrumb, .file, .button, .is-unselectable, .modal-close, .delete { + -webkit-touch-callout: none; + -webkit-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; } + +.navbar-link:not(.is-arrowless)::after, .select:not(.is-multiple):not(.is-loading)::after { + border: 3px solid transparent; + border-radius: 2px; + border-right: 0; + border-top: 0; + content: " "; + display: block; + height: 0.625em; + margin-top: -0.4375em; + pointer-events: none; + position: absolute; + top: 50%; + transform: rotate(-45deg); + transform-origin: center; + width: 0.625em; } + +.admonition:not(:last-child), .tabs:not(:last-child), .message:not(:last-child), .list:not(:last-child), .level:not(:last-child), .breadcrumb:not(:last-child), .highlight:not(:last-child), .block:not(:last-child), .title:not(:last-child), +.subtitle:not(:last-child), .table-container:not(:last-child), .table:not(:last-child), .progress:not(:last-child), .notification:not(:last-child), .content:not(:last-child), .box:not(:last-child) { + margin-bottom: 1.5rem; } + +.modal-close, .delete { + -moz-appearance: none; + -webkit-appearance: none; + background-color: rgba(10, 10, 10, 0.2); + border: none; + border-radius: 290486px; + cursor: pointer; + pointer-events: auto; + display: inline-block; + flex-grow: 0; + flex-shrink: 0; + font-size: 0; + height: 20px; + max-height: 20px; + max-width: 20px; + min-height: 20px; + min-width: 20px; + outline: none; + position: relative; + vertical-align: top; + width: 20px; } + .modal-close::before, .delete::before, .modal-close::after, .delete::after { + background-color: white; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + .modal-close::before, .delete::before { + height: 2px; + width: 50%; } + .modal-close::after, .delete::after { + height: 50%; + width: 2px; } + .modal-close:hover, .delete:hover, .modal-close:focus, .delete:focus { + background-color: rgba(10, 10, 10, 0.3); } + .modal-close:active, .delete:active { + background-color: rgba(10, 10, 10, 0.4); } + .is-small.modal-close, #documenter .docs-sidebar form.docs-search > input.modal-close, .is-small.delete, #documenter .docs-sidebar form.docs-search > input.delete { + height: 16px; + max-height: 16px; + max-width: 16px; + min-height: 16px; + min-width: 16px; + width: 16px; } + .is-medium.modal-close, .is-medium.delete { + height: 24px; + max-height: 24px; + max-width: 24px; + min-height: 24px; + min-width: 24px; + width: 24px; } + .is-large.modal-close, .is-large.delete { + height: 32px; + max-height: 32px; + max-width: 32px; + min-height: 32px; + min-width: 32px; + width: 32px; } + +.control.is-loading::after, .select.is-loading::after, .loader, .button.is-loading::after { + animation: spinAround 500ms infinite linear; + border: 2px solid #dbdbdb; + border-radius: 290486px; + border-right-color: transparent; + border-top-color: transparent; + content: ""; + display: block; + height: 1em; + position: relative; + width: 1em; } + +.hero-video, .modal-background, .modal, .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img, +.image.is-square .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img, +.image.is-1by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img, +.image.is-5by4 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img, +.image.is-4by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img, +.image.is-3by2 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img, +.image.is-5by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img, +.image.is-16by9 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img, +.image.is-2by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img, +.image.is-3by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img, +.image.is-4by5 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img, +.image.is-3by4 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img, +.image.is-2by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img, +.image.is-3by5 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img, +.image.is-9by16 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img, +.image.is-1by2 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img, +.image.is-1by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, .is-overlay { + bottom: 0; + left: 0; + position: absolute; + right: 0; + top: 0; } + +.pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis, .file-cta, +.file-name, .select select, .textarea, .input, #documenter .docs-sidebar form.docs-search > input, .button { + -moz-appearance: none; + -webkit-appearance: none; + align-items: center; + border: 1px solid transparent; + border-radius: 4px; + box-shadow: none; + display: inline-flex; + font-size: 1rem; + height: 2.25em; + justify-content: flex-start; + line-height: 1.5; + padding-bottom: calc(0.375em - 1px); + padding-left: calc(0.625em - 1px); + padding-right: calc(0.625em - 1px); + padding-top: calc(0.375em - 1px); + position: relative; + vertical-align: top; } + .pagination-previous:focus, + .pagination-next:focus, + .pagination-link:focus, + .pagination-ellipsis:focus, .file-cta:focus, + .file-name:focus, .select select:focus, .textarea:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .button:focus, .is-focused.pagination-previous, + .is-focused.pagination-next, + .is-focused.pagination-link, + .is-focused.pagination-ellipsis, .is-focused.file-cta, + .is-focused.file-name, .select select.is-focused, .is-focused.textarea, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-focused.button, .pagination-previous:active, + .pagination-next:active, + .pagination-link:active, + .pagination-ellipsis:active, .file-cta:active, + .file-name:active, .select select:active, .textarea:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .button:active, .is-active.pagination-previous, + .is-active.pagination-next, + .is-active.pagination-link, + .is-active.pagination-ellipsis, .is-active.file-cta, + .is-active.file-name, .select select.is-active, .is-active.textarea, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .is-active.button { + outline: none; } + .pagination-previous[disabled], + .pagination-next[disabled], + .pagination-link[disabled], + .pagination-ellipsis[disabled], .file-cta[disabled], + .file-name[disabled], .select select[disabled], .textarea[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], .button[disabled], fieldset[disabled] .pagination-previous, + fieldset[disabled] .pagination-next, + fieldset[disabled] .pagination-link, + fieldset[disabled] .pagination-ellipsis, fieldset[disabled] .file-cta, + fieldset[disabled] .file-name, fieldset[disabled] .select select, .select fieldset[disabled] select, fieldset[disabled] .textarea, fieldset[disabled] .input, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input, fieldset[disabled] .button { + cursor: not-allowed; } + +/*! minireset.css v0.0.4 | MIT License | github.com/jgthms/minireset.css */ +html, +body, +p, +ol, +ul, +li, +dl, +dt, +dd, +blockquote, +figure, +fieldset, +legend, +textarea, +pre, +iframe, +hr, +h1, +h2, +h3, +h4, +h5, +h6 { + margin: 0; + padding: 0; } + +h1, +h2, +h3, +h4, +h5, +h6 { + font-size: 100%; + font-weight: normal; } + +ul { + list-style: none; } + +button, +input, +select, +textarea { + margin: 0; } + +html { + box-sizing: border-box; } + +*, *::before, *::after { + box-sizing: inherit; } + +img, +embed, +iframe, +object, +video { + height: auto; + max-width: 100%; } + +audio { + max-width: 100%; } + +iframe { + border: 0; } + +table { + border-collapse: collapse; + border-spacing: 0; } + +td, +th { + padding: 0; } + td:not([align]), + th:not([align]) { + text-align: left; } + +html { + background-color: #fff; + font-size: 16px; + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + +article, +aside, +figure, +footer, +header, +hgroup, +section { + display: block; } + +body, +button, +input, +select, +textarea { + font-family: "Montserrat", sans-serif; } + +code, +pre { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; + font-family: "Source Code Pro", monospace; } + +body { + color: #202020; + font-size: 1em; + font-weight: 400; + line-height: 1.5; } + +a { + color: #149eaa; + cursor: pointer; + text-decoration: none; } + a strong { + color: currentColor; } + a:hover { + color: #107c85; } + +code { + background-color: #ebe8f4; + color: #000000; + font-size: 0.875em; + font-weight: normal; + padding: 0.1em; } + +hr { + background-color: whitesmoke; + border: none; + display: block; + height: 2px; + margin: 1.5rem 0; } + +img { + height: auto; + max-width: 100%; } + +input[type="checkbox"], +input[type="radio"] { + vertical-align: baseline; } + +small { + font-size: 0.875em; } + +span { + font-style: inherit; + font-weight: inherit; } + +strong { + color: #654ca3; + font-weight: 700; } + +fieldset { + border: none; } + +pre { + -webkit-overflow-scrolling: touch; + background-color: #ebe8f4; + color: #202020; + font-size: 0.875em; + overflow-x: auto; + padding: 1.25rem 1.5rem; + white-space: pre; + word-wrap: normal; } + pre code { + background-color: transparent; + color: currentColor; + font-size: 1em; + padding: 0; } + +table td, +table th { + vertical-align: top; } + table td:not([align]), + table th:not([align]) { + text-align: left; } + +table th { + color: #654ca3; } + +.is-clearfix::after { + clear: both; + content: " "; + display: table; } + +.is-pulled-left { + float: left !important; } + +.is-pulled-right { + float: right !important; } + +.is-clipped { + overflow: hidden !important; } + +.is-size-1 { + font-size: 3rem !important; } + +.is-size-2 { + font-size: 2.5rem !important; } + +.is-size-3 { + font-size: 2rem !important; } + +.is-size-4 { + font-size: 1.5rem !important; } + +.is-size-5 { + font-size: 1.25rem !important; } + +.is-size-6 { + font-size: 1rem !important; } + +.is-size-7, .docstring > section > a.docs-sourcelink { + font-size: 0.75rem !important; } + +@media screen and (max-width: 768px) { + .is-size-1-mobile { + font-size: 3rem !important; } + .is-size-2-mobile { + font-size: 2.5rem !important; } + .is-size-3-mobile { + font-size: 2rem !important; } + .is-size-4-mobile { + font-size: 1.5rem !important; } + .is-size-5-mobile { + font-size: 1.25rem !important; } + .is-size-6-mobile { + font-size: 1rem !important; } + .is-size-7-mobile { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 769px), print { + .is-size-1-tablet { + font-size: 3rem !important; } + .is-size-2-tablet { + font-size: 2.5rem !important; } + .is-size-3-tablet { + font-size: 2rem !important; } + .is-size-4-tablet { + font-size: 1.5rem !important; } + .is-size-5-tablet { + font-size: 1.25rem !important; } + .is-size-6-tablet { + font-size: 1rem !important; } + .is-size-7-tablet { + font-size: 0.75rem !important; } } + +@media screen and (max-width: 1055px) { + .is-size-1-touch { + font-size: 3rem !important; } + .is-size-2-touch { + font-size: 2.5rem !important; } + .is-size-3-touch { + font-size: 2rem !important; } + .is-size-4-touch { + font-size: 1.5rem !important; } + .is-size-5-touch { + font-size: 1.25rem !important; } + .is-size-6-touch { + font-size: 1rem !important; } + .is-size-7-touch { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1056px) { + .is-size-1-desktop { + font-size: 3rem !important; } + .is-size-2-desktop { + font-size: 2.5rem !important; } + .is-size-3-desktop { + font-size: 2rem !important; } + .is-size-4-desktop { + font-size: 1.5rem !important; } + .is-size-5-desktop { + font-size: 1.25rem !important; } + .is-size-6-desktop { + font-size: 1rem !important; } + .is-size-7-desktop { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1216px) { + .is-size-1-widescreen { + font-size: 3rem !important; } + .is-size-2-widescreen { + font-size: 2.5rem !important; } + .is-size-3-widescreen { + font-size: 2rem !important; } + .is-size-4-widescreen { + font-size: 1.5rem !important; } + .is-size-5-widescreen { + font-size: 1.25rem !important; } + .is-size-6-widescreen { + font-size: 1rem !important; } + .is-size-7-widescreen { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1408px) { + .is-size-1-fullhd { + font-size: 3rem !important; } + .is-size-2-fullhd { + font-size: 2.5rem !important; } + .is-size-3-fullhd { + font-size: 2rem !important; } + .is-size-4-fullhd { + font-size: 1.5rem !important; } + .is-size-5-fullhd { + font-size: 1.25rem !important; } + .is-size-6-fullhd { + font-size: 1rem !important; } + .is-size-7-fullhd { + font-size: 0.75rem !important; } } + +.has-text-centered { + text-align: center !important; } + +.has-text-justified { + text-align: justify !important; } + +.has-text-left { + text-align: left !important; } + +.has-text-right { + text-align: right !important; } + +@media screen and (max-width: 768px) { + .has-text-centered-mobile { + text-align: center !important; } } + +@media screen and (min-width: 769px), print { + .has-text-centered-tablet { + text-align: center !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-centered-tablet-only { + text-align: center !important; } } + +@media screen and (max-width: 1055px) { + .has-text-centered-touch { + text-align: center !important; } } + +@media screen and (min-width: 1056px) { + .has-text-centered-desktop { + text-align: center !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-centered-desktop-only { + text-align: center !important; } } + +@media screen and (min-width: 1216px) { + .has-text-centered-widescreen { + text-align: center !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-centered-widescreen-only { + text-align: center !important; } } + +@media screen and (min-width: 1408px) { + .has-text-centered-fullhd { + text-align: center !important; } } + +@media screen and (max-width: 768px) { + .has-text-justified-mobile { + text-align: justify !important; } } + +@media screen and (min-width: 769px), print { + .has-text-justified-tablet { + text-align: justify !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-justified-tablet-only { + text-align: justify !important; } } + +@media screen and (max-width: 1055px) { + .has-text-justified-touch { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) { + .has-text-justified-desktop { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-justified-desktop-only { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) { + .has-text-justified-widescreen { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-justified-widescreen-only { + text-align: justify !important; } } + +@media screen and (min-width: 1408px) { + .has-text-justified-fullhd { + text-align: justify !important; } } + +@media screen and (max-width: 768px) { + .has-text-left-mobile { + text-align: left !important; } } + +@media screen and (min-width: 769px), print { + .has-text-left-tablet { + text-align: left !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-left-tablet-only { + text-align: left !important; } } + +@media screen and (max-width: 1055px) { + .has-text-left-touch { + text-align: left !important; } } + +@media screen and (min-width: 1056px) { + .has-text-left-desktop { + text-align: left !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-left-desktop-only { + text-align: left !important; } } + +@media screen and (min-width: 1216px) { + .has-text-left-widescreen { + text-align: left !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-left-widescreen-only { + text-align: left !important; } } + +@media screen and (min-width: 1408px) { + .has-text-left-fullhd { + text-align: left !important; } } + +@media screen and (max-width: 768px) { + .has-text-right-mobile { + text-align: right !important; } } + +@media screen and (min-width: 769px), print { + .has-text-right-tablet { + text-align: right !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-right-tablet-only { + text-align: right !important; } } + +@media screen and (max-width: 1055px) { + .has-text-right-touch { + text-align: right !important; } } + +@media screen and (min-width: 1056px) { + .has-text-right-desktop { + text-align: right !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-right-desktop-only { + text-align: right !important; } } + +@media screen and (min-width: 1216px) { + .has-text-right-widescreen { + text-align: right !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-right-widescreen-only { + text-align: right !important; } } + +@media screen and (min-width: 1408px) { + .has-text-right-fullhd { + text-align: right !important; } } + +.is-capitalized { + text-transform: capitalize !important; } + +.is-lowercase { + text-transform: lowercase !important; } + +.is-uppercase { + text-transform: uppercase !important; } + +.is-italic { + font-style: italic !important; } + +.has-text-white { + color: white !important; } + +a.has-text-white:hover, a.has-text-white:focus { + color: #e6e6e6 !important; } + +.has-background-white { + background-color: white !important; } + +.has-text-black { + color: #0a0a0a !important; } + +a.has-text-black:hover, a.has-text-black:focus { + color: black !important; } + +.has-background-black { + background-color: #0a0a0a !important; } + +.has-text-light { + color: whitesmoke !important; } + +a.has-text-light:hover, a.has-text-light:focus { + color: #dbdbdb !important; } + +.has-background-light { + background-color: whitesmoke !important; } + +.has-text-dark { + color: #363636 !important; } + +a.has-text-dark:hover, a.has-text-dark:focus { + color: #1c1c1c !important; } + +.has-background-dark { + background-color: #363636 !important; } + +.has-text-primary { + color: #4eb5de !important; } + +a.has-text-primary:hover, a.has-text-primary:focus { + color: #27a1d2 !important; } + +.has-background-primary { + background-color: #4eb5de !important; } + +.has-text-link { + color: #149eaa !important; } + +a.has-text-link:hover, a.has-text-link:focus { + color: #0f747c !important; } + +.has-background-link { + background-color: #149eaa !important; } + +.has-text-info { + color: #209cee !important; } + +a.has-text-info:hover, a.has-text-info:focus { + color: #1081cb !important; } + +.has-background-info { + background-color: #209cee !important; } + +.has-text-success { + color: #22c35b !important; } + +a.has-text-success:hover, a.has-text-success:focus { + color: #1a9847 !important; } + +.has-background-success { + background-color: #22c35b !important; } + +.has-text-warning { + color: #ffdd57 !important; } + +a.has-text-warning:hover, a.has-text-warning:focus { + color: #ffd324 !important; } + +.has-background-warning { + background-color: #ffdd57 !important; } + +.has-text-danger { + color: #da0b00 !important; } + +a.has-text-danger:hover, a.has-text-danger:focus { + color: #a70800 !important; } + +.has-background-danger { + background-color: #da0b00 !important; } + +.has-text-black-bis { + color: #121212 !important; } + +.has-background-black-bis { + background-color: #121212 !important; } + +.has-text-black-ter { + color: #242424 !important; } + +.has-background-black-ter { + background-color: #242424 !important; } + +.has-text-grey-darker { + color: #363636 !important; } + +.has-background-grey-darker { + background-color: #363636 !important; } + +.has-text-grey-dark { + color: #4a4a4a !important; } + +.has-background-grey-dark { + background-color: #4a4a4a !important; } + +.has-text-grey { + color: #6b6b6b !important; } + +.has-background-grey { + background-color: #6b6b6b !important; } + +.has-text-grey-light { + color: #b5b5b5 !important; } + +.has-background-grey-light { + background-color: #b5b5b5 !important; } + +.has-text-grey-lighter { + color: #dbdbdb !important; } + +.has-background-grey-lighter { + background-color: #dbdbdb !important; } + +.has-text-white-ter { + color: whitesmoke !important; } + +.has-background-white-ter { + background-color: whitesmoke !important; } + +.has-text-white-bis { + color: #fafafa !important; } + +.has-background-white-bis { + background-color: #fafafa !important; } + +.has-text-weight-light { + font-weight: 300 !important; } + +.has-text-weight-normal { + font-weight: 400 !important; } + +.has-text-weight-medium { + font-weight: 500 !important; } + +.has-text-weight-semibold { + font-weight: 600 !important; } + +.has-text-weight-bold { + font-weight: 700 !important; } + +.is-family-primary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-secondary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-sans-serif { + font-family: "Montserrat", sans-serif !important; } + +.is-family-monospace { + font-family: "Source Code Pro", monospace !important; } + +.is-family-code { + font-family: "Source Code Pro", monospace !important; } + +.is-block { + display: block !important; } + +@media screen and (max-width: 768px) { + .is-block-mobile { + display: block !important; } } + +@media screen and (min-width: 769px), print { + .is-block-tablet { + display: block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-block-tablet-only { + display: block !important; } } + +@media screen and (max-width: 1055px) { + .is-block-touch { + display: block !important; } } + +@media screen and (min-width: 1056px) { + .is-block-desktop { + display: block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-block-desktop-only { + display: block !important; } } + +@media screen and (min-width: 1216px) { + .is-block-widescreen { + display: block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-block-widescreen-only { + display: block !important; } } + +@media screen and (min-width: 1408px) { + .is-block-fullhd { + display: block !important; } } + +.is-flex { + display: flex !important; } + +@media screen and (max-width: 768px) { + .is-flex-mobile { + display: flex !important; } } + +@media screen and (min-width: 769px), print { + .is-flex-tablet { + display: flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-flex-tablet-only { + display: flex !important; } } + +@media screen and (max-width: 1055px) { + .is-flex-touch { + display: flex !important; } } + +@media screen and (min-width: 1056px) { + .is-flex-desktop { + display: flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-flex-desktop-only { + display: flex !important; } } + +@media screen and (min-width: 1216px) { + .is-flex-widescreen { + display: flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-flex-widescreen-only { + display: flex !important; } } + +@media screen and (min-width: 1408px) { + .is-flex-fullhd { + display: flex !important; } } + +.is-inline { + display: inline !important; } + +@media screen and (max-width: 768px) { + .is-inline-mobile { + display: inline !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-tablet { + display: inline !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-tablet-only { + display: inline !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-touch { + display: inline !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-desktop { + display: inline !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-desktop-only { + display: inline !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-widescreen { + display: inline !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-widescreen-only { + display: inline !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-fullhd { + display: inline !important; } } + +.is-inline-block { + display: inline-block !important; } + +@media screen and (max-width: 768px) { + .is-inline-block-mobile { + display: inline-block !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-block-tablet { + display: inline-block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-block-tablet-only { + display: inline-block !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-block-touch { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-block-desktop { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-block-desktop-only { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-block-widescreen { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-block-widescreen-only { + display: inline-block !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-block-fullhd { + display: inline-block !important; } } + +.is-inline-flex { + display: inline-flex !important; } + +@media screen and (max-width: 768px) { + .is-inline-flex-mobile { + display: inline-flex !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-flex-tablet { + display: inline-flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-flex-tablet-only { + display: inline-flex !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-flex-touch { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-flex-desktop { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-flex-desktop-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-flex-widescreen { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-flex-widescreen-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-flex-fullhd { + display: inline-flex !important; } } + +.is-hidden { + display: none !important; } + +.is-sr-only { + border: none !important; + clip: rect(0, 0, 0, 0) !important; + height: 0.01em !important; + overflow: hidden !important; + padding: 0 !important; + position: absolute !important; + white-space: nowrap !important; + width: 0.01em !important; } + +@media screen and (max-width: 768px) { + .is-hidden-mobile { + display: none !important; } } + +@media screen and (min-width: 769px), print { + .is-hidden-tablet { + display: none !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-hidden-tablet-only { + display: none !important; } } + +@media screen and (max-width: 1055px) { + .is-hidden-touch { + display: none !important; } } + +@media screen and (min-width: 1056px) { + .is-hidden-desktop { + display: none !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-hidden-desktop-only { + display: none !important; } } + +@media screen and (min-width: 1216px) { + .is-hidden-widescreen { + display: none !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-hidden-widescreen-only { + display: none !important; } } + +@media screen and (min-width: 1408px) { + .is-hidden-fullhd { + display: none !important; } } + +.is-invisible { + visibility: hidden !important; } + +@media screen and (max-width: 768px) { + .is-invisible-mobile { + visibility: hidden !important; } } + +@media screen and (min-width: 769px), print { + .is-invisible-tablet { + visibility: hidden !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-invisible-tablet-only { + visibility: hidden !important; } } + +@media screen and (max-width: 1055px) { + .is-invisible-touch { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) { + .is-invisible-desktop { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-invisible-desktop-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) { + .is-invisible-widescreen { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-invisible-widescreen-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1408px) { + .is-invisible-fullhd { + visibility: hidden !important; } } + +.is-marginless { + margin: 0 !important; } + +.is-paddingless { + padding: 0 !important; } + +.is-radiusless { + border-radius: 0 !important; } + +.is-shadowless { + box-shadow: none !important; } + +.is-relative { + position: relative !important; } + +.box { + background-color: white; + border-radius: 6px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #202020; + display: block; + padding: 1.25rem; } + +a.box:hover, a.box:focus { + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #149eaa; } + +a.box:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #149eaa; } + +.button { + background-color: white; + border-color: #dbdbdb; + border-width: 1px; + color: #363636; + cursor: pointer; + justify-content: center; + padding-bottom: calc(0.375em - 1px); + padding-left: 0.75em; + padding-right: 0.75em; + padding-top: calc(0.375em - 1px); + text-align: center; + white-space: nowrap; } + .button strong { + color: inherit; } + .button .icon, .button .icon.is-small, .button #documenter .docs-sidebar form.docs-search > input.icon, #documenter .docs-sidebar .button form.docs-search > input.icon, .button .icon.is-medium, .button .icon.is-large { + height: 1.5em; + width: 1.5em; } + .button .icon:first-child:not(:last-child) { + margin-left: calc(-0.375em - 1px); + margin-right: 0.1875em; } + .button .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: calc(-0.375em - 1px); } + .button .icon:first-child:last-child { + margin-left: calc(-0.375em - 1px); + margin-right: calc(-0.375em - 1px); } + .button:hover, .button.is-hovered { + border-color: #b5b5b5; + color: #107c85; } + .button:focus, .button.is-focused { + border-color: #3c5dcd; + color: #363636; } + .button:focus:not(:active), .button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .button:active, .button.is-active { + border-color: #4a4a4a; + color: #363636; } + .button.is-text { + background-color: transparent; + border-color: transparent; + color: #202020; + text-decoration: underline; } + .button.is-text:hover, .button.is-text.is-hovered, .button.is-text:focus, .button.is-text.is-focused { + background-color: whitesmoke; + color: #654ca3; } + .button.is-text:active, .button.is-text.is-active { + background-color: #e8e8e8; + color: #654ca3; } + .button.is-text[disabled], fieldset[disabled] .button.is-text { + background-color: transparent; + border-color: transparent; + box-shadow: none; } + .button.is-white { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + .button.is-white:hover, .button.is-white.is-hovered { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + .button.is-white:focus, .button.is-white.is-focused { + border-color: transparent; + color: #0a0a0a; } + .button.is-white:focus:not(:active), .button.is-white.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .button.is-white:active, .button.is-white.is-active { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + .button.is-white[disabled], fieldset[disabled] .button.is-white { + background-color: white; + border-color: transparent; + box-shadow: none; } + .button.is-white.is-inverted { + background-color: #0a0a0a; + color: white; } + .button.is-white.is-inverted:hover, .button.is-white.is-inverted.is-hovered { + background-color: black; } + .button.is-white.is-inverted[disabled], fieldset[disabled] .button.is-white.is-inverted { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; + color: white; } + .button.is-white.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + .button.is-white.is-outlined:hover, .button.is-white.is-outlined.is-hovered, .button.is-white.is-outlined:focus, .button.is-white.is-outlined.is-focused { + background-color: white; + border-color: white; + color: #0a0a0a; } + .button.is-white.is-outlined.is-loading::after { + border-color: transparent transparent white white !important; } + .button.is-white.is-outlined.is-loading:hover::after, .button.is-white.is-outlined.is-loading.is-hovered::after, .button.is-white.is-outlined.is-loading:focus::after, .button.is-white.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-white.is-outlined[disabled], fieldset[disabled] .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + .button.is-white.is-inverted.is-outlined:hover, .button.is-white.is-inverted.is-outlined.is-hovered, .button.is-white.is-inverted.is-outlined:focus, .button.is-white.is-inverted.is-outlined.is-focused { + background-color: #0a0a0a; + color: white; } + .button.is-white.is-inverted.is-outlined.is-loading:hover::after, .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-white.is-inverted.is-outlined.is-loading:focus::after, .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + .button.is-white.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + .button.is-black:hover, .button.is-black.is-hovered { + background-color: #040404; + border-color: transparent; + color: white; } + .button.is-black:focus, .button.is-black.is-focused { + border-color: transparent; + color: white; } + .button.is-black:focus:not(:active), .button.is-black.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .button.is-black:active, .button.is-black.is-active { + background-color: black; + border-color: transparent; + color: white; } + .button.is-black[disabled], fieldset[disabled] .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; } + .button.is-black.is-inverted { + background-color: white; + color: #0a0a0a; } + .button.is-black.is-inverted:hover, .button.is-black.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-black.is-inverted[disabled], fieldset[disabled] .button.is-black.is-inverted { + background-color: white; + border-color: transparent; + box-shadow: none; + color: #0a0a0a; } + .button.is-black.is-loading::after { + border-color: transparent transparent white white !important; } + .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + .button.is-black.is-outlined:hover, .button.is-black.is-outlined.is-hovered, .button.is-black.is-outlined:focus, .button.is-black.is-outlined.is-focused { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .button.is-black.is-outlined.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-black.is-outlined.is-loading:hover::after, .button.is-black.is-outlined.is-loading.is-hovered::after, .button.is-black.is-outlined.is-loading:focus::after, .button.is-black.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + .button.is-black.is-outlined[disabled], fieldset[disabled] .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + .button.is-black.is-inverted.is-outlined:hover, .button.is-black.is-inverted.is-outlined.is-hovered, .button.is-black.is-inverted.is-outlined:focus, .button.is-black.is-inverted.is-outlined.is-focused { + background-color: white; + color: #0a0a0a; } + .button.is-black.is-inverted.is-outlined.is-loading:hover::after, .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-black.is-inverted.is-outlined.is-loading:focus::after, .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + .button.is-light { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + .button.is-light:hover, .button.is-light.is-hovered { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + .button.is-light:focus, .button.is-light.is-focused { + border-color: transparent; + color: #363636; } + .button.is-light:focus:not(:active), .button.is-light.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .button.is-light:active, .button.is-light.is-active { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + .button.is-light[disabled], fieldset[disabled] .button.is-light { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; } + .button.is-light.is-inverted { + background-color: #363636; + color: whitesmoke; } + .button.is-light.is-inverted:hover, .button.is-light.is-inverted.is-hovered { + background-color: #292929; } + .button.is-light.is-inverted[disabled], fieldset[disabled] .button.is-light.is-inverted { + background-color: #363636; + border-color: transparent; + box-shadow: none; + color: whitesmoke; } + .button.is-light.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + .button.is-light.is-outlined:hover, .button.is-light.is-outlined.is-hovered, .button.is-light.is-outlined:focus, .button.is-light.is-outlined.is-focused { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .button.is-light.is-outlined.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-light.is-outlined.is-loading:hover::after, .button.is-light.is-outlined.is-loading.is-hovered::after, .button.is-light.is-outlined.is-loading:focus::after, .button.is-light.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-light.is-outlined[disabled], fieldset[disabled] .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + .button.is-light.is-inverted.is-outlined:hover, .button.is-light.is-inverted.is-outlined.is-hovered, .button.is-light.is-inverted.is-outlined:focus, .button.is-light.is-inverted.is-outlined.is-focused { + background-color: #363636; + color: whitesmoke; } + .button.is-light.is-inverted.is-outlined.is-loading:hover::after, .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-light.is-inverted.is-outlined.is-loading:focus::after, .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + .button.is-dark, .content kbd.button { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + .button.is-dark:hover, .content kbd.button:hover, .button.is-dark.is-hovered, .content kbd.button.is-hovered { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + .button.is-dark:focus, .content kbd.button:focus, .button.is-dark.is-focused, .content kbd.button.is-focused { + border-color: transparent; + color: whitesmoke; } + .button.is-dark:focus:not(:active), .content kbd.button:focus:not(:active), .button.is-dark.is-focused:not(:active), .content kbd.button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .button.is-dark:active, .content kbd.button:active, .button.is-dark.is-active, .content kbd.button.is-active { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + .button.is-dark[disabled], .content kbd.button[disabled], fieldset[disabled] .button.is-dark, fieldset[disabled] .content kbd.button, .content fieldset[disabled] kbd.button { + background-color: #363636; + border-color: transparent; + box-shadow: none; } + .button.is-dark.is-inverted, .content kbd.button.is-inverted { + background-color: whitesmoke; + color: #363636; } + .button.is-dark.is-inverted:hover, .content kbd.button.is-inverted:hover, .button.is-dark.is-inverted.is-hovered, .content kbd.button.is-inverted.is-hovered { + background-color: #e8e8e8; } + .button.is-dark.is-inverted[disabled], .content kbd.button.is-inverted[disabled], fieldset[disabled] .button.is-dark.is-inverted, fieldset[disabled] .content kbd.button.is-inverted, .content fieldset[disabled] kbd.button.is-inverted { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; + color: #363636; } + .button.is-dark.is-loading::after, .content kbd.button.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-dark.is-outlined, .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + .button.is-dark.is-outlined:hover, .content kbd.button.is-outlined:hover, .button.is-dark.is-outlined.is-hovered, .content kbd.button.is-outlined.is-hovered, .button.is-dark.is-outlined:focus, .content kbd.button.is-outlined:focus, .button.is-dark.is-outlined.is-focused, .content kbd.button.is-outlined.is-focused { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .button.is-dark.is-outlined.is-loading::after, .content kbd.button.is-outlined.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-dark.is-outlined.is-loading:hover::after, .content kbd.button.is-outlined.is-loading:hover::after, .button.is-dark.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-outlined.is-loading:focus::after, .content kbd.button.is-outlined.is-loading:focus::after, .button.is-dark.is-outlined.is-loading.is-focused::after, .content kbd.button.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-dark.is-outlined[disabled], .content kbd.button.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-outlined, fieldset[disabled] .content kbd.button.is-outlined, .content fieldset[disabled] kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + .button.is-dark.is-inverted.is-outlined, .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + .button.is-dark.is-inverted.is-outlined:hover, .content kbd.button.is-inverted.is-outlined:hover, .button.is-dark.is-inverted.is-outlined.is-hovered, .content kbd.button.is-inverted.is-outlined.is-hovered, .button.is-dark.is-inverted.is-outlined:focus, .content kbd.button.is-inverted.is-outlined:focus, .button.is-dark.is-inverted.is-outlined.is-focused, .content kbd.button.is-inverted.is-outlined.is-focused { + background-color: whitesmoke; + color: #363636; } + .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-dark.is-inverted.is-outlined[disabled], .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-inverted.is-outlined, fieldset[disabled] .content kbd.button.is-inverted.is-outlined, .content fieldset[disabled] kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + .button.is-primary, .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + .button.is-primary:hover, .docstring > section > a.button.docs-sourcelink:hover, .button.is-primary.is-hovered, .docstring > section > a.button.is-hovered.docs-sourcelink { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + .button.is-primary:focus, .docstring > section > a.button.docs-sourcelink:focus, .button.is-primary.is-focused, .docstring > section > a.button.is-focused.docs-sourcelink { + border-color: transparent; + color: #fff; } + .button.is-primary:focus:not(:active), .docstring > section > a.button.docs-sourcelink:focus:not(:active), .button.is-primary.is-focused:not(:active), .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .button.is-primary:active, .docstring > section > a.button.docs-sourcelink:active, .button.is-primary.is-active, .docstring > section > a.button.is-active.docs-sourcelink { + background-color: #39acda; + border-color: transparent; + color: #fff; } + .button.is-primary[disabled], .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary, fieldset[disabled] .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + box-shadow: none; } + .button.is-primary.is-inverted, .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + .button.is-primary.is-inverted:hover, .docstring > section > a.button.is-inverted.docs-sourcelink:hover, .button.is-primary.is-inverted.is-hovered, .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { + background-color: #f2f2f2; } + .button.is-primary.is-inverted[disabled], .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted, fieldset[disabled] .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #4eb5de; } + .button.is-primary.is-loading::after, .docstring > section > a.button.is-loading.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-primary.is-outlined, .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + color: #4eb5de; } + .button.is-primary.is-outlined:hover, .docstring > section > a.button.is-outlined.docs-sourcelink:hover, .button.is-primary.is-outlined.is-hovered, .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-outlined:focus, .docstring > section > a.button.is-outlined.docs-sourcelink:focus, .button.is-primary.is-outlined.is-focused, .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + .button.is-primary.is-outlined.is-loading::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + .button.is-primary.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-primary.is-outlined[disabled], .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-outlined, fieldset[disabled] .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + box-shadow: none; + color: #4eb5de; } + .button.is-primary.is-inverted.is-outlined, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-primary.is-inverted.is-outlined:hover, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, .button.is-primary.is-inverted.is-outlined.is-hovered, .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-inverted.is-outlined:focus, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, .button.is-primary.is-inverted.is-outlined.is-focused, .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + .button.is-primary.is-inverted.is-outlined[disabled], .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted.is-outlined, fieldset[disabled] .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-link { + background-color: #149eaa; + border-color: transparent; + color: #fff; } + .button.is-link:hover, .button.is-link.is-hovered { + background-color: #13939f; + border-color: transparent; + color: #fff; } + .button.is-link:focus, .button.is-link.is-focused { + border-color: transparent; + color: #fff; } + .button.is-link:focus:not(:active), .button.is-link.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .button.is-link:active, .button.is-link.is-active { + background-color: #118993; + border-color: transparent; + color: #fff; } + .button.is-link[disabled], fieldset[disabled] .button.is-link { + background-color: #149eaa; + border-color: transparent; + box-shadow: none; } + .button.is-link.is-inverted { + background-color: #fff; + color: #149eaa; } + .button.is-link.is-inverted:hover, .button.is-link.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-link.is-inverted[disabled], fieldset[disabled] .button.is-link.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #149eaa; } + .button.is-link.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-link.is-outlined { + background-color: transparent; + border-color: #149eaa; + color: #149eaa; } + .button.is-link.is-outlined:hover, .button.is-link.is-outlined.is-hovered, .button.is-link.is-outlined:focus, .button.is-link.is-outlined.is-focused { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + .button.is-link.is-outlined.is-loading::after { + border-color: transparent transparent #149eaa #149eaa !important; } + .button.is-link.is-outlined.is-loading:hover::after, .button.is-link.is-outlined.is-loading.is-hovered::after, .button.is-link.is-outlined.is-loading:focus::after, .button.is-link.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-link.is-outlined[disabled], fieldset[disabled] .button.is-link.is-outlined { + background-color: transparent; + border-color: #149eaa; + box-shadow: none; + color: #149eaa; } + .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-link.is-inverted.is-outlined:hover, .button.is-link.is-inverted.is-outlined.is-hovered, .button.is-link.is-inverted.is-outlined:focus, .button.is-link.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #149eaa; } + .button.is-link.is-inverted.is-outlined.is-loading:hover::after, .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-link.is-inverted.is-outlined.is-loading:focus::after, .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #149eaa #149eaa !important; } + .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-info { + background-color: #209cee; + border-color: transparent; + color: #fff; } + .button.is-info:hover, .button.is-info.is-hovered { + background-color: #1497ed; + border-color: transparent; + color: #fff; } + .button.is-info:focus, .button.is-info.is-focused { + border-color: transparent; + color: #fff; } + .button.is-info:focus:not(:active), .button.is-info.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .button.is-info:active, .button.is-info.is-active { + background-color: #1190e3; + border-color: transparent; + color: #fff; } + .button.is-info[disabled], fieldset[disabled] .button.is-info { + background-color: #209cee; + border-color: transparent; + box-shadow: none; } + .button.is-info.is-inverted { + background-color: #fff; + color: #209cee; } + .button.is-info.is-inverted:hover, .button.is-info.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-info.is-inverted[disabled], fieldset[disabled] .button.is-info.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #209cee; } + .button.is-info.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-info.is-outlined { + background-color: transparent; + border-color: #209cee; + color: #209cee; } + .button.is-info.is-outlined:hover, .button.is-info.is-outlined.is-hovered, .button.is-info.is-outlined:focus, .button.is-info.is-outlined.is-focused { + background-color: #209cee; + border-color: #209cee; + color: #fff; } + .button.is-info.is-outlined.is-loading::after { + border-color: transparent transparent #209cee #209cee !important; } + .button.is-info.is-outlined.is-loading:hover::after, .button.is-info.is-outlined.is-loading.is-hovered::after, .button.is-info.is-outlined.is-loading:focus::after, .button.is-info.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-info.is-outlined[disabled], fieldset[disabled] .button.is-info.is-outlined { + background-color: transparent; + border-color: #209cee; + box-shadow: none; + color: #209cee; } + .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-info.is-inverted.is-outlined:hover, .button.is-info.is-inverted.is-outlined.is-hovered, .button.is-info.is-inverted.is-outlined:focus, .button.is-info.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #209cee; } + .button.is-info.is-inverted.is-outlined.is-loading:hover::after, .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-info.is-inverted.is-outlined.is-loading:focus::after, .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #209cee #209cee !important; } + .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-success { + background-color: #22c35b; + border-color: transparent; + color: #fff; } + .button.is-success:hover, .button.is-success.is-hovered { + background-color: #20b856; + border-color: transparent; + color: #fff; } + .button.is-success:focus, .button.is-success.is-focused { + border-color: transparent; + color: #fff; } + .button.is-success:focus:not(:active), .button.is-success.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .button.is-success:active, .button.is-success.is-active { + background-color: #1ead51; + border-color: transparent; + color: #fff; } + .button.is-success[disabled], fieldset[disabled] .button.is-success { + background-color: #22c35b; + border-color: transparent; + box-shadow: none; } + .button.is-success.is-inverted { + background-color: #fff; + color: #22c35b; } + .button.is-success.is-inverted:hover, .button.is-success.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-success.is-inverted[disabled], fieldset[disabled] .button.is-success.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #22c35b; } + .button.is-success.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-success.is-outlined { + background-color: transparent; + border-color: #22c35b; + color: #22c35b; } + .button.is-success.is-outlined:hover, .button.is-success.is-outlined.is-hovered, .button.is-success.is-outlined:focus, .button.is-success.is-outlined.is-focused { + background-color: #22c35b; + border-color: #22c35b; + color: #fff; } + .button.is-success.is-outlined.is-loading::after { + border-color: transparent transparent #22c35b #22c35b !important; } + .button.is-success.is-outlined.is-loading:hover::after, .button.is-success.is-outlined.is-loading.is-hovered::after, .button.is-success.is-outlined.is-loading:focus::after, .button.is-success.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-success.is-outlined[disabled], fieldset[disabled] .button.is-success.is-outlined { + background-color: transparent; + border-color: #22c35b; + box-shadow: none; + color: #22c35b; } + .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-success.is-inverted.is-outlined:hover, .button.is-success.is-inverted.is-outlined.is-hovered, .button.is-success.is-inverted.is-outlined:focus, .button.is-success.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #22c35b; } + .button.is-success.is-inverted.is-outlined.is-loading:hover::after, .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-success.is-inverted.is-outlined.is-loading:focus::after, .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #22c35b #22c35b !important; } + .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-warning { + background-color: #ffdd57; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:hover, .button.is-warning.is-hovered { + background-color: #ffda4a; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:focus, .button.is-warning.is-focused { + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:focus:not(:active), .button.is-warning.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .button.is-warning:active, .button.is-warning.is-active { + background-color: #ffd83e; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning[disabled], fieldset[disabled] .button.is-warning { + background-color: #ffdd57; + border-color: transparent; + box-shadow: none; } + .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .button.is-warning.is-inverted:hover, .button.is-warning.is-inverted.is-hovered { + background-color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-inverted[disabled], fieldset[disabled] .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + border-color: transparent; + box-shadow: none; + color: #ffdd57; } + .button.is-warning.is-loading::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + .button.is-warning.is-outlined { + background-color: transparent; + border-color: #ffdd57; + color: #ffdd57; } + .button.is-warning.is-outlined:hover, .button.is-warning.is-outlined.is-hovered, .button.is-warning.is-outlined:focus, .button.is-warning.is-outlined.is-focused { + background-color: #ffdd57; + border-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-outlined.is-loading::after { + border-color: transparent transparent #ffdd57 #ffdd57 !important; } + .button.is-warning.is-outlined.is-loading:hover::after, .button.is-warning.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-outlined.is-loading:focus::after, .button.is-warning.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + .button.is-warning.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-outlined { + background-color: transparent; + border-color: #ffdd57; + box-shadow: none; + color: #ffdd57; } + .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-inverted.is-outlined:hover, .button.is-warning.is-inverted.is-outlined.is-hovered, .button.is-warning.is-inverted.is-outlined:focus, .button.is-warning.is-inverted.is-outlined.is-focused { + background-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #ffdd57 #ffdd57 !important; } + .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + box-shadow: none; + color: rgba(0, 0, 0, 0.7); } + .button.is-danger { + background-color: #da0b00; + border-color: transparent; + color: #fff; } + .button.is-danger:hover, .button.is-danger.is-hovered { + background-color: #cd0a00; + border-color: transparent; + color: #fff; } + .button.is-danger:focus, .button.is-danger.is-focused { + border-color: transparent; + color: #fff; } + .button.is-danger:focus:not(:active), .button.is-danger.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .button.is-danger:active, .button.is-danger.is-active { + background-color: #c10a00; + border-color: transparent; + color: #fff; } + .button.is-danger[disabled], fieldset[disabled] .button.is-danger { + background-color: #da0b00; + border-color: transparent; + box-shadow: none; } + .button.is-danger.is-inverted { + background-color: #fff; + color: #da0b00; } + .button.is-danger.is-inverted:hover, .button.is-danger.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-danger.is-inverted[disabled], fieldset[disabled] .button.is-danger.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #da0b00; } + .button.is-danger.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-danger.is-outlined { + background-color: transparent; + border-color: #da0b00; + color: #da0b00; } + .button.is-danger.is-outlined:hover, .button.is-danger.is-outlined.is-hovered, .button.is-danger.is-outlined:focus, .button.is-danger.is-outlined.is-focused { + background-color: #da0b00; + border-color: #da0b00; + color: #fff; } + .button.is-danger.is-outlined.is-loading::after { + border-color: transparent transparent #da0b00 #da0b00 !important; } + .button.is-danger.is-outlined.is-loading:hover::after, .button.is-danger.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-outlined.is-loading:focus::after, .button.is-danger.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-danger.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-outlined { + background-color: transparent; + border-color: #da0b00; + box-shadow: none; + color: #da0b00; } + .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-danger.is-inverted.is-outlined:hover, .button.is-danger.is-inverted.is-outlined.is-hovered, .button.is-danger.is-inverted.is-outlined:focus, .button.is-danger.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #da0b00; } + .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #da0b00 #da0b00 !important; } + .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-small, #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 2px; + font-size: 0.75rem; } + .button.is-normal { + font-size: 1rem; } + .button.is-medium { + font-size: 1.25rem; } + .button.is-large { + font-size: 1.5rem; } + .button[disabled], fieldset[disabled] .button { + background-color: white; + border-color: #dbdbdb; + box-shadow: none; + opacity: 0.5; } + .button.is-fullwidth { + display: flex; + width: 100%; } + .button.is-loading { + color: transparent !important; + pointer-events: none; } + .button.is-loading::after { + position: absolute; + left: calc(50% - (1em / 2)); + top: calc(50% - (1em / 2)); + position: absolute !important; } + .button.is-static { + background-color: whitesmoke; + border-color: #dbdbdb; + color: #6b6b6b; + box-shadow: none; + pointer-events: none; } + .button.is-rounded, #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + +.buttons { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .buttons .button { + margin-bottom: 0.5rem; } + .buttons .button:not(:last-child):not(.is-fullwidth) { + margin-right: 0.5rem; } + .buttons:last-child { + margin-bottom: -0.5rem; } + .buttons:not(:last-child) { + margin-bottom: 1rem; } + .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { + border-radius: 2px; + font-size: 0.75rem; } + .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { + font-size: 1.25rem; } + .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { + font-size: 1.5rem; } + .buttons.has-addons .button:not(:first-child) { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .buttons.has-addons .button:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; + margin-right: -1px; } + .buttons.has-addons .button:last-child { + margin-right: 0; } + .buttons.has-addons .button:hover, .buttons.has-addons .button.is-hovered { + z-index: 2; } + .buttons.has-addons .button:focus, .buttons.has-addons .button.is-focused, .buttons.has-addons .button:active, .buttons.has-addons .button.is-active, .buttons.has-addons .button.is-selected { + z-index: 3; } + .buttons.has-addons .button:focus:hover, .buttons.has-addons .button.is-focused:hover, .buttons.has-addons .button:active:hover, .buttons.has-addons .button.is-active:hover, .buttons.has-addons .button.is-selected:hover { + z-index: 4; } + .buttons.has-addons .button.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .buttons.is-centered { + justify-content: center; } + .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + .buttons.is-right { + justify-content: flex-end; } + .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + +.container { + flex-grow: 1; + margin: 0 auto; + position: relative; + width: auto; } + @media screen and (min-width: 1056px) { + .container { + max-width: 992px; } + .container.is-fluid { + margin-left: 32px; + margin-right: 32px; + max-width: none; } } + @media screen and (max-width: 1215px) { + .container.is-widescreen { + max-width: 1152px; } } + @media screen and (max-width: 1407px) { + .container.is-fullhd { + max-width: 1344px; } } + @media screen and (min-width: 1216px) { + .container { + max-width: 1152px; } } + @media screen and (min-width: 1408px) { + .container { + max-width: 1344px; } } +.content li + li { + margin-top: 0.25em; } + +.content p:not(:last-child), +.content dl:not(:last-child), +.content ol:not(:last-child), +.content ul:not(:last-child), +.content blockquote:not(:last-child), +.content pre:not(:last-child), +.content table:not(:last-child) { + margin-bottom: 1em; } + +.content h1, +.content h2, +.content h3, +.content h4, +.content h5, +.content h6 { + color: #654ca3; + font-weight: 600; + line-height: 1.125; } + +.content h1 { + font-size: 2em; + margin-bottom: 0.5em; } + .content h1:not(:first-child) { + margin-top: 1em; } + +.content h2 { + font-size: 1.75em; + margin-bottom: 0.5714em; } + .content h2:not(:first-child) { + margin-top: 1.1428em; } + +.content h3 { + font-size: 1.5em; + margin-bottom: 0.6666em; } + .content h3:not(:first-child) { + margin-top: 1.3333em; } + +.content h4 { + font-size: 1.25em; + margin-bottom: 0.8em; } + +.content h5 { + font-size: 1.125em; + margin-bottom: 0.8888em; } + +.content h6 { + font-size: 1em; + margin-bottom: 1em; } + +.content blockquote { + background-color: whitesmoke; + border-left: 5px solid #dbdbdb; + padding: 1.25em 1.5em; } + +.content ol { + list-style-position: outside; + margin-left: 2em; + margin-top: 1em; } + .content ol:not([type]) { + list-style-type: decimal; } + .content ol.is-lower-alpha:not([type]) { + list-style-type: lower-alpha; } + .content ol.is-lower-roman:not([type]) { + list-style-type: lower-roman; } + .content ol.is-upper-alpha:not([type]) { + list-style-type: upper-alpha; } + .content ol.is-upper-roman:not([type]) { + list-style-type: upper-roman; } + +.content ul { + list-style: disc outside; + margin-left: 2em; + margin-top: 1em; } + .content ul ul { + list-style-type: circle; + margin-top: 0.5em; } + .content ul ul ul { + list-style-type: square; } + +.content dd { + margin-left: 2em; } + +.content figure { + margin-left: 2em; + margin-right: 2em; + text-align: center; } + .content figure:not(:first-child) { + margin-top: 2em; } + .content figure:not(:last-child) { + margin-bottom: 2em; } + .content figure img { + display: inline-block; } + .content figure figcaption { + font-style: italic; } + +.content pre { + -webkit-overflow-scrolling: touch; + overflow-x: auto; + padding: 0; + white-space: pre; + word-wrap: normal; } + +.content sup, +.content sub { + font-size: 75%; } + +.content table { + width: 100%; } + .content table td, + .content table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + .content table th { + color: #654ca3; } + .content table th:not([align]) { + text-align: left; } + .content table thead td, + .content table thead th { + border-width: 0 0 2px; + color: #654ca3; } + .content table tfoot td, + .content table tfoot th { + border-width: 2px 0 0; + color: #654ca3; } + .content table tbody tr:last-child td, + .content table tbody tr:last-child th { + border-bottom-width: 0; } + +.content .tabs li + li { + margin-top: 0; } + +.content.is-small, #documenter .docs-sidebar form.docs-search > input.content { + font-size: 0.75rem; } + +.content.is-medium { + font-size: 1.25rem; } + +.content.is-large { + font-size: 1.5rem; } + +.icon { + align-items: center; + display: inline-flex; + justify-content: center; + height: 1.5rem; + width: 1.5rem; } + .icon.is-small, #documenter .docs-sidebar form.docs-search > input.icon { + height: 1rem; + width: 1rem; } + .icon.is-medium { + height: 2rem; + width: 2rem; } + .icon.is-large { + height: 3rem; + width: 3rem; } + +.image, #documenter .docs-sidebar .docs-logo > img { + display: block; + position: relative; } + .image img, #documenter .docs-sidebar .docs-logo > img img { + display: block; + height: auto; + width: 100%; } + .image img.is-rounded, #documenter .docs-sidebar .docs-logo > img img.is-rounded { + border-radius: 290486px; } + .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img, + .image.is-square .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img, + .image.is-1by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img, + .image.is-5by4 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img, + .image.is-4by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img, + .image.is-3by2 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img, + .image.is-5by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img, + .image.is-16by9 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img, + .image.is-2by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img, + .image.is-3by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img, + .image.is-4by5 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img, + .image.is-3by4 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img, + .image.is-2by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img, + .image.is-3by5 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img, + .image.is-9by16 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img, + .image.is-1by2 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img, + .image.is-1by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { + height: 100%; + width: 100%; } + .image.is-square, #documenter .docs-sidebar .docs-logo > img.is-square, .image.is-1by1, #documenter .docs-sidebar .docs-logo > img.is-1by1 { + padding-top: 100%; } + .image.is-5by4, #documenter .docs-sidebar .docs-logo > img.is-5by4 { + padding-top: 80%; } + .image.is-4by3, #documenter .docs-sidebar .docs-logo > img.is-4by3 { + padding-top: 75%; } + .image.is-3by2, #documenter .docs-sidebar .docs-logo > img.is-3by2 { + padding-top: 66.6666%; } + .image.is-5by3, #documenter .docs-sidebar .docs-logo > img.is-5by3 { + padding-top: 60%; } + .image.is-16by9, #documenter .docs-sidebar .docs-logo > img.is-16by9 { + padding-top: 56.25%; } + .image.is-2by1, #documenter .docs-sidebar .docs-logo > img.is-2by1 { + padding-top: 50%; } + .image.is-3by1, #documenter .docs-sidebar .docs-logo > img.is-3by1 { + padding-top: 33.3333%; } + .image.is-4by5, #documenter .docs-sidebar .docs-logo > img.is-4by5 { + padding-top: 125%; } + .image.is-3by4, #documenter .docs-sidebar .docs-logo > img.is-3by4 { + padding-top: 133.3333%; } + .image.is-2by3, #documenter .docs-sidebar .docs-logo > img.is-2by3 { + padding-top: 150%; } + .image.is-3by5, #documenter .docs-sidebar .docs-logo > img.is-3by5 { + padding-top: 166.6666%; } + .image.is-9by16, #documenter .docs-sidebar .docs-logo > img.is-9by16 { + padding-top: 177.7777%; } + .image.is-1by2, #documenter .docs-sidebar .docs-logo > img.is-1by2 { + padding-top: 200%; } + .image.is-1by3, #documenter .docs-sidebar .docs-logo > img.is-1by3 { + padding-top: 300%; } + .image.is-16x16, #documenter .docs-sidebar .docs-logo > img.is-16x16 { + height: 16px; + width: 16px; } + .image.is-24x24, #documenter .docs-sidebar .docs-logo > img.is-24x24 { + height: 24px; + width: 24px; } + .image.is-32x32, #documenter .docs-sidebar .docs-logo > img.is-32x32 { + height: 32px; + width: 32px; } + .image.is-48x48, #documenter .docs-sidebar .docs-logo > img.is-48x48 { + height: 48px; + width: 48px; } + .image.is-64x64, #documenter .docs-sidebar .docs-logo > img.is-64x64 { + height: 64px; + width: 64px; } + .image.is-96x96, #documenter .docs-sidebar .docs-logo > img.is-96x96 { + height: 96px; + width: 96px; } + .image.is-128x128, #documenter .docs-sidebar .docs-logo > img.is-128x128 { + height: 128px; + width: 128px; } + +.notification { + background-color: whitesmoke; + border-radius: 4px; + padding: 1.25rem 2.5rem 1.25rem 1.5rem; + position: relative; } + .notification a:not(.button):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + .notification strong { + color: currentColor; } + .notification code, + .notification pre { + background: white; } + .notification pre code { + background: transparent; } + .notification > .delete { + position: absolute; + right: 0.5rem; + top: 0.5rem; } + .notification .title, + .notification .subtitle, + .notification .content { + color: currentColor; } + .notification.is-white { + background-color: white; + color: #0a0a0a; } + .notification.is-black { + background-color: #0a0a0a; + color: white; } + .notification.is-light { + background-color: whitesmoke; + color: #363636; } + .notification.is-dark, .content kbd.notification { + background-color: #363636; + color: whitesmoke; } + .notification.is-primary, .docstring > section > a.notification.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .notification.is-link { + background-color: #149eaa; + color: #fff; } + .notification.is-info { + background-color: #209cee; + color: #fff; } + .notification.is-success { + background-color: #22c35b; + color: #fff; } + .notification.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .notification.is-danger { + background-color: #da0b00; + color: #fff; } + +.progress { + -moz-appearance: none; + -webkit-appearance: none; + border: none; + border-radius: 290486px; + display: block; + height: 1rem; + overflow: hidden; + padding: 0; + width: 100%; } + .progress::-webkit-progress-bar { + background-color: #dbdbdb; } + .progress::-webkit-progress-value { + background-color: #202020; } + .progress::-moz-progress-bar { + background-color: #202020; } + .progress::-ms-fill { + background-color: #202020; + border: none; } + .progress.is-white::-webkit-progress-value { + background-color: white; } + .progress.is-white::-moz-progress-bar { + background-color: white; } + .progress.is-white::-ms-fill { + background-color: white; } + .progress.is-white:indeterminate { + background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); } + .progress.is-black::-webkit-progress-value { + background-color: #0a0a0a; } + .progress.is-black::-moz-progress-bar { + background-color: #0a0a0a; } + .progress.is-black::-ms-fill { + background-color: #0a0a0a; } + .progress.is-black:indeterminate { + background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); } + .progress.is-light::-webkit-progress-value { + background-color: whitesmoke; } + .progress.is-light::-moz-progress-bar { + background-color: whitesmoke; } + .progress.is-light::-ms-fill { + background-color: whitesmoke; } + .progress.is-light:indeterminate { + background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); } + .progress.is-dark::-webkit-progress-value, .content kbd.progress::-webkit-progress-value { + background-color: #363636; } + .progress.is-dark::-moz-progress-bar, .content kbd.progress::-moz-progress-bar { + background-color: #363636; } + .progress.is-dark::-ms-fill, .content kbd.progress::-ms-fill { + background-color: #363636; } + .progress.is-dark:indeterminate, .content kbd.progress:indeterminate { + background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); } + .progress.is-primary::-webkit-progress-value, .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { + background-color: #4eb5de; } + .progress.is-primary::-moz-progress-bar, .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { + background-color: #4eb5de; } + .progress.is-primary::-ms-fill, .docstring > section > a.progress.docs-sourcelink::-ms-fill { + background-color: #4eb5de; } + .progress.is-primary:indeterminate, .docstring > section > a.progress.docs-sourcelink:indeterminate { + background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); } + .progress.is-link::-webkit-progress-value { + background-color: #149eaa; } + .progress.is-link::-moz-progress-bar { + background-color: #149eaa; } + .progress.is-link::-ms-fill { + background-color: #149eaa; } + .progress.is-link:indeterminate { + background-image: linear-gradient(to right, #149eaa 30%, #dbdbdb 30%); } + .progress.is-info::-webkit-progress-value { + background-color: #209cee; } + .progress.is-info::-moz-progress-bar { + background-color: #209cee; } + .progress.is-info::-ms-fill { + background-color: #209cee; } + .progress.is-info:indeterminate { + background-image: linear-gradient(to right, #209cee 30%, #dbdbdb 30%); } + .progress.is-success::-webkit-progress-value { + background-color: #22c35b; } + .progress.is-success::-moz-progress-bar { + background-color: #22c35b; } + .progress.is-success::-ms-fill { + background-color: #22c35b; } + .progress.is-success:indeterminate { + background-image: linear-gradient(to right, #22c35b 30%, #dbdbdb 30%); } + .progress.is-warning::-webkit-progress-value { + background-color: #ffdd57; } + .progress.is-warning::-moz-progress-bar { + background-color: #ffdd57; } + .progress.is-warning::-ms-fill { + background-color: #ffdd57; } + .progress.is-warning:indeterminate { + background-image: linear-gradient(to right, #ffdd57 30%, #dbdbdb 30%); } + .progress.is-danger::-webkit-progress-value { + background-color: #da0b00; } + .progress.is-danger::-moz-progress-bar { + background-color: #da0b00; } + .progress.is-danger::-ms-fill { + background-color: #da0b00; } + .progress.is-danger:indeterminate { + background-image: linear-gradient(to right, #da0b00 30%, #dbdbdb 30%); } + .progress:indeterminate { + animation-duration: 1.5s; + animation-iteration-count: infinite; + animation-name: moveIndeterminate; + animation-timing-function: linear; + background-color: #dbdbdb; + background-image: linear-gradient(to right, #202020 30%, #dbdbdb 30%); + background-position: top left; + background-repeat: no-repeat; + background-size: 150% 150%; } + .progress:indeterminate::-webkit-progress-bar { + background-color: transparent; } + .progress:indeterminate::-moz-progress-bar { + background-color: transparent; } + .progress.is-small, #documenter .docs-sidebar form.docs-search > input.progress { + height: 0.75rem; } + .progress.is-medium { + height: 1.25rem; } + .progress.is-large { + height: 1.5rem; } + +@keyframes moveIndeterminate { + from { + background-position: 200% 0; } + to { + background-position: -200% 0; } } + +.table { + background-color: white; + color: #363636; } + .table td, + .table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + .table td.is-white, + .table th.is-white { + background-color: white; + border-color: white; + color: #0a0a0a; } + .table td.is-black, + .table th.is-black { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .table td.is-light, + .table th.is-light { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .table td.is-dark, + .table th.is-dark { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .table td.is-primary, + .table th.is-primary { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + .table td.is-link, + .table th.is-link { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + .table td.is-info, + .table th.is-info { + background-color: #209cee; + border-color: #209cee; + color: #fff; } + .table td.is-success, + .table th.is-success { + background-color: #22c35b; + border-color: #22c35b; + color: #fff; } + .table td.is-warning, + .table th.is-warning { + background-color: #ffdd57; + border-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .table td.is-danger, + .table th.is-danger { + background-color: #da0b00; + border-color: #da0b00; + color: #fff; } + .table td.is-narrow, + .table th.is-narrow { + white-space: nowrap; + width: 1%; } + .table td.is-selected, + .table th.is-selected { + background-color: #4eb5de; + color: #fff; } + .table td.is-selected a, + .table td.is-selected strong, + .table th.is-selected a, + .table th.is-selected strong { + color: currentColor; } + .table th { + color: #654ca3; } + .table th:not([align]) { + text-align: left; } + .table tr.is-selected { + background-color: #4eb5de; + color: #fff; } + .table tr.is-selected a, + .table tr.is-selected strong { + color: currentColor; } + .table tr.is-selected td, + .table tr.is-selected th { + border-color: #fff; + color: currentColor; } + .table thead { + background-color: transparent; } + .table thead td, + .table thead th { + border-width: 0 0 2px; + color: #654ca3; } + .table tfoot { + background-color: transparent; } + .table tfoot td, + .table tfoot th { + border-width: 2px 0 0; + color: #654ca3; } + .table tbody { + background-color: transparent; } + .table tbody tr:last-child td, + .table tbody tr:last-child th { + border-bottom-width: 0; } + .table.is-bordered td, + .table.is-bordered th { + border-width: 1px; } + .table.is-bordered tr:last-child td, + .table.is-bordered tr:last-child th { + border-bottom-width: 1px; } + .table.is-fullwidth { + width: 100%; } + .table.is-hoverable tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { + background-color: whitesmoke; } + .table.is-narrow td, + .table.is-narrow th { + padding: 0.25em 0.5em; } + .table.is-striped tbody tr:not(.is-selected):nth-child(even) { + background-color: #fafafa; } + +.table-container { + -webkit-overflow-scrolling: touch; + overflow: auto; + overflow-y: hidden; + max-width: 100%; } + +.tags { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .tags .tag, .tags .content kbd, .content .tags kbd, .tags .docstring > section > a.docs-sourcelink { + margin-bottom: 0.5rem; } + .tags .tag:not(:last-child), .tags .content kbd:not(:last-child), .content .tags kbd:not(:last-child), .tags .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0.5rem; } + .tags:last-child { + margin-bottom: -0.5rem; } + .tags:not(:last-child) { + margin-bottom: 1rem; } + .tags.are-medium .tag:not(.is-normal):not(.is-large), .tags.are-medium .content kbd:not(.is-normal):not(.is-large), .content .tags.are-medium kbd:not(.is-normal):not(.is-large), .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { + font-size: 1rem; } + .tags.are-large .tag:not(.is-normal):not(.is-medium), .tags.are-large .content kbd:not(.is-normal):not(.is-medium), .content .tags.are-large kbd:not(.is-normal):not(.is-medium), .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { + font-size: 1.25rem; } + .tags.is-centered { + justify-content: center; } + .tags.is-centered .tag, .tags.is-centered .content kbd, .content .tags.is-centered kbd, .tags.is-centered .docstring > section > a.docs-sourcelink { + margin-right: 0.25rem; + margin-left: 0.25rem; } + .tags.is-right { + justify-content: flex-end; } + .tags.is-right .tag:not(:first-child), .tags.is-right .content kbd:not(:first-child), .content .tags.is-right kbd:not(:first-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0.5rem; } + .tags.is-right .tag:not(:last-child), .tags.is-right .content kbd:not(:last-child), .content .tags.is-right kbd:not(:last-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0; } + .tags.has-addons .tag, .tags.has-addons .content kbd, .content .tags.has-addons kbd, .tags.has-addons .docstring > section > a.docs-sourcelink { + margin-right: 0; } + .tags.has-addons .tag:not(:first-child), .tags.has-addons .content kbd:not(:first-child), .content .tags.has-addons kbd:not(:first-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0; + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .tags.has-addons .tag:not(:last-child), .tags.has-addons .content kbd:not(:last-child), .content .tags.has-addons kbd:not(:last-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + +.tag:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink:not(body) { + align-items: center; + background-color: whitesmoke; + border-radius: 4px; + color: #202020; + display: inline-flex; + font-size: 0.75rem; + height: 2em; + justify-content: center; + line-height: 1.5; + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + .tag:not(body) .delete, .content kbd:not(body) .delete, .docstring > section > a.docs-sourcelink:not(body) .delete { + margin-left: 0.25rem; + margin-right: -0.375rem; } + .tag.is-white:not(body), .content kbd.is-white:not(body), .docstring > section > a.docs-sourcelink.is-white:not(body) { + background-color: white; + color: #0a0a0a; } + .tag.is-black:not(body), .content kbd.is-black:not(body), .docstring > section > a.docs-sourcelink.is-black:not(body) { + background-color: #0a0a0a; + color: white; } + .tag.is-light:not(body), .content kbd.is-light:not(body), .docstring > section > a.docs-sourcelink.is-light:not(body) { + background-color: whitesmoke; + color: #363636; } + .tag.is-dark:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink.is-dark:not(body), .content .docstring > section > kbd:not(body) { + background-color: #363636; + color: whitesmoke; } + .tag.is-primary:not(body), .content kbd.is-primary:not(body), .docstring > section > a.docs-sourcelink:not(body) { + background-color: #4eb5de; + color: #fff; } + .tag.is-link:not(body), .content kbd.is-link:not(body), .docstring > section > a.docs-sourcelink.is-link:not(body) { + background-color: #149eaa; + color: #fff; } + .tag.is-info:not(body), .content kbd.is-info:not(body), .docstring > section > a.docs-sourcelink.is-info:not(body) { + background-color: #209cee; + color: #fff; } + .tag.is-success:not(body), .content kbd.is-success:not(body), .docstring > section > a.docs-sourcelink.is-success:not(body) { + background-color: #22c35b; + color: #fff; } + .tag.is-warning:not(body), .content kbd.is-warning:not(body), .docstring > section > a.docs-sourcelink.is-warning:not(body) { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .tag.is-danger:not(body), .content kbd.is-danger:not(body), .docstring > section > a.docs-sourcelink.is-danger:not(body) { + background-color: #da0b00; + color: #fff; } + .tag.is-normal:not(body), .content kbd.is-normal:not(body), .docstring > section > a.docs-sourcelink.is-normal:not(body) { + font-size: 0.75rem; } + .tag.is-medium:not(body), .content kbd.is-medium:not(body), .docstring > section > a.docs-sourcelink.is-medium:not(body) { + font-size: 1rem; } + .tag.is-large:not(body), .content kbd.is-large:not(body), .docstring > section > a.docs-sourcelink.is-large:not(body) { + font-size: 1.25rem; } + .tag:not(body) .icon:first-child:not(:last-child), .content kbd:not(body) .icon:first-child:not(:last-child), .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { + margin-left: -0.375em; + margin-right: 0.1875em; } + .tag:not(body) .icon:last-child:not(:first-child), .content kbd:not(body) .icon:last-child:not(:first-child), .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: -0.375em; } + .tag:not(body) .icon:first-child:last-child, .content kbd:not(body) .icon:first-child:last-child, .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { + margin-left: -0.375em; + margin-right: -0.375em; } + .tag.is-delete:not(body), .content kbd.is-delete:not(body), .docstring > section > a.docs-sourcelink.is-delete:not(body) { + margin-left: 1px; + padding: 0; + position: relative; + width: 2em; } + .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + background-color: currentColor; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { + height: 1px; + width: 50%; } + .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + height: 50%; + width: 1px; } + .tag.is-delete:not(body):hover, .content kbd.is-delete:not(body):hover, .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, .tag.is-delete:not(body):focus, .content kbd.is-delete:not(body):focus, .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { + background-color: #e8e8e8; } + .tag.is-delete:not(body):active, .content kbd.is-delete:not(body):active, .docstring > section > a.docs-sourcelink.is-delete:not(body):active { + background-color: #dbdbdb; } + .tag.is-rounded:not(body), #documenter .docs-sidebar form.docs-search > input:not(body), .content kbd.is-rounded:not(body), #documenter .docs-sidebar .content form.docs-search > input:not(body), .docstring > section > a.docs-sourcelink.is-rounded:not(body) { + border-radius: 290486px; } + +a.tag:hover, .docstring > section > a.docs-sourcelink:hover { + text-decoration: underline; } + +.title, +.subtitle { + word-break: break-word; } + .title em, + .title span, + .subtitle em, + .subtitle span { + font-weight: inherit; } + .title sub, + .subtitle sub { + font-size: 0.75em; } + .title sup, + .subtitle sup { + font-size: 0.75em; } + .title .tag, .title .content kbd, .content .title kbd, .title .docstring > section > a.docs-sourcelink, + .subtitle .tag, + .subtitle .content kbd, + .content .subtitle kbd, + .subtitle .docstring > section > a.docs-sourcelink { + vertical-align: middle; } + +.title { + color: #363636; + font-size: 2rem; + font-weight: 600; + line-height: 1.125; } + .title strong { + color: inherit; + font-weight: inherit; } + .title + .highlight { + margin-top: -0.75rem; } + .title:not(.is-spaced) + .subtitle { + margin-top: -1.25rem; } + .title.is-1 { + font-size: 3rem; } + .title.is-2 { + font-size: 2.5rem; } + .title.is-3 { + font-size: 2rem; } + .title.is-4 { + font-size: 1.5rem; } + .title.is-5 { + font-size: 1.25rem; } + .title.is-6 { + font-size: 1rem; } + .title.is-7 { + font-size: 0.75rem; } + +.subtitle { + color: #4a4a4a; + font-size: 1.25rem; + font-weight: 400; + line-height: 1.25; } + .subtitle strong { + color: #363636; + font-weight: 600; } + .subtitle:not(.is-spaced) + .title { + margin-top: -1.25rem; } + .subtitle.is-1 { + font-size: 3rem; } + .subtitle.is-2 { + font-size: 2.5rem; } + .subtitle.is-3 { + font-size: 2rem; } + .subtitle.is-4 { + font-size: 1.5rem; } + .subtitle.is-5 { + font-size: 1.25rem; } + .subtitle.is-6 { + font-size: 1rem; } + .subtitle.is-7 { + font-size: 0.75rem; } + +.heading { + display: block; + font-size: 11px; + letter-spacing: 1px; + margin-bottom: 5px; + text-transform: uppercase; } + +.highlight { + font-weight: 400; + max-width: 100%; + overflow: hidden; + padding: 0; } + .highlight pre { + overflow: auto; + max-width: 100%; } + +.number { + align-items: center; + background-color: whitesmoke; + border-radius: 290486px; + display: inline-flex; + font-size: 1.25rem; + height: 2em; + justify-content: center; + margin-right: 1.5rem; + min-width: 2.5em; + padding: 0.25rem 0.5rem; + text-align: center; + vertical-align: top; } + +.select select, .textarea, .input, #documenter .docs-sidebar form.docs-search > input { + background-color: white; + border-color: #dbdbdb; + border-radius: 4px; + color: #363636; } + .select select::-moz-placeholder, .textarea::-moz-placeholder, .input::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select::-webkit-input-placeholder, .textarea::-webkit-input-placeholder, .input::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:-moz-placeholder, .textarea:-moz-placeholder, .input:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:-ms-input-placeholder, .textarea:-ms-input-placeholder, .input:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:hover, .textarea:hover, .input:hover, #documenter .docs-sidebar form.docs-search > input:hover, .select select.is-hovered, .is-hovered.textarea, .is-hovered.input, #documenter .docs-sidebar form.docs-search > input.is-hovered { + border-color: #149eaa; } + .select select:focus, .textarea:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .select select.is-focused, .is-focused.textarea, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .select select:active, .textarea:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .select select.is-active, .is-active.textarea, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + border-color: #fff; + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .select select[disabled], .textarea[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] .select select, .select fieldset[disabled] select, fieldset[disabled] .textarea, fieldset[disabled] .input, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input { + background-color: whitesmoke; + border-color: whitesmoke; + box-shadow: none; + color: #6b6b6b; } + .select select[disabled]::-moz-placeholder, .textarea[disabled]::-moz-placeholder, .input[disabled]::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] .select select::-moz-placeholder, .select fieldset[disabled] select::-moz-placeholder, fieldset[disabled] .textarea::-moz-placeholder, fieldset[disabled] .input::-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-moz-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]::-webkit-input-placeholder, .textarea[disabled]::-webkit-input-placeholder, .input[disabled]::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] .select select::-webkit-input-placeholder, .select fieldset[disabled] select::-webkit-input-placeholder, fieldset[disabled] .textarea::-webkit-input-placeholder, fieldset[disabled] .input::-webkit-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-webkit-input-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]:-moz-placeholder, .textarea[disabled]:-moz-placeholder, .input[disabled]:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] .select select:-moz-placeholder, .select fieldset[disabled] select:-moz-placeholder, fieldset[disabled] .textarea:-moz-placeholder, fieldset[disabled] .input:-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-moz-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]:-ms-input-placeholder, .textarea[disabled]:-ms-input-placeholder, .input[disabled]:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] .select select:-ms-input-placeholder, .select fieldset[disabled] select:-ms-input-placeholder, fieldset[disabled] .textarea:-ms-input-placeholder, fieldset[disabled] .input:-ms-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-ms-input-placeholder { + color: rgba(107, 107, 107, 0.3); } + +.textarea, .input, #documenter .docs-sidebar form.docs-search > input { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); + max-width: 100%; + width: 100%; } + .textarea[readonly], .input[readonly], #documenter .docs-sidebar form.docs-search > input[readonly] { + box-shadow: none; } + .is-white.textarea, .is-white.input, #documenter .docs-sidebar form.docs-search > input.is-white { + border-color: white; } + .is-white.textarea:focus, .is-white.input:focus, #documenter .docs-sidebar form.docs-search > input.is-white:focus, .is-white.is-focused.textarea, .is-white.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-white.textarea:active, .is-white.input:active, #documenter .docs-sidebar form.docs-search > input.is-white:active, .is-white.is-active.textarea, .is-white.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .is-black.textarea, .is-black.input, #documenter .docs-sidebar form.docs-search > input.is-black { + border-color: #0a0a0a; } + .is-black.textarea:focus, .is-black.input:focus, #documenter .docs-sidebar form.docs-search > input.is-black:focus, .is-black.is-focused.textarea, .is-black.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-black.textarea:active, .is-black.input:active, #documenter .docs-sidebar form.docs-search > input.is-black:active, .is-black.is-active.textarea, .is-black.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .is-light.textarea, .is-light.input, #documenter .docs-sidebar form.docs-search > input.is-light { + border-color: whitesmoke; } + .is-light.textarea:focus, .is-light.input:focus, #documenter .docs-sidebar form.docs-search > input.is-light:focus, .is-light.is-focused.textarea, .is-light.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-light.textarea:active, .is-light.input:active, #documenter .docs-sidebar form.docs-search > input.is-light:active, .is-light.is-active.textarea, .is-light.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .is-dark.textarea, .content kbd.textarea, .is-dark.input, #documenter .docs-sidebar form.docs-search > input.is-dark, .content kbd.input { + border-color: #363636; } + .is-dark.textarea:focus, .content kbd.textarea:focus, .is-dark.input:focus, #documenter .docs-sidebar form.docs-search > input.is-dark:focus, .content kbd.input:focus, .is-dark.is-focused.textarea, .content kbd.is-focused.textarea, .is-dark.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .content kbd.is-focused.input, #documenter .docs-sidebar .content form.docs-search > input.is-focused, .is-dark.textarea:active, .content kbd.textarea:active, .is-dark.input:active, #documenter .docs-sidebar form.docs-search > input.is-dark:active, .content kbd.input:active, .is-dark.is-active.textarea, .content kbd.is-active.textarea, .is-dark.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .content kbd.is-active.input, #documenter .docs-sidebar .content form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .is-primary.textarea, .docstring > section > a.textarea.docs-sourcelink, .is-primary.input, #documenter .docs-sidebar form.docs-search > input.is-primary, .docstring > section > a.input.docs-sourcelink { + border-color: #4eb5de; } + .is-primary.textarea:focus, .docstring > section > a.textarea.docs-sourcelink:focus, .is-primary.input:focus, #documenter .docs-sidebar form.docs-search > input.is-primary:focus, .docstring > section > a.input.docs-sourcelink:focus, .is-primary.is-focused.textarea, .docstring > section > a.is-focused.textarea.docs-sourcelink, .is-primary.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .docstring > section > a.is-focused.input.docs-sourcelink, .is-primary.textarea:active, .docstring > section > a.textarea.docs-sourcelink:active, .is-primary.input:active, #documenter .docs-sidebar form.docs-search > input.is-primary:active, .docstring > section > a.input.docs-sourcelink:active, .is-primary.is-active.textarea, .docstring > section > a.is-active.textarea.docs-sourcelink, .is-primary.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .docstring > section > a.is-active.input.docs-sourcelink { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .is-link.textarea, .is-link.input, #documenter .docs-sidebar form.docs-search > input.is-link { + border-color: #149eaa; } + .is-link.textarea:focus, .is-link.input:focus, #documenter .docs-sidebar form.docs-search > input.is-link:focus, .is-link.is-focused.textarea, .is-link.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-link.textarea:active, .is-link.input:active, #documenter .docs-sidebar form.docs-search > input.is-link:active, .is-link.is-active.textarea, .is-link.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .is-info.textarea, .is-info.input, #documenter .docs-sidebar form.docs-search > input.is-info { + border-color: #209cee; } + .is-info.textarea:focus, .is-info.input:focus, #documenter .docs-sidebar form.docs-search > input.is-info:focus, .is-info.is-focused.textarea, .is-info.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-info.textarea:active, .is-info.input:active, #documenter .docs-sidebar form.docs-search > input.is-info:active, .is-info.is-active.textarea, .is-info.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .is-success.textarea, .is-success.input, #documenter .docs-sidebar form.docs-search > input.is-success { + border-color: #22c35b; } + .is-success.textarea:focus, .is-success.input:focus, #documenter .docs-sidebar form.docs-search > input.is-success:focus, .is-success.is-focused.textarea, .is-success.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-success.textarea:active, .is-success.input:active, #documenter .docs-sidebar form.docs-search > input.is-success:active, .is-success.is-active.textarea, .is-success.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .is-warning.textarea, .is-warning.input, #documenter .docs-sidebar form.docs-search > input.is-warning { + border-color: #ffdd57; } + .is-warning.textarea:focus, .is-warning.input:focus, #documenter .docs-sidebar form.docs-search > input.is-warning:focus, .is-warning.is-focused.textarea, .is-warning.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-warning.textarea:active, .is-warning.input:active, #documenter .docs-sidebar form.docs-search > input.is-warning:active, .is-warning.is-active.textarea, .is-warning.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .is-danger.textarea, .is-danger.input, #documenter .docs-sidebar form.docs-search > input.is-danger { + border-color: #da0b00; } + .is-danger.textarea:focus, .is-danger.input:focus, #documenter .docs-sidebar form.docs-search > input.is-danger:focus, .is-danger.is-focused.textarea, .is-danger.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-danger.textarea:active, .is-danger.input:active, #documenter .docs-sidebar form.docs-search > input.is-danger:active, .is-danger.is-active.textarea, .is-danger.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .is-small.textarea, .is-small.input, #documenter .docs-sidebar form.docs-search > input { + border-radius: 2px; + font-size: 0.75rem; } + .is-medium.textarea, .is-medium.input, #documenter .docs-sidebar form.docs-search > input.is-medium { + font-size: 1.25rem; } + .is-large.textarea, .is-large.input, #documenter .docs-sidebar form.docs-search > input.is-large { + font-size: 1.5rem; } + .is-fullwidth.textarea, .is-fullwidth.input, #documenter .docs-sidebar form.docs-search > input.is-fullwidth { + display: block; + width: 100%; } + .is-inline.textarea, .is-inline.input, #documenter .docs-sidebar form.docs-search > input.is-inline { + display: inline; + width: auto; } + +.input.is-rounded, #documenter .docs-sidebar form.docs-search > input { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + +.input.is-static, #documenter .docs-sidebar form.docs-search > input.is-static { + background-color: transparent; + border-color: transparent; + box-shadow: none; + padding-left: 0; + padding-right: 0; } + +.textarea { + display: block; + max-width: 100%; + min-width: 100%; + padding: 0.625em; + resize: vertical; } + .textarea:not([rows]) { + max-height: 600px; + min-height: 120px; } + .textarea[rows] { + height: initial; } + .textarea.has-fixed-size { + resize: none; } + +.radio, .checkbox { + cursor: pointer; + display: inline-block; + line-height: 1.25; + position: relative; } + .radio input, .checkbox input { + cursor: pointer; } + .radio:hover, .checkbox:hover { + color: #363636; } + .radio[disabled], .checkbox[disabled], fieldset[disabled] .radio, fieldset[disabled] .checkbox { + color: #6b6b6b; + cursor: not-allowed; } + +.radio + .radio { + margin-left: 0.5em; } + +.select { + display: inline-block; + max-width: 100%; + position: relative; + vertical-align: top; } + .select:not(.is-multiple) { + height: 2.25em; } + .select:not(.is-multiple):not(.is-loading)::after { + border-color: #149eaa; + right: 1.125em; + z-index: 4; } + .select.is-rounded select, #documenter .docs-sidebar form.docs-search > input.select select { + border-radius: 290486px; + padding-left: 1em; } + .select select { + cursor: pointer; + display: block; + font-size: 1em; + max-width: 100%; + outline: none; } + .select select::-ms-expand { + display: none; } + .select select[disabled]:hover, fieldset[disabled] .select select:hover { + border-color: whitesmoke; } + .select select:not([multiple]) { + padding-right: 2.5em; } + .select select[multiple] { + height: auto; + padding: 0; } + .select select[multiple] option { + padding: 0.5em 1em; } + .select:not(.is-multiple):not(.is-loading):hover::after { + border-color: #363636; } + .select.is-white:not(:hover)::after { + border-color: white; } + .select.is-white select { + border-color: white; } + .select.is-white select:hover, .select.is-white select.is-hovered { + border-color: #f2f2f2; } + .select.is-white select:focus, .select.is-white select.is-focused, .select.is-white select:active, .select.is-white select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .select.is-black:not(:hover)::after { + border-color: #0a0a0a; } + .select.is-black select { + border-color: #0a0a0a; } + .select.is-black select:hover, .select.is-black select.is-hovered { + border-color: black; } + .select.is-black select:focus, .select.is-black select.is-focused, .select.is-black select:active, .select.is-black select.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .select.is-light:not(:hover)::after { + border-color: whitesmoke; } + .select.is-light select { + border-color: whitesmoke; } + .select.is-light select:hover, .select.is-light select.is-hovered { + border-color: #e8e8e8; } + .select.is-light select:focus, .select.is-light select.is-focused, .select.is-light select:active, .select.is-light select.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .select.is-dark:not(:hover)::after, .content kbd.select:not(:hover)::after { + border-color: #363636; } + .select.is-dark select, .content kbd.select select { + border-color: #363636; } + .select.is-dark select:hover, .content kbd.select select:hover, .select.is-dark select.is-hovered, .content kbd.select select.is-hovered { + border-color: #292929; } + .select.is-dark select:focus, .content kbd.select select:focus, .select.is-dark select.is-focused, .content kbd.select select.is-focused, .select.is-dark select:active, .content kbd.select select:active, .select.is-dark select.is-active, .content kbd.select select.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .select.is-primary:not(:hover)::after, .docstring > section > a.select.docs-sourcelink:not(:hover)::after { + border-color: #4eb5de; } + .select.is-primary select, .docstring > section > a.select.docs-sourcelink select { + border-color: #4eb5de; } + .select.is-primary select:hover, .docstring > section > a.select.docs-sourcelink select:hover, .select.is-primary select.is-hovered, .docstring > section > a.select.docs-sourcelink select.is-hovered { + border-color: #39acda; } + .select.is-primary select:focus, .docstring > section > a.select.docs-sourcelink select:focus, .select.is-primary select.is-focused, .docstring > section > a.select.docs-sourcelink select.is-focused, .select.is-primary select:active, .docstring > section > a.select.docs-sourcelink select:active, .select.is-primary select.is-active, .docstring > section > a.select.docs-sourcelink select.is-active { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .select.is-link:not(:hover)::after { + border-color: #149eaa; } + .select.is-link select { + border-color: #149eaa; } + .select.is-link select:hover, .select.is-link select.is-hovered { + border-color: #118993; } + .select.is-link select:focus, .select.is-link select.is-focused, .select.is-link select:active, .select.is-link select.is-active { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .select.is-info:not(:hover)::after { + border-color: #209cee; } + .select.is-info select { + border-color: #209cee; } + .select.is-info select:hover, .select.is-info select.is-hovered { + border-color: #1190e3; } + .select.is-info select:focus, .select.is-info select.is-focused, .select.is-info select:active, .select.is-info select.is-active { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .select.is-success:not(:hover)::after { + border-color: #22c35b; } + .select.is-success select { + border-color: #22c35b; } + .select.is-success select:hover, .select.is-success select.is-hovered { + border-color: #1ead51; } + .select.is-success select:focus, .select.is-success select.is-focused, .select.is-success select:active, .select.is-success select.is-active { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .select.is-warning:not(:hover)::after { + border-color: #ffdd57; } + .select.is-warning select { + border-color: #ffdd57; } + .select.is-warning select:hover, .select.is-warning select.is-hovered { + border-color: #ffd83e; } + .select.is-warning select:focus, .select.is-warning select.is-focused, .select.is-warning select:active, .select.is-warning select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .select.is-danger:not(:hover)::after { + border-color: #da0b00; } + .select.is-danger select { + border-color: #da0b00; } + .select.is-danger select:hover, .select.is-danger select.is-hovered { + border-color: #c10a00; } + .select.is-danger select:focus, .select.is-danger select.is-focused, .select.is-danger select:active, .select.is-danger select.is-active { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .select.is-small, #documenter .docs-sidebar form.docs-search > input.select { + border-radius: 2px; + font-size: 0.75rem; } + .select.is-medium { + font-size: 1.25rem; } + .select.is-large { + font-size: 1.5rem; } + .select.is-disabled::after { + border-color: #6b6b6b; } + .select.is-fullwidth { + width: 100%; } + .select.is-fullwidth select { + width: 100%; } + .select.is-loading::after { + margin-top: 0; + position: absolute; + right: 0.625em; + top: 0.625em; + transform: none; } + .select.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + .select.is-loading.is-medium:after { + font-size: 1.25rem; } + .select.is-loading.is-large:after { + font-size: 1.5rem; } + +.file { + align-items: stretch; + display: flex; + justify-content: flex-start; + position: relative; } + .file.is-white .file-cta { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + .file.is-white:hover .file-cta, .file.is-white.is-hovered .file-cta { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + .file.is-white:focus .file-cta, .file.is-white.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); + color: #0a0a0a; } + .file.is-white:active .file-cta, .file.is-white.is-active .file-cta { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + .file.is-black .file-cta { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + .file.is-black:hover .file-cta, .file.is-black.is-hovered .file-cta { + background-color: #040404; + border-color: transparent; + color: white; } + .file.is-black:focus .file-cta, .file.is-black.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); + color: white; } + .file.is-black:active .file-cta, .file.is-black.is-active .file-cta { + background-color: black; + border-color: transparent; + color: white; } + .file.is-light .file-cta { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + .file.is-light:hover .file-cta, .file.is-light.is-hovered .file-cta { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + .file.is-light:focus .file-cta, .file.is-light.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25); + color: #363636; } + .file.is-light:active .file-cta, .file.is-light.is-active .file-cta { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + .file.is-dark .file-cta, .content kbd.file .file-cta { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + .file.is-dark:hover .file-cta, .content kbd.file:hover .file-cta, .file.is-dark.is-hovered .file-cta, .content kbd.file.is-hovered .file-cta { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + .file.is-dark:focus .file-cta, .content kbd.file:focus .file-cta, .file.is-dark.is-focused .file-cta, .content kbd.file.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25); + color: whitesmoke; } + .file.is-dark:active .file-cta, .content kbd.file:active .file-cta, .file.is-dark.is-active .file-cta, .content kbd.file.is-active .file-cta { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + .file.is-primary .file-cta, .docstring > section > a.file.docs-sourcelink .file-cta { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + .file.is-primary:hover .file-cta, .docstring > section > a.file.docs-sourcelink:hover .file-cta, .file.is-primary.is-hovered .file-cta, .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + .file.is-primary:focus .file-cta, .docstring > section > a.file.docs-sourcelink:focus .file-cta, .file.is-primary.is-focused .file-cta, .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25); + color: #fff; } + .file.is-primary:active .file-cta, .docstring > section > a.file.docs-sourcelink:active .file-cta, .file.is-primary.is-active .file-cta, .docstring > section > a.file.is-active.docs-sourcelink .file-cta { + background-color: #39acda; + border-color: transparent; + color: #fff; } + .file.is-link .file-cta { + background-color: #149eaa; + border-color: transparent; + color: #fff; } + .file.is-link:hover .file-cta, .file.is-link.is-hovered .file-cta { + background-color: #13939f; + border-color: transparent; + color: #fff; } + .file.is-link:focus .file-cta, .file.is-link.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(20, 158, 170, 0.25); + color: #fff; } + .file.is-link:active .file-cta, .file.is-link.is-active .file-cta { + background-color: #118993; + border-color: transparent; + color: #fff; } + .file.is-info .file-cta { + background-color: #209cee; + border-color: transparent; + color: #fff; } + .file.is-info:hover .file-cta, .file.is-info.is-hovered .file-cta { + background-color: #1497ed; + border-color: transparent; + color: #fff; } + .file.is-info:focus .file-cta, .file.is-info.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(32, 156, 238, 0.25); + color: #fff; } + .file.is-info:active .file-cta, .file.is-info.is-active .file-cta { + background-color: #1190e3; + border-color: transparent; + color: #fff; } + .file.is-success .file-cta { + background-color: #22c35b; + border-color: transparent; + color: #fff; } + .file.is-success:hover .file-cta, .file.is-success.is-hovered .file-cta { + background-color: #20b856; + border-color: transparent; + color: #fff; } + .file.is-success:focus .file-cta, .file.is-success.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(34, 195, 91, 0.25); + color: #fff; } + .file.is-success:active .file-cta, .file.is-success.is-active .file-cta { + background-color: #1ead51; + border-color: transparent; + color: #fff; } + .file.is-warning .file-cta { + background-color: #ffdd57; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:hover .file-cta, .file.is-warning.is-hovered .file-cta { + background-color: #ffda4a; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:focus .file-cta, .file.is-warning.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 221, 87, 0.25); + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:active .file-cta, .file.is-warning.is-active .file-cta { + background-color: #ffd83e; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-danger .file-cta { + background-color: #da0b00; + border-color: transparent; + color: #fff; } + .file.is-danger:hover .file-cta, .file.is-danger.is-hovered .file-cta { + background-color: #cd0a00; + border-color: transparent; + color: #fff; } + .file.is-danger:focus .file-cta, .file.is-danger.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(218, 11, 0, 0.25); + color: #fff; } + .file.is-danger:active .file-cta, .file.is-danger.is-active .file-cta { + background-color: #c10a00; + border-color: transparent; + color: #fff; } + .file.is-small, #documenter .docs-sidebar form.docs-search > input.file { + font-size: 0.75rem; } + .file.is-medium { + font-size: 1.25rem; } + .file.is-medium .file-icon .fa { + font-size: 21px; } + .file.is-large { + font-size: 1.5rem; } + .file.is-large .file-icon .fa { + font-size: 28px; } + .file.has-name .file-cta { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + .file.has-name .file-name { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .file.has-name.is-empty .file-cta { + border-radius: 4px; } + .file.has-name.is-empty .file-name { + display: none; } + .file.is-boxed .file-label { + flex-direction: column; } + .file.is-boxed .file-cta { + flex-direction: column; + height: auto; + padding: 1em 3em; } + .file.is-boxed .file-name { + border-width: 0 1px 1px; } + .file.is-boxed .file-icon { + height: 1.5em; + width: 1.5em; } + .file.is-boxed .file-icon .fa { + font-size: 21px; } + .file.is-boxed.is-small .file-icon .fa, #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { + font-size: 14px; } + .file.is-boxed.is-medium .file-icon .fa { + font-size: 28px; } + .file.is-boxed.is-large .file-icon .fa { + font-size: 35px; } + .file.is-boxed.has-name .file-cta { + border-radius: 4px 4px 0 0; } + .file.is-boxed.has-name .file-name { + border-radius: 0 0 4px 4px; + border-width: 0 1px 1px; } + .file.is-centered { + justify-content: center; } + .file.is-fullwidth .file-label { + width: 100%; } + .file.is-fullwidth .file-name { + flex-grow: 1; + max-width: none; } + .file.is-right { + justify-content: flex-end; } + .file.is-right .file-cta { + border-radius: 0 4px 4px 0; } + .file.is-right .file-name { + border-radius: 4px 0 0 4px; + border-width: 1px 0 1px 1px; + order: -1; } + +.file-label { + align-items: stretch; + display: flex; + cursor: pointer; + justify-content: flex-start; + overflow: hidden; + position: relative; } + .file-label:hover .file-cta { + background-color: #eeeeee; + color: #363636; } + .file-label:hover .file-name { + border-color: #d5d5d5; } + .file-label:active .file-cta { + background-color: #e8e8e8; + color: #363636; } + .file-label:active .file-name { + border-color: #cfcfcf; } + +.file-input { + height: 100%; + left: 0; + opacity: 0; + outline: none; + position: absolute; + top: 0; + width: 100%; } + +.file-cta, +.file-name { + border-color: #dbdbdb; + border-radius: 4px; + font-size: 1em; + padding-left: 1em; + padding-right: 1em; + white-space: nowrap; } + +.file-cta { + background-color: whitesmoke; + color: #4a4a4a; } + +.file-name { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px 1px 1px 0; + display: block; + max-width: 16em; + overflow: hidden; + text-align: left; + text-overflow: ellipsis; } + +.file-icon { + align-items: center; + display: flex; + height: 1em; + justify-content: center; + margin-right: 0.5em; + width: 1em; } + .file-icon .fa { + font-size: 14px; } + +.label { + color: #363636; + display: block; + font-size: 1rem; + font-weight: 700; } + .label:not(:last-child) { + margin-bottom: 0.5em; } + .label.is-small, #documenter .docs-sidebar form.docs-search > input.label { + font-size: 0.75rem; } + .label.is-medium { + font-size: 1.25rem; } + .label.is-large { + font-size: 1.5rem; } + +.help { + display: block; + font-size: 0.75rem; + margin-top: 0.25rem; } + .help.is-white { + color: white; } + .help.is-black { + color: #0a0a0a; } + .help.is-light { + color: whitesmoke; } + .help.is-dark, .content kbd.help { + color: #363636; } + .help.is-primary, .docstring > section > a.help.docs-sourcelink { + color: #4eb5de; } + .help.is-link { + color: #149eaa; } + .help.is-info { + color: #209cee; } + .help.is-success { + color: #22c35b; } + .help.is-warning { + color: #ffdd57; } + .help.is-danger { + color: #da0b00; } + +.field:not(:last-child) { + margin-bottom: 0.75rem; } + +.field.has-addons { + display: flex; + justify-content: flex-start; } + .field.has-addons .control:not(:last-child) { + margin-right: -1px; } + .field.has-addons .control:not(:first-child):not(:last-child) .button, + .field.has-addons .control:not(:first-child):not(:last-child) .input, + .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, + .field.has-addons .control:not(:first-child):not(:last-child) .select select { + border-radius: 0; } + .field.has-addons .control:first-child:not(:only-child) .button, + .field.has-addons .control:first-child:not(:only-child) .input, + .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, + .field.has-addons .control:first-child:not(:only-child) .select select { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + .field.has-addons .control:last-child:not(:only-child) .button, + .field.has-addons .control:last-child:not(:only-child) .input, + .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, + .field.has-addons .control:last-child:not(:only-child) .select select { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .field.has-addons .control .button:not([disabled]):hover, .field.has-addons .control .button.is-hovered:not([disabled]), + .field.has-addons .control .input:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, + .field.has-addons .control .input.is-hovered:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), + .field.has-addons .control .select select:not([disabled]):hover, + .field.has-addons .control .select select.is-hovered:not([disabled]) { + z-index: 2; } + .field.has-addons .control .button:not([disabled]):focus, .field.has-addons .control .button.is-focused:not([disabled]), .field.has-addons .control .button:not([disabled]):active, .field.has-addons .control .button.is-active:not([disabled]), + .field.has-addons .control .input:not([disabled]):focus, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, + .field.has-addons .control .input.is-focused:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), + .field.has-addons .control .input:not([disabled]):active, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, + .field.has-addons .control .input.is-active:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), + .field.has-addons .control .select select:not([disabled]):focus, + .field.has-addons .control .select select.is-focused:not([disabled]), + .field.has-addons .control .select select:not([disabled]):active, + .field.has-addons .control .select select.is-active:not([disabled]) { + z-index: 3; } + .field.has-addons .control .button:not([disabled]):focus:hover, .field.has-addons .control .button.is-focused:not([disabled]):hover, .field.has-addons .control .button:not([disabled]):active:hover, .field.has-addons .control .button.is-active:not([disabled]):hover, + .field.has-addons .control .input:not([disabled]):focus:hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, + .field.has-addons .control .input.is-focused:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, + .field.has-addons .control .input:not([disabled]):active:hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, + .field.has-addons .control .input.is-active:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, + .field.has-addons .control .select select:not([disabled]):focus:hover, + .field.has-addons .control .select select.is-focused:not([disabled]):hover, + .field.has-addons .control .select select:not([disabled]):active:hover, + .field.has-addons .control .select select.is-active:not([disabled]):hover { + z-index: 4; } + .field.has-addons .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .field.has-addons.has-addons-centered { + justify-content: center; } + .field.has-addons.has-addons-right { + justify-content: flex-end; } + .field.has-addons.has-addons-fullwidth .control { + flex-grow: 1; + flex-shrink: 0; } + +.field.is-grouped { + display: flex; + justify-content: flex-start; } + .field.is-grouped > .control { + flex-shrink: 0; } + .field.is-grouped > .control:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + .field.is-grouped > .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .field.is-grouped.is-grouped-centered { + justify-content: center; } + .field.is-grouped.is-grouped-right { + justify-content: flex-end; } + .field.is-grouped.is-grouped-multiline { + flex-wrap: wrap; } + .field.is-grouped.is-grouped-multiline > .control:last-child, .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { + margin-bottom: 0.75rem; } + .field.is-grouped.is-grouped-multiline:last-child { + margin-bottom: -0.75rem; } + .field.is-grouped.is-grouped-multiline:not(:last-child) { + margin-bottom: 0; } + +@media screen and (min-width: 769px), print { + .field.is-horizontal { + display: flex; } } + +.field-label .label { + font-size: inherit; } + +@media screen and (max-width: 768px) { + .field-label { + margin-bottom: 0.5rem; } } + +@media screen and (min-width: 769px), print { + .field-label { + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + margin-right: 1.5rem; + text-align: right; } + .field-label.is-small, #documenter .docs-sidebar form.docs-search > input.field-label { + font-size: 0.75rem; + padding-top: 0.375em; } + .field-label.is-normal { + padding-top: 0.375em; } + .field-label.is-medium { + font-size: 1.25rem; + padding-top: 0.375em; } + .field-label.is-large { + font-size: 1.5rem; + padding-top: 0.375em; } } + +.field-body .field .field { + margin-bottom: 0; } + +@media screen and (min-width: 769px), print { + .field-body { + display: flex; + flex-basis: 0; + flex-grow: 5; + flex-shrink: 1; } + .field-body .field { + margin-bottom: 0; } + .field-body > .field { + flex-shrink: 1; } + .field-body > .field:not(.is-narrow) { + flex-grow: 1; } + .field-body > .field:not(:last-child) { + margin-right: 0.75rem; } } + +.control { + box-sizing: border-box; + clear: both; + font-size: 1rem; + position: relative; + text-align: left; } + .control.has-icons-left .input:focus ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, + .control.has-icons-left .select:focus ~ .icon, .control.has-icons-right .input:focus ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, + .control.has-icons-right .select:focus ~ .icon { + color: #6b6b6b; } + .control.has-icons-left .input.is-small ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, + .control.has-icons-left .select.is-small ~ .icon, .control.has-icons-right .input.is-small ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, + .control.has-icons-right .select.is-small ~ .icon { + font-size: 0.75rem; } + .control.has-icons-left .input.is-medium ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, + .control.has-icons-left .select.is-medium ~ .icon, .control.has-icons-right .input.is-medium ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, + .control.has-icons-right .select.is-medium ~ .icon { + font-size: 1.25rem; } + .control.has-icons-left .input.is-large ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, + .control.has-icons-left .select.is-large ~ .icon, .control.has-icons-right .input.is-large ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, + .control.has-icons-right .select.is-large ~ .icon { + font-size: 1.5rem; } + .control.has-icons-left .icon, .control.has-icons-right .icon { + color: #dbdbdb; + height: 2.25em; + pointer-events: none; + position: absolute; + top: 0; + width: 2.25em; + z-index: 4; } + .control.has-icons-left .input, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, + .control.has-icons-left .select select { + padding-left: 2.25em; } + .control.has-icons-left .icon.is-left { + left: 0; } + .control.has-icons-right .input, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, + .control.has-icons-right .select select { + padding-right: 2.25em; } + .control.has-icons-right .icon.is-right { + right: 0; } + .control.is-loading::after { + position: absolute !important; + right: 0.625em; + top: 0.625em; + z-index: 4; } + .control.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + .control.is-loading.is-medium:after { + font-size: 1.25rem; } + .control.is-loading.is-large:after { + font-size: 1.5rem; } + +.breadcrumb { + font-size: 1rem; + white-space: nowrap; } + .breadcrumb a { + align-items: center; + color: #149eaa; + display: flex; + justify-content: center; + padding: 0 0.75em; } + .breadcrumb a:hover { + color: #107c85; } + .breadcrumb li { + align-items: center; + display: flex; } + .breadcrumb li:first-child a { + padding-left: 0; } + .breadcrumb li.is-active a { + color: #654ca3; + cursor: default; + pointer-events: none; } + .breadcrumb li + li::before { + color: #b5b5b5; + content: "\0002f"; } + .breadcrumb ul, + .breadcrumb ol { + align-items: flex-start; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .breadcrumb .icon:first-child { + margin-right: 0.5em; } + .breadcrumb .icon:last-child { + margin-left: 0.5em; } + .breadcrumb.is-centered ol, + .breadcrumb.is-centered ul { + justify-content: center; } + .breadcrumb.is-right ol, + .breadcrumb.is-right ul { + justify-content: flex-end; } + .breadcrumb.is-small, #documenter .docs-sidebar form.docs-search > input.breadcrumb { + font-size: 0.75rem; } + .breadcrumb.is-medium { + font-size: 1.25rem; } + .breadcrumb.is-large { + font-size: 1.5rem; } + .breadcrumb.has-arrow-separator li + li::before { + content: "\02192"; } + .breadcrumb.has-bullet-separator li + li::before { + content: "\02022"; } + .breadcrumb.has-dot-separator li + li::before { + content: "\000b7"; } + .breadcrumb.has-succeeds-separator li + li::before { + content: "\0227B"; } + +.card { + background-color: white; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #202020; + max-width: 100%; + position: relative; } + +.card-header { + background-color: transparent; + align-items: stretch; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + display: flex; } + +.card-header-title { + align-items: center; + color: #654ca3; + display: flex; + flex-grow: 1; + font-weight: 700; + padding: 0.75rem; } + .card-header-title.is-centered { + justify-content: center; } + +.card-header-icon { + align-items: center; + cursor: pointer; + display: flex; + justify-content: center; + padding: 0.75rem; } + +.card-image { + display: block; + position: relative; } + +.card-content { + background-color: transparent; + padding: 1.5rem; } + +.card-footer { + background-color: transparent; + border-top: 1px solid #dbdbdb; + align-items: stretch; + display: flex; } + +.card-footer-item { + align-items: center; + display: flex; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + justify-content: center; + padding: 0.75rem; } + .card-footer-item:not(:last-child) { + border-right: 1px solid #dbdbdb; } + +.card .media:not(:last-child) { + margin-bottom: 1.5rem; } + +.dropdown { + display: inline-flex; + position: relative; + vertical-align: top; } + .dropdown.is-active .dropdown-menu, .dropdown.is-hoverable:hover .dropdown-menu { + display: block; } + .dropdown.is-right .dropdown-menu { + left: auto; + right: 0; } + .dropdown.is-up .dropdown-menu { + bottom: 100%; + padding-bottom: 4px; + padding-top: initial; + top: auto; } + +.dropdown-menu { + display: none; + left: 0; + min-width: 12rem; + padding-top: 4px; + position: absolute; + top: 100%; + z-index: 20; } + +.dropdown-content { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + +.dropdown-item { + color: #4a4a4a; + display: block; + font-size: 0.875rem; + line-height: 1.5; + padding: 0.375rem 1rem; + position: relative; } + +a.dropdown-item, +button.dropdown-item { + padding-right: 3rem; + text-align: left; + white-space: nowrap; + width: 100%; } + a.dropdown-item:hover, + button.dropdown-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + a.dropdown-item.is-active, + button.dropdown-item.is-active { + background-color: #149eaa; + color: #fff; } + +.dropdown-divider { + background-color: #dbdbdb; + border: none; + display: block; + height: 1px; + margin: 0.5rem 0; } + +.level { + align-items: center; + justify-content: space-between; } + .level code { + border-radius: 4px; } + .level img { + display: inline-block; + vertical-align: top; } + .level.is-mobile { + display: flex; } + .level.is-mobile .level-left, + .level.is-mobile .level-right { + display: flex; } + .level.is-mobile .level-left + .level-right { + margin-top: 0; } + .level.is-mobile .level-item:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + .level.is-mobile .level-item:not(.is-narrow) { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + .level { + display: flex; } + .level > .level-item:not(.is-narrow) { + flex-grow: 1; } } +.level-item { + align-items: center; + display: flex; + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; + justify-content: center; } + .level-item .title, + .level-item .subtitle { + margin-bottom: 0; } + @media screen and (max-width: 768px) { + .level-item:not(:last-child) { + margin-bottom: 0.75rem; } } +.level-left, +.level-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + .level-left .level-item.is-flexible, + .level-right .level-item.is-flexible { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + .level-left .level-item:not(:last-child), + .level-right .level-item:not(:last-child) { + margin-right: 0.75rem; } } +.level-left { + align-items: center; + justify-content: flex-start; } + @media screen and (max-width: 768px) { + .level-left + .level-right { + margin-top: 1.5rem; } } + @media screen and (min-width: 769px), print { + .level-left { + display: flex; } } +.level-right { + align-items: center; + justify-content: flex-end; } + @media screen and (min-width: 769px), print { + .level-right { + display: flex; } } +.list { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } + +.list-item { + display: block; + padding: 0.5em 1em; } + .list-item:not(a) { + color: #202020; } + .list-item:first-child { + border-top-left-radius: 4px; + border-top-right-radius: 4px; } + .list-item:last-child { + border-bottom-left-radius: 4px; + border-bottom-right-radius: 4px; } + .list-item:not(:last-child) { + border-bottom: 1px solid #dbdbdb; } + .list-item.is-active { + background-color: #149eaa; + color: #fff; } + +a.list-item { + background-color: whitesmoke; + cursor: pointer; } + +.media { + align-items: flex-start; + display: flex; + text-align: left; } + .media .content:not(:last-child) { + margin-bottom: 0.75rem; } + .media .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + display: flex; + padding-top: 0.75rem; } + .media .media .content:not(:last-child), + .media .media .control:not(:last-child) { + margin-bottom: 0.5rem; } + .media .media .media { + padding-top: 0.5rem; } + .media .media .media + .media { + margin-top: 0.5rem; } + .media + .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + margin-top: 1rem; + padding-top: 1rem; } + .media.is-large + .media { + margin-top: 1.5rem; + padding-top: 1.5rem; } + +.media-left, +.media-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + +.media-left { + margin-right: 1rem; } + +.media-right { + margin-left: 1rem; } + +.media-content { + flex-basis: auto; + flex-grow: 1; + flex-shrink: 1; + text-align: left; } + +@media screen and (max-width: 768px) { + .media-content { + overflow-x: auto; } } + +.menu { + font-size: 1rem; } + .menu.is-small, #documenter .docs-sidebar form.docs-search > input.menu { + font-size: 0.75rem; } + .menu.is-medium { + font-size: 1.25rem; } + .menu.is-large { + font-size: 1.5rem; } + +.menu-list { + line-height: 1.25; } + .menu-list a { + border-radius: 2px; + color: #202020; + display: block; + padding: 0.5em 0.75em; } + .menu-list a:hover { + background-color: whitesmoke; + color: #654ca3; } + .menu-list a.is-active { + background-color: #149eaa; + color: #fff; } + .menu-list li ul { + border-left: 1px solid #dbdbdb; + margin: 0.75em; + padding-left: 0.75em; } + +.menu-label { + color: #6b6b6b; + font-size: 0.75em; + letter-spacing: 0.1em; + text-transform: uppercase; } + .menu-label:not(:first-child) { + margin-top: 1em; } + .menu-label:not(:last-child) { + margin-bottom: 1em; } + +.message { + background-color: whitesmoke; + border-radius: 4px; + font-size: 1rem; } + .message strong { + color: currentColor; } + .message a:not(.button):not(.tag):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + .message.is-small, #documenter .docs-sidebar form.docs-search > input.message { + font-size: 0.75rem; } + .message.is-medium { + font-size: 1.25rem; } + .message.is-large { + font-size: 1.5rem; } + .message.is-white { + background-color: white; } + .message.is-white .message-header { + background-color: white; + color: #0a0a0a; } + .message.is-white .message-body { + border-color: white; + color: #4d4d4d; } + .message.is-black { + background-color: #fafafa; } + .message.is-black .message-header { + background-color: #0a0a0a; + color: white; } + .message.is-black .message-body { + border-color: #0a0a0a; + color: #090909; } + .message.is-light { + background-color: #fafafa; } + .message.is-light .message-header { + background-color: whitesmoke; + color: #363636; } + .message.is-light .message-body { + border-color: whitesmoke; + color: #505050; } + .message.is-dark, .content kbd.message { + background-color: #fafafa; } + .message.is-dark .message-header, .content kbd.message .message-header { + background-color: #363636; + color: whitesmoke; } + .message.is-dark .message-body, .content kbd.message .message-body { + border-color: #363636; + color: #2a2a2a; } + .message.is-primary, .docstring > section > a.message.docs-sourcelink { + background-color: #f6fbfd; } + .message.is-primary .message-header, .docstring > section > a.message.docs-sourcelink .message-header { + background-color: #4eb5de; + color: #fff; } + .message.is-primary .message-body, .docstring > section > a.message.docs-sourcelink .message-body { + border-color: #4eb5de; + color: #1f556a; } + .message.is-link { + background-color: #f6fdfe; } + .message.is-link .message-header { + background-color: #149eaa; + color: #fff; } + .message.is-link .message-body { + border-color: #149eaa; + color: #0b393d; } + .message.is-info { + background-color: #f6fbfe; } + .message.is-info .message-header { + background-color: #209cee; + color: #fff; } + .message.is-info .message-body { + border-color: #209cee; + color: #12537d; } + .message.is-success { + background-color: #f6fdf9; } + .message.is-success .message-header { + background-color: #22c35b; + color: #fff; } + .message.is-success .message-body { + border-color: #22c35b; + color: #0f361d; } + .message.is-warning { + background-color: #fffdf5; } + .message.is-warning .message-header { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .message.is-warning .message-body { + border-color: #ffdd57; + color: #3c3108; } + .message.is-danger { + background-color: #fff5f5; } + .message.is-danger .message-header { + background-color: #da0b00; + color: #fff; } + .message.is-danger .message-body { + border-color: #da0b00; + color: #9b0c04; } + +.message-header { + align-items: center; + background-color: #202020; + border-radius: 4px 4px 0 0; + color: #fff; + display: flex; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.75em 1em; + position: relative; } + .message-header .delete { + flex-grow: 0; + flex-shrink: 0; + margin-left: 0.75em; } + .message-header + .message-body { + border-width: 0; + border-top-left-radius: 0; + border-top-right-radius: 0; } + +.message-body { + border-color: #dbdbdb; + border-radius: 4px; + border-style: solid; + border-width: 0 0 0 4px; + color: #202020; + padding: 1.25em 1.5em; } + .message-body code, + .message-body pre { + background-color: white; } + .message-body pre code { + background-color: transparent; } + +.modal { + align-items: center; + display: none; + flex-direction: column; + justify-content: center; + overflow: hidden; + position: fixed; + z-index: 40; } + .modal.is-active { + display: flex; } + +.modal-background { + background-color: rgba(10, 10, 10, 0.86); } + +.modal-content, +.modal-card { + margin: 0 20px; + max-height: calc(100vh - 160px); + overflow: auto; + position: relative; + width: 100%; } + @media screen and (min-width: 769px), print { + .modal-content, + .modal-card { + margin: 0 auto; + max-height: calc(100vh - 40px); + width: 640px; } } +.modal-close { + background: none; + height: 40px; + position: fixed; + right: 20px; + top: 20px; + width: 40px; } + +.modal-card { + display: flex; + flex-direction: column; + max-height: calc(100vh - 40px); + overflow: hidden; + -ms-overflow-y: visible; } + +.modal-card-head, +.modal-card-foot { + align-items: center; + background-color: whitesmoke; + display: flex; + flex-shrink: 0; + justify-content: flex-start; + padding: 20px; + position: relative; } + +.modal-card-head { + border-bottom: 1px solid #dbdbdb; + border-top-left-radius: 6px; + border-top-right-radius: 6px; } + +.modal-card-title { + color: #654ca3; + flex-grow: 1; + flex-shrink: 0; + font-size: 1.5rem; + line-height: 1; } + +.modal-card-foot { + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 1px solid #dbdbdb; } + .modal-card-foot .button:not(:last-child) { + margin-right: 0.5em; } + +.modal-card-body { + -webkit-overflow-scrolling: touch; + background-color: white; + flex-grow: 1; + flex-shrink: 1; + overflow: auto; + padding: 20px; } + +.navbar { + background-color: white; + min-height: 3.25rem; + position: relative; + z-index: 30; } + .navbar.is-white { + background-color: white; + color: #0a0a0a; } + .navbar.is-white .navbar-brand > .navbar-item, + .navbar.is-white .navbar-brand .navbar-link { + color: #0a0a0a; } + .navbar.is-white .navbar-brand > a.navbar-item:focus, .navbar.is-white .navbar-brand > a.navbar-item:hover, .navbar.is-white .navbar-brand > a.navbar-item.is-active, + .navbar.is-white .navbar-brand .navbar-link:focus, + .navbar.is-white .navbar-brand .navbar-link:hover, + .navbar.is-white .navbar-brand .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-brand .navbar-link::after { + border-color: #0a0a0a; } + .navbar.is-white .navbar-burger { + color: #0a0a0a; } + @media screen and (min-width: 1056px) { + .navbar.is-white .navbar-start > .navbar-item, + .navbar.is-white .navbar-start .navbar-link, + .navbar.is-white .navbar-end > .navbar-item, + .navbar.is-white .navbar-end .navbar-link { + color: #0a0a0a; } + .navbar.is-white .navbar-start > a.navbar-item:focus, .navbar.is-white .navbar-start > a.navbar-item:hover, .navbar.is-white .navbar-start > a.navbar-item.is-active, + .navbar.is-white .navbar-start .navbar-link:focus, + .navbar.is-white .navbar-start .navbar-link:hover, + .navbar.is-white .navbar-start .navbar-link.is-active, + .navbar.is-white .navbar-end > a.navbar-item:focus, + .navbar.is-white .navbar-end > a.navbar-item:hover, + .navbar.is-white .navbar-end > a.navbar-item.is-active, + .navbar.is-white .navbar-end .navbar-link:focus, + .navbar.is-white .navbar-end .navbar-link:hover, + .navbar.is-white .navbar-end .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-start .navbar-link::after, + .navbar.is-white .navbar-end .navbar-link::after { + border-color: #0a0a0a; } + .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-dropdown a.navbar-item.is-active { + background-color: white; + color: #0a0a0a; } } + .navbar.is-black { + background-color: #0a0a0a; + color: white; } + .navbar.is-black .navbar-brand > .navbar-item, + .navbar.is-black .navbar-brand .navbar-link { + color: white; } + .navbar.is-black .navbar-brand > a.navbar-item:focus, .navbar.is-black .navbar-brand > a.navbar-item:hover, .navbar.is-black .navbar-brand > a.navbar-item.is-active, + .navbar.is-black .navbar-brand .navbar-link:focus, + .navbar.is-black .navbar-brand .navbar-link:hover, + .navbar.is-black .navbar-brand .navbar-link.is-active { + background-color: black; + color: white; } + .navbar.is-black .navbar-brand .navbar-link::after { + border-color: white; } + .navbar.is-black .navbar-burger { + color: white; } + @media screen and (min-width: 1056px) { + .navbar.is-black .navbar-start > .navbar-item, + .navbar.is-black .navbar-start .navbar-link, + .navbar.is-black .navbar-end > .navbar-item, + .navbar.is-black .navbar-end .navbar-link { + color: white; } + .navbar.is-black .navbar-start > a.navbar-item:focus, .navbar.is-black .navbar-start > a.navbar-item:hover, .navbar.is-black .navbar-start > a.navbar-item.is-active, + .navbar.is-black .navbar-start .navbar-link:focus, + .navbar.is-black .navbar-start .navbar-link:hover, + .navbar.is-black .navbar-start .navbar-link.is-active, + .navbar.is-black .navbar-end > a.navbar-item:focus, + .navbar.is-black .navbar-end > a.navbar-item:hover, + .navbar.is-black .navbar-end > a.navbar-item.is-active, + .navbar.is-black .navbar-end .navbar-link:focus, + .navbar.is-black .navbar-end .navbar-link:hover, + .navbar.is-black .navbar-end .navbar-link.is-active { + background-color: black; + color: white; } + .navbar.is-black .navbar-start .navbar-link::after, + .navbar.is-black .navbar-end .navbar-link::after { + border-color: white; } + .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { + background-color: black; + color: white; } + .navbar.is-black .navbar-dropdown a.navbar-item.is-active { + background-color: #0a0a0a; + color: white; } } + .navbar.is-light { + background-color: whitesmoke; + color: #363636; } + .navbar.is-light .navbar-brand > .navbar-item, + .navbar.is-light .navbar-brand .navbar-link { + color: #363636; } + .navbar.is-light .navbar-brand > a.navbar-item:focus, .navbar.is-light .navbar-brand > a.navbar-item:hover, .navbar.is-light .navbar-brand > a.navbar-item.is-active, + .navbar.is-light .navbar-brand .navbar-link:focus, + .navbar.is-light .navbar-brand .navbar-link:hover, + .navbar.is-light .navbar-brand .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-brand .navbar-link::after { + border-color: #363636; } + .navbar.is-light .navbar-burger { + color: #363636; } + @media screen and (min-width: 1056px) { + .navbar.is-light .navbar-start > .navbar-item, + .navbar.is-light .navbar-start .navbar-link, + .navbar.is-light .navbar-end > .navbar-item, + .navbar.is-light .navbar-end .navbar-link { + color: #363636; } + .navbar.is-light .navbar-start > a.navbar-item:focus, .navbar.is-light .navbar-start > a.navbar-item:hover, .navbar.is-light .navbar-start > a.navbar-item.is-active, + .navbar.is-light .navbar-start .navbar-link:focus, + .navbar.is-light .navbar-start .navbar-link:hover, + .navbar.is-light .navbar-start .navbar-link.is-active, + .navbar.is-light .navbar-end > a.navbar-item:focus, + .navbar.is-light .navbar-end > a.navbar-item:hover, + .navbar.is-light .navbar-end > a.navbar-item.is-active, + .navbar.is-light .navbar-end .navbar-link:focus, + .navbar.is-light .navbar-end .navbar-link:hover, + .navbar.is-light .navbar-end .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-start .navbar-link::after, + .navbar.is-light .navbar-end .navbar-link::after { + border-color: #363636; } + .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #363636; } } + .navbar.is-dark, .content kbd.navbar { + background-color: #363636; + color: whitesmoke; } + .navbar.is-dark .navbar-brand > .navbar-item, .content kbd.navbar .navbar-brand > .navbar-item, + .navbar.is-dark .navbar-brand .navbar-link, + .content kbd.navbar .navbar-brand .navbar-link { + color: whitesmoke; } + .navbar.is-dark .navbar-brand > a.navbar-item:focus, .content kbd.navbar .navbar-brand > a.navbar-item:focus, .navbar.is-dark .navbar-brand > a.navbar-item:hover, .content kbd.navbar .navbar-brand > a.navbar-item:hover, .navbar.is-dark .navbar-brand > a.navbar-item.is-active, .content kbd.navbar .navbar-brand > a.navbar-item.is-active, + .navbar.is-dark .navbar-brand .navbar-link:focus, + .content kbd.navbar .navbar-brand .navbar-link:focus, + .navbar.is-dark .navbar-brand .navbar-link:hover, + .content kbd.navbar .navbar-brand .navbar-link:hover, + .navbar.is-dark .navbar-brand .navbar-link.is-active, + .content kbd.navbar .navbar-brand .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-brand .navbar-link::after, .content kbd.navbar .navbar-brand .navbar-link::after { + border-color: whitesmoke; } + .navbar.is-dark .navbar-burger, .content kbd.navbar .navbar-burger { + color: whitesmoke; } + @media screen and (min-width: 1056px) { + .navbar.is-dark .navbar-start > .navbar-item, .content kbd.navbar .navbar-start > .navbar-item, + .navbar.is-dark .navbar-start .navbar-link, + .content kbd.navbar .navbar-start .navbar-link, + .navbar.is-dark .navbar-end > .navbar-item, + .content kbd.navbar .navbar-end > .navbar-item, + .navbar.is-dark .navbar-end .navbar-link, + .content kbd.navbar .navbar-end .navbar-link { + color: whitesmoke; } + .navbar.is-dark .navbar-start > a.navbar-item:focus, .content kbd.navbar .navbar-start > a.navbar-item:focus, .navbar.is-dark .navbar-start > a.navbar-item:hover, .content kbd.navbar .navbar-start > a.navbar-item:hover, .navbar.is-dark .navbar-start > a.navbar-item.is-active, .content kbd.navbar .navbar-start > a.navbar-item.is-active, + .navbar.is-dark .navbar-start .navbar-link:focus, + .content kbd.navbar .navbar-start .navbar-link:focus, + .navbar.is-dark .navbar-start .navbar-link:hover, + .content kbd.navbar .navbar-start .navbar-link:hover, + .navbar.is-dark .navbar-start .navbar-link.is-active, + .content kbd.navbar .navbar-start .navbar-link.is-active, + .navbar.is-dark .navbar-end > a.navbar-item:focus, + .content kbd.navbar .navbar-end > a.navbar-item:focus, + .navbar.is-dark .navbar-end > a.navbar-item:hover, + .content kbd.navbar .navbar-end > a.navbar-item:hover, + .navbar.is-dark .navbar-end > a.navbar-item.is-active, + .content kbd.navbar .navbar-end > a.navbar-item.is-active, + .navbar.is-dark .navbar-end .navbar-link:focus, + .content kbd.navbar .navbar-end .navbar-link:focus, + .navbar.is-dark .navbar-end .navbar-link:hover, + .content kbd.navbar .navbar-end .navbar-link:hover, + .navbar.is-dark .navbar-end .navbar-link.is-active, + .content kbd.navbar .navbar-end .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-start .navbar-link::after, .content kbd.navbar .navbar-start .navbar-link::after, + .navbar.is-dark .navbar-end .navbar-link::after, + .content kbd.navbar .navbar-end .navbar-link::after { + border-color: whitesmoke; } + .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, + .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, + .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { + background-color: #363636; + color: whitesmoke; } } + .navbar.is-primary, .docstring > section > a.navbar.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .navbar.is-primary .navbar-brand > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, + .navbar.is-primary .navbar-brand .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-primary .navbar-brand > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, .navbar.is-primary .navbar-brand > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, .navbar.is-primary .navbar-brand > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, + .navbar.is-primary .navbar-brand .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, + .navbar.is-primary .navbar-brand .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, + .navbar.is-primary .navbar-brand .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-brand .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-primary .navbar-burger, .docstring > section > a.navbar.docs-sourcelink .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-primary .navbar-start > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, + .navbar.is-primary .navbar-start .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, + .navbar.is-primary .navbar-end > .navbar-item, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, + .navbar.is-primary .navbar-end .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { + color: #fff; } + .navbar.is-primary .navbar-start > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, .navbar.is-primary .navbar-start > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, .navbar.is-primary .navbar-start > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, + .navbar.is-primary .navbar-start .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, + .navbar.is-primary .navbar-start .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, + .navbar.is-primary .navbar-start .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, + .navbar.is-primary .navbar-end > a.navbar-item:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, + .navbar.is-primary .navbar-end > a.navbar-item:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, + .navbar.is-primary .navbar-end > a.navbar-item.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, + .navbar.is-primary .navbar-end .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, + .navbar.is-primary .navbar-end .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, + .navbar.is-primary .navbar-end .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-start .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, + .navbar.is-primary .navbar-end .navbar-link::after, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { + background-color: #4eb5de; + color: #fff; } } + .navbar.is-link { + background-color: #149eaa; + color: #fff; } + .navbar.is-link .navbar-brand > .navbar-item, + .navbar.is-link .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-link .navbar-brand > a.navbar-item:focus, .navbar.is-link .navbar-brand > a.navbar-item:hover, .navbar.is-link .navbar-brand > a.navbar-item.is-active, + .navbar.is-link .navbar-brand .navbar-link:focus, + .navbar.is-link .navbar-brand .navbar-link:hover, + .navbar.is-link .navbar-brand .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-link .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-link .navbar-start > .navbar-item, + .navbar.is-link .navbar-start .navbar-link, + .navbar.is-link .navbar-end > .navbar-item, + .navbar.is-link .navbar-end .navbar-link { + color: #fff; } + .navbar.is-link .navbar-start > a.navbar-item:focus, .navbar.is-link .navbar-start > a.navbar-item:hover, .navbar.is-link .navbar-start > a.navbar-item.is-active, + .navbar.is-link .navbar-start .navbar-link:focus, + .navbar.is-link .navbar-start .navbar-link:hover, + .navbar.is-link .navbar-start .navbar-link.is-active, + .navbar.is-link .navbar-end > a.navbar-item:focus, + .navbar.is-link .navbar-end > a.navbar-item:hover, + .navbar.is-link .navbar-end > a.navbar-item.is-active, + .navbar.is-link .navbar-end .navbar-link:focus, + .navbar.is-link .navbar-end .navbar-link:hover, + .navbar.is-link .navbar-end .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-start .navbar-link::after, + .navbar.is-link .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-dropdown a.navbar-item.is-active { + background-color: #149eaa; + color: #fff; } } + .navbar.is-info { + background-color: #209cee; + color: #fff; } + .navbar.is-info .navbar-brand > .navbar-item, + .navbar.is-info .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-info .navbar-brand > a.navbar-item:focus, .navbar.is-info .navbar-brand > a.navbar-item:hover, .navbar.is-info .navbar-brand > a.navbar-item.is-active, + .navbar.is-info .navbar-brand .navbar-link:focus, + .navbar.is-info .navbar-brand .navbar-link:hover, + .navbar.is-info .navbar-brand .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-info .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-info .navbar-start > .navbar-item, + .navbar.is-info .navbar-start .navbar-link, + .navbar.is-info .navbar-end > .navbar-item, + .navbar.is-info .navbar-end .navbar-link { + color: #fff; } + .navbar.is-info .navbar-start > a.navbar-item:focus, .navbar.is-info .navbar-start > a.navbar-item:hover, .navbar.is-info .navbar-start > a.navbar-item.is-active, + .navbar.is-info .navbar-start .navbar-link:focus, + .navbar.is-info .navbar-start .navbar-link:hover, + .navbar.is-info .navbar-start .navbar-link.is-active, + .navbar.is-info .navbar-end > a.navbar-item:focus, + .navbar.is-info .navbar-end > a.navbar-item:hover, + .navbar.is-info .navbar-end > a.navbar-item.is-active, + .navbar.is-info .navbar-end .navbar-link:focus, + .navbar.is-info .navbar-end .navbar-link:hover, + .navbar.is-info .navbar-end .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-start .navbar-link::after, + .navbar.is-info .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-dropdown a.navbar-item.is-active { + background-color: #209cee; + color: #fff; } } + .navbar.is-success { + background-color: #22c35b; + color: #fff; } + .navbar.is-success .navbar-brand > .navbar-item, + .navbar.is-success .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-success .navbar-brand > a.navbar-item:focus, .navbar.is-success .navbar-brand > a.navbar-item:hover, .navbar.is-success .navbar-brand > a.navbar-item.is-active, + .navbar.is-success .navbar-brand .navbar-link:focus, + .navbar.is-success .navbar-brand .navbar-link:hover, + .navbar.is-success .navbar-brand .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-success .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-success .navbar-start > .navbar-item, + .navbar.is-success .navbar-start .navbar-link, + .navbar.is-success .navbar-end > .navbar-item, + .navbar.is-success .navbar-end .navbar-link { + color: #fff; } + .navbar.is-success .navbar-start > a.navbar-item:focus, .navbar.is-success .navbar-start > a.navbar-item:hover, .navbar.is-success .navbar-start > a.navbar-item.is-active, + .navbar.is-success .navbar-start .navbar-link:focus, + .navbar.is-success .navbar-start .navbar-link:hover, + .navbar.is-success .navbar-start .navbar-link.is-active, + .navbar.is-success .navbar-end > a.navbar-item:focus, + .navbar.is-success .navbar-end > a.navbar-item:hover, + .navbar.is-success .navbar-end > a.navbar-item.is-active, + .navbar.is-success .navbar-end .navbar-link:focus, + .navbar.is-success .navbar-end .navbar-link:hover, + .navbar.is-success .navbar-end .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-start .navbar-link::after, + .navbar.is-success .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-dropdown a.navbar-item.is-active { + background-color: #22c35b; + color: #fff; } } + .navbar.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand > .navbar-item, + .navbar.is-warning .navbar-brand .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand > a.navbar-item:focus, .navbar.is-warning .navbar-brand > a.navbar-item:hover, .navbar.is-warning .navbar-brand > a.navbar-item.is-active, + .navbar.is-warning .navbar-brand .navbar-link:focus, + .navbar.is-warning .navbar-brand .navbar-link:hover, + .navbar.is-warning .navbar-brand .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-burger { + color: rgba(0, 0, 0, 0.7); } + @media screen and (min-width: 1056px) { + .navbar.is-warning .navbar-start > .navbar-item, + .navbar.is-warning .navbar-start .navbar-link, + .navbar.is-warning .navbar-end > .navbar-item, + .navbar.is-warning .navbar-end .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-start > a.navbar-item:focus, .navbar.is-warning .navbar-start > a.navbar-item:hover, .navbar.is-warning .navbar-start > a.navbar-item.is-active, + .navbar.is-warning .navbar-start .navbar-link:focus, + .navbar.is-warning .navbar-start .navbar-link:hover, + .navbar.is-warning .navbar-start .navbar-link.is-active, + .navbar.is-warning .navbar-end > a.navbar-item:focus, + .navbar.is-warning .navbar-end > a.navbar-item:hover, + .navbar.is-warning .navbar-end > a.navbar-item.is-active, + .navbar.is-warning .navbar-end .navbar-link:focus, + .navbar.is-warning .navbar-end .navbar-link:hover, + .navbar.is-warning .navbar-end .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-start .navbar-link::after, + .navbar.is-warning .navbar-end .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } } + .navbar.is-danger { + background-color: #da0b00; + color: #fff; } + .navbar.is-danger .navbar-brand > .navbar-item, + .navbar.is-danger .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-danger .navbar-brand > a.navbar-item:focus, .navbar.is-danger .navbar-brand > a.navbar-item:hover, .navbar.is-danger .navbar-brand > a.navbar-item.is-active, + .navbar.is-danger .navbar-brand .navbar-link:focus, + .navbar.is-danger .navbar-brand .navbar-link:hover, + .navbar.is-danger .navbar-brand .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-danger .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-danger .navbar-start > .navbar-item, + .navbar.is-danger .navbar-start .navbar-link, + .navbar.is-danger .navbar-end > .navbar-item, + .navbar.is-danger .navbar-end .navbar-link { + color: #fff; } + .navbar.is-danger .navbar-start > a.navbar-item:focus, .navbar.is-danger .navbar-start > a.navbar-item:hover, .navbar.is-danger .navbar-start > a.navbar-item.is-active, + .navbar.is-danger .navbar-start .navbar-link:focus, + .navbar.is-danger .navbar-start .navbar-link:hover, + .navbar.is-danger .navbar-start .navbar-link.is-active, + .navbar.is-danger .navbar-end > a.navbar-item:focus, + .navbar.is-danger .navbar-end > a.navbar-item:hover, + .navbar.is-danger .navbar-end > a.navbar-item.is-active, + .navbar.is-danger .navbar-end .navbar-link:focus, + .navbar.is-danger .navbar-end .navbar-link:hover, + .navbar.is-danger .navbar-end .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-start .navbar-link::after, + .navbar.is-danger .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { + background-color: #da0b00; + color: #fff; } } + .navbar > .container { + align-items: stretch; + display: flex; + min-height: 3.25rem; + width: 100%; } + .navbar.has-shadow { + box-shadow: 0 2px 0 0 whitesmoke; } + .navbar.is-fixed-bottom, .navbar.is-fixed-top { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom { + bottom: 0; } + .navbar.is-fixed-bottom.has-shadow { + box-shadow: 0 -2px 0 0 whitesmoke; } + .navbar.is-fixed-top { + top: 0; } + +html.has-navbar-fixed-top, +body.has-navbar-fixed-top { + padding-top: 3.25rem; } + +html.has-navbar-fixed-bottom, +body.has-navbar-fixed-bottom { + padding-bottom: 3.25rem; } + +.navbar-brand, +.navbar-tabs { + align-items: stretch; + display: flex; + flex-shrink: 0; + min-height: 3.25rem; } + +.navbar-brand a.navbar-item:focus, .navbar-brand a.navbar-item:hover { + background-color: transparent; } + +.navbar-tabs { + -webkit-overflow-scrolling: touch; + max-width: 100vw; + overflow-x: auto; + overflow-y: hidden; } + +.navbar-burger { + color: #4a4a4a; + cursor: pointer; + display: block; + height: 3.25rem; + position: relative; + width: 3.25rem; + margin-left: auto; } + .navbar-burger span { + background-color: currentColor; + display: block; + height: 1px; + left: calc(50% - 8px); + position: absolute; + transform-origin: center; + transition-duration: 86ms; + transition-property: background-color, opacity, transform; + transition-timing-function: ease-out; + width: 16px; } + .navbar-burger span:nth-child(1) { + top: calc(50% - 6px); } + .navbar-burger span:nth-child(2) { + top: calc(50% - 1px); } + .navbar-burger span:nth-child(3) { + top: calc(50% + 4px); } + .navbar-burger:hover { + background-color: rgba(0, 0, 0, 0.05); } + .navbar-burger.is-active span:nth-child(1) { + transform: translateY(5px) rotate(45deg); } + .navbar-burger.is-active span:nth-child(2) { + opacity: 0; } + .navbar-burger.is-active span:nth-child(3) { + transform: translateY(-5px) rotate(-45deg); } + +.navbar-menu { + display: none; } + +.navbar-item, +.navbar-link { + color: #4a4a4a; + display: block; + line-height: 1.5; + padding: 0.5rem 0.75rem; + position: relative; } + .navbar-item .icon:only-child, + .navbar-link .icon:only-child { + margin-left: -0.25rem; + margin-right: -0.25rem; } + +a.navbar-item, +.navbar-link { + cursor: pointer; } + a.navbar-item:focus, a.navbar-item:focus-within, a.navbar-item:hover, a.navbar-item.is-active, + .navbar-link:focus, + .navbar-link:focus-within, + .navbar-link:hover, + .navbar-link.is-active { + background-color: #fafafa; + color: #149eaa; } + +.navbar-item { + display: block; + flex-grow: 0; + flex-shrink: 0; } + .navbar-item img { + max-height: 1.75rem; } + .navbar-item.has-dropdown { + padding: 0; } + .navbar-item.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .navbar-item.is-tab { + border-bottom: 1px solid transparent; + min-height: 3.25rem; + padding-bottom: calc(0.5rem - 1px); } + .navbar-item.is-tab:focus, .navbar-item.is-tab:hover { + background-color: transparent; + border-bottom-color: #149eaa; } + .navbar-item.is-tab.is-active { + background-color: transparent; + border-bottom-color: #149eaa; + border-bottom-style: solid; + border-bottom-width: 3px; + color: #149eaa; + padding-bottom: calc(0.5rem - 3px); } + +.navbar-content { + flex-grow: 1; + flex-shrink: 1; } + +.navbar-link:not(.is-arrowless) { + padding-right: 2.5em; } + .navbar-link:not(.is-arrowless)::after { + border-color: #149eaa; + margin-top: -0.375em; + right: 1.125em; } + +.navbar-dropdown { + font-size: 0.875rem; + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + .navbar-dropdown .navbar-item { + padding-left: 1.5rem; + padding-right: 1.5rem; } + +.navbar-divider { + background-color: whitesmoke; + border: none; + display: none; + height: 2px; + margin: 0.5rem 0; } + +@media screen and (max-width: 1055px) { + .navbar > .container { + display: block; } + .navbar-brand .navbar-item, + .navbar-tabs .navbar-item { + align-items: center; + display: flex; } + .navbar-link::after { + display: none; } + .navbar-menu { + background-color: white; + box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); + padding: 0.5rem 0; } + .navbar-menu.is-active { + display: block; } + .navbar.is-fixed-bottom-touch, .navbar.is-fixed-top-touch { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom-touch { + bottom: 0; } + .navbar.is-fixed-bottom-touch.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + .navbar.is-fixed-top-touch { + top: 0; } + .navbar.is-fixed-top .navbar-menu, .navbar.is-fixed-top-touch .navbar-menu { + -webkit-overflow-scrolling: touch; + max-height: calc(100vh - 3.25rem); + overflow: auto; } + html.has-navbar-fixed-top-touch, + body.has-navbar-fixed-top-touch { + padding-top: 3.25rem; } + html.has-navbar-fixed-bottom-touch, + body.has-navbar-fixed-bottom-touch { + padding-bottom: 3.25rem; } } + +@media screen and (min-width: 1056px) { + .navbar, + .navbar-menu, + .navbar-start, + .navbar-end { + align-items: stretch; + display: flex; } + .navbar { + min-height: 3.25rem; } + .navbar.is-spaced { + padding: 1rem 2rem; } + .navbar.is-spaced .navbar-start, + .navbar.is-spaced .navbar-end { + align-items: center; } + .navbar.is-spaced a.navbar-item, + .navbar.is-spaced .navbar-link { + border-radius: 4px; } + .navbar.is-transparent a.navbar-item:focus, .navbar.is-transparent a.navbar-item:hover, .navbar.is-transparent a.navbar-item.is-active, + .navbar.is-transparent .navbar-link:focus, + .navbar.is-transparent .navbar-link:hover, + .navbar.is-transparent .navbar-link.is-active { + background-color: transparent !important; } + .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { + background-color: transparent !important; } + .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #149eaa; } + .navbar-burger { + display: none; } + .navbar-item, + .navbar-link { + align-items: center; + display: flex; } + .navbar-item { + display: flex; } + .navbar-item.has-dropdown { + align-items: stretch; } + .navbar-item.has-dropdown-up .navbar-link::after { + transform: rotate(135deg) translate(0.25em, -0.25em); } + .navbar-item.has-dropdown-up .navbar-dropdown { + border-bottom: 2px solid #dbdbdb; + border-radius: 6px 6px 0 0; + border-top: none; + bottom: 100%; + box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); + top: auto; } + .navbar-item.is-active .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown { + display: block; } + .navbar.is-spaced .navbar-item.is-active .navbar-dropdown, .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:hover .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { + opacity: 1; + pointer-events: auto; + transform: translateY(0); } + .navbar-menu { + flex-grow: 1; + flex-shrink: 0; } + .navbar-start { + justify-content: flex-start; + margin-right: auto; } + .navbar-end { + justify-content: flex-end; + margin-left: auto; } + .navbar-dropdown { + background-color: white; + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 2px solid #dbdbdb; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); + display: none; + font-size: 0.875rem; + left: 0; + min-width: 100%; + position: absolute; + top: 100%; + z-index: 20; } + .navbar-dropdown .navbar-item { + padding: 0.375rem 1rem; + white-space: nowrap; } + .navbar-dropdown a.navbar-item { + padding-right: 3rem; } + .navbar-dropdown a.navbar-item:focus, .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #149eaa; } + .navbar.is-spaced .navbar-dropdown, .navbar-dropdown.is-boxed { + border-radius: 6px; + border-top: none; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + display: block; + opacity: 0; + pointer-events: none; + top: calc(100% + (-4px)); + transform: translateY(-5px); + transition-duration: 86ms; + transition-property: opacity, transform; } + .navbar-dropdown.is-right { + left: auto; + right: 0; } + .navbar-divider { + display: block; } + .navbar > .container .navbar-brand, + .container > .navbar .navbar-brand { + margin-left: -.75rem; } + .navbar > .container .navbar-menu, + .container > .navbar .navbar-menu { + margin-right: -.75rem; } + .navbar.is-fixed-bottom-desktop, .navbar.is-fixed-top-desktop { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom-desktop { + bottom: 0; } + .navbar.is-fixed-bottom-desktop.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + .navbar.is-fixed-top-desktop { + top: 0; } + html.has-navbar-fixed-top-desktop, + body.has-navbar-fixed-top-desktop { + padding-top: 3.25rem; } + html.has-navbar-fixed-bottom-desktop, + body.has-navbar-fixed-bottom-desktop { + padding-bottom: 3.25rem; } + html.has-spaced-navbar-fixed-top, + body.has-spaced-navbar-fixed-top { + padding-top: 5.25rem; } + html.has-spaced-navbar-fixed-bottom, + body.has-spaced-navbar-fixed-bottom { + padding-bottom: 5.25rem; } + a.navbar-item.is-active, + .navbar-link.is-active { + color: #0a0a0a; } + a.navbar-item.is-active:not(:focus):not(:hover), + .navbar-link.is-active:not(:focus):not(:hover) { + background-color: transparent; } + .navbar-item.has-dropdown:focus .navbar-link, .navbar-item.has-dropdown:hover .navbar-link, .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #fafafa; } } + +.hero.is-fullheight-with-navbar { + min-height: calc(100vh - 3.25rem); } + +.pagination { + font-size: 1rem; + margin: -0.25rem; } + .pagination.is-small, #documenter .docs-sidebar form.docs-search > input.pagination { + font-size: 0.75rem; } + .pagination.is-medium { + font-size: 1.25rem; } + .pagination.is-large { + font-size: 1.5rem; } + .pagination.is-rounded .pagination-previous, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, + .pagination.is-rounded .pagination-next, + #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { + padding-left: 1em; + padding-right: 1em; + border-radius: 290486px; } + .pagination.is-rounded .pagination-link, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { + border-radius: 290486px; } + +.pagination, +.pagination-list { + align-items: center; + display: flex; + justify-content: center; + text-align: center; } + +.pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis { + font-size: 1em; + justify-content: center; + margin: 0.25rem; + padding-left: 0.5em; + padding-right: 0.5em; + text-align: center; } + +.pagination-previous, +.pagination-next, +.pagination-link { + border-color: #dbdbdb; + color: #363636; + min-width: 2.25em; } + .pagination-previous:hover, + .pagination-next:hover, + .pagination-link:hover { + border-color: #b5b5b5; + color: #107c85; } + .pagination-previous:focus, + .pagination-next:focus, + .pagination-link:focus { + border-color: #3c5dcd; } + .pagination-previous:active, + .pagination-next:active, + .pagination-link:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } + .pagination-previous[disabled], + .pagination-next[disabled], + .pagination-link[disabled] { + background-color: #dbdbdb; + border-color: #dbdbdb; + box-shadow: none; + color: #6b6b6b; + opacity: 0.5; } + +.pagination-previous, +.pagination-next { + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + +.pagination-link.is-current { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + +.pagination-ellipsis { + color: #b5b5b5; + pointer-events: none; } + +.pagination-list { + flex-wrap: wrap; } + +@media screen and (max-width: 768px) { + .pagination { + flex-wrap: wrap; } + .pagination-previous, + .pagination-next { + flex-grow: 1; + flex-shrink: 1; } + .pagination-list li { + flex-grow: 1; + flex-shrink: 1; } } + +@media screen and (min-width: 769px), print { + .pagination-list { + flex-grow: 1; + flex-shrink: 1; + justify-content: flex-start; + order: 1; } + .pagination-previous { + order: 2; } + .pagination-next { + order: 3; } + .pagination { + justify-content: space-between; } + .pagination.is-centered .pagination-previous { + order: 1; } + .pagination.is-centered .pagination-list { + justify-content: center; + order: 2; } + .pagination.is-centered .pagination-next { + order: 3; } + .pagination.is-right .pagination-previous { + order: 1; } + .pagination.is-right .pagination-next { + order: 2; } + .pagination.is-right .pagination-list { + justify-content: flex-end; + order: 3; } } + +.panel { + font-size: 1rem; } + .panel:not(:last-child) { + margin-bottom: 1.5rem; } + +.panel-heading, +.panel-tabs, +.panel-block { + border-bottom: 1px solid #dbdbdb; + border-left: 1px solid #dbdbdb; + border-right: 1px solid #dbdbdb; } + .panel-heading:first-child, + .panel-tabs:first-child, + .panel-block:first-child { + border-top: 1px solid #dbdbdb; } + +.panel-heading { + background-color: whitesmoke; + border-radius: 4px 4px 0 0; + color: #654ca3; + font-size: 1.25em; + font-weight: 300; + line-height: 1.25; + padding: 0.5em 0.75em; } + +.panel-tabs { + align-items: flex-end; + display: flex; + font-size: 0.875em; + justify-content: center; } + .panel-tabs a { + border-bottom: 1px solid #dbdbdb; + margin-bottom: -1px; + padding: 0.5em; } + .panel-tabs a.is-active { + border-bottom-color: #4a4a4a; + color: #363636; } + +.panel-list a { + color: #202020; } + .panel-list a:hover { + color: #149eaa; } + +.panel-block { + align-items: center; + color: #654ca3; + display: flex; + justify-content: flex-start; + padding: 0.5em 0.75em; } + .panel-block input[type="checkbox"] { + margin-right: 0.75em; } + .panel-block > .control { + flex-grow: 1; + flex-shrink: 1; + width: 100%; } + .panel-block.is-wrapped { + flex-wrap: wrap; } + .panel-block.is-active { + border-left-color: #149eaa; + color: #363636; } + .panel-block.is-active .panel-icon { + color: #149eaa; } + +a.panel-block, +label.panel-block { + cursor: pointer; } + a.panel-block:hover, + label.panel-block:hover { + background-color: whitesmoke; } + +.panel-icon { + display: inline-block; + font-size: 14px; + height: 1em; + line-height: 1em; + text-align: center; + vertical-align: top; + width: 1em; + color: #6b6b6b; + margin-right: 0.75em; } + .panel-icon .fa { + font-size: inherit; + line-height: inherit; } + +.tabs { + -webkit-overflow-scrolling: touch; + align-items: stretch; + display: flex; + font-size: 1rem; + justify-content: space-between; + overflow: hidden; + overflow-x: auto; + white-space: nowrap; } + .tabs a { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + color: #202020; + display: flex; + justify-content: center; + margin-bottom: -1px; + padding: 0.5em 1em; + vertical-align: top; } + .tabs a:hover { + border-bottom-color: #654ca3; + color: #654ca3; } + .tabs li { + display: block; } + .tabs li.is-active a { + border-bottom-color: #149eaa; + color: #149eaa; } + .tabs ul { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + display: flex; + flex-grow: 1; + flex-shrink: 0; + justify-content: flex-start; } + .tabs ul.is-left { + padding-right: 0.75em; } + .tabs ul.is-center { + flex: none; + justify-content: center; + padding-left: 0.75em; + padding-right: 0.75em; } + .tabs ul.is-right { + justify-content: flex-end; + padding-left: 0.75em; } + .tabs .icon:first-child { + margin-right: 0.5em; } + .tabs .icon:last-child { + margin-left: 0.5em; } + .tabs.is-centered ul { + justify-content: center; } + .tabs.is-right ul { + justify-content: flex-end; } + .tabs.is-boxed a { + border: 1px solid transparent; + border-radius: 4px 4px 0 0; } + .tabs.is-boxed a:hover { + background-color: whitesmoke; + border-bottom-color: #dbdbdb; } + .tabs.is-boxed li.is-active a { + background-color: white; + border-color: #dbdbdb; + border-bottom-color: transparent !important; } + .tabs.is-fullwidth li { + flex-grow: 1; + flex-shrink: 0; } + .tabs.is-toggle a { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px; + margin-bottom: 0; + position: relative; } + .tabs.is-toggle a:hover { + background-color: whitesmoke; + border-color: #b5b5b5; + z-index: 2; } + .tabs.is-toggle li + li { + margin-left: -1px; } + .tabs.is-toggle li:first-child a { + border-radius: 4px 0 0 4px; } + .tabs.is-toggle li:last-child a { + border-radius: 0 4px 4px 0; } + .tabs.is-toggle li.is-active a { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; + z-index: 1; } + .tabs.is-toggle ul { + border-bottom: none; } + .tabs.is-toggle.is-toggle-rounded li:first-child a { + border-bottom-left-radius: 290486px; + border-top-left-radius: 290486px; + padding-left: 1.25em; } + .tabs.is-toggle.is-toggle-rounded li:last-child a { + border-bottom-right-radius: 290486px; + border-top-right-radius: 290486px; + padding-right: 1.25em; } + .tabs.is-small, #documenter .docs-sidebar form.docs-search > input.tabs { + font-size: 0.75rem; } + .tabs.is-medium { + font-size: 1.25rem; } + .tabs.is-large { + font-size: 1.5rem; } + +.column { + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + padding: 0.75rem; } + .columns.is-mobile > .column.is-narrow { + flex: none; } + .columns.is-mobile > .column.is-full { + flex: none; + width: 100%; } + .columns.is-mobile > .column.is-three-quarters { + flex: none; + width: 75%; } + .columns.is-mobile > .column.is-two-thirds { + flex: none; + width: 66.6666%; } + .columns.is-mobile > .column.is-half { + flex: none; + width: 50%; } + .columns.is-mobile > .column.is-one-third { + flex: none; + width: 33.3333%; } + .columns.is-mobile > .column.is-one-quarter { + flex: none; + width: 25%; } + .columns.is-mobile > .column.is-one-fifth { + flex: none; + width: 20%; } + .columns.is-mobile > .column.is-two-fifths { + flex: none; + width: 40%; } + .columns.is-mobile > .column.is-three-fifths { + flex: none; + width: 60%; } + .columns.is-mobile > .column.is-four-fifths { + flex: none; + width: 80%; } + .columns.is-mobile > .column.is-offset-three-quarters { + margin-left: 75%; } + .columns.is-mobile > .column.is-offset-two-thirds { + margin-left: 66.6666%; } + .columns.is-mobile > .column.is-offset-half { + margin-left: 50%; } + .columns.is-mobile > .column.is-offset-one-third { + margin-left: 33.3333%; } + .columns.is-mobile > .column.is-offset-one-quarter { + margin-left: 25%; } + .columns.is-mobile > .column.is-offset-one-fifth { + margin-left: 20%; } + .columns.is-mobile > .column.is-offset-two-fifths { + margin-left: 40%; } + .columns.is-mobile > .column.is-offset-three-fifths { + margin-left: 60%; } + .columns.is-mobile > .column.is-offset-four-fifths { + margin-left: 80%; } + .columns.is-mobile > .column.is-0 { + flex: none; + width: 0%; } + .columns.is-mobile > .column.is-offset-0 { + margin-left: 0%; } + .columns.is-mobile > .column.is-1 { + flex: none; + width: 8.3333333333%; } + .columns.is-mobile > .column.is-offset-1 { + margin-left: 8.3333333333%; } + .columns.is-mobile > .column.is-2 { + flex: none; + width: 16.6666666667%; } + .columns.is-mobile > .column.is-offset-2 { + margin-left: 16.6666666667%; } + .columns.is-mobile > .column.is-3 { + flex: none; + width: 25%; } + .columns.is-mobile > .column.is-offset-3 { + margin-left: 25%; } + .columns.is-mobile > .column.is-4 { + flex: none; + width: 33.3333333333%; } + .columns.is-mobile > .column.is-offset-4 { + margin-left: 33.3333333333%; } + .columns.is-mobile > .column.is-5 { + flex: none; + width: 41.6666666667%; } + .columns.is-mobile > .column.is-offset-5 { + margin-left: 41.6666666667%; } + .columns.is-mobile > .column.is-6 { + flex: none; + width: 50%; } + .columns.is-mobile > .column.is-offset-6 { + margin-left: 50%; } + .columns.is-mobile > .column.is-7 { + flex: none; + width: 58.3333333333%; } + .columns.is-mobile > .column.is-offset-7 { + margin-left: 58.3333333333%; } + .columns.is-mobile > .column.is-8 { + flex: none; + width: 66.6666666667%; } + .columns.is-mobile > .column.is-offset-8 { + margin-left: 66.6666666667%; } + .columns.is-mobile > .column.is-9 { + flex: none; + width: 75%; } + .columns.is-mobile > .column.is-offset-9 { + margin-left: 75%; } + .columns.is-mobile > .column.is-10 { + flex: none; + width: 83.3333333333%; } + .columns.is-mobile > .column.is-offset-10 { + margin-left: 83.3333333333%; } + .columns.is-mobile > .column.is-11 { + flex: none; + width: 91.6666666667%; } + .columns.is-mobile > .column.is-offset-11 { + margin-left: 91.6666666667%; } + .columns.is-mobile > .column.is-12 { + flex: none; + width: 100%; } + .columns.is-mobile > .column.is-offset-12 { + margin-left: 100%; } + @media screen and (max-width: 768px) { + .column.is-narrow-mobile { + flex: none; } + .column.is-full-mobile { + flex: none; + width: 100%; } + .column.is-three-quarters-mobile { + flex: none; + width: 75%; } + .column.is-two-thirds-mobile { + flex: none; + width: 66.6666%; } + .column.is-half-mobile { + flex: none; + width: 50%; } + .column.is-one-third-mobile { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-mobile { + flex: none; + width: 25%; } + .column.is-one-fifth-mobile { + flex: none; + width: 20%; } + .column.is-two-fifths-mobile { + flex: none; + width: 40%; } + .column.is-three-fifths-mobile { + flex: none; + width: 60%; } + .column.is-four-fifths-mobile { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-mobile { + margin-left: 75%; } + .column.is-offset-two-thirds-mobile { + margin-left: 66.6666%; } + .column.is-offset-half-mobile { + margin-left: 50%; } + .column.is-offset-one-third-mobile { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-mobile { + margin-left: 25%; } + .column.is-offset-one-fifth-mobile { + margin-left: 20%; } + .column.is-offset-two-fifths-mobile { + margin-left: 40%; } + .column.is-offset-three-fifths-mobile { + margin-left: 60%; } + .column.is-offset-four-fifths-mobile { + margin-left: 80%; } + .column.is-0-mobile { + flex: none; + width: 0%; } + .column.is-offset-0-mobile { + margin-left: 0%; } + .column.is-1-mobile { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-mobile { + margin-left: 8.3333333333%; } + .column.is-2-mobile { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-mobile { + margin-left: 16.6666666667%; } + .column.is-3-mobile { + flex: none; + width: 25%; } + .column.is-offset-3-mobile { + margin-left: 25%; } + .column.is-4-mobile { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-mobile { + margin-left: 33.3333333333%; } + .column.is-5-mobile { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-mobile { + margin-left: 41.6666666667%; } + .column.is-6-mobile { + flex: none; + width: 50%; } + .column.is-offset-6-mobile { + margin-left: 50%; } + .column.is-7-mobile { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-mobile { + margin-left: 58.3333333333%; } + .column.is-8-mobile { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-mobile { + margin-left: 66.6666666667%; } + .column.is-9-mobile { + flex: none; + width: 75%; } + .column.is-offset-9-mobile { + margin-left: 75%; } + .column.is-10-mobile { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-mobile { + margin-left: 83.3333333333%; } + .column.is-11-mobile { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-mobile { + margin-left: 91.6666666667%; } + .column.is-12-mobile { + flex: none; + width: 100%; } + .column.is-offset-12-mobile { + margin-left: 100%; } } + @media screen and (min-width: 769px), print { + .column.is-narrow, .column.is-narrow-tablet { + flex: none; } + .column.is-full, .column.is-full-tablet { + flex: none; + width: 100%; } + .column.is-three-quarters, .column.is-three-quarters-tablet { + flex: none; + width: 75%; } + .column.is-two-thirds, .column.is-two-thirds-tablet { + flex: none; + width: 66.6666%; } + .column.is-half, .column.is-half-tablet { + flex: none; + width: 50%; } + .column.is-one-third, .column.is-one-third-tablet { + flex: none; + width: 33.3333%; } + .column.is-one-quarter, .column.is-one-quarter-tablet { + flex: none; + width: 25%; } + .column.is-one-fifth, .column.is-one-fifth-tablet { + flex: none; + width: 20%; } + .column.is-two-fifths, .column.is-two-fifths-tablet { + flex: none; + width: 40%; } + .column.is-three-fifths, .column.is-three-fifths-tablet { + flex: none; + width: 60%; } + .column.is-four-fifths, .column.is-four-fifths-tablet { + flex: none; + width: 80%; } + .column.is-offset-three-quarters, .column.is-offset-three-quarters-tablet { + margin-left: 75%; } + .column.is-offset-two-thirds, .column.is-offset-two-thirds-tablet { + margin-left: 66.6666%; } + .column.is-offset-half, .column.is-offset-half-tablet { + margin-left: 50%; } + .column.is-offset-one-third, .column.is-offset-one-third-tablet { + margin-left: 33.3333%; } + .column.is-offset-one-quarter, .column.is-offset-one-quarter-tablet { + margin-left: 25%; } + .column.is-offset-one-fifth, .column.is-offset-one-fifth-tablet { + margin-left: 20%; } + .column.is-offset-two-fifths, .column.is-offset-two-fifths-tablet { + margin-left: 40%; } + .column.is-offset-three-fifths, .column.is-offset-three-fifths-tablet { + margin-left: 60%; } + .column.is-offset-four-fifths, .column.is-offset-four-fifths-tablet { + margin-left: 80%; } + .column.is-0, .column.is-0-tablet { + flex: none; + width: 0%; } + .column.is-offset-0, .column.is-offset-0-tablet { + margin-left: 0%; } + .column.is-1, .column.is-1-tablet { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1, .column.is-offset-1-tablet { + margin-left: 8.3333333333%; } + .column.is-2, .column.is-2-tablet { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2, .column.is-offset-2-tablet { + margin-left: 16.6666666667%; } + .column.is-3, .column.is-3-tablet { + flex: none; + width: 25%; } + .column.is-offset-3, .column.is-offset-3-tablet { + margin-left: 25%; } + .column.is-4, .column.is-4-tablet { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4, .column.is-offset-4-tablet { + margin-left: 33.3333333333%; } + .column.is-5, .column.is-5-tablet { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5, .column.is-offset-5-tablet { + margin-left: 41.6666666667%; } + .column.is-6, .column.is-6-tablet { + flex: none; + width: 50%; } + .column.is-offset-6, .column.is-offset-6-tablet { + margin-left: 50%; } + .column.is-7, .column.is-7-tablet { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7, .column.is-offset-7-tablet { + margin-left: 58.3333333333%; } + .column.is-8, .column.is-8-tablet { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8, .column.is-offset-8-tablet { + margin-left: 66.6666666667%; } + .column.is-9, .column.is-9-tablet { + flex: none; + width: 75%; } + .column.is-offset-9, .column.is-offset-9-tablet { + margin-left: 75%; } + .column.is-10, .column.is-10-tablet { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10, .column.is-offset-10-tablet { + margin-left: 83.3333333333%; } + .column.is-11, .column.is-11-tablet { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11, .column.is-offset-11-tablet { + margin-left: 91.6666666667%; } + .column.is-12, .column.is-12-tablet { + flex: none; + width: 100%; } + .column.is-offset-12, .column.is-offset-12-tablet { + margin-left: 100%; } } + @media screen and (max-width: 1055px) { + .column.is-narrow-touch { + flex: none; } + .column.is-full-touch { + flex: none; + width: 100%; } + .column.is-three-quarters-touch { + flex: none; + width: 75%; } + .column.is-two-thirds-touch { + flex: none; + width: 66.6666%; } + .column.is-half-touch { + flex: none; + width: 50%; } + .column.is-one-third-touch { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-touch { + flex: none; + width: 25%; } + .column.is-one-fifth-touch { + flex: none; + width: 20%; } + .column.is-two-fifths-touch { + flex: none; + width: 40%; } + .column.is-three-fifths-touch { + flex: none; + width: 60%; } + .column.is-four-fifths-touch { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-touch { + margin-left: 75%; } + .column.is-offset-two-thirds-touch { + margin-left: 66.6666%; } + .column.is-offset-half-touch { + margin-left: 50%; } + .column.is-offset-one-third-touch { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-touch { + margin-left: 25%; } + .column.is-offset-one-fifth-touch { + margin-left: 20%; } + .column.is-offset-two-fifths-touch { + margin-left: 40%; } + .column.is-offset-three-fifths-touch { + margin-left: 60%; } + .column.is-offset-four-fifths-touch { + margin-left: 80%; } + .column.is-0-touch { + flex: none; + width: 0%; } + .column.is-offset-0-touch { + margin-left: 0%; } + .column.is-1-touch { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-touch { + margin-left: 8.3333333333%; } + .column.is-2-touch { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-touch { + margin-left: 16.6666666667%; } + .column.is-3-touch { + flex: none; + width: 25%; } + .column.is-offset-3-touch { + margin-left: 25%; } + .column.is-4-touch { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-touch { + margin-left: 33.3333333333%; } + .column.is-5-touch { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-touch { + margin-left: 41.6666666667%; } + .column.is-6-touch { + flex: none; + width: 50%; } + .column.is-offset-6-touch { + margin-left: 50%; } + .column.is-7-touch { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-touch { + margin-left: 58.3333333333%; } + .column.is-8-touch { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-touch { + margin-left: 66.6666666667%; } + .column.is-9-touch { + flex: none; + width: 75%; } + .column.is-offset-9-touch { + margin-left: 75%; } + .column.is-10-touch { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-touch { + margin-left: 83.3333333333%; } + .column.is-11-touch { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-touch { + margin-left: 91.6666666667%; } + .column.is-12-touch { + flex: none; + width: 100%; } + .column.is-offset-12-touch { + margin-left: 100%; } } + @media screen and (min-width: 1056px) { + .column.is-narrow-desktop { + flex: none; } + .column.is-full-desktop { + flex: none; + width: 100%; } + .column.is-three-quarters-desktop { + flex: none; + width: 75%; } + .column.is-two-thirds-desktop { + flex: none; + width: 66.6666%; } + .column.is-half-desktop { + flex: none; + width: 50%; } + .column.is-one-third-desktop { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-desktop { + flex: none; + width: 25%; } + .column.is-one-fifth-desktop { + flex: none; + width: 20%; } + .column.is-two-fifths-desktop { + flex: none; + width: 40%; } + .column.is-three-fifths-desktop { + flex: none; + width: 60%; } + .column.is-four-fifths-desktop { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-desktop { + margin-left: 75%; } + .column.is-offset-two-thirds-desktop { + margin-left: 66.6666%; } + .column.is-offset-half-desktop { + margin-left: 50%; } + .column.is-offset-one-third-desktop { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-desktop { + margin-left: 25%; } + .column.is-offset-one-fifth-desktop { + margin-left: 20%; } + .column.is-offset-two-fifths-desktop { + margin-left: 40%; } + .column.is-offset-three-fifths-desktop { + margin-left: 60%; } + .column.is-offset-four-fifths-desktop { + margin-left: 80%; } + .column.is-0-desktop { + flex: none; + width: 0%; } + .column.is-offset-0-desktop { + margin-left: 0%; } + .column.is-1-desktop { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-desktop { + margin-left: 8.3333333333%; } + .column.is-2-desktop { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-desktop { + margin-left: 16.6666666667%; } + .column.is-3-desktop { + flex: none; + width: 25%; } + .column.is-offset-3-desktop { + margin-left: 25%; } + .column.is-4-desktop { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-desktop { + margin-left: 33.3333333333%; } + .column.is-5-desktop { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-desktop { + margin-left: 41.6666666667%; } + .column.is-6-desktop { + flex: none; + width: 50%; } + .column.is-offset-6-desktop { + margin-left: 50%; } + .column.is-7-desktop { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-desktop { + margin-left: 58.3333333333%; } + .column.is-8-desktop { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-desktop { + margin-left: 66.6666666667%; } + .column.is-9-desktop { + flex: none; + width: 75%; } + .column.is-offset-9-desktop { + margin-left: 75%; } + .column.is-10-desktop { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-desktop { + margin-left: 83.3333333333%; } + .column.is-11-desktop { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-desktop { + margin-left: 91.6666666667%; } + .column.is-12-desktop { + flex: none; + width: 100%; } + .column.is-offset-12-desktop { + margin-left: 100%; } } + @media screen and (min-width: 1216px) { + .column.is-narrow-widescreen { + flex: none; } + .column.is-full-widescreen { + flex: none; + width: 100%; } + .column.is-three-quarters-widescreen { + flex: none; + width: 75%; } + .column.is-two-thirds-widescreen { + flex: none; + width: 66.6666%; } + .column.is-half-widescreen { + flex: none; + width: 50%; } + .column.is-one-third-widescreen { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-widescreen { + flex: none; + width: 25%; } + .column.is-one-fifth-widescreen { + flex: none; + width: 20%; } + .column.is-two-fifths-widescreen { + flex: none; + width: 40%; } + .column.is-three-fifths-widescreen { + flex: none; + width: 60%; } + .column.is-four-fifths-widescreen { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-widescreen { + margin-left: 75%; } + .column.is-offset-two-thirds-widescreen { + margin-left: 66.6666%; } + .column.is-offset-half-widescreen { + margin-left: 50%; } + .column.is-offset-one-third-widescreen { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-widescreen { + margin-left: 25%; } + .column.is-offset-one-fifth-widescreen { + margin-left: 20%; } + .column.is-offset-two-fifths-widescreen { + margin-left: 40%; } + .column.is-offset-three-fifths-widescreen { + margin-left: 60%; } + .column.is-offset-four-fifths-widescreen { + margin-left: 80%; } + .column.is-0-widescreen { + flex: none; + width: 0%; } + .column.is-offset-0-widescreen { + margin-left: 0%; } + .column.is-1-widescreen { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-widescreen { + margin-left: 8.3333333333%; } + .column.is-2-widescreen { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-widescreen { + margin-left: 16.6666666667%; } + .column.is-3-widescreen { + flex: none; + width: 25%; } + .column.is-offset-3-widescreen { + margin-left: 25%; } + .column.is-4-widescreen { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-widescreen { + margin-left: 33.3333333333%; } + .column.is-5-widescreen { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-widescreen { + margin-left: 41.6666666667%; } + .column.is-6-widescreen { + flex: none; + width: 50%; } + .column.is-offset-6-widescreen { + margin-left: 50%; } + .column.is-7-widescreen { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-widescreen { + margin-left: 58.3333333333%; } + .column.is-8-widescreen { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-widescreen { + margin-left: 66.6666666667%; } + .column.is-9-widescreen { + flex: none; + width: 75%; } + .column.is-offset-9-widescreen { + margin-left: 75%; } + .column.is-10-widescreen { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-widescreen { + margin-left: 83.3333333333%; } + .column.is-11-widescreen { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-widescreen { + margin-left: 91.6666666667%; } + .column.is-12-widescreen { + flex: none; + width: 100%; } + .column.is-offset-12-widescreen { + margin-left: 100%; } } + @media screen and (min-width: 1408px) { + .column.is-narrow-fullhd { + flex: none; } + .column.is-full-fullhd { + flex: none; + width: 100%; } + .column.is-three-quarters-fullhd { + flex: none; + width: 75%; } + .column.is-two-thirds-fullhd { + flex: none; + width: 66.6666%; } + .column.is-half-fullhd { + flex: none; + width: 50%; } + .column.is-one-third-fullhd { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-fullhd { + flex: none; + width: 25%; } + .column.is-one-fifth-fullhd { + flex: none; + width: 20%; } + .column.is-two-fifths-fullhd { + flex: none; + width: 40%; } + .column.is-three-fifths-fullhd { + flex: none; + width: 60%; } + .column.is-four-fifths-fullhd { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-fullhd { + margin-left: 75%; } + .column.is-offset-two-thirds-fullhd { + margin-left: 66.6666%; } + .column.is-offset-half-fullhd { + margin-left: 50%; } + .column.is-offset-one-third-fullhd { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-fullhd { + margin-left: 25%; } + .column.is-offset-one-fifth-fullhd { + margin-left: 20%; } + .column.is-offset-two-fifths-fullhd { + margin-left: 40%; } + .column.is-offset-three-fifths-fullhd { + margin-left: 60%; } + .column.is-offset-four-fifths-fullhd { + margin-left: 80%; } + .column.is-0-fullhd { + flex: none; + width: 0%; } + .column.is-offset-0-fullhd { + margin-left: 0%; } + .column.is-1-fullhd { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-fullhd { + margin-left: 8.3333333333%; } + .column.is-2-fullhd { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-fullhd { + margin-left: 16.6666666667%; } + .column.is-3-fullhd { + flex: none; + width: 25%; } + .column.is-offset-3-fullhd { + margin-left: 25%; } + .column.is-4-fullhd { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-fullhd { + margin-left: 33.3333333333%; } + .column.is-5-fullhd { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-fullhd { + margin-left: 41.6666666667%; } + .column.is-6-fullhd { + flex: none; + width: 50%; } + .column.is-offset-6-fullhd { + margin-left: 50%; } + .column.is-7-fullhd { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-fullhd { + margin-left: 58.3333333333%; } + .column.is-8-fullhd { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-fullhd { + margin-left: 66.6666666667%; } + .column.is-9-fullhd { + flex: none; + width: 75%; } + .column.is-offset-9-fullhd { + margin-left: 75%; } + .column.is-10-fullhd { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-fullhd { + margin-left: 83.3333333333%; } + .column.is-11-fullhd { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-fullhd { + margin-left: 91.6666666667%; } + .column.is-12-fullhd { + flex: none; + width: 100%; } + .column.is-offset-12-fullhd { + margin-left: 100%; } } +.columns { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + .columns:last-child { + margin-bottom: -0.75rem; } + .columns:not(:last-child) { + margin-bottom: calc(1.5rem - 0.75rem); } + .columns.is-centered { + justify-content: center; } + .columns.is-gapless { + margin-left: 0; + margin-right: 0; + margin-top: 0; } + .columns.is-gapless > .column { + margin: 0; + padding: 0 !important; } + .columns.is-gapless:not(:last-child) { + margin-bottom: 1.5rem; } + .columns.is-gapless:last-child { + margin-bottom: 0; } + .columns.is-mobile { + display: flex; } + .columns.is-multiline { + flex-wrap: wrap; } + .columns.is-vcentered { + align-items: center; } + @media screen and (min-width: 769px), print { + .columns:not(.is-desktop) { + display: flex; } } + @media screen and (min-width: 1056px) { + .columns.is-desktop { + display: flex; } } +.columns.is-variable { + --columnGap: 0.75rem; + margin-left: calc(-1 * var(--columnGap)); + margin-right: calc(-1 * var(--columnGap)); } + .columns.is-variable .column { + padding-left: var(--columnGap); + padding-right: var(--columnGap); } + .columns.is-variable.is-0 { + --columnGap: 0rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-0-mobile { + --columnGap: 0rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-0-tablet { + --columnGap: 0rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-0-tablet-only { + --columnGap: 0rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-0-touch { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-0-desktop { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-0-desktop-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-0-widescreen { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-0-widescreen-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-0-fullhd { + --columnGap: 0rem; } } + .columns.is-variable.is-1 { + --columnGap: 0.25rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-1-mobile { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-1-tablet { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-1-tablet-only { + --columnGap: 0.25rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-1-touch { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-1-desktop { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-1-desktop-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-1-widescreen { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-1-widescreen-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-1-fullhd { + --columnGap: 0.25rem; } } + .columns.is-variable.is-2 { + --columnGap: 0.5rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-2-mobile { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-2-tablet { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-2-tablet-only { + --columnGap: 0.5rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-2-touch { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-2-desktop { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-2-desktop-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-2-widescreen { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-2-widescreen-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-2-fullhd { + --columnGap: 0.5rem; } } + .columns.is-variable.is-3 { + --columnGap: 0.75rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-3-mobile { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-3-tablet { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-3-tablet-only { + --columnGap: 0.75rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-3-touch { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-3-desktop { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-3-desktop-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-3-widescreen { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-3-widescreen-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-3-fullhd { + --columnGap: 0.75rem; } } + .columns.is-variable.is-4 { + --columnGap: 1rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-4-mobile { + --columnGap: 1rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-4-tablet { + --columnGap: 1rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-4-tablet-only { + --columnGap: 1rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-4-touch { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-4-desktop { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-4-desktop-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-4-widescreen { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-4-widescreen-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-4-fullhd { + --columnGap: 1rem; } } + .columns.is-variable.is-5 { + --columnGap: 1.25rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-5-mobile { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-5-tablet { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-5-tablet-only { + --columnGap: 1.25rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-5-touch { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-5-desktop { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-5-desktop-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-5-widescreen { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-5-widescreen-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-5-fullhd { + --columnGap: 1.25rem; } } + .columns.is-variable.is-6 { + --columnGap: 1.5rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-6-mobile { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-6-tablet { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-6-tablet-only { + --columnGap: 1.5rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-6-touch { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-6-desktop { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-6-desktop-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-6-widescreen { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-6-widescreen-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-6-fullhd { + --columnGap: 1.5rem; } } + .columns.is-variable.is-7 { + --columnGap: 1.75rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-7-mobile { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-7-tablet { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-7-tablet-only { + --columnGap: 1.75rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-7-touch { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-7-desktop { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-7-desktop-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-7-widescreen { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-7-widescreen-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-7-fullhd { + --columnGap: 1.75rem; } } + .columns.is-variable.is-8 { + --columnGap: 2rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-8-mobile { + --columnGap: 2rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-8-tablet { + --columnGap: 2rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-8-tablet-only { + --columnGap: 2rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-8-touch { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-8-desktop { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-8-desktop-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-8-widescreen { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-8-widescreen-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-8-fullhd { + --columnGap: 2rem; } } +.tile { + align-items: stretch; + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + min-height: min-content; } + .tile.is-ancestor { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + .tile.is-ancestor:last-child { + margin-bottom: -0.75rem; } + .tile.is-ancestor:not(:last-child) { + margin-bottom: 0.75rem; } + .tile.is-child { + margin: 0 !important; } + .tile.is-parent { + padding: 0.75rem; } + .tile.is-vertical { + flex-direction: column; } + .tile.is-vertical > .tile.is-child:not(:last-child) { + margin-bottom: 1.5rem !important; } + @media screen and (min-width: 769px), print { + .tile:not(.is-child) { + display: flex; } + .tile.is-1 { + flex: none; + width: 8.3333333333%; } + .tile.is-2 { + flex: none; + width: 16.6666666667%; } + .tile.is-3 { + flex: none; + width: 25%; } + .tile.is-4 { + flex: none; + width: 33.3333333333%; } + .tile.is-5 { + flex: none; + width: 41.6666666667%; } + .tile.is-6 { + flex: none; + width: 50%; } + .tile.is-7 { + flex: none; + width: 58.3333333333%; } + .tile.is-8 { + flex: none; + width: 66.6666666667%; } + .tile.is-9 { + flex: none; + width: 75%; } + .tile.is-10 { + flex: none; + width: 83.3333333333%; } + .tile.is-11 { + flex: none; + width: 91.6666666667%; } + .tile.is-12 { + flex: none; + width: 100%; } } +.hero { + align-items: stretch; + display: flex; + flex-direction: column; + justify-content: space-between; } + .hero .navbar { + background: none; } + .hero .tabs ul { + border-bottom: none; } + .hero.is-white { + background-color: white; + color: #0a0a0a; } + .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-white strong { + color: inherit; } + .hero.is-white .title { + color: #0a0a0a; } + .hero.is-white .subtitle { + color: rgba(10, 10, 10, 0.9); } + .hero.is-white .subtitle a:not(.button), + .hero.is-white .subtitle strong { + color: #0a0a0a; } + @media screen and (max-width: 1055px) { + .hero.is-white .navbar-menu { + background-color: white; } } + .hero.is-white .navbar-item, + .hero.is-white .navbar-link { + color: rgba(10, 10, 10, 0.7); } + .hero.is-white a.navbar-item:hover, .hero.is-white a.navbar-item.is-active, + .hero.is-white .navbar-link:hover, + .hero.is-white .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .hero.is-white .tabs a { + color: #0a0a0a; + opacity: 0.9; } + .hero.is-white .tabs a:hover { + opacity: 1; } + .hero.is-white .tabs li.is-active a { + opacity: 1; } + .hero.is-white .tabs.is-boxed a, .hero.is-white .tabs.is-toggle a { + color: #0a0a0a; } + .hero.is-white .tabs.is-boxed a:hover, .hero.is-white .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-white .tabs.is-boxed li.is-active a, .hero.is-white .tabs.is-boxed li.is-active a:hover, .hero.is-white .tabs.is-toggle li.is-active a, .hero.is-white .tabs.is-toggle li.is-active a:hover { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .hero.is-white.is-bold { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } + @media screen and (max-width: 768px) { + .hero.is-white.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } + .hero.is-black { + background-color: #0a0a0a; + color: white; } + .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-black strong { + color: inherit; } + .hero.is-black .title { + color: white; } + .hero.is-black .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-black .subtitle a:not(.button), + .hero.is-black .subtitle strong { + color: white; } + @media screen and (max-width: 1055px) { + .hero.is-black .navbar-menu { + background-color: #0a0a0a; } } + .hero.is-black .navbar-item, + .hero.is-black .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-black a.navbar-item:hover, .hero.is-black a.navbar-item.is-active, + .hero.is-black .navbar-link:hover, + .hero.is-black .navbar-link.is-active { + background-color: black; + color: white; } + .hero.is-black .tabs a { + color: white; + opacity: 0.9; } + .hero.is-black .tabs a:hover { + opacity: 1; } + .hero.is-black .tabs li.is-active a { + opacity: 1; } + .hero.is-black .tabs.is-boxed a, .hero.is-black .tabs.is-toggle a { + color: white; } + .hero.is-black .tabs.is-boxed a:hover, .hero.is-black .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-black .tabs.is-boxed li.is-active a, .hero.is-black .tabs.is-boxed li.is-active a:hover, .hero.is-black .tabs.is-toggle li.is-active a, .hero.is-black .tabs.is-toggle li.is-active a:hover { + background-color: white; + border-color: white; + color: #0a0a0a; } + .hero.is-black.is-bold { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } + @media screen and (max-width: 768px) { + .hero.is-black.is-bold .navbar-menu { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } + .hero.is-light { + background-color: whitesmoke; + color: #363636; } + .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-light strong { + color: inherit; } + .hero.is-light .title { + color: #363636; } + .hero.is-light .subtitle { + color: rgba(54, 54, 54, 0.9); } + .hero.is-light .subtitle a:not(.button), + .hero.is-light .subtitle strong { + color: #363636; } + @media screen and (max-width: 1055px) { + .hero.is-light .navbar-menu { + background-color: whitesmoke; } } + .hero.is-light .navbar-item, + .hero.is-light .navbar-link { + color: rgba(54, 54, 54, 0.7); } + .hero.is-light a.navbar-item:hover, .hero.is-light a.navbar-item.is-active, + .hero.is-light .navbar-link:hover, + .hero.is-light .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .hero.is-light .tabs a { + color: #363636; + opacity: 0.9; } + .hero.is-light .tabs a:hover { + opacity: 1; } + .hero.is-light .tabs li.is-active a { + opacity: 1; } + .hero.is-light .tabs.is-boxed a, .hero.is-light .tabs.is-toggle a { + color: #363636; } + .hero.is-light .tabs.is-boxed a:hover, .hero.is-light .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-light .tabs.is-boxed li.is-active a, .hero.is-light .tabs.is-boxed li.is-active a:hover, .hero.is-light .tabs.is-toggle li.is-active a, .hero.is-light .tabs.is-toggle li.is-active a:hover { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .hero.is-light.is-bold { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } + @media screen and (max-width: 768px) { + .hero.is-light.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } } + .hero.is-dark, .content kbd.hero { + background-color: #363636; + color: whitesmoke; } + .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-dark strong, + .content kbd.hero strong { + color: inherit; } + .hero.is-dark .title, .content kbd.hero .title { + color: whitesmoke; } + .hero.is-dark .subtitle, .content kbd.hero .subtitle { + color: rgba(245, 245, 245, 0.9); } + .hero.is-dark .subtitle a:not(.button), .content kbd.hero .subtitle a:not(.button), + .hero.is-dark .subtitle strong, + .content kbd.hero .subtitle strong { + color: whitesmoke; } + @media screen and (max-width: 1055px) { + .hero.is-dark .navbar-menu, .content kbd.hero .navbar-menu { + background-color: #363636; } } + .hero.is-dark .navbar-item, .content kbd.hero .navbar-item, + .hero.is-dark .navbar-link, + .content kbd.hero .navbar-link { + color: rgba(245, 245, 245, 0.7); } + .hero.is-dark a.navbar-item:hover, .content kbd.hero a.navbar-item:hover, .hero.is-dark a.navbar-item.is-active, .content kbd.hero a.navbar-item.is-active, + .hero.is-dark .navbar-link:hover, + .content kbd.hero .navbar-link:hover, + .hero.is-dark .navbar-link.is-active, + .content kbd.hero .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .hero.is-dark .tabs a, .content kbd.hero .tabs a { + color: whitesmoke; + opacity: 0.9; } + .hero.is-dark .tabs a:hover, .content kbd.hero .tabs a:hover { + opacity: 1; } + .hero.is-dark .tabs li.is-active a, .content kbd.hero .tabs li.is-active a { + opacity: 1; } + .hero.is-dark .tabs.is-boxed a, .content kbd.hero .tabs.is-boxed a, .hero.is-dark .tabs.is-toggle a, .content kbd.hero .tabs.is-toggle a { + color: whitesmoke; } + .hero.is-dark .tabs.is-boxed a:hover, .content kbd.hero .tabs.is-boxed a:hover, .hero.is-dark .tabs.is-toggle a:hover, .content kbd.hero .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-dark .tabs.is-boxed li.is-active a, .content kbd.hero .tabs.is-boxed li.is-active a, .hero.is-dark .tabs.is-boxed li.is-active a:hover, .hero.is-dark .tabs.is-toggle li.is-active a, .content kbd.hero .tabs.is-toggle li.is-active a, .hero.is-dark .tabs.is-toggle li.is-active a:hover { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .hero.is-dark.is-bold, .content kbd.hero.is-bold { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } + @media screen and (max-width: 768px) { + .hero.is-dark.is-bold .navbar-menu, .content kbd.hero.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } } + .hero.is-primary, .docstring > section > a.hero.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-primary strong, + .docstring > section > a.hero.docs-sourcelink strong { + color: inherit; } + .hero.is-primary .title, .docstring > section > a.hero.docs-sourcelink .title { + color: #fff; } + .hero.is-primary .subtitle, .docstring > section > a.hero.docs-sourcelink .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-primary .subtitle a:not(.button), .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), + .hero.is-primary .subtitle strong, + .docstring > section > a.hero.docs-sourcelink .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-primary .navbar-menu, .docstring > section > a.hero.docs-sourcelink .navbar-menu { + background-color: #4eb5de; } } + .hero.is-primary .navbar-item, .docstring > section > a.hero.docs-sourcelink .navbar-item, + .hero.is-primary .navbar-link, + .docstring > section > a.hero.docs-sourcelink .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-primary a.navbar-item:hover, .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, .hero.is-primary a.navbar-item.is-active, .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, + .hero.is-primary .navbar-link:hover, + .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, + .hero.is-primary .navbar-link.is-active, + .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .hero.is-primary .tabs a, .docstring > section > a.hero.docs-sourcelink .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-primary .tabs a:hover, .docstring > section > a.hero.docs-sourcelink .tabs a:hover { + opacity: 1; } + .hero.is-primary .tabs li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { + opacity: 1; } + .hero.is-primary .tabs.is-boxed a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, .hero.is-primary .tabs.is-toggle a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { + color: #fff; } + .hero.is-primary .tabs.is-boxed a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, .hero.is-primary .tabs.is-toggle a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-primary .tabs.is-boxed li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, .hero.is-primary .tabs.is-boxed li.is-active a:hover, .hero.is-primary .tabs.is-toggle li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, .hero.is-primary .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #4eb5de; } + .hero.is-primary.is-bold, .docstring > section > a.hero.is-bold.docs-sourcelink { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } + @media screen and (max-width: 768px) { + .hero.is-primary.is-bold .navbar-menu, .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } } + .hero.is-link { + background-color: #149eaa; + color: #fff; } + .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-link strong { + color: inherit; } + .hero.is-link .title { + color: #fff; } + .hero.is-link .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-link .subtitle a:not(.button), + .hero.is-link .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-link .navbar-menu { + background-color: #149eaa; } } + .hero.is-link .navbar-item, + .hero.is-link .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-link a.navbar-item:hover, .hero.is-link a.navbar-item.is-active, + .hero.is-link .navbar-link:hover, + .hero.is-link .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .hero.is-link .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-link .tabs a:hover { + opacity: 1; } + .hero.is-link .tabs li.is-active a { + opacity: 1; } + .hero.is-link .tabs.is-boxed a, .hero.is-link .tabs.is-toggle a { + color: #fff; } + .hero.is-link .tabs.is-boxed a:hover, .hero.is-link .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-link .tabs.is-boxed li.is-active a, .hero.is-link .tabs.is-boxed li.is-active a:hover, .hero.is-link .tabs.is-toggle li.is-active a, .hero.is-link .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #149eaa; } + .hero.is-link.is-bold { + background-image: linear-gradient(141deg, #088379 0%, #149eaa 71%, #119ac6 100%); } + @media screen and (max-width: 768px) { + .hero.is-link.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #088379 0%, #149eaa 71%, #119ac6 100%); } } + .hero.is-info { + background-color: #209cee; + color: #fff; } + .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-info strong { + color: inherit; } + .hero.is-info .title { + color: #fff; } + .hero.is-info .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-info .subtitle a:not(.button), + .hero.is-info .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-info .navbar-menu { + background-color: #209cee; } } + .hero.is-info .navbar-item, + .hero.is-info .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-info a.navbar-item:hover, .hero.is-info a.navbar-item.is-active, + .hero.is-info .navbar-link:hover, + .hero.is-info .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .hero.is-info .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-info .tabs a:hover { + opacity: 1; } + .hero.is-info .tabs li.is-active a { + opacity: 1; } + .hero.is-info .tabs.is-boxed a, .hero.is-info .tabs.is-toggle a { + color: #fff; } + .hero.is-info .tabs.is-boxed a:hover, .hero.is-info .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-info .tabs.is-boxed li.is-active a, .hero.is-info .tabs.is-boxed li.is-active a:hover, .hero.is-info .tabs.is-toggle li.is-active a, .hero.is-info .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #209cee; } + .hero.is-info.is-bold { + background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } + @media screen and (max-width: 768px) { + .hero.is-info.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } } + .hero.is-success { + background-color: #22c35b; + color: #fff; } + .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-success strong { + color: inherit; } + .hero.is-success .title { + color: #fff; } + .hero.is-success .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-success .subtitle a:not(.button), + .hero.is-success .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-success .navbar-menu { + background-color: #22c35b; } } + .hero.is-success .navbar-item, + .hero.is-success .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-success a.navbar-item:hover, .hero.is-success a.navbar-item.is-active, + .hero.is-success .navbar-link:hover, + .hero.is-success .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .hero.is-success .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-success .tabs a:hover { + opacity: 1; } + .hero.is-success .tabs li.is-active a { + opacity: 1; } + .hero.is-success .tabs.is-boxed a, .hero.is-success .tabs.is-toggle a { + color: #fff; } + .hero.is-success .tabs.is-boxed a:hover, .hero.is-success .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-success .tabs.is-boxed li.is-active a, .hero.is-success .tabs.is-boxed li.is-active a:hover, .hero.is-success .tabs.is-toggle li.is-active a, .hero.is-success .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #22c35b; } + .hero.is-success.is-bold { + background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } + @media screen and (max-width: 768px) { + .hero.is-success.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } } + .hero.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-warning strong { + color: inherit; } + .hero.is-warning .title { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .subtitle { + color: rgba(0, 0, 0, 0.9); } + .hero.is-warning .subtitle a:not(.button), + .hero.is-warning .subtitle strong { + color: rgba(0, 0, 0, 0.7); } + @media screen and (max-width: 1055px) { + .hero.is-warning .navbar-menu { + background-color: #ffdd57; } } + .hero.is-warning .navbar-item, + .hero.is-warning .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning a.navbar-item:hover, .hero.is-warning a.navbar-item.is-active, + .hero.is-warning .navbar-link:hover, + .hero.is-warning .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .tabs a { + color: rgba(0, 0, 0, 0.7); + opacity: 0.9; } + .hero.is-warning .tabs a:hover { + opacity: 1; } + .hero.is-warning .tabs li.is-active a { + opacity: 1; } + .hero.is-warning .tabs.is-boxed a, .hero.is-warning .tabs.is-toggle a { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .tabs.is-boxed a:hover, .hero.is-warning .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-warning .tabs.is-boxed li.is-active a, .hero.is-warning .tabs.is-boxed li.is-active a:hover, .hero.is-warning .tabs.is-toggle li.is-active a, .hero.is-warning .tabs.is-toggle li.is-active a:hover { + background-color: rgba(0, 0, 0, 0.7); + border-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .hero.is-warning.is-bold { + background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } + @media screen and (max-width: 768px) { + .hero.is-warning.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } } + .hero.is-danger { + background-color: #da0b00; + color: #fff; } + .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-danger strong { + color: inherit; } + .hero.is-danger .title { + color: #fff; } + .hero.is-danger .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-danger .subtitle a:not(.button), + .hero.is-danger .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-danger .navbar-menu { + background-color: #da0b00; } } + .hero.is-danger .navbar-item, + .hero.is-danger .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-danger a.navbar-item:hover, .hero.is-danger a.navbar-item.is-active, + .hero.is-danger .navbar-link:hover, + .hero.is-danger .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .hero.is-danger .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-danger .tabs a:hover { + opacity: 1; } + .hero.is-danger .tabs li.is-active a { + opacity: 1; } + .hero.is-danger .tabs.is-boxed a, .hero.is-danger .tabs.is-toggle a { + color: #fff; } + .hero.is-danger .tabs.is-boxed a:hover, .hero.is-danger .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-danger .tabs.is-boxed li.is-active a, .hero.is-danger .tabs.is-boxed li.is-active a:hover, .hero.is-danger .tabs.is-toggle li.is-active a, .hero.is-danger .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #da0b00; } + .hero.is-danger.is-bold { + background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } + @media screen and (max-width: 768px) { + .hero.is-danger.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } } + .hero.is-small .hero-body, #documenter .docs-sidebar form.docs-search > input.hero .hero-body { + padding-bottom: 1.5rem; + padding-top: 1.5rem; } + @media screen and (min-width: 769px), print { + .hero.is-medium .hero-body { + padding-bottom: 9rem; + padding-top: 9rem; } } + @media screen and (min-width: 769px), print { + .hero.is-large .hero-body { + padding-bottom: 18rem; + padding-top: 18rem; } } + .hero.is-halfheight .hero-body, .hero.is-fullheight .hero-body, .hero.is-fullheight-with-navbar .hero-body { + align-items: center; + display: flex; } + .hero.is-halfheight .hero-body > .container, .hero.is-fullheight .hero-body > .container, .hero.is-fullheight-with-navbar .hero-body > .container { + flex-grow: 1; + flex-shrink: 1; } + .hero.is-halfheight { + min-height: 50vh; } + .hero.is-fullheight { + min-height: 100vh; } + +.hero-video { + overflow: hidden; } + .hero-video video { + left: 50%; + min-height: 100%; + min-width: 100%; + position: absolute; + top: 50%; + transform: translate3d(-50%, -50%, 0); } + .hero-video.is-transparent { + opacity: 0.3; } + @media screen and (max-width: 768px) { + .hero-video { + display: none; } } +.hero-buttons { + margin-top: 1.5rem; } + @media screen and (max-width: 768px) { + .hero-buttons .button { + display: flex; } + .hero-buttons .button:not(:last-child) { + margin-bottom: 0.75rem; } } + @media screen and (min-width: 769px), print { + .hero-buttons { + display: flex; + justify-content: center; } + .hero-buttons .button:not(:last-child) { + margin-right: 1.5rem; } } +.hero-head, +.hero-foot { + flex-grow: 0; + flex-shrink: 0; } + +.hero-body { + flex-grow: 1; + flex-shrink: 0; + padding: 3rem 1.5rem; } + +.section { + padding: 3rem 1.5rem; } + @media screen and (min-width: 1056px) { + .section.is-medium { + padding: 9rem 1.5rem; } + .section.is-large { + padding: 18rem 1.5rem; } } +.footer { + background-color: #fafafa; + padding: 3rem 1.5rem 6rem; } + +h1 .docs-heading-anchor, h1 .docs-heading-anchor:hover, h1 .docs-heading-anchor:visited, h2 .docs-heading-anchor, h2 .docs-heading-anchor:hover, h2 .docs-heading-anchor:visited, h3 .docs-heading-anchor, h3 .docs-heading-anchor:hover, h3 .docs-heading-anchor:visited, h4 .docs-heading-anchor, h4 .docs-heading-anchor:hover, h4 .docs-heading-anchor:visited, h5 .docs-heading-anchor, h5 .docs-heading-anchor:hover, h5 .docs-heading-anchor:visited, h6 .docs-heading-anchor, h6 .docs-heading-anchor:hover, h6 .docs-heading-anchor:visited { + color: #654ca3; } + +h1 .docs-heading-anchor-permalink, h2 .docs-heading-anchor-permalink, h3 .docs-heading-anchor-permalink, h4 .docs-heading-anchor-permalink, h5 .docs-heading-anchor-permalink, h6 .docs-heading-anchor-permalink { + visibility: hidden; + vertical-align: middle; + margin-left: 0.5em; + font-size: 0.7rem; } + h1 .docs-heading-anchor-permalink::before, h2 .docs-heading-anchor-permalink::before, h3 .docs-heading-anchor-permalink::before, h4 .docs-heading-anchor-permalink::before, h5 .docs-heading-anchor-permalink::before, h6 .docs-heading-anchor-permalink::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f0c1"; } + +h1:hover .docs-heading-anchor-permalink, h2:hover .docs-heading-anchor-permalink, h3:hover .docs-heading-anchor-permalink, h4:hover .docs-heading-anchor-permalink, h5:hover .docs-heading-anchor-permalink, h6:hover .docs-heading-anchor-permalink { + visibility: visible; } + +.docs-dark-only { + display: none !important; } + +pre { + position: relative; + overflow: hidden; } + pre code, pre code.hljs { + padding: 0 0.75rem !important; + overflow: auto; + display: block; } + pre code:first-of-type, pre code.hljs:first-of-type { + padding-top: 0.5rem !important; } + pre code:last-of-type, pre code.hljs:last-of-type { + padding-bottom: 0.5rem !important; } + pre .copy-button { + opacity: 0.2; + transition: opacity 0.2s; + position: absolute; + right: 0em; + top: 0em; + padding: 0.5em; + width: 2.5em; + height: 2.5em; + background: transparent; + border: none; + font-family: "Font Awesome 5 Free"; + color: #202020; + cursor: pointer; + text-align: center; } + pre .copy-button:focus, pre .copy-button:hover { + opacity: 1; + background: rgba(32, 32, 32, 0.1); + color: #149eaa; } + pre .copy-button.success { + color: #259a12; + opacity: 1; } + pre .copy-button.error { + color: #cb3c33; + opacity: 1; } + pre:hover .copy-button { + opacity: 1; } + +.admonition { + background-color: #b5b5b5; + border-style: solid; + border-width: 1px; + border-color: #363636; + border-radius: 4px; + font-size: 1rem; } + .admonition strong { + color: currentColor; } + .admonition.is-small, #documenter .docs-sidebar form.docs-search > input.admonition { + font-size: 0.75rem; } + .admonition.is-medium { + font-size: 1.25rem; } + .admonition.is-large { + font-size: 1.5rem; } + .admonition.is-default { + background-color: #b5b5b5; + border-color: #363636; } + .admonition.is-default > .admonition-header { + background-color: #363636; + color: #fff; } + .admonition.is-default > .admonition-body { + color: #fff; } + .admonition.is-info { + background-color: #def0fc; + border-color: #209cee; } + .admonition.is-info > .admonition-header { + background-color: #209cee; + color: #fff; } + .admonition.is-info > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-success { + background-color: #bdf4d1; + border-color: #22c35b; } + .admonition.is-success > .admonition-header { + background-color: #22c35b; + color: #fff; } + .admonition.is-success > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-warning { + background-color: #fff3c5; + border-color: #ffdd57; } + .admonition.is-warning > .admonition-header { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .admonition.is-warning > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-danger { + background-color: #ffaba7; + border-color: #da0b00; } + .admonition.is-danger > .admonition-header { + background-color: #da0b00; + color: #fff; } + .admonition.is-danger > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-compat { + background-color: #bdeff5; + border-color: #1db5c9; } + .admonition.is-compat > .admonition-header { + background-color: #1db5c9; + color: #fff; } + .admonition.is-compat > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + +.admonition-header { + color: #fff; + background-color: #363636; + align-items: center; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.5rem 0.75rem; + position: relative; } + .admonition-header:before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + margin-right: 0.75rem; + content: "\f06a"; } + +.admonition-body { + color: #202020; + padding: 0.5rem 0.75rem; } + .admonition-body pre { + background-color: #ebe8f4; } + .admonition-body code { + background-color: #ebe8f4; } + +.docstring { + margin-bottom: 1em; + background-color: transparent; + border: 1px solid #dbdbdb; + box-shadow: 2px 2px 3px rgba(10, 10, 10, 0.1); + max-width: 100%; } + .docstring > header { + display: flex; + flex-grow: 1; + align-items: stretch; + padding: 0.5rem 0.75rem; + background-color: #f7f7f7; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + box-shadow: none; + border-bottom: 1px solid #dbdbdb; } + .docstring > header code { + background-color: transparent; } + .docstring > header .docstring-binding { + margin-right: 0.3em; } + .docstring > header .docstring-category { + margin-left: 0.3em; } + .docstring > section { + position: relative; + padding: 0.75rem 0.75rem; + border-bottom: 1px solid #dbdbdb; } + .docstring > section:last-child { + border-bottom: none; } + .docstring > section > a.docs-sourcelink { + transition: opacity 0.3s; + opacity: 0; + position: absolute; + right: 0.375rem; + bottom: 0.375rem; } + .docstring > section > a.docs-sourcelink:focus { + opacity: 1 !important; } + .docstring:hover > section > a.docs-sourcelink { + opacity: 0.2; } + .docstring:focus-within > section > a.docs-sourcelink { + opacity: 0.2; } + .docstring > section:hover a.docs-sourcelink { + opacity: 1; } + +.documenter-example-output { + background-color: #fff; } + +.outdated-warning-overlay { + position: fixed; + top: 0; + left: 0; + right: 0; + box-shadow: 0 0 10px rgba(0, 0, 0, 0.3); + z-index: 999; + background-color: #ffaba7; + color: rgba(0, 0, 0, 0.7); + border-bottom: 3px solid #da0b00; + padding: 10px 35px; + text-align: center; + font-size: 15px; } + .outdated-warning-overlay .outdated-warning-closer { + position: absolute; + top: calc(50% - 10px); + right: 18px; + cursor: pointer; + width: 12px; } + .outdated-warning-overlay a { + color: #149eaa; } + .outdated-warning-overlay a:hover { + color: #107c85; } + +.content pre { + border: 1px solid #dbdbdb; } + +.content code { + font-weight: inherit; } + +.content a code { + color: #149eaa; } + +.content h1 code, .content h2 code, .content h3 code, .content h4 code, .content h5 code, .content h6 code { + color: #654ca3; } + +.content table { + display: block; + width: initial; + max-width: 100%; + overflow-x: auto; } + +.content blockquote > ul:first-child, .content blockquote > ol:first-child, .content .admonition-body > ul:first-child, .content .admonition-body > ol:first-child { + margin-top: 0; } + +pre, code { + font-variant-ligatures: no-contextual; } + +.breadcrumb a.is-disabled { + cursor: default; + pointer-events: none; } + .breadcrumb a.is-disabled, .breadcrumb a.is-disabled:hover { + color: #654ca3; } + +.hljs { + background: initial !important; } + +.katex .katex-mathml { + top: 0; + right: 0; } + +.katex-display, mjx-container, .MathJax_Display { + margin: 0.5em 0 !important; } + +html { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; } + +li.no-marker { + list-style: none; } + +/* This file contain the overall layout. + * + * The main container is
        that is identified by id #documenter. + */ +#documenter .docs-main > article { + overflow-wrap: break-word; } + #documenter .docs-main > article .math-container { + overflow-x: auto; + overflow-y: hidden; } + +@media screen and (min-width: 1056px) { + #documenter .docs-main { + max-width: 52rem; + margin-left: 20rem; + padding-right: 1rem; } } + +@media screen and (max-width: 1055px) { + #documenter .docs-main { + width: 100%; } + #documenter .docs-main > article { + max-width: 52rem; + margin-left: auto; + margin-right: auto; + margin-bottom: 1rem; + padding: 0 1rem; } + #documenter .docs-main > header, #documenter .docs-main > nav { + max-width: 100%; + width: 100%; + margin: 0; } } + +#documenter .docs-main header.docs-navbar { + background-color: #fff; + border-bottom: 1px solid #dbdbdb; + z-index: 2; + min-height: 4rem; + margin-bottom: 1rem; + display: flex; } + #documenter .docs-main header.docs-navbar .breadcrumb { + flex-grow: 1; } + #documenter .docs-main header.docs-navbar .docs-right { + display: flex; + white-space: nowrap; } + #documenter .docs-main header.docs-navbar .docs-right .docs-icon, #documenter .docs-main header.docs-navbar .docs-right .docs-label, #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + display: inline-block; } + #documenter .docs-main header.docs-navbar .docs-right .docs-label { + padding: 0; + margin-left: 0.3em; } + #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button { + margin: auto 0 auto 1rem; } + #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + font-size: 1.5rem; + margin: auto 0 auto 1rem; } + #documenter .docs-main header.docs-navbar > * { + margin: auto 0; } + @media screen and (max-width: 1055px) { + #documenter .docs-main header.docs-navbar { + position: sticky; + top: 0; + padding: 0 1rem; + /* For Headroom.js */ + transition-property: top, box-shadow; + -webkit-transition-property: top, box-shadow; + /* Safari */ + transition-duration: 0.3s; + -webkit-transition-duration: 0.3s; + /* Safari */ } + #documenter .docs-main header.docs-navbar.headroom--not-top { + box-shadow: 0.2rem 0rem 0.4rem #bbb; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } + #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { + top: -4.5rem; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } } +#documenter .docs-main section.footnotes { + border-top: 1px solid #dbdbdb; } + #documenter .docs-main section.footnotes li .tag:first-child, #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, #documenter .docs-main section.footnotes li .content kbd:first-child, .content #documenter .docs-main section.footnotes li kbd:first-child { + margin-right: 1em; + margin-bottom: 0.4em; } + +#documenter .docs-main .docs-footer { + display: flex; + flex-wrap: wrap; + margin-left: 0; + margin-right: 0; + border-top: 1px solid #dbdbdb; + padding-top: 1rem; + padding-bottom: 1rem; } + @media screen and (max-width: 1055px) { + #documenter .docs-main .docs-footer { + padding-left: 1rem; + padding-right: 1rem; } } + #documenter .docs-main .docs-footer .docs-footer-nextpage, #documenter .docs-main .docs-footer .docs-footer-prevpage { + flex-grow: 1; } + #documenter .docs-main .docs-footer .docs-footer-nextpage { + text-align: right; } + #documenter .docs-main .docs-footer .flexbox-break { + flex-basis: 100%; + height: 0; } + #documenter .docs-main .docs-footer .footer-message { + font-size: 0.8em; + margin: 0.5em auto 0 auto; + text-align: center; } + +#documenter .docs-sidebar { + display: flex; + flex-direction: column; + color: #fff; + background-color: #654ca3; + border-right: 1px solid #dbdbdb; + padding: 0; + flex: 0 0 18rem; + z-index: 5; + font-size: 1em; + position: fixed; + left: -18rem; + width: 18rem; + height: 100%; + transition: left 0.3s; + /* Setting up a nicer theme style for the scrollbar */ } + #documenter .docs-sidebar.visible { + left: 0; + box-shadow: 0.4rem 0rem 0.8rem #bbb; } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar.visible { + box-shadow: none; } } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar { + left: 0; + top: 0; } } + #documenter .docs-sidebar .docs-logo { + margin-top: 1rem; + padding: 0 1rem; } + #documenter .docs-sidebar .docs-logo > img { + max-height: 6rem; + margin: auto; } + #documenter .docs-sidebar .docs-package-name { + flex-shrink: 0; + font-size: 1.5rem; + font-weight: 700; + text-align: center; + white-space: nowrap; + overflow: hidden; + padding: 0.5rem 0; } + #documenter .docs-sidebar .docs-package-name .docs-autofit { + max-width: 16.2rem; } + #documenter .docs-sidebar .docs-package-name a, #documenter .docs-sidebar .docs-package-name a:hover { + color: #fff; } + #documenter .docs-sidebar .docs-version-selector { + border-top: 1px solid #dbdbdb; + display: none; + padding: 0.5rem; } + #documenter .docs-sidebar .docs-version-selector.visible { + display: flex; } + #documenter .docs-sidebar ul.docs-menu { + flex-grow: 1; + user-select: none; + border-top: 1px solid #dbdbdb; + padding-bottom: 1.5rem; + /* Managing collapsible submenus */ } + #documenter .docs-sidebar ul.docs-menu > li > .tocitem { + font-weight: bold; } + #documenter .docs-sidebar ul.docs-menu > li li { + font-size: 0.95em; + margin-left: 1em; + border-left: 1px solid #dbdbdb; } + #documenter .docs-sidebar ul.docs-menu input.collapse-toggle { + display: none; } + #documenter .docs-sidebar ul.docs-menu ul.collapsed { + display: none; } + #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed { + display: block; } + #documenter .docs-sidebar ul.docs-menu label.tocitem { + display: flex; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label { + flex-grow: 2; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron { + display: inline-block; + font-style: normal; + font-variant: normal; + text-rendering: auto; + line-height: 1; + font-size: 0.75em; + margin-left: 1rem; + margin-top: auto; + margin-bottom: auto; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f054"; } + #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before { + content: "\f078"; } + #documenter .docs-sidebar ul.docs-menu .tocitem { + display: block; + padding: 0.5rem 0.5rem; } + #documenter .docs-sidebar ul.docs-menu .tocitem, #documenter .docs-sidebar ul.docs-menu .tocitem:hover { + color: #fff; + background: #654ca3; } + #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, #documenter .docs-sidebar ul.docs-menu label.tocitem:hover { + color: #fff; + background-color: #4b3979; } + #documenter .docs-sidebar ul.docs-menu li.is-active { + border-top: 1px solid #dbdbdb; + border-bottom: 1px solid #dbdbdb; + background-color: #fff; } + #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover { + background-color: #fff; + color: #202020; } + #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover { + background-color: #ddd7ec; + color: #202020; } + #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child { + border-top: none; } + #documenter .docs-sidebar ul.docs-menu ul.internal { + margin: 0 0.5rem 0.5rem; + border-top: 1px solid #dbdbdb; } + #documenter .docs-sidebar ul.docs-menu ul.internal li { + font-size: 0.85em; + border-left: none; + margin-left: 0; + margin-top: 0.5rem; } + #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem { + width: 100%; + padding: 0; } + #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before { + content: "⚬"; + margin-right: 0.4em; } + #documenter .docs-sidebar form.docs-search { + margin: auto; + margin-top: 0.5rem; + margin-bottom: 0.5rem; } + #documenter .docs-sidebar form.docs-search > input { + width: 14.4rem; } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar ul.docs-menu { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar { + width: .3rem; + background: none; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #543f87; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover { + background: #43326b; } } + @media screen and (max-width: 1055px) { + #documenter .docs-sidebar { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + #documenter .docs-sidebar::-webkit-scrollbar { + width: .3rem; + background: none; } + #documenter .docs-sidebar::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #543f87; } + #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover { + background: #43326b; } } +#documenter .docs-main #documenter-search-info { + margin-bottom: 1rem; } + +#documenter .docs-main #documenter-search-results { + list-style-type: circle; + list-style-position: outside; } + #documenter .docs-main #documenter-search-results li { + margin-left: 2rem; 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Gets put into the tag.. +function set_theme_from_local_storage() { + // Intialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if(window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the browser supports user color preference + var darkPreference = false; + // Check if the users preference is for dark color scheme + if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { + darkPreference = true; + } + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; var disabled = []; var darkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. 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Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return + }; + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return + }; + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement('meta'); + meta.name = 'robots'; + meta.content = 'noindex'; + + document.getElementsByTagName('head')[0].appendChild(meta); + }; + + const div = document.createElement('div'); + div.classList.add('outdated-warning-overlay'); + const closer = document.createElement('button'); + closer.classList.add('outdated-warning-closer', 'delete'); + closer.addEventListener('click', function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + '/../' + window.DOCUMENTER_STABLE; + div.innerHTML = 'This documentation is not for the latest stable release, but for either the development version or an older release.
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        Edit on GitHub

        TransitionIndicators.jl

        TransitionIndicators.jl

        TransitionIndicators — Module

        TransitionIndicators.jl

        CI codecov Package Downloads

        A Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

        To install it, run import Pkg; Pkg.add("TransitionIndicators").

        All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

        source
        Star us on GitHub!

        If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

        Content

        Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionIndicators.jl sticks to the latter terminology and provides an interface that:

        • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
        • Makes the surrogate analysis to test for significance under the hub.
        • Can be easily extended by any user without touching the source code.
        • Reduces the programming overhead for any researcher willing to benchmark new methods.
        • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
        • Increases trustworthiness thanks to a large test suite.
        Similar projects

        An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

        Approaches

        Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system with continuous right-hand side approaches a bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionIndicators.jl is designed to allow these cutting-edge methods and foster the development of new ones.

        diff --git a/previews/PR19/search/index.html b/previews/PR19/search/index.html new file mode 100644 index 00000000..4c486547 --- /dev/null +++ b/previews/PR19/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionIndicators.jl

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          diff --git a/previews/PR19/search_index.js b/previews/PR19/search_index.js new file mode 100644 index 00000000..0273d5e9 --- /dev/null +++ b/previews/PR19/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionIndicators.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionIndicators.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"api/#Indicators-analysis","page":"API","title":"Indicators analysis","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"IndicatorsConfig\nSignificanceConfig\nindicators_analysis","category":"page"},{"location":"api/#TransitionIndicators.IndicatorsConfig","page":"API","title":"TransitionIndicators.IndicatorsConfig","text":"IndicatorsConfig(indicators...; window_kwargs...)\n\nA configuration for computing indicators from timeseries. Indicators are standard Julia functions that input an AbstractVector and output a real number. Any number of indicators can be given. Indicators typically used in the literature are listed in the documentation section Indicators.\n\nKeywords are propagated into WindowViewer to create a sliding window for estimating the indicators.\n\nAlong with SignificanceConfig it is given to indicators_analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.SignificanceConfig","page":"API","title":"TransitionIndicators.SignificanceConfig","text":"SignificanceConfig(change_metrics...; kwargs...)\n\nA configuration for estimating a significant change of indicators computed from timeseries. Along with IndicatorsConfig it is given to indicators_analysis.\n\nchange_metrics can be a single Julia function, in which case the same metric is applied over all indicators in IndicatorsConfig. change_metrics can also be many functions, each one for each indicator.\n\nKeyword arguments\n\nn_surrogates::Int = 10_000: how many surrogates to create.\nsurrogate_method::S = RandomFourier(): what method to use to create the surrogates. Any Surrogate subtype from TimeseriesSurrogates.jl is valid.\nrng::AbstractRNG = Random.default_rng()`: a random number generator for the surrogates. See the Julia manual for more.\nwv_indicator_width::Int = 100,\nwv_indicator_stride::Int = 5,\nwidth, stride = 20, 1: width and stride given to the WindowViewer of the indicator timeseries. Notice that here the default values are different.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.indicators_analysis","page":"API","title":"TransitionIndicators.indicators_analysis","text":"indicators_analysis(x, indicators::IndicatorsConfig, significance::SignificanceConfig)\n\nPerform an analysis of transition indicators for input timeseries x by specifying which indicators to use and with what sliding window (IndicatorsConfig), as well as how to measure significant changes in the indicators (SignificanceConfig).\n\nReturn the output as IndicatorsResults.\n\nThis function performs the analysis described in the documentation Example sections. It computes various indicators over sliding windows of x, and then computes change metrics of over sliding windows of the indicators. In parallel it does exactly the same computations for surrogates of x. The returned output contains all these computed timeseries and can be given to indicators_significance.\n\n\n\n\n\n","category":"function"},{"location":"api/#Indicators-significance","page":"API","title":"Indicators significance","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"indicators_significance\nSignificanceTest\nQuantile\nSigma\nsignificant","category":"page"},{"location":"api/#TransitionIndicators.indicators_significance","page":"API","title":"TransitionIndicators.indicators_significance","text":"indicators_significance(res::IndicatorsResults, q::SignificanceTest) → out\n\nGiven the output of indicators_analysis, estimate when the computed indicators have a statistically significant change, with \"significant\" defined by q, which is a subtype of SignificanceTest.\n\nThe output is returned as an n×m matrix with n the length of the time vector of the change metric timeseries, and m the number of change metrics (which is the same as the number of indicators). The values of the matrix are Booleans (true for significant).\n\nYou can use prod(out; dim = 2) for logical & product across indicators.\n\n\n\n\n\n","category":"function"},{"location":"api/#indicator_functions","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"ar1_whitenoise\nStatistics.mean(::Any)\nStatistics.var(::AbstractArray)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#TransitionIndicators.ar1_whitenoise","page":"API","title":"TransitionIndicators.ar1_whitenoise","text":"ar1_whitenoise(x) → ̂θ\n\nEstimate the AR1 regression coefficient θ of a vector time series x. Computation based on the analytic solution of the least-square parameter estimation:\n\n hattheta = dfracsum_i=2^n x_i x_i-1sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1)). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). 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The output rr can then be used as a function to perform the regression and extract the slope! If lambda = 0, linear regression is recovered (default case). For more information, visit: https://en.wikipedia.org/wiki/Ridge_regression.\n\nExamples\n\njulia> t = 0.0:1.0:100;\njulia> x = 2.3 .* t .+ 1.2;\njulia> rr = RidgeRegression(t);\njulia> rr(x)\n2.299999999999999\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.kendalltau","page":"API","title":"TransitionIndicators.kendalltau","text":"kendalltau(x)\n\nCompute the kendall-τ correlation coefficient of the time series x.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.spearman","page":"API","title":"TransitionIndicators.spearman","text":"spearman(x)\n\nCompute the spearman correlation coefficient of the time series x.\n\n\n\n\n\n","category":"function"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Significance-metrics","page":"API","title":"Significance metrics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"threshold_indicators\nmeasure_significance\nconfidence_interval\nnormalized_percentile","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionIndicators.WindowViewer","page":"API","title":"TransitionIndicators.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride as taken as length(x)÷100 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.windowmap","page":"API","title":"TransitionIndicators.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.windowmap!","page":"API","title":"TransitionIndicators.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"#TransitionIndicators.jl","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"(Image: TransitionIndicators.jl)","category":"page"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"TransitionIndicators","category":"page"},{"location":"#TransitionIndicators","page":"TransitionIndicators.jl","title":"TransitionIndicators","text":"TransitionIndicators.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\nTo install it, run import Pkg; Pkg.add(\"TransitionIndicators\").\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionIndicators.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionIndicators.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionIndicators.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system with continuous right-hand side approaches a bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionIndicators.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any pre-processing of raw data first such as detrending (not part of TransitionIndicators.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend or jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionIndicators.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionIndicators\nusing CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionIndicators.jl\nAny timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionIndicators.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\nt_indicator = windowmap(midpoint, tfluct; indicator_window...)\n\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\n\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a ridge regression","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 20, stride = 1)\nridgereg = RidgeRegression(t_indicator, change_window.width)\n\nt_change = windowmap(midpoint, t_indicator; change_window...)\nchange_l = windowmap(ridgereg, indicator_l; change_window...)\nchange_nl = windowmap(ridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionIndicators, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\nfig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))\nlines!(ax, tfluct, s .- 0.05; color = Cycled(3))\nax.title = \"real signal vs. surrogate(s)\"\n\n# compute and plot change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(ridgereg, indicator_s; change_window...)\n\nax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = \"nonlin\")\nlines!(ax, t_change, change_s; color = Cycled(3), label = \"surrogate\")\naxislegend()\nax.title = \"change metric\"\n\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test. We calculate the change metric for thousands of surrogates of the input timeseries, and then detect the points in time where the change metric timeseries exceeds a threshold (such as the 95-quantile) of the change metrics of the surrogates.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To visualize significant trends, we plot the bands giving the (-2 sigma 2 sigma) and (-3 sigma 3 sigma) intervals of the surrogate values, with sigma the standard-deviation of indicator slope across the surrogate timeseries:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig = Figure()\naxl = Axis(fig[1,1]; title = \"linear\")\naxnl = Axis(fig[1,2]; title = \"nonlinear\")\n\nfor (j, ax, x) in zip(1:2, (axl, axnl), (x_l_fluct, x_nl_fluct))\n\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n change_s_distr = zeros(n_surrogates, length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(ridgereg, indicator_s; change_window...)\n change_s_distr[i, :] .= change_s\n end\n\n mu = vec(mean(change_s_distr, dims = 1))\n sigma = vec(std(change_s_distr, dims = 1))\n\n # Plot (real signal) change metric and various confidence intervals\n orig_change = j == 1 ? change_l : change_nl\n lines!(ax, t_change, orig_change; color = Cycled(j))\n band!(ax, t_change, mu .- 2 .* sigma, mu .+ 2 .* sigma, color = (:red, 0.2) )\n band!(ax, t_change, mu .- 3 .* sigma, mu .+ 3 .* sigma, color = (:red, 0.1) )\nend\n\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, while the data generated by the linear model does not.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionIndicators.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionIndicators.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several different indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow as follows:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Create an instance of IndicatorsConfig, that dictates which indicators will be used, and over what sliding window.\nCreate an instance of SignificanceConfig, that dictates what change metrics, surrogate types, and sliding window will be used to quantify a significant change of the indicators.\nAlong with the input timeseries x these three are plugged into indicators_analysis.\nThe output, which is an IndicatorsResults, can be used to visualize the results, or given to indicators_significance to provide flags of the timepoints where there is a significant change of each indicator.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks apply this process, and visualize it, for the examples we used in the educational part of the tutorial.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"First we load, and do the necessary pre-processing, to get input data","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionIndicators, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_nl_fluct)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Then we decide what indicators and change metrices to use","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# these indicators are suitable for Critical Slowing Down\nindicators = [var, ar1_whitenoise]\nind_conf = IndicatorsConfig(indicators; width = 400)\n\n# use spearman correlation for both indicators\nchange_metric = spearman\nsig_conf = SignificanceConfig(change_metric; width = 20, n_surrogates = 1000)\n\n# perform the full analysis\nresult = indicators_analysis(x_nl_fluct, ind_conf, sig_conf)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"And lastly, obtain some flags for when there is a significant indicator change","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"sig = indicators_significance(result, 0.99)\n\n# Plot the original timeseries\nfig, ax = lines(tfluct, x_nl_fluct; label = \"input\")\n# Scatter the significance of each indicator\nfor i in size(sig, 2)\n signif_idxs = findall(sig[:, i])\n isempty(signif_idxs) && continue\n # get timepoints in real time\n tflags = tfluct[result.t_change[signif_idxs]]\n vlines!(ax, tflags; label = \"indicator $(indicators[i])\", color = Cycled(1+i))\nend\naxislegend()\nfig","category":"page"}] +} diff --git a/previews/PR19/siteinfo.js b/previews/PR19/siteinfo.js new file mode 100644 index 00000000..97d10c4e --- /dev/null +++ b/previews/PR19/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR19"; diff --git a/previews/PR19/tutorial/index.html b/previews/PR19/tutorial/index.html new file mode 100644 index 00000000..59270810 --- /dev/null +++ b/previews/PR19/tutorial/index.html @@ -0,0 +1,121 @@ + +Tutorial · TransitionIndicators.jl
          Edit on GitHub

          Tutorial

          Workflow

          Computing transition indicators consists of the following steps:

          1. Doing any pre-processing of raw data first such as detrending (not part of TransitionIndicators.jl). This yields the input timeseries.
          2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
          3. Computing the changes of the indicator by sliding a window over its timeseries.
          4. Generating many surrogates that preserve important statistical properties of the original timeseries.
          5. Performing step 2 and 3 for the surrogate timeseries.
          6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend or jump or anything else) when compared to the surrogate data.

          These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionIndicators.jl exports.

          Tutorial – Educational

          Raw input data

          Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

          \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

          with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

          using TransitionIndicators
+using CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig

          Preprocessing

          Not part of TransitionIndicators.jl

          Any timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionIndicators.jl and is the responsibility of the researcher.

          The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

          x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

          At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

          Detrending in Julia

          Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

          Indicator timeseries

          We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

          indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+t_indicator = windowmap(midpoint, tfluct; indicator_window...)
+
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

          The lines plotted above are the indicator timeseries.

          Change metric timeseries

          From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a ridge regression

          change_window = (width = 20, stride = 1)
+ridgereg = RidgeRegression(t_indicator, change_window.width)
+
+t_change = windowmap(midpoint, t_indicator; change_window...)
+change_l = windowmap(ridgereg, indicator_l; change_window...)
+change_nl = windowmap(ridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

          Timeseries surrogates

          As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

          In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionIndicators, so that you don't have to using both of them.

          To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

          # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))
+lines!(ax, tfluct, s .- 0.05; color = Cycled(3))
+ax.title = "real signal vs. surrogate(s)"
+
+# compute and plot change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(ridgereg, indicator_s; change_window...)
+
+ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin")
+lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate")
+axislegend()
+ax.title = "change metric"
+
+fig

          Quantifying significance

          To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test. We calculate the change metric for thousands of surrogates of the input timeseries, and then detect the points in time where the change metric timeseries exceeds a threshold (such as the 95-quantile) of the change metrics of the surrogates.

          To visualize significant trends, we plot the bands giving the $(-2 \, \sigma, 2 \, \sigma)$ and $(-3 \, \sigma, 3 \, \sigma)$ intervals of the surrogate values, with $\sigma$ the standard-deviation of indicator slope across the surrogate timeseries:

          n_surrogates = 1_000
+fig = Figure()
+axl = Axis(fig[1,1]; title = "linear")
+axnl = Axis(fig[1,2]; title = "nonlinear")
+
+for (j, ax, x) in zip(1:2, (axl, axnl), (x_l_fluct, x_nl_fluct))
+
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    change_s_distr =  zeros(n_surrogates, length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(ridgereg, indicator_s; change_window...)
+        change_s_distr[i, :] .= change_s
+    end
+
+    mu = vec(mean(change_s_distr, dims = 1))
+    sigma = vec(std(change_s_distr, dims = 1))
+
+    # Plot (real signal) change metric and various confidence intervals
+    orig_change = j == 1 ? change_l : change_nl
+    lines!(ax, t_change, orig_change; color = Cycled(j))
+    band!(ax, t_change, mu .- 2 .* sigma, mu .+ 2 .* sigma, color = (:red, 0.2) )
+    band!(ax, t_change, mu .- 3 .* sigma, mu .+ 3 .* sigma, color = (:red, 0.1) )
+end
+
+fig

          As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, while the data generated by the linear model does not.

          Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

          Tutorial – TransitionIndicators.jl

          TransitionIndicators.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several different indicators / change metrics in one go.

          The interface is simple, and directly parallelizes the Workflow as follows:

          1. Create an instance of IndicatorsConfig, that dictates which indicators will be used, and over what sliding window.
          2. Create an instance of SignificanceConfig, that dictates what change metrics, surrogate types, and sliding window will be used to quantify a significant change of the indicators.
          3. Along with the input timeseries x these three are plugged into indicators_analysis.
          4. The output, which is an IndicatorsResults, can be used to visualize the results, or given to indicators_significance to provide flags of the timepoints where there is a significant change of each indicator.

          The following blocks apply this process, and visualize it, for the examples we used in the educational part of the tutorial.

          First we load, and do the necessary pre-processing, to get input data

          using TransitionIndicators, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_nl_fluct)
+ax.title = "input timeseries"
+fig

          Then we decide what indicators and change metrices to use

          # these indicators are suitable for Critical Slowing Down
+indicators = [var, ar1_whitenoise]
+ind_conf = IndicatorsConfig(indicators; width = 400)
+
+# use spearman correlation for both indicators
+change_metric = spearman
+sig_conf = SignificanceConfig(change_metric; width = 20, n_surrogates = 1000)
+
+# perform the full analysis
+result = indicators_analysis(x_nl_fluct, ind_conf, sig_conf)
          IndicatorsResults
+ input timeseries: 2500-element Vector{Float64}
+ indicators:       Function[Statistics.var, TransitionIndicators.ar1_whitenoise]
+ indicator length: 2100
+ change metrics:   [TransitionIndicators.spearman]
+ surrogate:        RandomFourier(true)
+ surrogate #:      1000
+

          And lastly, obtain some flags for when there is a significant indicator change

          sig = indicators_significance(result, 0.99)
+
+# Plot the original timeseries
+fig, ax = lines(tfluct, x_nl_fluct; label = "input")
+# Scatter the significance of each indicator
+for i in size(sig, 2)
+    signif_idxs = findall(sig[:, i])
+    isempty(signif_idxs) && continue
+    # get timepoints in real time
+    tflags = tfluct[result.t_change[signif_idxs]]
+    vlines!(ax, tflags; label = "indicator $(indicators[i])", color = Cycled(1+i))
+end
+axislegend()
+fig
          diff --git a/previews/PR19/tutorial_literate.jl b/previews/PR19/tutorial_literate.jl new file mode 100644 index 00000000..7817d0f2 --- /dev/null +++ b/previews/PR19/tutorial_literate.jl @@ -0,0 +1,202 @@ +using TransitionIndicators, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_nlinear) +lines!(ax, t, x_linear) +ax.title = "raw data" +fig + +# +x_nl_fluct = diff(x_nlinear) +x_l_fluct = diff(x_linear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_nl_fluct) +ax.title = "input timeseries" +fig + +# +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +t_indicator = windowmap(midpoint, tfluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +# +change_window = (width = 20, stride = 1) +ridgereg = RidgeRegression(t_indicator, change_window.width) + +t_change = windowmap(midpoint, t_indicator; change_window...) +change_l = windowmap(ridgereg, indicator_l; change_window...) +change_nl = windowmap(ridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_nl) +# lines!(ax, t_change, change_l) +ax.title = "change metric timeseries" +fig + + +# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) +fig, ax = lines(tfluct, x_nl_fluct) +lines!(ax, tfluct, s .- 0.05; color = Cycled(3)) +ax.title = "real signal vs. surrogate(s)" + +# compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(ridgereg, indicator_s; change_window...) +fig, ax = lines(t_indicator, indicator_nl) +lines!(ax, t_indicator, indicator_s; color = Cycled(3)) +ax.ylabel = "indicator" +ax, = lines(fig[1,2], t_change, change_nl) +lines!(ax, t_change, change_s; color = Cycled(3)) +ax.ylabel = "change metric" +Label(fig[0, :], "real signal vs. surrogate(s)"; + tellheight = true, tellwidth = false, valign = :bottom, font = "TeX Gyre Heros Bold" +) +fig + + + + +lines!(ax, tfluct, s .- 0.05; color = Cycled(3)) +ax.title = "real signal vs. surrogate(s)" + + + +ax, = lines(fig[1,2], t_change, change_nl; label = "real") +lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate") +axislegend() +ax.title = "change metric" + +fig + +# %% + +n_surrogates = 1_000 +fig = Figure() +axnl = Axis(fig[1,1]; title = "nonlinear") +# axl = Axis(fig[1,2]; title = "linear") +axl = nothing + +for (j, ax, x) in zip(1:2, (axnl, axl), (x_nl_fluct, x_l_fluct)) + + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + change_s_distr = zeros(n_surrogates, length(change_s)) + + # Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(ridgereg, indicator_s; change_window...) + change_s_distr[i, :] .= change_s + end + + mu = vec(mean(change_s_distr, dims = 1)) + sigma = vec(std(change_s_distr, dims = 1)) + + # Plot (real signal) change metric and various confidence intervals + orig_change = j == 1 ? change_nl : change_l + lines!(ax, t_change, orig_change; color = Cycled(j)) + # band!(ax, t_change, mu .- 2 .* sigma, mu .+ 2 .* sigma, color = (:red, 0.2) ) + band!(ax, t_change, mu .- 3 .* sigma, mu .+ 3 .* sigma, color = (Main.COLORS[3], 0.2), + label = "±3σ") + axislegend(ax) + j == 1 && break +end + +fig + +# %% + +# these indicators are suitable for Critical Slowing Down +indicators = [var, ar1_whitenoise] +ind_conf = IndicatorsConfig(indicators; width = 400) + +# use spearman correlation for both indicators +change_metric = spearman +sig_conf = SignificanceConfig(change_metric; width = 20, n_surrogates = 1000) + +# perform the full analysis +result = indicators_analysis(x_nl_fluct, ind_conf, sig_conf) + +# And lastly, obtain some flags for when there is a significant indicator change +sig = indicators_significance(result, 0.99) + +# Plot the original timeseries +fig, ax = lines(tfluct, x_nl_fluct; label = "input") +# Scatter the significance of each indicator +for i in size(sig, 2) + signif_idxs = findall(sig[:, i]) + isempty(signif_idxs) && continue + # get timepoints in real time + tflags = tfluct[result.t_change[signif_idxs]] + vlines!(ax, tflags; label = "flags for $(indicators[i])", color = Cycled(3)) +end +axislegend() +fig + + + +# Tutorial short + +using TransitionIndicators, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +fig, ax = lines(t, x_nlinear;z) +ax.title = "original timeseries" +fig + +input = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(tfluct, input; color = Cycled(2)) +ax.title = "input timeseries" +fig + + + +# these indicators are suitable for Critical Slowing Down +indicators = [var, ar1_whitenoise] +ind_conf = IndicatorsConfig(indicators; + width = 400 +) +# use spearman correlation for both indicators +change_metric = spearman +sig_conf = SignificanceConfig(change_metric; + width = 20, n_surrogates = 10_000, + surrogate_method = RandomFourier(), +) + +# perform the full analysis +result = indicators_analysis(input, ind_conf, sig_conf) + +# And lastly, obtain some flags for when there +# is a significant indicator change +sig = indicators_significance(result, 0.99) + +sig + +# Plot the original timeseries +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2), label = "input") +# Scatter the significance of each indicator +for i in size(sig, 2) + signif_idxs = findall(sig[:, i]) + isempty(signif_idxs) && continue + # get timepoints in real time + tflags = tfluct[result.t_change[signif_idxs]] + vlines!(ax, tflags; label = "indicator $(indicators[i])", color = Cycled(2+i)) +end +axislegend() +fig + + diff --git a/previews/PR31/api/index.html b/previews/PR31/api/index.html new file mode 100644 index 00000000..6db8a27f --- /dev/null +++ b/previews/PR31/api/index.html @@ -0,0 +1,15 @@ + +API · TransitionIndicators.jl
          Edit on GitHub

          API

          Load data

          Indicators analysis

          TransitionIndicators.IndicatorsConfig — Type
          IndicatorsConfig(indicators...; window_kwargs...)

          A configuration for computing indicators from timeseries. Indicators are standard Julia functions that input an AbstractVector and output a real number. Any number of indicators can be given. Indicators typically used in the literature are listed in the documentation section Indicators.

          Keywords are propagated into WindowViewer to create a sliding window for estimating the indicators.

          Along with SignificanceConfig it is given to indicators_analysis.

          source
          TransitionIndicators.SignificanceConfig — Type
          SignificanceConfig(change_metrics...; kwargs...)

          A configuration for estimating a significant change of indicators computed from timeseries. Along with IndicatorsConfig it is given to indicators_analysis.

          change_metrics can be a single Julia function, in which case the same metric is applied over all indicators in IndicatorsConfig. change_metrics can also be many functions, each one for each indicator.

          Keyword arguments

          • n_surrogates::Int = 10_000: how many surrogates to create.
          • surrogate_method::S = RandomFourier(): what method to use to create the surrogates. Any Surrogate subtype from TimeseriesSurrogates.jl is valid.
          • rng::AbstractRNG = Random.default_rng()`: a random number generator for the surrogates. See the Julia manual for more.
          • wv_indicator_width::Int = 100,
          • wv_indicator_stride::Int = 5,
          • width, stride = 20, 1: width and stride given to the WindowViewer of the indicator timeseries. Notice that here the default values are different.
          source
          TransitionIndicators.indicators_analysis — Function
          indicators_analysis(x, indicators::IndicatorsConfig, significance::SignificanceConfig)

          Perform an analysis of transition indicators for input timeseries x by specifying which indicators to use and with what sliding window (IndicatorsConfig), as well as how to measure significant changes in the indicators (SignificanceConfig).

          Return the output as IndicatorsResults.

          This function performs the analysis described in the documentation Example sections. It computes various indicators over sliding windows of x, and then computes change metrics of over sliding windows of the indicators. In parallel it does exactly the same computations for surrogates of x. The returned output contains all these computed timeseries and can be given to indicators_significance.

          source

          Indicators significance

          TransitionIndicators.indicators_significance — Function
          indicators_significance(res::IndicatorsResults, q::SignificanceTest) → out

          Given the output of indicators_analysis, estimate when the computed indicators have a statistically significant change, with "significant" defined by q, which is a subtype of SignificanceTest.

          The output is returned as an n×m matrix with n the length of the time vector of the change metric timeseries, and m the number of change metrics (which is the same as the number of indicators). The values of the matrix are Booleans (true for significant).

          You can use prod(out; dim = 2) for logical & product across indicators.

          source
          Missing docstring.

          Missing docstring for SignificanceTest. Check Documenter's build log for details.

          TransitionIndicators.Quantile — Type
          Quantile(q = 0.99, dir::Symbol = :updown) <: SignificanceTest

          Significance is claimed by comparing the real value v with the q-th quantile of the surrogate distribution. Three possibilities are provided depending on dir:

          • dir = :updown: Significance is claimed if v is more than the q-th or is less than the 1-q-th quantile
          • dir = :up: if v is more than q-th
          • dir = :down: if v is less than 1-q-th
          source
          TransitionIndicators.Sigma — Type
          Sigma(n::Real = 3, dir::Symbol = :updown) <: SignificanceTest

          Significance is claimed by comparing the real value v with the mean μ and standard deviation σ of the surrogate distribution. Three possibilities are provided depending on dir:

          • dir = :updown: significance is claimed if v is more than μ + n*σ or less than μ - n*σ.
          • dir = :up: if v is more than μ + n*σ
          • dir = :down: if v is less than μ - n*σ
          source
          TransitionIndicators.significant — Function
          significant(v::Real, s_vals::AbstractVector, q::Significance) → true/false

          Return true if the value v is significant when compared to distribution of surrogate values s_vals according to the criterion q (see SignificanceTest). If not significant, return false.

          If given q::Real, then Quantile is used.

          source

          Indicators

          TransitionIndicators.ar1_whitenoise — Function
          ar1_whitenoise(x) → ̂θ

          Estimate the AR1 regression coefficient θ of a vector time series x. Computation based on the analytic solution of the least-square parameter estimation:

          \[ \hat{\theta} = \dfrac{\sum_{i=2}^{n} x_i \, x_{i-1}}{\sum_{i=2}^{n} x_{i-1}^2}\]

          source
          Statistics.mean — Method
          mean(itr)

          Compute the mean of all elements in a collection.

          Note

          If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

          Examples

          julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
          Statistics.var — Method
          var(itr; corrected::Bool=true, mean=nothing[, dims])

          Compute the sample variance of collection itr.

          The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1)). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

          If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

          A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

          Note

          If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

          StatsBase.skewness — Function
          skewness(v, [wv::AbstractWeights], m=mean(v))

          Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

          StatsBase.kurtosis — Function
          kurtosis(v, [wv::AbstractWeights], m=mean(v))

          Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

          Change metrics

          TransitionIndicators.RidgeRegression — Type
          RidgeRegression(t, width; lambda = 0.0) → rr

          Initialize a ridge regression for a time vector t, a sliding-window width and an optional regularizeation term lambda. The output rr can then be used as a function to perform the regression and extract the slope! If lambda = 0, linear regression is recovered (default case). For more information, visit: https://en.wikipedia.org/wiki/Ridge_regression.

          Examples

          julia> t = 0.0:1.0:100;
+julia> x = 2.3 .* t .+ 1.2;
+julia> rr = RidgeRegression(t);
+julia> rr(x)
+2.299999999999999
          source

          Surrogates

          For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

          Significance metrics

          Missing docstring.

          Missing docstring for threshold_indicators. Check Documenter's build log for details.

          Missing docstring.

          Missing docstring for measure_significance. Check Documenter's build log for details.

          Missing docstring.

          Missing docstring for confidence_interval. Check Documenter's build log for details.

          Missing docstring.

          Missing docstring for normalized_percentile. Check Documenter's build log for details.

          Sliding windows

          TransitionIndicators.WindowViewer — Type
          WindowViewer(x; width, stride)

          Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

          If not given, the keywords width, stride as taken as length(x)÷100 and 1.

          source
          TransitionIndicators.windowmap — Function
          windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

          A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

          source
          diff --git a/previews/PR31/assets/documenter.js b/previews/PR31/assets/documenter.js new file mode 100644 index 00000000..6adfbbbf --- /dev/null +++ b/previews/PR31/assets/documenter.js @@ -0,0 +1,331 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); 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+ var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR31/assets/search.js b/previews/PR31/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR31/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
        • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR31/assets/themes/documenter-dark.css b/previews/PR31/assets/themes/documenter-dark.css new file mode 100644 index 00000000..aedf20e6 --- /dev/null +++ b/previews/PR31/assets/themes/documenter-dark.css @@ -0,0 +1,7396 @@ +@charset "UTF-8"; +/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */ +@keyframes spinAround { + from { + transform: rotate(0deg); } + to { + transform: rotate(359deg); } } + +html.theme--documenter-dark .tabs, html.theme--documenter-dark .pagination-previous, +html.theme--documenter-dark .pagination-next, +html.theme--documenter-dark .pagination-link, +html.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .breadcrumb, html.theme--documenter-dark .file, html.theme--documenter-dark .button, .is-unselectable, html.theme--documenter-dark .modal-close, html.theme--documenter-dark .delete { + -webkit-touch-callout: none; + -webkit-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; } + +html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after, html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after { + border: 3px solid transparent; + border-radius: 2px; + border-right: 0; + border-top: 0; + content: " "; + display: block; + height: 0.625em; + margin-top: -0.4375em; + pointer-events: none; + position: absolute; + top: 50%; + transform: rotate(-45deg); + transform-origin: center; + width: 0.625em; } + +html.theme--documenter-dark .admonition:not(:last-child), html.theme--documenter-dark .tabs:not(:last-child), html.theme--documenter-dark .message:not(:last-child), html.theme--documenter-dark .list:not(:last-child), html.theme--documenter-dark .level:not(:last-child), html.theme--documenter-dark .breadcrumb:not(:last-child), html.theme--documenter-dark .highlight:not(:last-child), html.theme--documenter-dark .block:not(:last-child), html.theme--documenter-dark .title:not(:last-child), +html.theme--documenter-dark .subtitle:not(:last-child), html.theme--documenter-dark .table-container:not(:last-child), html.theme--documenter-dark .table:not(:last-child), html.theme--documenter-dark .progress:not(:last-child), html.theme--documenter-dark .notification:not(:last-child), html.theme--documenter-dark .content:not(:last-child), html.theme--documenter-dark .box:not(:last-child) { + margin-bottom: 1.5rem; } + +html.theme--documenter-dark .modal-close, html.theme--documenter-dark .delete { + -moz-appearance: none; + -webkit-appearance: none; + background-color: rgba(10, 10, 10, 0.2); + border: none; + border-radius: 290486px; + cursor: pointer; + pointer-events: auto; + display: inline-block; + flex-grow: 0; + flex-shrink: 0; + font-size: 0; + height: 20px; + max-height: 20px; + max-width: 20px; + min-height: 20px; + min-width: 20px; + outline: none; + position: relative; + vertical-align: top; + width: 20px; } + html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::before, html.theme--documenter-dark .modal-close::after, html.theme--documenter-dark .delete::after { + background-color: white; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::before { + height: 2px; + width: 50%; } + html.theme--documenter-dark .modal-close::after, html.theme--documenter-dark .delete::after { + height: 50%; + width: 2px; } + html.theme--documenter-dark .modal-close:hover, html.theme--documenter-dark .delete:hover, html.theme--documenter-dark .modal-close:focus, html.theme--documenter-dark .delete:focus { + background-color: rgba(10, 10, 10, 0.3); } + html.theme--documenter-dark .modal-close:active, html.theme--documenter-dark .delete:active { + background-color: rgba(10, 10, 10, 0.4); } + html.theme--documenter-dark .is-small.modal-close, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.modal-close, html.theme--documenter-dark .is-small.delete, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.delete { + height: 16px; + max-height: 16px; + max-width: 16px; + min-height: 16px; + min-width: 16px; + width: 16px; } + html.theme--documenter-dark .is-medium.modal-close, html.theme--documenter-dark .is-medium.delete { + height: 24px; + max-height: 24px; + max-width: 24px; + min-height: 24px; + min-width: 24px; + width: 24px; } + html.theme--documenter-dark .is-large.modal-close, html.theme--documenter-dark .is-large.delete { + height: 32px; + max-height: 32px; + max-width: 32px; + min-height: 32px; + min-width: 32px; + width: 32px; } + +html.theme--documenter-dark .control.is-loading::after, html.theme--documenter-dark .select.is-loading::after, html.theme--documenter-dark .loader, html.theme--documenter-dark .button.is-loading::after { + animation: spinAround 500ms infinite linear; + border: 2px solid #dbdbdb; + border-radius: 290486px; + border-right-color: transparent; + border-top-color: transparent; + content: ""; + display: block; + height: 1em; + position: relative; + width: 1em; } + +html.theme--documenter-dark .hero-video, html.theme--documenter-dark .modal-background, html.theme--documenter-dark .modal, html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img, +html.theme--documenter-dark .image.is-square .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img, +html.theme--documenter-dark .image.is-1by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img, +html.theme--documenter-dark .image.is-5by4 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img, +html.theme--documenter-dark .image.is-4by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img, +html.theme--documenter-dark .image.is-3by2 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img, +html.theme--documenter-dark .image.is-5by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img, +html.theme--documenter-dark .image.is-16by9 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img, +html.theme--documenter-dark .image.is-2by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img, +html.theme--documenter-dark .image.is-3by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img, +html.theme--documenter-dark .image.is-4by5 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img, +html.theme--documenter-dark .image.is-3by4 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img, +html.theme--documenter-dark .image.is-2by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img, +html.theme--documenter-dark .image.is-3by5 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img, +html.theme--documenter-dark .image.is-9by16 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img, +html.theme--documenter-dark .image.is-1by2 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img, +html.theme--documenter-dark .image.is-1by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, .is-overlay { + bottom: 0; + left: 0; + position: absolute; + right: 0; + top: 0; } + +html.theme--documenter-dark .pagination-previous, +html.theme--documenter-dark .pagination-next, +html.theme--documenter-dark .pagination-link, +html.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .file-cta, +html.theme--documenter-dark .file-name, html.theme--documenter-dark .select select, html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .button { + -moz-appearance: none; + -webkit-appearance: none; + align-items: center; + border: 1px solid transparent; + border-radius: 4px; + box-shadow: none; + display: inline-flex; + font-size: 1rem; + height: 2.25em; + justify-content: flex-start; + line-height: 1.5; + padding-bottom: calc(0.375em - 1px); + padding-left: calc(0.625em - 1px); + padding-right: calc(0.625em - 1px); + padding-top: calc(0.375em - 1px); + position: relative; + vertical-align: top; } + html.theme--documenter-dark .pagination-previous:focus, + html.theme--documenter-dark .pagination-next:focus, + html.theme--documenter-dark .pagination-link:focus, + html.theme--documenter-dark .pagination-ellipsis:focus, html.theme--documenter-dark .file-cta:focus, + html.theme--documenter-dark .file-name:focus, html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .button:focus, html.theme--documenter-dark .is-focused.pagination-previous, + html.theme--documenter-dark .is-focused.pagination-next, + html.theme--documenter-dark .is-focused.pagination-link, + html.theme--documenter-dark .is-focused.pagination-ellipsis, html.theme--documenter-dark .is-focused.file-cta, + html.theme--documenter-dark .is-focused.file-name, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-focused.button, html.theme--documenter-dark .pagination-previous:active, + html.theme--documenter-dark .pagination-next:active, + html.theme--documenter-dark .pagination-link:active, + html.theme--documenter-dark .pagination-ellipsis:active, html.theme--documenter-dark .file-cta:active, + html.theme--documenter-dark .file-name:active, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .button:active, html.theme--documenter-dark .is-active.pagination-previous, + html.theme--documenter-dark .is-active.pagination-next, + html.theme--documenter-dark .is-active.pagination-link, + html.theme--documenter-dark .is-active.pagination-ellipsis, html.theme--documenter-dark .is-active.file-cta, + html.theme--documenter-dark .is-active.file-name, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .is-active.button { + outline: none; } + html.theme--documenter-dark .pagination-previous[disabled], + html.theme--documenter-dark .pagination-next[disabled], + html.theme--documenter-dark .pagination-link[disabled], + html.theme--documenter-dark .pagination-ellipsis[disabled], html.theme--documenter-dark .file-cta[disabled], + html.theme--documenter-dark .file-name[disabled], html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], html.theme--documenter-dark .button[disabled], fieldset[disabled] html.theme--documenter-dark .pagination-previous, html.theme--documenter-dark fieldset[disabled] .pagination-previous, + 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+ box-sizing: inherit; } + +img, +embed, +iframe, +object, +video { + height: auto; + max-width: 100%; } + +audio { + max-width: 100%; } + +iframe { + border: 0; } + +table { + border-collapse: collapse; + border-spacing: 0; } + +td, +th { + padding: 0; } + td:not([align]), + th:not([align]) { + text-align: left; } + +.is-clearfix::after { + clear: both; + content: " "; + display: table; } + +.is-pulled-left { + float: left !important; } + +.is-pulled-right { + float: right !important; } + +.is-clipped { + overflow: hidden !important; } + +.is-size-1 { + font-size: 3rem !important; } + +.is-size-2 { + font-size: 2.5rem !important; } + +.is-size-3 { + font-size: 2rem !important; } + +.is-size-4 { + font-size: 1.5rem !important; } + +.is-size-5 { + font-size: 1.25rem !important; } + +.is-size-6 { + font-size: 1rem !important; } + +.is-size-7, html.theme--documenter-dark .docstring > section > a.docs-sourcelink { + font-size: 0.75rem !important; } + +@media screen and (max-width: 768px) { 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(max-width: 1055px) { + .is-inline-flex-touch { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-flex-desktop { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-flex-desktop-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-flex-widescreen { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-flex-widescreen-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-flex-fullhd { + display: inline-flex !important; } } + +.is-hidden { + display: none !important; } + +.is-sr-only { + border: none !important; + clip: rect(0, 0, 0, 0) !important; + height: 0.01em !important; + overflow: hidden !important; + padding: 0 !important; + position: absolute !important; + white-space: nowrap !important; + width: 0.01em !important; } + +@media screen and (max-width: 768px) { + .is-hidden-mobile { + display: none !important; } } + +@media screen and (min-width: 769px), print { + .is-hidden-tablet { + display: none !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-hidden-tablet-only { + display: none !important; } } + +@media screen and (max-width: 1055px) { + .is-hidden-touch { + display: none !important; } } + +@media screen and (min-width: 1056px) { + .is-hidden-desktop { + display: none !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-hidden-desktop-only { + display: none !important; } } + +@media screen and (min-width: 1216px) { + .is-hidden-widescreen { + display: none !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-hidden-widescreen-only { + display: none !important; } } + +@media screen and (min-width: 1408px) { + .is-hidden-fullhd { + display: none !important; } } + +.is-invisible { + visibility: hidden !important; } + +@media screen and (max-width: 768px) { + .is-invisible-mobile { + visibility: hidden !important; } } + +@media screen and (min-width: 769px), print { + .is-invisible-tablet { + visibility: hidden !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-invisible-tablet-only { + visibility: hidden !important; } } + +@media screen and (max-width: 1055px) { + .is-invisible-touch { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) { + .is-invisible-desktop { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-invisible-desktop-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) { + .is-invisible-widescreen { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-invisible-widescreen-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1408px) { + .is-invisible-fullhd { + visibility: hidden !important; } } + +.is-marginless { + margin: 0 !important; } + +.is-paddingless { + padding: 0 !important; } + +.is-radiusless { + border-radius: 0 !important; } + +.is-shadowless { + box-shadow: none !important; } + +.is-relative { + position: relative !important; } + +html.theme--documenter-dark { + /* This file contain the overall layout. + * + * The main container is
          that is identified by id #documenter. + */ + /*! + Theme: a11y-dark + Author: @ericwbailey + Maintainer: @ericwbailey + + Based on the Tomorrow Night Eighties theme: https://github.com/isagalaev/highlight.js/blob/master/src/styles/tomorrow-night-eighties.css +*/ + /* Comment */ + /* Red */ + /* Orange */ + /* Yellow */ + /* Green */ + /* Blue */ + /* Purple */ } + html.theme--documenter-dark html { + background-color: #1e1e20; + font-size: 16px; + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + html.theme--documenter-dark article, + html.theme--documenter-dark aside, + html.theme--documenter-dark figure, + html.theme--documenter-dark footer, + html.theme--documenter-dark header, + html.theme--documenter-dark hgroup, + html.theme--documenter-dark section { + display: block; } + html.theme--documenter-dark body, + html.theme--documenter-dark button, + html.theme--documenter-dark input, + html.theme--documenter-dark select, + html.theme--documenter-dark textarea { + font-family: "Montserrat", sans-serif; } + html.theme--documenter-dark code, + html.theme--documenter-dark pre { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; + font-family: "Source Code Pro", monospace; } + html.theme--documenter-dark body { + color: #fbfbfb; + font-size: 1em; + font-weight: 400; + line-height: 1.5; } + html.theme--documenter-dark a { + color: #2ad7e6; + cursor: pointer; + text-decoration: none; } + html.theme--documenter-dark a strong { + color: currentColor; } + html.theme--documenter-dark a:hover { + color: #97ebf3; } + html.theme--documenter-dark code { + background-color: #312550; + color: #fff; + font-size: 0.875em; + font-weight: normal; + padding: 0.1em; } + html.theme--documenter-dark hr { + background-color: whitesmoke; + border: none; + display: block; + height: 2px; + margin: 1.5rem 0; } + html.theme--documenter-dark img { + height: auto; + max-width: 100%; } + html.theme--documenter-dark input[type="checkbox"], + html.theme--documenter-dark input[type="radio"] { + vertical-align: baseline; } + html.theme--documenter-dark small { + font-size: 0.875em; } + html.theme--documenter-dark span { + font-style: inherit; + font-weight: inherit; } + html.theme--documenter-dark strong { + color: #cdc3e3; + font-weight: 700; } + html.theme--documenter-dark fieldset { + border: none; } + html.theme--documenter-dark pre { + -webkit-overflow-scrolling: touch; + background-color: #312550; + color: #fbfbfb; + font-size: 0.875em; + overflow-x: auto; + padding: 1.25rem 1.5rem; + white-space: pre; + word-wrap: normal; } + html.theme--documenter-dark pre code { + background-color: transparent; + color: currentColor; + font-size: 1em; + padding: 0; } + html.theme--documenter-dark table td, + html.theme--documenter-dark table th { + vertical-align: top; } + html.theme--documenter-dark table td:not([align]), + html.theme--documenter-dark table th:not([align]) { + text-align: left; } + html.theme--documenter-dark table th { + color: #cdc3e3; } + html.theme--documenter-dark .box { + background-color: white; + border-radius: 6px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #fbfbfb; + display: block; + padding: 1.25rem; } + html.theme--documenter-dark a.box:hover, html.theme--documenter-dark a.box:focus { + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #2ad7e6; } + html.theme--documenter-dark a.box:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #2ad7e6; } + html.theme--documenter-dark .button { + background-color: white; + border-color: #dbdbdb; + border-width: 1px; + color: #363636; + cursor: pointer; + justify-content: center; + padding-bottom: calc(0.375em - 1px); + padding-left: 0.75em; + padding-right: 0.75em; + padding-top: calc(0.375em - 1px); + text-align: center; + white-space: nowrap; } + html.theme--documenter-dark .button strong { + color: inherit; } + html.theme--documenter-dark .button .icon, html.theme--documenter-dark .button .icon.is-small, html.theme--documenter-dark .button #documenter .docs-sidebar form.docs-search > input.icon, html.theme--documenter-dark #documenter .docs-sidebar .button form.docs-search > input.icon, html.theme--documenter-dark .button .icon.is-medium, html.theme--documenter-dark .button .icon.is-large { + height: 1.5em; + width: 1.5em; } + html.theme--documenter-dark .button .icon:first-child:not(:last-child) { + margin-left: calc(-0.375em - 1px); + margin-right: 0.1875em; } + html.theme--documenter-dark .button .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: calc(-0.375em - 1px); } + html.theme--documenter-dark .button .icon:first-child:last-child { + margin-left: calc(-0.375em - 1px); + margin-right: calc(-0.375em - 1px); } + html.theme--documenter-dark .button:hover, html.theme--documenter-dark .button.is-hovered { + border-color: #b5b5b5; + color: #97ebf3; } + html.theme--documenter-dark .button:focus, html.theme--documenter-dark .button.is-focused { + border-color: #3c5dcd; + color: #363636; } + html.theme--documenter-dark .button:focus:not(:active), html.theme--documenter-dark .button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .button:active, html.theme--documenter-dark .button.is-active { + border-color: #4a4a4a; + color: #363636; } + html.theme--documenter-dark .button.is-text { + background-color: transparent; + border-color: transparent; + color: #fbfbfb; + text-decoration: underline; } + html.theme--documenter-dark .button.is-text:hover, html.theme--documenter-dark .button.is-text.is-hovered, html.theme--documenter-dark .button.is-text:focus, html.theme--documenter-dark .button.is-text.is-focused { + background-color: whitesmoke; + color: #cdc3e3; } + html.theme--documenter-dark .button.is-text:active, html.theme--documenter-dark .button.is-text.is-active { + background-color: #e8e8e8; + color: #cdc3e3; } + html.theme--documenter-dark .button.is-text[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-text { + background-color: transparent; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-white { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:hover, html.theme--documenter-dark .button.is-white.is-hovered { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:focus, html.theme--documenter-dark .button.is-white.is-focused { + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:focus:not(:active), html.theme--documenter-dark .button.is-white.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .button.is-white:active, html.theme--documenter-dark .button.is-white.is-active { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white { + background-color: white; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-white.is-inverted { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-hovered { + background-color: black; } + html.theme--documenter-dark .button.is-white.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-white.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + html.theme--documenter-dark .button.is-white.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-outlined.is-focused { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-white.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:hover, html.theme--documenter-dark .button.is-black.is-hovered { + background-color: #040404; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:focus, html.theme--documenter-dark .button.is-black.is-focused { + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:focus:not(:active), html.theme--documenter-dark .button.is-black.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .button.is-black:active, html.theme--documenter-dark .button.is-black.is-active { + background-color: black; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-black.is-inverted { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-black.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted { + background-color: white; + border-color: transparent; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-loading::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-outlined.is-focused { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-black.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-light { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:hover, html.theme--documenter-dark .button.is-light.is-hovered { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:focus, html.theme--documenter-dark .button.is-light.is-focused { + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:focus:not(:active), html.theme--documenter-dark .button.is-light.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .button.is-light:active, html.theme--documenter-dark .button.is-light.is-active { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-light.is-inverted { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-hovered { + background-color: #292929; } + html.theme--documenter-dark .button.is-light.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted { + background-color: #363636; + border-color: transparent; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-outlined.is-focused { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-light.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark, html.theme--documenter-dark .content kbd.button { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:hover, html.theme--documenter-dark .content kbd.button:hover, html.theme--documenter-dark .button.is-dark.is-hovered, html.theme--documenter-dark .content kbd.button.is-hovered { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:focus, html.theme--documenter-dark .content kbd.button:focus, html.theme--documenter-dark .button.is-dark.is-focused, html.theme--documenter-dark .content kbd.button.is-focused { + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:focus:not(:active), html.theme--documenter-dark .content kbd.button:focus:not(:active), html.theme--documenter-dark .button.is-dark.is-focused:not(:active), html.theme--documenter-dark .content kbd.button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .button.is-dark:active, html.theme--documenter-dark .content kbd.button:active, html.theme--documenter-dark .button.is-dark.is-active, html.theme--documenter-dark .content kbd.button.is-active { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark[disabled], html.theme--documenter-dark .content kbd.button[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark, fieldset[disabled] html.theme--documenter-dark .content kbd.button { + background-color: #363636; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-dark.is-inverted, html.theme--documenter-dark .content kbd.button.is-inverted { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted:hover, html.theme--documenter-dark .content kbd.button.is-inverted:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered { + background-color: #e8e8e8; } + html.theme--documenter-dark .button.is-dark.is-inverted[disabled], html.theme--documenter-dark .content kbd.button.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-loading::after, html.theme--documenter-dark .content kbd.button.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-dark.is-outlined, html.theme--documenter-dark .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-outlined.is-focused { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-dark.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-primary, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:hover, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-hovered.docs-sourcelink { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:focus, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:focus:not(:active), html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus:not(:active), html.theme--documenter-dark .button.is-primary.is-focused:not(:active), html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .button.is-primary:active, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:active, html.theme--documenter-dark .button.is-primary.is-active, html.theme--documenter-dark .docstring > section > a.button.is-active.docs-sourcelink { + background-color: #39acda; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary[disabled], html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-primary.is-inverted, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-primary.is-inverted[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-loading.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-primary.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-primary.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + box-shadow: none; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-link { + background-color: #2ad7e6; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:hover, html.theme--documenter-dark .button.is-link.is-hovered { + background-color: #1ed5e5; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:focus, html.theme--documenter-dark .button.is-link.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:focus:not(:active), html.theme--documenter-dark .button.is-link.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .button.is-link:active, html.theme--documenter-dark .button.is-link.is-active { + background-color: #1acddc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link { + background-color: #2ad7e6; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-link.is-inverted { + background-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-link.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-link.is-outlined { + background-color: transparent; + border-color: #2ad7e6; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-outlined.is-focused { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after { + border-color: transparent transparent #2ad7e6 #2ad7e6 !important; } + html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-link.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined { + background-color: transparent; + border-color: #2ad7e6; + box-shadow: none; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #2ad7e6 #2ad7e6 !important; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-info { + background-color: #3489da; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:hover, html.theme--documenter-dark .button.is-info.is-hovered { + background-color: #2983d8; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:focus, html.theme--documenter-dark .button.is-info.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:focus:not(:active), html.theme--documenter-dark .button.is-info.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .button.is-info:active, html.theme--documenter-dark .button.is-info.is-active { + background-color: #267ccf; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info { + background-color: #3489da; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-info.is-inverted { + background-color: #fff; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-info.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-info.is-outlined { + background-color: transparent; + border-color: #3489da; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-outlined.is-focused { + background-color: #3489da; + border-color: #3489da; + color: #fff; } + html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after { + border-color: transparent transparent #3489da #3489da !important; } + html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-info.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined { + background-color: transparent; + border-color: #3489da; + box-shadow: none; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #3489da #3489da !important; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-success { + background-color: #259a12; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:hover, html.theme--documenter-dark .button.is-success.is-hovered { + background-color: #228f11; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:focus, html.theme--documenter-dark .button.is-success.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:focus:not(:active), html.theme--documenter-dark .button.is-success.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .button.is-success:active, html.theme--documenter-dark .button.is-success.is-active { + background-color: #20830f; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success { + background-color: #259a12; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-success.is-inverted { + background-color: #fff; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-success.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-success.is-outlined { + background-color: transparent; + border-color: #259a12; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-outlined.is-focused { + background-color: #259a12; + border-color: #259a12; + color: #fff; } + html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after { + border-color: transparent transparent #259a12 #259a12 !important; } + html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-success.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined { + background-color: transparent; + border-color: #259a12; + box-shadow: none; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #259a12 #259a12 !important; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-warning { + background-color: #f4c72f; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:hover, html.theme--documenter-dark .button.is-warning.is-hovered { + background-color: #f3c423; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:focus, html.theme--documenter-dark .button.is-warning.is-focused { + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:focus:not(:active), html.theme--documenter-dark .button.is-warning.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .button.is-warning:active, html.theme--documenter-dark .button.is-warning.is-active { + background-color: #f3c017; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning { + background-color: #f4c72f; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered { + background-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + border-color: transparent; + box-shadow: none; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-loading::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + html.theme--documenter-dark .button.is-warning.is-outlined { + background-color: transparent; + border-color: #f4c72f; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-outlined.is-focused { + background-color: #f4c72f; + border-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after { + border-color: transparent transparent #f4c72f #f4c72f !important; } + html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + html.theme--documenter-dark .button.is-warning.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined { + background-color: transparent; + border-color: #f4c72f; + box-shadow: none; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused { + background-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #f4c72f #f4c72f !important; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + box-shadow: none; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-danger { + background-color: #cb3c33; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:hover, html.theme--documenter-dark .button.is-danger.is-hovered { + background-color: #c13930; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:focus, html.theme--documenter-dark .button.is-danger.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:focus:not(:active), html.theme--documenter-dark .button.is-danger.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .button.is-danger:active, html.theme--documenter-dark .button.is-danger.is-active { + background-color: #b7362e; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger { + background-color: #cb3c33; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-danger.is-inverted { + background-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-danger.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-danger.is-outlined { + background-color: transparent; + border-color: #cb3c33; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-outlined.is-focused { + background-color: #cb3c33; + border-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after { + border-color: transparent transparent #cb3c33 #cb3c33 !important; } + html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-danger.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined { + background-color: transparent; + border-color: #cb3c33; + box-shadow: none; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #cb3c33 #cb3c33 !important; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .button.is-normal { + font-size: 1rem; } + html.theme--documenter-dark .button.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .button.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .button[disabled], fieldset[disabled] html.theme--documenter-dark .button { + background-color: white; + border-color: #dbdbdb; + box-shadow: none; + opacity: 0.5; } + html.theme--documenter-dark .button.is-fullwidth { + display: flex; + width: 100%; } + html.theme--documenter-dark .button.is-loading { + color: transparent !important; + pointer-events: none; } + html.theme--documenter-dark .button.is-loading::after { + position: absolute; + left: calc(50% - (1em / 2)); + top: calc(50% - (1em / 2)); + position: absolute !important; } + html.theme--documenter-dark .button.is-static { + background-color: whitesmoke; + border-color: #dbdbdb; + color: #7a7a7a; + box-shadow: none; + pointer-events: none; } + html.theme--documenter-dark .button.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + html.theme--documenter-dark .buttons { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .buttons .button { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth) { + margin-right: 0.5rem; } + html.theme--documenter-dark .buttons:last-child { + margin-bottom: -0.5rem; } + html.theme--documenter-dark .buttons:not(:last-child) { + margin-bottom: 1rem; } + html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { + font-size: 1.25rem; } + html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { + font-size: 1.5rem; } + html.theme--documenter-dark .buttons.has-addons .button:not(:first-child) { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .buttons.has-addons .button:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; + margin-right: -1px; } + html.theme--documenter-dark .buttons.has-addons .button:last-child { + margin-right: 0; } + html.theme--documenter-dark .buttons.has-addons .button:hover, html.theme--documenter-dark .buttons.has-addons .button.is-hovered { + z-index: 2; } + html.theme--documenter-dark .buttons.has-addons .button:focus, html.theme--documenter-dark .buttons.has-addons .button.is-focused, html.theme--documenter-dark .buttons.has-addons .button:active, html.theme--documenter-dark .buttons.has-addons .button.is-active, html.theme--documenter-dark .buttons.has-addons .button.is-selected { + z-index: 3; } + html.theme--documenter-dark .buttons.has-addons .button:focus:hover, html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover, html.theme--documenter-dark .buttons.has-addons .button:active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover { + z-index: 4; } + html.theme--documenter-dark .buttons.has-addons .button.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .buttons.is-centered { + justify-content: center; } + html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + html.theme--documenter-dark .buttons.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + html.theme--documenter-dark .container { + flex-grow: 1; + margin: 0 auto; + position: relative; + width: auto; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .container { + max-width: 992px; } + html.theme--documenter-dark .container.is-fluid { + margin-left: 32px; + margin-right: 32px; + max-width: none; } } + @media screen and (max-width: 1215px) { + html.theme--documenter-dark .container.is-widescreen { + max-width: 1152px; } } + @media screen and (max-width: 1407px) { + html.theme--documenter-dark .container.is-fullhd { + max-width: 1344px; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .container { + max-width: 1152px; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .container { + max-width: 1344px; } } + html.theme--documenter-dark .content li + li { + margin-top: 0.25em; } + html.theme--documenter-dark .content p:not(:last-child), + html.theme--documenter-dark .content dl:not(:last-child), + html.theme--documenter-dark .content ol:not(:last-child), + html.theme--documenter-dark .content ul:not(:last-child), + html.theme--documenter-dark .content blockquote:not(:last-child), + html.theme--documenter-dark .content pre:not(:last-child), + html.theme--documenter-dark .content table:not(:last-child) { + margin-bottom: 1em; } + html.theme--documenter-dark .content h1, + html.theme--documenter-dark .content h2, + html.theme--documenter-dark .content h3, + html.theme--documenter-dark .content h4, + html.theme--documenter-dark .content h5, + html.theme--documenter-dark .content h6 { + color: #cdc3e3; + font-weight: 600; + line-height: 1.125; } + html.theme--documenter-dark .content h1 { + font-size: 2em; + margin-bottom: 0.5em; } + html.theme--documenter-dark .content h1:not(:first-child) { + margin-top: 1em; } + html.theme--documenter-dark .content h2 { + font-size: 1.75em; + margin-bottom: 0.5714em; } + html.theme--documenter-dark .content h2:not(:first-child) { + margin-top: 1.1428em; } + html.theme--documenter-dark .content h3 { + font-size: 1.5em; + margin-bottom: 0.6666em; } + html.theme--documenter-dark .content h3:not(:first-child) { + margin-top: 1.3333em; } + html.theme--documenter-dark .content h4 { + font-size: 1.25em; + margin-bottom: 0.8em; } + html.theme--documenter-dark .content h5 { + font-size: 1.125em; + margin-bottom: 0.8888em; } + html.theme--documenter-dark .content h6 { + font-size: 1em; + margin-bottom: 1em; } + html.theme--documenter-dark .content blockquote { + background-color: whitesmoke; + border-left: 5px solid #dbdbdb; + padding: 1.25em 1.5em; } + html.theme--documenter-dark .content ol { + list-style-position: outside; + margin-left: 2em; + margin-top: 1em; } + html.theme--documenter-dark .content ol:not([type]) { + list-style-type: decimal; } + html.theme--documenter-dark .content ol.is-lower-alpha:not([type]) { + list-style-type: lower-alpha; } + html.theme--documenter-dark .content ol.is-lower-roman:not([type]) { + list-style-type: lower-roman; } + html.theme--documenter-dark .content ol.is-upper-alpha:not([type]) { + list-style-type: upper-alpha; } + html.theme--documenter-dark .content ol.is-upper-roman:not([type]) { + list-style-type: upper-roman; } + html.theme--documenter-dark .content ul { + list-style: disc outside; + margin-left: 2em; + margin-top: 1em; } + html.theme--documenter-dark .content ul ul { + list-style-type: circle; + margin-top: 0.5em; } + html.theme--documenter-dark .content ul ul ul { + list-style-type: square; } + html.theme--documenter-dark .content dd { + margin-left: 2em; } + html.theme--documenter-dark .content figure { + margin-left: 2em; + margin-right: 2em; + text-align: center; } + html.theme--documenter-dark .content figure:not(:first-child) { + margin-top: 2em; } + html.theme--documenter-dark .content figure:not(:last-child) { + margin-bottom: 2em; } + html.theme--documenter-dark .content figure img { + display: inline-block; } + html.theme--documenter-dark .content figure figcaption { + font-style: italic; } + html.theme--documenter-dark .content pre { + -webkit-overflow-scrolling: touch; + overflow-x: auto; + padding: 0; + white-space: pre; + word-wrap: normal; } + html.theme--documenter-dark .content sup, + html.theme--documenter-dark .content sub { + font-size: 75%; } + html.theme--documenter-dark .content table { + width: 100%; } + html.theme--documenter-dark .content table td, + html.theme--documenter-dark .content table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + html.theme--documenter-dark .content table th { + color: #cdc3e3; } + html.theme--documenter-dark .content table th:not([align]) { + text-align: left; } + html.theme--documenter-dark .content table thead td, + html.theme--documenter-dark .content table thead th { + border-width: 0 0 2px; + color: #cdc3e3; } + html.theme--documenter-dark .content table tfoot td, + html.theme--documenter-dark .content table tfoot th { + border-width: 2px 0 0; + color: #cdc3e3; } + html.theme--documenter-dark .content table tbody tr:last-child td, + html.theme--documenter-dark .content table tbody tr:last-child th { + border-bottom-width: 0; } + html.theme--documenter-dark .content .tabs li + li { + margin-top: 0; } + html.theme--documenter-dark .content.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.content { + font-size: 0.75rem; } + html.theme--documenter-dark .content.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .content.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .icon { + align-items: center; + display: inline-flex; + justify-content: center; + height: 1.5rem; + width: 1.5rem; } + html.theme--documenter-dark .icon.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.icon { + height: 1rem; + width: 1rem; } + html.theme--documenter-dark .icon.is-medium { + height: 2rem; + width: 2rem; } + html.theme--documenter-dark .icon.is-large { + height: 3rem; + width: 3rem; } + html.theme--documenter-dark .image, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { + display: block; + position: relative; } + html.theme--documenter-dark .image img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img { + display: block; + height: auto; + width: 100%; } + html.theme--documenter-dark .image img.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img.is-rounded { + border-radius: 290486px; } + html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img, + html.theme--documenter-dark .image.is-square .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img, + html.theme--documenter-dark .image.is-1by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img, + html.theme--documenter-dark .image.is-5by4 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img, + html.theme--documenter-dark .image.is-4by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img, + html.theme--documenter-dark .image.is-3by2 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img, + html.theme--documenter-dark .image.is-5by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img, + html.theme--documenter-dark .image.is-16by9 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img, + html.theme--documenter-dark .image.is-2by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img, + html.theme--documenter-dark .image.is-3by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img, + html.theme--documenter-dark .image.is-4by5 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img, + html.theme--documenter-dark .image.is-3by4 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img, + html.theme--documenter-dark .image.is-2by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img, + html.theme--documenter-dark .image.is-3by5 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img, + html.theme--documenter-dark .image.is-9by16 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img, + html.theme--documenter-dark .image.is-1by2 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img, + html.theme--documenter-dark .image.is-1by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { + height: 100%; + width: 100%; } + html.theme--documenter-dark .image.is-square, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square, html.theme--documenter-dark .image.is-1by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 { + padding-top: 100%; } + html.theme--documenter-dark .image.is-5by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 { + padding-top: 80%; } + html.theme--documenter-dark .image.is-4by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 { + padding-top: 75%; } + html.theme--documenter-dark .image.is-3by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 { + padding-top: 66.6666%; } + html.theme--documenter-dark .image.is-5by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 { + padding-top: 60%; } + html.theme--documenter-dark .image.is-16by9, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 { + padding-top: 56.25%; } + html.theme--documenter-dark .image.is-2by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 { + padding-top: 50%; } + html.theme--documenter-dark .image.is-3by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 { + padding-top: 33.3333%; } + html.theme--documenter-dark .image.is-4by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 { + padding-top: 125%; } + html.theme--documenter-dark .image.is-3by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 { + padding-top: 133.3333%; } + html.theme--documenter-dark .image.is-2by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 { + padding-top: 150%; } + html.theme--documenter-dark .image.is-3by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 { + padding-top: 166.6666%; } + html.theme--documenter-dark .image.is-9by16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 { + padding-top: 177.7777%; } + html.theme--documenter-dark .image.is-1by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 { + padding-top: 200%; } + html.theme--documenter-dark .image.is-1by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 { + padding-top: 300%; } + html.theme--documenter-dark .image.is-16x16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16x16 { + height: 16px; + width: 16px; } + html.theme--documenter-dark .image.is-24x24, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-24x24 { + height: 24px; + width: 24px; } + html.theme--documenter-dark .image.is-32x32, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-32x32 { + height: 32px; + width: 32px; } + html.theme--documenter-dark .image.is-48x48, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-48x48 { + height: 48px; + width: 48px; } + html.theme--documenter-dark .image.is-64x64, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-64x64 { + height: 64px; + width: 64px; } + html.theme--documenter-dark .image.is-96x96, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-96x96 { + height: 96px; + width: 96px; } + html.theme--documenter-dark .image.is-128x128, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-128x128 { + height: 128px; + width: 128px; } + html.theme--documenter-dark .notification { + background-color: whitesmoke; + border-radius: 4px; + padding: 1.25rem 2.5rem 1.25rem 1.5rem; + position: relative; } + html.theme--documenter-dark .notification a:not(.button):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + html.theme--documenter-dark .notification strong { + color: currentColor; } + html.theme--documenter-dark .notification code, + html.theme--documenter-dark .notification pre { + background: white; } + html.theme--documenter-dark .notification pre code { + background: transparent; } + html.theme--documenter-dark .notification > .delete { + position: absolute; + right: 0.5rem; + top: 0.5rem; } + html.theme--documenter-dark .notification .title, + html.theme--documenter-dark .notification .subtitle, + html.theme--documenter-dark .notification .content { + color: currentColor; } + html.theme--documenter-dark .notification.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .notification.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .notification.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .notification.is-dark, html.theme--documenter-dark .content kbd.notification { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .notification.is-primary, html.theme--documenter-dark .docstring > section > a.notification.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .notification.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .notification.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .notification.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .notification.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .notification.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .progress { + -moz-appearance: none; + -webkit-appearance: none; + border: none; + border-radius: 290486px; + display: block; + height: 1rem; + overflow: hidden; + padding: 0; + width: 100%; } + html.theme--documenter-dark .progress::-webkit-progress-bar { + background-color: #dbdbdb; } + html.theme--documenter-dark .progress::-webkit-progress-value { + background-color: #fbfbfb; } + html.theme--documenter-dark .progress::-moz-progress-bar { + background-color: #fbfbfb; } + html.theme--documenter-dark .progress::-ms-fill { + background-color: #fbfbfb; + border: none; } + html.theme--documenter-dark .progress.is-white::-webkit-progress-value { + background-color: white; } + html.theme--documenter-dark .progress.is-white::-moz-progress-bar { + background-color: white; } + html.theme--documenter-dark .progress.is-white::-ms-fill { + background-color: white; } + html.theme--documenter-dark .progress.is-white:indeterminate { + background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-black::-webkit-progress-value { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black::-moz-progress-bar { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black::-ms-fill { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black:indeterminate { + background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-light::-webkit-progress-value { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light::-moz-progress-bar { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light::-ms-fill { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light:indeterminate { + background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-dark::-webkit-progress-value, html.theme--documenter-dark .content kbd.progress::-webkit-progress-value { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark::-moz-progress-bar, html.theme--documenter-dark .content kbd.progress::-moz-progress-bar { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark::-ms-fill, html.theme--documenter-dark .content kbd.progress::-ms-fill { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark:indeterminate, html.theme--documenter-dark .content kbd.progress:indeterminate { + background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-primary::-webkit-progress-value, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary::-moz-progress-bar, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary::-ms-fill, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-ms-fill { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary:indeterminate, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink:indeterminate { + background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-link::-webkit-progress-value { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link::-moz-progress-bar { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link::-ms-fill { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link:indeterminate { + background-image: linear-gradient(to right, #2ad7e6 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-info::-webkit-progress-value { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info::-moz-progress-bar { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info::-ms-fill { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info:indeterminate { + background-image: linear-gradient(to right, #3489da 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-success::-webkit-progress-value { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success::-moz-progress-bar { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success::-ms-fill { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success:indeterminate { + background-image: linear-gradient(to right, #259a12 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-warning::-webkit-progress-value { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning::-moz-progress-bar { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning::-ms-fill { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning:indeterminate { + background-image: linear-gradient(to right, #f4c72f 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-danger::-webkit-progress-value { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger::-moz-progress-bar { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger::-ms-fill { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger:indeterminate { + background-image: linear-gradient(to right, #cb3c33 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress:indeterminate { + animation-duration: 1.5s; + animation-iteration-count: infinite; + animation-name: moveIndeterminate; + animation-timing-function: linear; + background-color: #dbdbdb; + background-image: linear-gradient(to right, #fbfbfb 30%, #dbdbdb 30%); + background-position: top left; + background-repeat: no-repeat; + background-size: 150% 150%; } + html.theme--documenter-dark .progress:indeterminate::-webkit-progress-bar { + background-color: transparent; } + html.theme--documenter-dark .progress:indeterminate::-moz-progress-bar { + background-color: transparent; } + html.theme--documenter-dark .progress.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.progress { + height: 0.75rem; } + html.theme--documenter-dark .progress.is-medium { + height: 1.25rem; } + html.theme--documenter-dark .progress.is-large { + height: 1.5rem; } + +@keyframes moveIndeterminate { + from { + background-position: 200% 0; } + to { + background-position: -200% 0; } } + html.theme--documenter-dark .table { + background-color: white; + color: #363636; } + html.theme--documenter-dark .table td, + html.theme--documenter-dark .table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + html.theme--documenter-dark .table td.is-white, + html.theme--documenter-dark .table th.is-white { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .table td.is-black, + html.theme--documenter-dark .table th.is-black { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .table td.is-light, + html.theme--documenter-dark .table th.is-light { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .table td.is-dark, + html.theme--documenter-dark .table th.is-dark { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .table td.is-primary, + html.theme--documenter-dark .table th.is-primary { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table td.is-link, + html.theme--documenter-dark .table th.is-link { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .table td.is-info, + html.theme--documenter-dark .table th.is-info { + background-color: #3489da; + border-color: #3489da; + color: #fff; } + html.theme--documenter-dark .table td.is-success, + html.theme--documenter-dark .table th.is-success { + background-color: #259a12; + border-color: #259a12; + color: #fff; } + html.theme--documenter-dark .table td.is-warning, + html.theme--documenter-dark .table th.is-warning { + background-color: #f4c72f; + border-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .table td.is-danger, + html.theme--documenter-dark .table th.is-danger { + background-color: #cb3c33; + border-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .table td.is-narrow, + html.theme--documenter-dark .table th.is-narrow { + white-space: nowrap; + width: 1%; } + html.theme--documenter-dark .table td.is-selected, + html.theme--documenter-dark .table th.is-selected { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table td.is-selected a, + html.theme--documenter-dark .table td.is-selected strong, + html.theme--documenter-dark .table th.is-selected a, + html.theme--documenter-dark .table th.is-selected strong { + color: currentColor; } + html.theme--documenter-dark .table th { + color: #cdc3e3; } + html.theme--documenter-dark .table th:not([align]) { + text-align: left; } + html.theme--documenter-dark .table tr.is-selected { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table tr.is-selected a, + html.theme--documenter-dark .table tr.is-selected strong { + color: currentColor; } + html.theme--documenter-dark .table tr.is-selected td, + html.theme--documenter-dark .table tr.is-selected th { + border-color: #fff; + color: currentColor; } + html.theme--documenter-dark .table thead { + background-color: transparent; } + html.theme--documenter-dark .table thead td, + html.theme--documenter-dark .table thead th { + border-width: 0 0 2px; + color: #cdc3e3; } + html.theme--documenter-dark .table tfoot { + background-color: transparent; } + html.theme--documenter-dark .table tfoot td, + html.theme--documenter-dark .table tfoot th { + border-width: 2px 0 0; + color: #cdc3e3; } + html.theme--documenter-dark .table tbody { + background-color: transparent; } + html.theme--documenter-dark .table tbody tr:last-child td, + html.theme--documenter-dark .table tbody tr:last-child th { + border-bottom-width: 0; } + html.theme--documenter-dark .table.is-bordered td, + html.theme--documenter-dark .table.is-bordered th { + border-width: 1px; } + html.theme--documenter-dark .table.is-bordered tr:last-child td, + html.theme--documenter-dark .table.is-bordered tr:last-child th { + border-bottom-width: 1px; } + html.theme--documenter-dark .table.is-fullwidth { + width: 100%; } + html.theme--documenter-dark .table.is-hoverable tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { + background-color: whitesmoke; } + html.theme--documenter-dark .table.is-narrow td, + html.theme--documenter-dark .table.is-narrow th { + padding: 0.25em 0.5em; } + html.theme--documenter-dark .table.is-striped tbody tr:not(.is-selected):nth-child(even) { + background-color: #fafafa; } + html.theme--documenter-dark .table-container { + -webkit-overflow-scrolling: touch; + overflow: auto; + overflow-y: hidden; + max-width: 100%; } + html.theme--documenter-dark .tags { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .tags .tag, html.theme--documenter-dark .tags .content kbd, html.theme--documenter-dark .content .tags kbd, html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .tags .tag:not(:last-child), html.theme--documenter-dark .tags .content kbd:not(:last-child), html.theme--documenter-dark .content .tags kbd:not(:last-child), html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0.5rem; } + html.theme--documenter-dark .tags:last-child { + margin-bottom: -0.5rem; } + html.theme--documenter-dark .tags:not(:last-child) { + margin-bottom: 1rem; } + html.theme--documenter-dark .tags.are-medium .tag:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .content kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .content .tags.are-medium kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { + font-size: 1rem; } + html.theme--documenter-dark .tags.are-large .tag:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .content kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .content .tags.are-large kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { + font-size: 1.25rem; } + html.theme--documenter-dark .tags.is-centered { + justify-content: center; } + html.theme--documenter-dark .tags.is-centered .tag, html.theme--documenter-dark .tags.is-centered .content kbd, html.theme--documenter-dark .content .tags.is-centered kbd, html.theme--documenter-dark .tags.is-centered .docstring > section > a.docs-sourcelink { + margin-right: 0.25rem; + margin-left: 0.25rem; } + html.theme--documenter-dark .tags.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .tags.is-right .tag:not(:first-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:first-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0.5rem; } + html.theme--documenter-dark .tags.is-right .tag:not(:last-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:last-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0; } + html.theme--documenter-dark .tags.has-addons .tag, html.theme--documenter-dark .tags.has-addons .content kbd, html.theme--documenter-dark .content .tags.has-addons kbd, html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink { + margin-right: 0; } + html.theme--documenter-dark .tags.has-addons .tag:not(:first-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:first-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0; + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .tags.has-addons .tag:not(:last-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:last-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .tag:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { + align-items: center; + background-color: whitesmoke; + border-radius: 4px; + color: #fbfbfb; + display: inline-flex; + font-size: 0.75rem; + height: 2em; + justify-content: center; + line-height: 1.5; + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + html.theme--documenter-dark .tag:not(body) .delete, html.theme--documenter-dark .content kbd:not(body) .delete, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .delete { + margin-left: 0.25rem; + margin-right: -0.375rem; } + html.theme--documenter-dark .tag.is-white:not(body), html.theme--documenter-dark .content kbd.is-white:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-white:not(body) { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .tag.is-black:not(body), html.theme--documenter-dark .content kbd.is-black:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-black:not(body) { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .tag.is-light:not(body), html.theme--documenter-dark .content kbd.is-light:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-light:not(body) { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .tag.is-dark:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-dark:not(body), html.theme--documenter-dark .content .docstring > section > kbd:not(body) { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .tag.is-primary:not(body), html.theme--documenter-dark .content kbd.is-primary:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .tag.is-link:not(body), html.theme--documenter-dark .content kbd.is-link:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-link:not(body) { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .tag.is-info:not(body), html.theme--documenter-dark .content kbd.is-info:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-info:not(body) { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .tag.is-success:not(body), html.theme--documenter-dark .content kbd.is-success:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-success:not(body) { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .tag.is-warning:not(body), html.theme--documenter-dark .content kbd.is-warning:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-warning:not(body) { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .tag.is-danger:not(body), html.theme--documenter-dark .content kbd.is-danger:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-danger:not(body) { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .tag.is-normal:not(body), html.theme--documenter-dark .content kbd.is-normal:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-normal:not(body) { + font-size: 0.75rem; } + html.theme--documenter-dark .tag.is-medium:not(body), html.theme--documenter-dark .content kbd.is-medium:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-medium:not(body) { + font-size: 1rem; } + html.theme--documenter-dark .tag.is-large:not(body), html.theme--documenter-dark .content kbd.is-large:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-large:not(body) { + font-size: 1.25rem; } + html.theme--documenter-dark .tag:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .content kbd:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { + margin-left: -0.375em; + margin-right: 0.1875em; } + html.theme--documenter-dark .tag:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .content kbd:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: -0.375em; } + html.theme--documenter-dark .tag:not(body) .icon:first-child:last-child, html.theme--documenter-dark .content kbd:not(body) .icon:first-child:last-child, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { + margin-left: -0.375em; + margin-right: -0.375em; } + html.theme--documenter-dark .tag.is-delete:not(body), html.theme--documenter-dark .content kbd.is-delete:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body) { + margin-left: 1px; + padding: 0; + position: relative; + width: 2em; } + html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + background-color: currentColor; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { + height: 1px; + width: 50%; } + html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + height: 50%; + width: 1px; } + html.theme--documenter-dark .tag.is-delete:not(body):hover, html.theme--documenter-dark .content kbd.is-delete:not(body):hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, html.theme--documenter-dark .tag.is-delete:not(body):focus, html.theme--documenter-dark .content kbd.is-delete:not(body):focus, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { + background-color: #e8e8e8; } + html.theme--documenter-dark .tag.is-delete:not(body):active, html.theme--documenter-dark .content kbd.is-delete:not(body):active, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):active { + background-color: #dbdbdb; } + html.theme--documenter-dark .tag.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:not(body), html.theme--documenter-dark .content kbd.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-rounded:not(body) { + border-radius: 290486px; } + html.theme--documenter-dark a.tag:hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:hover { + text-decoration: underline; } + html.theme--documenter-dark .title, + html.theme--documenter-dark .subtitle { + word-break: break-word; } + html.theme--documenter-dark .title em, + html.theme--documenter-dark .title span, + html.theme--documenter-dark .subtitle em, + html.theme--documenter-dark .subtitle span { + font-weight: inherit; } + html.theme--documenter-dark .title sub, + html.theme--documenter-dark .subtitle sub { + font-size: 0.75em; } + html.theme--documenter-dark .title sup, + html.theme--documenter-dark .subtitle sup { + font-size: 0.75em; } + html.theme--documenter-dark .title .tag, html.theme--documenter-dark .title .content kbd, html.theme--documenter-dark .content .title kbd, html.theme--documenter-dark .title .docstring > section > a.docs-sourcelink, + html.theme--documenter-dark .subtitle .tag, + html.theme--documenter-dark .subtitle .content kbd, + html.theme--documenter-dark .content .subtitle kbd, + html.theme--documenter-dark .subtitle .docstring > section > a.docs-sourcelink { + vertical-align: middle; } + html.theme--documenter-dark .title { + color: #363636; + font-size: 2rem; + font-weight: 600; + line-height: 1.125; } + html.theme--documenter-dark .title strong { + color: inherit; + font-weight: inherit; } + html.theme--documenter-dark .title + .highlight { + margin-top: -0.75rem; } + html.theme--documenter-dark .title:not(.is-spaced) + .subtitle { + margin-top: -1.25rem; } + html.theme--documenter-dark .title.is-1 { + font-size: 3rem; } + html.theme--documenter-dark .title.is-2 { + font-size: 2.5rem; } + html.theme--documenter-dark .title.is-3 { + font-size: 2rem; } + html.theme--documenter-dark .title.is-4 { + font-size: 1.5rem; } + html.theme--documenter-dark .title.is-5 { + font-size: 1.25rem; } + html.theme--documenter-dark .title.is-6 { + font-size: 1rem; } + html.theme--documenter-dark .title.is-7 { + font-size: 0.75rem; } + html.theme--documenter-dark .subtitle { + color: #4a4a4a; + font-size: 1.25rem; + font-weight: 400; + line-height: 1.25; } + html.theme--documenter-dark .subtitle strong { + color: #363636; + font-weight: 600; } + html.theme--documenter-dark .subtitle:not(.is-spaced) + .title { + margin-top: -1.25rem; } + html.theme--documenter-dark .subtitle.is-1 { + font-size: 3rem; } + html.theme--documenter-dark .subtitle.is-2 { + font-size: 2.5rem; } + html.theme--documenter-dark .subtitle.is-3 { + font-size: 2rem; } + html.theme--documenter-dark .subtitle.is-4 { + font-size: 1.5rem; } + html.theme--documenter-dark .subtitle.is-5 { + font-size: 1.25rem; } + html.theme--documenter-dark .subtitle.is-6 { + font-size: 1rem; } + html.theme--documenter-dark .subtitle.is-7 { + font-size: 0.75rem; } + html.theme--documenter-dark .heading { + display: block; + font-size: 11px; + letter-spacing: 1px; + margin-bottom: 5px; + text-transform: uppercase; } + html.theme--documenter-dark .highlight { + font-weight: 400; + max-width: 100%; + overflow: hidden; + padding: 0; } + html.theme--documenter-dark .highlight pre { + overflow: auto; + max-width: 100%; } + html.theme--documenter-dark .number { + align-items: center; + background-color: whitesmoke; + border-radius: 290486px; + display: inline-flex; + font-size: 1.25rem; + height: 2em; + justify-content: center; + margin-right: 1.5rem; + min-width: 2.5em; + padding: 0.25rem 0.5rem; + text-align: center; + vertical-align: top; } + html.theme--documenter-dark .select select, html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + background-color: white; + border-color: #dbdbdb; + border-radius: 4px; + color: #363636; } + html.theme--documenter-dark .select select::-moz-placeholder, html.theme--documenter-dark .textarea::-moz-placeholder, html.theme--documenter-dark .input::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select::-webkit-input-placeholder, html.theme--documenter-dark .textarea::-webkit-input-placeholder, html.theme--documenter-dark .input::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:-moz-placeholder, html.theme--documenter-dark .textarea:-moz-placeholder, html.theme--documenter-dark .input:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:-ms-input-placeholder, html.theme--documenter-dark .textarea:-ms-input-placeholder, html.theme--documenter-dark .input:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:hover, html.theme--documenter-dark .textarea:hover, html.theme--documenter-dark .input:hover, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:hover, html.theme--documenter-dark .select select.is-hovered, html.theme--documenter-dark .is-hovered.textarea, html.theme--documenter-dark .is-hovered.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-hovered { + border-color: #149eaa; } + html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + border-color: #fff; + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] html.theme--documenter-dark .select select, fieldset[disabled] html.theme--documenter-dark .textarea, fieldset[disabled] html.theme--documenter-dark .input, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + background-color: whitesmoke; + border-color: whitesmoke; + box-shadow: none; + color: #7a7a7a; } + html.theme--documenter-dark .select select[disabled]::-moz-placeholder, html.theme--documenter-dark .textarea[disabled]::-moz-placeholder, html.theme--documenter-dark .input[disabled]::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .textarea[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .input[disabled]::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]:-moz-placeholder, html.theme--documenter-dark .textarea[disabled]:-moz-placeholder, html.theme--documenter-dark .input[disabled]:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]:-ms-input-placeholder, html.theme--documenter-dark .textarea[disabled]:-ms-input-placeholder, html.theme--documenter-dark .input[disabled]:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); + max-width: 100%; + width: 100%; } + html.theme--documenter-dark .textarea[readonly], html.theme--documenter-dark .input[readonly], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[readonly] { + box-shadow: none; } + html.theme--documenter-dark .is-white.textarea, html.theme--documenter-dark .is-white.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white { + border-color: white; } + html.theme--documenter-dark .is-white.textarea:focus, html.theme--documenter-dark .is-white.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:focus, html.theme--documenter-dark .is-white.is-focused.textarea, html.theme--documenter-dark .is-white.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-white.textarea:active, html.theme--documenter-dark .is-white.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:active, html.theme--documenter-dark .is-white.is-active.textarea, html.theme--documenter-dark .is-white.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .is-black.textarea, html.theme--documenter-dark .is-black.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black { + border-color: #0a0a0a; } + html.theme--documenter-dark .is-black.textarea:focus, html.theme--documenter-dark .is-black.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:focus, html.theme--documenter-dark .is-black.is-focused.textarea, html.theme--documenter-dark .is-black.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-black.textarea:active, html.theme--documenter-dark .is-black.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:active, html.theme--documenter-dark .is-black.is-active.textarea, html.theme--documenter-dark .is-black.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .is-light.textarea, html.theme--documenter-dark .is-light.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light { + border-color: whitesmoke; } + html.theme--documenter-dark .is-light.textarea:focus, html.theme--documenter-dark .is-light.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:focus, html.theme--documenter-dark .is-light.is-focused.textarea, html.theme--documenter-dark .is-light.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-light.textarea:active, html.theme--documenter-dark .is-light.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:active, html.theme--documenter-dark .is-light.is-active.textarea, html.theme--documenter-dark .is-light.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .is-dark.textarea, html.theme--documenter-dark .content kbd.textarea, html.theme--documenter-dark .is-dark.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark, html.theme--documenter-dark .content kbd.input { + border-color: #363636; } + html.theme--documenter-dark .is-dark.textarea:focus, html.theme--documenter-dark .content kbd.textarea:focus, html.theme--documenter-dark .is-dark.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:focus, html.theme--documenter-dark .content kbd.input:focus, html.theme--documenter-dark .is-dark.is-focused.textarea, html.theme--documenter-dark .content kbd.is-focused.textarea, html.theme--documenter-dark .is-dark.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .content kbd.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-focused, html.theme--documenter-dark .is-dark.textarea:active, html.theme--documenter-dark .content kbd.textarea:active, html.theme--documenter-dark .is-dark.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:active, html.theme--documenter-dark .content kbd.input:active, html.theme--documenter-dark .is-dark.is-active.textarea, html.theme--documenter-dark .content kbd.is-active.textarea, html.theme--documenter-dark .is-dark.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .content kbd.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .is-primary.textarea, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink { + border-color: #4eb5de; } + html.theme--documenter-dark .is-primary.textarea:focus, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:focus, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.is-focused.textarea, html.theme--documenter-dark .docstring > section > a.is-focused.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .docstring > section > a.is-focused.input.docs-sourcelink, html.theme--documenter-dark .is-primary.textarea:active, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:active, html.theme--documenter-dark .is-primary.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:active, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:active, html.theme--documenter-dark .is-primary.is-active.textarea, html.theme--documenter-dark .docstring > section > a.is-active.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .docstring > section > a.is-active.input.docs-sourcelink { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .is-link.textarea, html.theme--documenter-dark .is-link.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link { + border-color: #2ad7e6; } + html.theme--documenter-dark .is-link.textarea:focus, html.theme--documenter-dark .is-link.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:focus, html.theme--documenter-dark .is-link.is-focused.textarea, html.theme--documenter-dark .is-link.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-link.textarea:active, html.theme--documenter-dark .is-link.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:active, html.theme--documenter-dark .is-link.is-active.textarea, html.theme--documenter-dark .is-link.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .is-info.textarea, html.theme--documenter-dark .is-info.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info { + border-color: #3489da; } + html.theme--documenter-dark .is-info.textarea:focus, html.theme--documenter-dark .is-info.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:focus, html.theme--documenter-dark .is-info.is-focused.textarea, html.theme--documenter-dark .is-info.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-info.textarea:active, html.theme--documenter-dark .is-info.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:active, html.theme--documenter-dark .is-info.is-active.textarea, html.theme--documenter-dark .is-info.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .is-success.textarea, html.theme--documenter-dark .is-success.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success { + border-color: #259a12; } + html.theme--documenter-dark .is-success.textarea:focus, html.theme--documenter-dark .is-success.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:focus, html.theme--documenter-dark .is-success.is-focused.textarea, html.theme--documenter-dark .is-success.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-success.textarea:active, html.theme--documenter-dark .is-success.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:active, html.theme--documenter-dark .is-success.is-active.textarea, html.theme--documenter-dark .is-success.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .is-warning.textarea, html.theme--documenter-dark .is-warning.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning { + border-color: #f4c72f; } + html.theme--documenter-dark .is-warning.textarea:focus, html.theme--documenter-dark .is-warning.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:focus, html.theme--documenter-dark .is-warning.is-focused.textarea, html.theme--documenter-dark .is-warning.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-warning.textarea:active, html.theme--documenter-dark .is-warning.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:active, html.theme--documenter-dark .is-warning.is-active.textarea, html.theme--documenter-dark .is-warning.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .is-danger.textarea, html.theme--documenter-dark .is-danger.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger { + border-color: #cb3c33; } + html.theme--documenter-dark .is-danger.textarea:focus, html.theme--documenter-dark .is-danger.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:focus, html.theme--documenter-dark .is-danger.is-focused.textarea, html.theme--documenter-dark .is-danger.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-danger.textarea:active, html.theme--documenter-dark .is-danger.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:active, html.theme--documenter-dark .is-danger.is-active.textarea, html.theme--documenter-dark .is-danger.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .is-small.textarea, html.theme--documenter-dark .is-small.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .is-medium.textarea, html.theme--documenter-dark .is-medium.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .is-large.textarea, html.theme--documenter-dark .is-large.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .is-fullwidth.textarea, html.theme--documenter-dark .is-fullwidth.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-fullwidth { + display: block; + width: 100%; } + html.theme--documenter-dark .is-inline.textarea, html.theme--documenter-dark .is-inline.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-inline { + display: inline; + width: auto; } + html.theme--documenter-dark .input.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + html.theme--documenter-dark .input.is-static, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-static { + background-color: transparent; + border-color: transparent; + box-shadow: none; + padding-left: 0; + padding-right: 0; } + html.theme--documenter-dark .textarea { + display: block; + max-width: 100%; + min-width: 100%; + padding: 0.625em; + resize: vertical; } + html.theme--documenter-dark .textarea:not([rows]) { + max-height: 600px; + min-height: 120px; } + html.theme--documenter-dark .textarea[rows] { + height: initial; } + html.theme--documenter-dark .textarea.has-fixed-size { + resize: none; } + html.theme--documenter-dark .radio, html.theme--documenter-dark .checkbox { + cursor: pointer; + display: inline-block; + line-height: 1.25; + position: relative; } + html.theme--documenter-dark .radio input, html.theme--documenter-dark .checkbox input { + cursor: pointer; } + html.theme--documenter-dark .radio:hover, html.theme--documenter-dark .checkbox:hover { + color: #363636; } + html.theme--documenter-dark .radio[disabled], html.theme--documenter-dark .checkbox[disabled], fieldset[disabled] html.theme--documenter-dark .radio, fieldset[disabled] html.theme--documenter-dark .checkbox { + color: #7a7a7a; + cursor: not-allowed; } + html.theme--documenter-dark .radio + .radio { + margin-left: 0.5em; } + html.theme--documenter-dark .select { + display: inline-block; + max-width: 100%; + position: relative; + vertical-align: top; } + html.theme--documenter-dark .select:not(.is-multiple) { + height: 2.25em; } + html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after { + border-color: #2ad7e6; + right: 1.125em; + z-index: 4; } + html.theme--documenter-dark .select.is-rounded select, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select select { + border-radius: 290486px; + padding-left: 1em; } + html.theme--documenter-dark .select select { + cursor: pointer; + display: block; + font-size: 1em; + max-width: 100%; + outline: none; } + html.theme--documenter-dark .select select::-ms-expand { + display: none; } + html.theme--documenter-dark .select select[disabled]:hover, fieldset[disabled] html.theme--documenter-dark .select select:hover { + border-color: whitesmoke; } + html.theme--documenter-dark .select select:not([multiple]) { + padding-right: 2.5em; } + html.theme--documenter-dark .select select[multiple] { + height: auto; + padding: 0; } + html.theme--documenter-dark .select select[multiple] option { + padding: 0.5em 1em; } + html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading):hover::after { + border-color: #363636; } + html.theme--documenter-dark .select.is-white:not(:hover)::after { + border-color: white; } + html.theme--documenter-dark .select.is-white select { + border-color: white; } + html.theme--documenter-dark .select.is-white select:hover, html.theme--documenter-dark .select.is-white select.is-hovered { + border-color: #f2f2f2; } + html.theme--documenter-dark .select.is-white select:focus, html.theme--documenter-dark .select.is-white select.is-focused, html.theme--documenter-dark .select.is-white select:active, html.theme--documenter-dark .select.is-white select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .select.is-black:not(:hover)::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .select.is-black select { + border-color: #0a0a0a; } + html.theme--documenter-dark .select.is-black select:hover, html.theme--documenter-dark .select.is-black select.is-hovered { + border-color: black; } + html.theme--documenter-dark .select.is-black select:focus, html.theme--documenter-dark .select.is-black select.is-focused, html.theme--documenter-dark .select.is-black select:active, html.theme--documenter-dark .select.is-black select.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .select.is-light:not(:hover)::after { + border-color: whitesmoke; } + html.theme--documenter-dark .select.is-light select { + border-color: whitesmoke; } + html.theme--documenter-dark .select.is-light select:hover, html.theme--documenter-dark .select.is-light select.is-hovered { + border-color: #e8e8e8; } + html.theme--documenter-dark .select.is-light select:focus, html.theme--documenter-dark .select.is-light select.is-focused, html.theme--documenter-dark .select.is-light select:active, html.theme--documenter-dark .select.is-light select.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .select.is-dark:not(:hover)::after, html.theme--documenter-dark .content kbd.select:not(:hover)::after { + border-color: #363636; } + html.theme--documenter-dark .select.is-dark select, html.theme--documenter-dark .content kbd.select select { + border-color: #363636; } + html.theme--documenter-dark .select.is-dark select:hover, html.theme--documenter-dark .content kbd.select select:hover, html.theme--documenter-dark .select.is-dark select.is-hovered, html.theme--documenter-dark .content kbd.select select.is-hovered { + border-color: #292929; } + html.theme--documenter-dark .select.is-dark select:focus, html.theme--documenter-dark .content kbd.select select:focus, html.theme--documenter-dark .select.is-dark select.is-focused, html.theme--documenter-dark .content kbd.select select.is-focused, html.theme--documenter-dark .select.is-dark select:active, html.theme--documenter-dark .content kbd.select select:active, html.theme--documenter-dark .select.is-dark select.is-active, html.theme--documenter-dark .content kbd.select select.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .select.is-primary:not(:hover)::after, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink:not(:hover)::after { + border-color: #4eb5de; } + html.theme--documenter-dark .select.is-primary select, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select { + border-color: #4eb5de; } + html.theme--documenter-dark .select.is-primary select:hover, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:hover, html.theme--documenter-dark .select.is-primary select.is-hovered, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-hovered { + border-color: #39acda; } + html.theme--documenter-dark .select.is-primary select:focus, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:focus, html.theme--documenter-dark .select.is-primary select.is-focused, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-focused, html.theme--documenter-dark .select.is-primary select:active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:active, html.theme--documenter-dark .select.is-primary select.is-active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-active { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .select.is-link:not(:hover)::after { + border-color: #2ad7e6; } + html.theme--documenter-dark .select.is-link select { + border-color: #2ad7e6; } + html.theme--documenter-dark .select.is-link select:hover, html.theme--documenter-dark .select.is-link select.is-hovered { + border-color: #1acddc; } + html.theme--documenter-dark .select.is-link select:focus, html.theme--documenter-dark .select.is-link select.is-focused, html.theme--documenter-dark .select.is-link select:active, html.theme--documenter-dark .select.is-link select.is-active { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .select.is-info:not(:hover)::after { + border-color: #3489da; } + html.theme--documenter-dark .select.is-info select { + border-color: #3489da; } + html.theme--documenter-dark .select.is-info select:hover, html.theme--documenter-dark .select.is-info select.is-hovered { + border-color: #267ccf; } + html.theme--documenter-dark .select.is-info select:focus, html.theme--documenter-dark .select.is-info select.is-focused, html.theme--documenter-dark .select.is-info select:active, html.theme--documenter-dark .select.is-info select.is-active { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .select.is-success:not(:hover)::after { + border-color: #259a12; } + html.theme--documenter-dark .select.is-success select { + border-color: #259a12; } + html.theme--documenter-dark .select.is-success select:hover, html.theme--documenter-dark .select.is-success select.is-hovered { + border-color: #20830f; } + html.theme--documenter-dark .select.is-success select:focus, html.theme--documenter-dark .select.is-success select.is-focused, html.theme--documenter-dark .select.is-success select:active, html.theme--documenter-dark .select.is-success select.is-active { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .select.is-warning:not(:hover)::after { + border-color: #f4c72f; } + html.theme--documenter-dark .select.is-warning select { + border-color: #f4c72f; } + html.theme--documenter-dark .select.is-warning select:hover, html.theme--documenter-dark .select.is-warning select.is-hovered { + border-color: #f3c017; } + html.theme--documenter-dark .select.is-warning select:focus, html.theme--documenter-dark .select.is-warning select.is-focused, html.theme--documenter-dark .select.is-warning select:active, html.theme--documenter-dark .select.is-warning select.is-active { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .select.is-danger:not(:hover)::after { + border-color: #cb3c33; } + html.theme--documenter-dark .select.is-danger select { + border-color: #cb3c33; } + html.theme--documenter-dark .select.is-danger select:hover, html.theme--documenter-dark .select.is-danger select.is-hovered { + border-color: #b7362e; } + html.theme--documenter-dark .select.is-danger select:focus, html.theme--documenter-dark .select.is-danger select.is-focused, html.theme--documenter-dark .select.is-danger select:active, html.theme--documenter-dark .select.is-danger select.is-active { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .select.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .select.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .select.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .select.is-disabled::after { + border-color: #7a7a7a; } + html.theme--documenter-dark .select.is-fullwidth { + width: 100%; } + html.theme--documenter-dark .select.is-fullwidth select { + width: 100%; } + html.theme--documenter-dark .select.is-loading::after { + margin-top: 0; + position: absolute; + right: 0.625em; + top: 0.625em; + transform: none; } + html.theme--documenter-dark .select.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + html.theme--documenter-dark .select.is-loading.is-medium:after { + font-size: 1.25rem; } + html.theme--documenter-dark .select.is-loading.is-large:after { + font-size: 1.5rem; } + html.theme--documenter-dark .file { + align-items: stretch; + display: flex; + justify-content: flex-start; + position: relative; } + html.theme--documenter-dark .file.is-white .file-cta { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:hover .file-cta, html.theme--documenter-dark .file.is-white.is-hovered .file-cta { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:focus .file-cta, html.theme--documenter-dark .file.is-white.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:active .file-cta, html.theme--documenter-dark .file.is-white.is-active .file-cta { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-black .file-cta { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-black:hover .file-cta, html.theme--documenter-dark .file.is-black.is-hovered .file-cta { + background-color: #040404; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-black:focus .file-cta, html.theme--documenter-dark .file.is-black.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); + color: white; } + html.theme--documenter-dark .file.is-black:active .file-cta, html.theme--documenter-dark .file.is-black.is-active .file-cta { + background-color: black; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-light .file-cta { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-light:hover .file-cta, html.theme--documenter-dark .file.is-light.is-hovered .file-cta { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-light:focus .file-cta, html.theme--documenter-dark .file.is-light.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25); + color: #363636; } + html.theme--documenter-dark .file.is-light:active .file-cta, html.theme--documenter-dark .file.is-light.is-active .file-cta { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-dark .file-cta, html.theme--documenter-dark .content kbd.file .file-cta { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:hover .file-cta, html.theme--documenter-dark .content kbd.file:hover .file-cta, html.theme--documenter-dark .file.is-dark.is-hovered .file-cta, html.theme--documenter-dark .content kbd.file.is-hovered .file-cta { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:focus .file-cta, html.theme--documenter-dark .content kbd.file:focus .file-cta, html.theme--documenter-dark .file.is-dark.is-focused .file-cta, html.theme--documenter-dark .content kbd.file.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25); + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:active .file-cta, html.theme--documenter-dark .content kbd.file:active .file-cta, html.theme--documenter-dark .file.is-dark.is-active .file-cta, html.theme--documenter-dark .content kbd.file.is-active .file-cta { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-primary .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink .file-cta { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-primary:hover .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:hover .file-cta, html.theme--documenter-dark .file.is-primary.is-hovered .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-primary:focus .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:focus .file-cta, html.theme--documenter-dark .file.is-primary.is-focused .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-primary:active .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:active .file-cta, html.theme--documenter-dark .file.is-primary.is-active .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-active.docs-sourcelink .file-cta { + background-color: #39acda; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link .file-cta { + background-color: #2ad7e6; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link:hover .file-cta, html.theme--documenter-dark .file.is-link.is-hovered .file-cta { + background-color: #1ed5e5; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link:focus .file-cta, html.theme--documenter-dark .file.is-link.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(42, 215, 230, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-link:active .file-cta, html.theme--documenter-dark .file.is-link.is-active .file-cta { + background-color: #1acddc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info .file-cta { + background-color: #3489da; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info:hover .file-cta, html.theme--documenter-dark .file.is-info.is-hovered .file-cta { + background-color: #2983d8; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info:focus .file-cta, html.theme--documenter-dark .file.is-info.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(52, 137, 218, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-info:active .file-cta, html.theme--documenter-dark .file.is-info.is-active .file-cta { + background-color: #267ccf; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success .file-cta { + background-color: #259a12; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success:hover .file-cta, html.theme--documenter-dark .file.is-success.is-hovered .file-cta { + background-color: #228f11; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success:focus .file-cta, html.theme--documenter-dark .file.is-success.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(37, 154, 18, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-success:active .file-cta, html.theme--documenter-dark .file.is-success.is-active .file-cta { + background-color: #20830f; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-warning .file-cta { + background-color: #f4c72f; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:hover .file-cta, html.theme--documenter-dark .file.is-warning.is-hovered .file-cta { + background-color: #f3c423; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:focus .file-cta, html.theme--documenter-dark .file.is-warning.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(244, 199, 47, 0.25); + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:active .file-cta, html.theme--documenter-dark .file.is-warning.is-active .file-cta { + background-color: #f3c017; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-danger .file-cta { + background-color: #cb3c33; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-danger:hover .file-cta, html.theme--documenter-dark .file.is-danger.is-hovered .file-cta { + background-color: #c13930; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-danger:focus .file-cta, html.theme--documenter-dark .file.is-danger.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(203, 60, 51, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-danger:active .file-cta, html.theme--documenter-dark .file.is-danger.is-active .file-cta { + background-color: #b7362e; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.file { + font-size: 0.75rem; } + html.theme--documenter-dark .file.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .file.is-medium .file-icon .fa { + font-size: 21px; } + html.theme--documenter-dark .file.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .file.is-large .file-icon .fa { + font-size: 28px; } + html.theme--documenter-dark .file.has-name .file-cta { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .file.has-name .file-name { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .file.has-name.is-empty .file-cta { + border-radius: 4px; } + html.theme--documenter-dark .file.has-name.is-empty .file-name { + display: none; } + html.theme--documenter-dark .file.is-boxed .file-label { + flex-direction: column; } + html.theme--documenter-dark .file.is-boxed .file-cta { + flex-direction: column; + height: auto; + padding: 1em 3em; } + html.theme--documenter-dark .file.is-boxed .file-name { + border-width: 0 1px 1px; } + html.theme--documenter-dark .file.is-boxed .file-icon { + height: 1.5em; + width: 1.5em; } + html.theme--documenter-dark .file.is-boxed .file-icon .fa { + font-size: 21px; } + html.theme--documenter-dark .file.is-boxed.is-small .file-icon .fa, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { + font-size: 14px; } + html.theme--documenter-dark .file.is-boxed.is-medium .file-icon .fa { + font-size: 28px; } + html.theme--documenter-dark .file.is-boxed.is-large .file-icon .fa { + font-size: 35px; } + html.theme--documenter-dark .file.is-boxed.has-name .file-cta { + border-radius: 4px 4px 0 0; } + html.theme--documenter-dark .file.is-boxed.has-name .file-name { + border-radius: 0 0 4px 4px; + border-width: 0 1px 1px; } + html.theme--documenter-dark .file.is-centered { + justify-content: center; } + html.theme--documenter-dark .file.is-fullwidth .file-label { + width: 100%; } + html.theme--documenter-dark .file.is-fullwidth .file-name { + flex-grow: 1; + max-width: none; } + html.theme--documenter-dark .file.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .file.is-right .file-cta { + border-radius: 0 4px 4px 0; } + html.theme--documenter-dark .file.is-right .file-name { + border-radius: 4px 0 0 4px; + border-width: 1px 0 1px 1px; + order: -1; } + html.theme--documenter-dark .file-label { + align-items: stretch; + display: flex; + cursor: pointer; + justify-content: flex-start; + overflow: hidden; + position: relative; } + html.theme--documenter-dark .file-label:hover .file-cta { + background-color: #eeeeee; + color: #363636; } + html.theme--documenter-dark .file-label:hover .file-name { + border-color: #d5d5d5; } + html.theme--documenter-dark .file-label:active .file-cta { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .file-label:active .file-name { + border-color: #cfcfcf; } + html.theme--documenter-dark .file-input { + height: 100%; + left: 0; + opacity: 0; + outline: none; + position: absolute; + top: 0; + width: 100%; } + html.theme--documenter-dark .file-cta, + html.theme--documenter-dark .file-name { + border-color: #dbdbdb; + border-radius: 4px; + font-size: 1em; + padding-left: 1em; + padding-right: 1em; + white-space: nowrap; } + html.theme--documenter-dark .file-cta { + background-color: whitesmoke; + color: #4a4a4a; } + html.theme--documenter-dark .file-name { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px 1px 1px 0; + display: block; + max-width: 16em; + overflow: hidden; + text-align: left; + text-overflow: ellipsis; } + html.theme--documenter-dark .file-icon { + align-items: center; + display: flex; + height: 1em; + justify-content: center; + margin-right: 0.5em; + width: 1em; } + html.theme--documenter-dark .file-icon .fa { + font-size: 14px; } + html.theme--documenter-dark .label { + color: #363636; + display: block; + font-size: 1rem; + font-weight: 700; } + html.theme--documenter-dark .label:not(:last-child) { + margin-bottom: 0.5em; } + html.theme--documenter-dark .label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.label { + font-size: 0.75rem; } + html.theme--documenter-dark .label.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .label.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .help { + display: block; + font-size: 0.75rem; + margin-top: 0.25rem; } + html.theme--documenter-dark .help.is-white { + color: white; } + html.theme--documenter-dark .help.is-black { + color: #0a0a0a; } + html.theme--documenter-dark .help.is-light { + color: whitesmoke; } + html.theme--documenter-dark .help.is-dark, html.theme--documenter-dark .content kbd.help { + color: #363636; } + html.theme--documenter-dark .help.is-primary, html.theme--documenter-dark .docstring > section > a.help.docs-sourcelink { + color: #4eb5de; } + html.theme--documenter-dark .help.is-link { + color: #2ad7e6; } + html.theme--documenter-dark .help.is-info { + color: #3489da; } + html.theme--documenter-dark .help.is-success { + color: #259a12; } + html.theme--documenter-dark .help.is-warning { + color: #f4c72f; } + html.theme--documenter-dark .help.is-danger { + color: #cb3c33; } + html.theme--documenter-dark .field:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .field.has-addons { + display: flex; + justify-content: flex-start; } + html.theme--documenter-dark .field.has-addons .control:not(:last-child) { + margin-right: -1px; } + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .button, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .input, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .select select { + border-radius: 0; } + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .button, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .input, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .select select { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .button, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .input, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .select select { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-hovered:not([disabled]) { + z-index: 2; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]), html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]) { + z-index: 3; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus:hover, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active:hover, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]):hover { + z-index: 4; } + html.theme--documenter-dark .field.has-addons .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .field.has-addons.has-addons-centered { + justify-content: center; } + html.theme--documenter-dark .field.has-addons.has-addons-right { + justify-content: flex-end; } + html.theme--documenter-dark .field.has-addons.has-addons-fullwidth .control { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .field.is-grouped { + display: flex; + justify-content: flex-start; } + html.theme--documenter-dark .field.is-grouped > .control { + flex-shrink: 0; } + html.theme--documenter-dark .field.is-grouped > .control:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + html.theme--documenter-dark .field.is-grouped > .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .field.is-grouped.is-grouped-centered { + justify-content: center; } + html.theme--documenter-dark .field.is-grouped.is-grouped-right { + justify-content: flex-end; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline { + flex-wrap: wrap; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:last-child, html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:not(:last-child) { + margin-bottom: 0; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field.is-horizontal { + display: flex; } } + html.theme--documenter-dark .field-label .label { + font-size: inherit; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .field-label { + margin-bottom: 0.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field-label { + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + margin-right: 1.5rem; + text-align: right; } + html.theme--documenter-dark .field-label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.field-label { + font-size: 0.75rem; + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-normal { + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-medium { + font-size: 1.25rem; + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-large { + font-size: 1.5rem; + padding-top: 0.375em; } } + html.theme--documenter-dark .field-body .field .field { + margin-bottom: 0; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field-body { + display: flex; + flex-basis: 0; + flex-grow: 5; + flex-shrink: 1; } + html.theme--documenter-dark .field-body .field { + margin-bottom: 0; } + html.theme--documenter-dark .field-body > .field { + flex-shrink: 1; } + html.theme--documenter-dark .field-body > .field:not(.is-narrow) { + flex-grow: 1; } + html.theme--documenter-dark .field-body > .field:not(:last-child) { + margin-right: 0.75rem; } } + html.theme--documenter-dark .control { + box-sizing: border-box; + clear: both; + font-size: 1rem; + position: relative; + text-align: left; } + html.theme--documenter-dark .control.has-icons-left .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select:focus ~ .icon { + color: #7a7a7a; } + html.theme--documenter-dark .control.has-icons-left .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-small ~ .icon { + font-size: 0.75rem; } + html.theme--documenter-dark .control.has-icons-left .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-medium ~ .icon { + font-size: 1.25rem; } + html.theme--documenter-dark .control.has-icons-left .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-large ~ .icon { + font-size: 1.5rem; } + html.theme--documenter-dark .control.has-icons-left .icon, html.theme--documenter-dark .control.has-icons-right .icon { + color: #dbdbdb; + height: 2.25em; + pointer-events: none; + position: absolute; + top: 0; + width: 2.25em; + z-index: 4; } + html.theme--documenter-dark .control.has-icons-left .input, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, + html.theme--documenter-dark .control.has-icons-left .select select { + padding-left: 2.25em; } + html.theme--documenter-dark .control.has-icons-left .icon.is-left { + left: 0; } + html.theme--documenter-dark .control.has-icons-right .input, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, + html.theme--documenter-dark .control.has-icons-right .select select { + padding-right: 2.25em; } + html.theme--documenter-dark .control.has-icons-right .icon.is-right { + right: 0; } + html.theme--documenter-dark .control.is-loading::after { + position: absolute !important; + right: 0.625em; + top: 0.625em; + z-index: 4; } + html.theme--documenter-dark .control.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + html.theme--documenter-dark .control.is-loading.is-medium:after { + font-size: 1.25rem; } + html.theme--documenter-dark .control.is-loading.is-large:after { + font-size: 1.5rem; } + html.theme--documenter-dark .breadcrumb { + font-size: 1rem; + white-space: nowrap; } + html.theme--documenter-dark .breadcrumb a { + align-items: center; + color: #2ad7e6; + display: flex; + justify-content: center; + padding: 0 0.75em; } + html.theme--documenter-dark .breadcrumb a:hover { + color: #97ebf3; } + html.theme--documenter-dark .breadcrumb li { + align-items: center; + display: flex; } + html.theme--documenter-dark .breadcrumb li:first-child a { + padding-left: 0; } + html.theme--documenter-dark .breadcrumb li.is-active a { + color: #cdc3e3; + cursor: default; + pointer-events: none; } + html.theme--documenter-dark .breadcrumb li + li::before { + color: #b5b5b5; + content: "\0002f"; } + html.theme--documenter-dark .breadcrumb ul, + html.theme--documenter-dark .breadcrumb ol { + align-items: flex-start; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .breadcrumb .icon:first-child { + margin-right: 0.5em; } + html.theme--documenter-dark .breadcrumb .icon:last-child { + margin-left: 0.5em; } + html.theme--documenter-dark .breadcrumb.is-centered ol, + html.theme--documenter-dark .breadcrumb.is-centered ul { + justify-content: center; } + html.theme--documenter-dark .breadcrumb.is-right ol, + html.theme--documenter-dark .breadcrumb.is-right ul { + justify-content: flex-end; } + html.theme--documenter-dark .breadcrumb.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.breadcrumb { + font-size: 0.75rem; } + html.theme--documenter-dark .breadcrumb.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .breadcrumb.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .breadcrumb.has-arrow-separator li + li::before { + content: "\02192"; } + html.theme--documenter-dark .breadcrumb.has-bullet-separator li + li::before { + content: "\02022"; } + html.theme--documenter-dark .breadcrumb.has-dot-separator li + li::before { + content: "\000b7"; } + html.theme--documenter-dark .breadcrumb.has-succeeds-separator li + li::before { + content: "\0227B"; } + html.theme--documenter-dark .card { + background-color: white; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #fbfbfb; + max-width: 100%; + position: relative; } + html.theme--documenter-dark .card-header { + background-color: transparent; + align-items: stretch; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + display: flex; } + html.theme--documenter-dark .card-header-title { + align-items: center; + color: #cdc3e3; + display: flex; + flex-grow: 1; + font-weight: 700; + padding: 0.75rem; } + html.theme--documenter-dark .card-header-title.is-centered { + justify-content: center; } + html.theme--documenter-dark .card-header-icon { + align-items: center; + cursor: pointer; + display: flex; + justify-content: center; + padding: 0.75rem; } + html.theme--documenter-dark .card-image { + display: block; + position: relative; } + html.theme--documenter-dark .card-content { + background-color: transparent; + padding: 1.5rem; } + html.theme--documenter-dark .card-footer { + background-color: transparent; + border-top: 1px solid #dbdbdb; + align-items: stretch; + display: flex; } + html.theme--documenter-dark .card-footer-item { + align-items: center; + display: flex; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + justify-content: center; + padding: 0.75rem; } + html.theme--documenter-dark .card-footer-item:not(:last-child) { + border-right: 1px solid #dbdbdb; } + html.theme--documenter-dark .card .media:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .dropdown { + display: inline-flex; + position: relative; + vertical-align: top; } + html.theme--documenter-dark .dropdown.is-active .dropdown-menu, html.theme--documenter-dark .dropdown.is-hoverable:hover .dropdown-menu { + display: block; } + html.theme--documenter-dark .dropdown.is-right .dropdown-menu { + left: auto; + right: 0; } + html.theme--documenter-dark .dropdown.is-up .dropdown-menu { + bottom: 100%; + padding-bottom: 4px; + padding-top: initial; + top: auto; } + html.theme--documenter-dark .dropdown-menu { + display: none; + left: 0; + min-width: 12rem; + padding-top: 4px; + position: absolute; + top: 100%; + z-index: 20; } + html.theme--documenter-dark .dropdown-content { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + html.theme--documenter-dark .dropdown-item { + color: #4a4a4a; + display: block; + font-size: 0.875rem; + line-height: 1.5; + padding: 0.375rem 1rem; + position: relative; } + html.theme--documenter-dark a.dropdown-item, + html.theme--documenter-dark button.dropdown-item { + padding-right: 3rem; + text-align: left; + white-space: nowrap; + width: 100%; } + html.theme--documenter-dark a.dropdown-item:hover, + html.theme--documenter-dark button.dropdown-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark a.dropdown-item.is-active, + html.theme--documenter-dark button.dropdown-item.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .dropdown-divider { + background-color: #dbdbdb; + border: none; + display: block; + height: 1px; + margin: 0.5rem 0; } + html.theme--documenter-dark .level { + align-items: center; + justify-content: space-between; } + html.theme--documenter-dark .level code { + border-radius: 4px; } + html.theme--documenter-dark .level img { + display: inline-block; + vertical-align: top; } + html.theme--documenter-dark .level.is-mobile { + display: flex; } + html.theme--documenter-dark .level.is-mobile .level-left, + html.theme--documenter-dark .level.is-mobile .level-right { + display: flex; } + html.theme--documenter-dark .level.is-mobile .level-left + .level-right { + margin-top: 0; } + html.theme--documenter-dark .level.is-mobile .level-item:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + html.theme--documenter-dark .level.is-mobile .level-item:not(.is-narrow) { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level { + display: flex; } + html.theme--documenter-dark .level > .level-item:not(.is-narrow) { + flex-grow: 1; } } + html.theme--documenter-dark .level-item { + align-items: center; + display: flex; + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; + justify-content: center; } + html.theme--documenter-dark .level-item .title, + html.theme--documenter-dark .level-item .subtitle { + margin-bottom: 0; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .level-item:not(:last-child) { + margin-bottom: 0.75rem; } } + html.theme--documenter-dark .level-left, + html.theme--documenter-dark .level-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .level-left .level-item.is-flexible, + html.theme--documenter-dark .level-right .level-item.is-flexible { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-left .level-item:not(:last-child), + html.theme--documenter-dark .level-right .level-item:not(:last-child) { + margin-right: 0.75rem; } } + html.theme--documenter-dark .level-left { + align-items: center; + justify-content: flex-start; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .level-left + .level-right { + margin-top: 1.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-left { + display: flex; } } + html.theme--documenter-dark .level-right { + align-items: center; + justify-content: flex-end; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-right { + display: flex; } } + html.theme--documenter-dark .list { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .list-item { + display: block; + padding: 0.5em 1em; } + html.theme--documenter-dark .list-item:not(a) { + color: #fbfbfb; } + html.theme--documenter-dark .list-item:first-child { + border-top-left-radius: 4px; + border-top-right-radius: 4px; } + html.theme--documenter-dark .list-item:last-child { + border-bottom-left-radius: 4px; + border-bottom-right-radius: 4px; } + html.theme--documenter-dark .list-item:not(:last-child) { + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .list-item.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark a.list-item { + background-color: whitesmoke; + cursor: pointer; } + html.theme--documenter-dark .media { + align-items: flex-start; + display: flex; + text-align: left; } + html.theme--documenter-dark .media .content:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .media .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + display: flex; + padding-top: 0.75rem; } + html.theme--documenter-dark .media .media .content:not(:last-child), + html.theme--documenter-dark .media .media .control:not(:last-child) { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .media .media .media { + padding-top: 0.5rem; } + html.theme--documenter-dark .media .media .media + .media { + margin-top: 0.5rem; } + html.theme--documenter-dark .media + .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + margin-top: 1rem; + padding-top: 1rem; } + html.theme--documenter-dark .media.is-large + .media { + margin-top: 1.5rem; + padding-top: 1.5rem; } + html.theme--documenter-dark .media-left, + html.theme--documenter-dark .media-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .media-left { + margin-right: 1rem; } + html.theme--documenter-dark .media-right { + margin-left: 1rem; } + html.theme--documenter-dark .media-content { + flex-basis: auto; + flex-grow: 1; + flex-shrink: 1; + text-align: left; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .media-content { + overflow-x: auto; } } + html.theme--documenter-dark .menu { + font-size: 1rem; } + html.theme--documenter-dark .menu.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.menu { + font-size: 0.75rem; } + html.theme--documenter-dark .menu.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .menu.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .menu-list { + line-height: 1.25; } + html.theme--documenter-dark .menu-list a { + border-radius: 2px; + color: #fbfbfb; + display: block; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .menu-list a:hover { + background-color: whitesmoke; + color: #cdc3e3; } + html.theme--documenter-dark .menu-list a.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .menu-list li ul { + border-left: 1px solid #dbdbdb; + margin: 0.75em; + padding-left: 0.75em; } + html.theme--documenter-dark .menu-label { + color: #7a7a7a; + font-size: 0.75em; + letter-spacing: 0.1em; + text-transform: uppercase; } + html.theme--documenter-dark .menu-label:not(:first-child) { + margin-top: 1em; } + html.theme--documenter-dark .menu-label:not(:last-child) { + margin-bottom: 1em; } + html.theme--documenter-dark .message { + background-color: whitesmoke; + border-radius: 4px; + font-size: 1rem; } + html.theme--documenter-dark .message strong { + color: currentColor; } + html.theme--documenter-dark .message a:not(.button):not(.tag):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + html.theme--documenter-dark .message.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.message { + font-size: 0.75rem; } + html.theme--documenter-dark .message.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .message.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .message.is-white { + background-color: white; } + html.theme--documenter-dark .message.is-white .message-header { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .message.is-white .message-body { + border-color: white; + color: #4d4d4d; } + html.theme--documenter-dark .message.is-black { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-black .message-header { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .message.is-black .message-body { + border-color: #0a0a0a; + color: #090909; } + html.theme--documenter-dark .message.is-light { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-light .message-header { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .message.is-light .message-body { + border-color: whitesmoke; + color: #505050; } + html.theme--documenter-dark .message.is-dark, html.theme--documenter-dark .content kbd.message { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-dark .message-header, html.theme--documenter-dark .content kbd.message .message-header { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .message.is-dark .message-body, html.theme--documenter-dark .content kbd.message .message-body { + border-color: #363636; + color: #2a2a2a; } + html.theme--documenter-dark .message.is-primary, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink { + background-color: #f6fbfd; } + html.theme--documenter-dark .message.is-primary .message-header, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-header { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .message.is-primary .message-body, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-body { + border-color: #4eb5de; + color: #1f556a; } + html.theme--documenter-dark .message.is-link { + background-color: #f6fdfe; } + html.theme--documenter-dark .message.is-link .message-header { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .message.is-link .message-body { + border-color: #2ad7e6; + color: #0c2f32; } + html.theme--documenter-dark .message.is-info { + background-color: #f6fafd; } + html.theme--documenter-dark .message.is-info .message-header { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .message.is-info .message-body { + border-color: #3489da; + color: #215485; } + html.theme--documenter-dark .message.is-success { + background-color: #f7fef6; } + html.theme--documenter-dark .message.is-success .message-header { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .message.is-success .message-body { + border-color: #259a12; + color: #113b0a; } + html.theme--documenter-dark .message.is-warning { + background-color: #fefcf5; } + html.theme--documenter-dark .message.is-warning .message-header { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .message.is-warning .message-body { + border-color: #f4c72f; + color: #332909; } + html.theme--documenter-dark .message.is-danger { + background-color: #fdf7f7; } + html.theme--documenter-dark .message.is-danger .message-header { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .message.is-danger .message-body { + border-color: #cb3c33; + color: #8d302a; } + html.theme--documenter-dark .message-header { + align-items: center; + background-color: #fbfbfb; + border-radius: 4px 4px 0 0; + color: rgba(0, 0, 0, 0.7); + display: flex; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.75em 1em; + position: relative; } + html.theme--documenter-dark .message-header .delete { + flex-grow: 0; + flex-shrink: 0; + margin-left: 0.75em; } + html.theme--documenter-dark .message-header + .message-body { + border-width: 0; + border-top-left-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .message-body { + border-color: #dbdbdb; + border-radius: 4px; + border-style: solid; + border-width: 0 0 0 4px; + color: #fbfbfb; + padding: 1.25em 1.5em; } + html.theme--documenter-dark .message-body code, + html.theme--documenter-dark .message-body pre { + background-color: white; } + html.theme--documenter-dark .message-body pre code { + background-color: transparent; } + html.theme--documenter-dark .modal { + align-items: center; + display: none; + flex-direction: column; + justify-content: center; + overflow: hidden; + position: fixed; + z-index: 40; } + html.theme--documenter-dark .modal.is-active { + display: flex; } + html.theme--documenter-dark .modal-background { + background-color: rgba(10, 10, 10, 0.86); } + html.theme--documenter-dark .modal-content, + html.theme--documenter-dark .modal-card { + margin: 0 20px; + max-height: calc(100vh - 160px); + overflow: auto; + position: relative; + width: 100%; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .modal-content, + html.theme--documenter-dark .modal-card { + margin: 0 auto; + max-height: calc(100vh - 40px); + width: 640px; } } + html.theme--documenter-dark .modal-close { + background: none; + height: 40px; + position: fixed; + right: 20px; + top: 20px; + width: 40px; } + html.theme--documenter-dark .modal-card { + display: flex; + flex-direction: column; + max-height: calc(100vh - 40px); + overflow: hidden; + -ms-overflow-y: visible; } + html.theme--documenter-dark .modal-card-head, + html.theme--documenter-dark .modal-card-foot { + align-items: center; + background-color: whitesmoke; + display: flex; + flex-shrink: 0; + justify-content: flex-start; + padding: 20px; + position: relative; } + html.theme--documenter-dark .modal-card-head { + border-bottom: 1px solid #dbdbdb; + border-top-left-radius: 6px; + border-top-right-radius: 6px; } + html.theme--documenter-dark .modal-card-title { + color: #cdc3e3; + flex-grow: 1; + flex-shrink: 0; + font-size: 1.5rem; + line-height: 1; } + html.theme--documenter-dark .modal-card-foot { + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark .modal-card-foot .button:not(:last-child) { + margin-right: 0.5em; } + html.theme--documenter-dark .modal-card-body { + -webkit-overflow-scrolling: touch; + background-color: white; + flex-grow: 1; + flex-shrink: 1; + overflow: auto; + padding: 20px; } + html.theme--documenter-dark .navbar { + background-color: white; + min-height: 3.25rem; + position: relative; + z-index: 30; } + html.theme--documenter-dark .navbar.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link { + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-burger { + color: #0a0a0a; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-white .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link { + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-dropdown a.navbar-item.is-active { + background-color: white; + color: #0a0a0a; } } + html.theme--documenter-dark .navbar.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link { + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link::after { + border-color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-burger { + color: white; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-black .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link { + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link::after { + border-color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-dropdown a.navbar-item.is-active { + background-color: #0a0a0a; + color: white; } } + html.theme--documenter-dark .navbar.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link { + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link::after { + border-color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-burger { + color: #363636; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-light .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link { + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link::after { + border-color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #363636; } } + html.theme--documenter-dark .navbar.is-dark, html.theme--documenter-dark .content kbd.navbar { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link { + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link::after { + border-color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-burger, html.theme--documenter-dark .content kbd.navbar .navbar-burger { + color: whitesmoke; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-dark .navbar-start > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-end > .navbar-item, + html.theme--documenter-dark .content kbd.navbar .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link { + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link::after, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link::after { + border-color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { + background-color: #363636; + color: whitesmoke; } } + html.theme--documenter-dark .navbar.is-primary, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-burger, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-primary .navbar-start > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-end > .navbar-item, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link::after, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { + background-color: #4eb5de; + color: #fff; } } + html.theme--documenter-dark .navbar.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-link .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-dropdown a.navbar-item.is-active { + background-color: #2ad7e6; + color: #fff; } } + html.theme--documenter-dark .navbar.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-info .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-dropdown a.navbar-item.is-active { + background-color: #3489da; + color: #fff; } } + html.theme--documenter-dark .navbar.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-success .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-dropdown a.navbar-item.is-active { + background-color: #259a12; + color: #fff; } } + html.theme--documenter-dark .navbar.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-burger { + color: rgba(0, 0, 0, 0.7); } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-warning .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } } + html.theme--documenter-dark .navbar.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-danger .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { + background-color: #cb3c33; + color: #fff; } } + html.theme--documenter-dark .navbar > .container { + align-items: stretch; + display: flex; + min-height: 3.25rem; + width: 100%; } + html.theme--documenter-dark .navbar.has-shadow { + box-shadow: 0 2px 0 0 whitesmoke; } + html.theme--documenter-dark .navbar.is-fixed-bottom, html.theme--documenter-dark .navbar.is-fixed-top { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom.has-shadow { + box-shadow: 0 -2px 0 0 whitesmoke; } + html.theme--documenter-dark .navbar.is-fixed-top { + top: 0; } + html.theme--documenter-dark html.has-navbar-fixed-top, + html.theme--documenter-dark body.has-navbar-fixed-top { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom, + html.theme--documenter-dark body.has-navbar-fixed-bottom { + padding-bottom: 3.25rem; } + html.theme--documenter-dark .navbar-brand, + html.theme--documenter-dark .navbar-tabs { + align-items: stretch; + display: flex; + flex-shrink: 0; + min-height: 3.25rem; } + html.theme--documenter-dark .navbar-brand a.navbar-item:focus, html.theme--documenter-dark .navbar-brand a.navbar-item:hover { + background-color: transparent; } + html.theme--documenter-dark .navbar-tabs { + -webkit-overflow-scrolling: touch; + max-width: 100vw; + overflow-x: auto; + overflow-y: hidden; } + html.theme--documenter-dark .navbar-burger { + color: #4a4a4a; + cursor: pointer; + display: block; + height: 3.25rem; + position: relative; + width: 3.25rem; + margin-left: auto; } + html.theme--documenter-dark .navbar-burger span { + background-color: currentColor; + display: block; + height: 1px; + left: calc(50% - 8px); + position: absolute; + transform-origin: center; + transition-duration: 86ms; + transition-property: background-color, opacity, transform; + transition-timing-function: ease-out; + width: 16px; } + html.theme--documenter-dark .navbar-burger span:nth-child(1) { + top: calc(50% - 6px); } + html.theme--documenter-dark .navbar-burger span:nth-child(2) { + top: calc(50% - 1px); } + html.theme--documenter-dark .navbar-burger span:nth-child(3) { + top: calc(50% + 4px); } + html.theme--documenter-dark .navbar-burger:hover { + background-color: rgba(0, 0, 0, 0.05); } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(1) { + transform: translateY(5px) rotate(45deg); } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(2) { + opacity: 0; } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(3) { + transform: translateY(-5px) rotate(-45deg); } + html.theme--documenter-dark .navbar-menu { + display: none; } + html.theme--documenter-dark .navbar-item, + html.theme--documenter-dark .navbar-link { + color: #4a4a4a; + display: block; + line-height: 1.5; + padding: 0.5rem 0.75rem; + position: relative; } + html.theme--documenter-dark .navbar-item .icon:only-child, + html.theme--documenter-dark .navbar-link .icon:only-child { + margin-left: -0.25rem; + margin-right: -0.25rem; } + html.theme--documenter-dark a.navbar-item, + html.theme--documenter-dark .navbar-link { + cursor: pointer; } + html.theme--documenter-dark a.navbar-item:focus, html.theme--documenter-dark a.navbar-item:focus-within, html.theme--documenter-dark a.navbar-item:hover, html.theme--documenter-dark a.navbar-item.is-active, + html.theme--documenter-dark .navbar-link:focus, + html.theme--documenter-dark .navbar-link:focus-within, + html.theme--documenter-dark .navbar-link:hover, + html.theme--documenter-dark .navbar-link.is-active { + background-color: #fafafa; + color: #2ad7e6; } + html.theme--documenter-dark .navbar-item { + display: block; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .navbar-item img { + max-height: 1.75rem; } + html.theme--documenter-dark .navbar-item.has-dropdown { + padding: 0; } + html.theme--documenter-dark .navbar-item.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .navbar-item.is-tab { + border-bottom: 1px solid transparent; + min-height: 3.25rem; + padding-bottom: calc(0.5rem - 1px); } + html.theme--documenter-dark .navbar-item.is-tab:focus, html.theme--documenter-dark .navbar-item.is-tab:hover { + background-color: transparent; + border-bottom-color: #2ad7e6; } + html.theme--documenter-dark .navbar-item.is-tab.is-active { + background-color: transparent; + border-bottom-color: #2ad7e6; + border-bottom-style: solid; + border-bottom-width: 3px; + color: #2ad7e6; + padding-bottom: calc(0.5rem - 3px); } + html.theme--documenter-dark .navbar-content { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .navbar-link:not(.is-arrowless) { + padding-right: 2.5em; } + html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after { + border-color: #2ad7e6; + margin-top: -0.375em; + right: 1.125em; } + html.theme--documenter-dark .navbar-dropdown { + font-size: 0.875rem; + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + html.theme--documenter-dark .navbar-dropdown .navbar-item { + padding-left: 1.5rem; + padding-right: 1.5rem; } + html.theme--documenter-dark .navbar-divider { + background-color: whitesmoke; + border: none; + display: none; + height: 2px; + margin: 0.5rem 0; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .navbar > .container { + display: block; } + html.theme--documenter-dark .navbar-brand .navbar-item, + html.theme--documenter-dark .navbar-tabs .navbar-item { + align-items: center; + display: flex; } + html.theme--documenter-dark .navbar-link::after { + display: none; } + html.theme--documenter-dark .navbar-menu { + background-color: white; + box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); + padding: 0.5rem 0; } + html.theme--documenter-dark .navbar-menu.is-active { + display: block; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch, html.theme--documenter-dark .navbar.is-fixed-top-touch { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .navbar.is-fixed-top-touch { + top: 0; } + html.theme--documenter-dark .navbar.is-fixed-top .navbar-menu, html.theme--documenter-dark .navbar.is-fixed-top-touch .navbar-menu { + -webkit-overflow-scrolling: touch; + max-height: calc(100vh - 3.25rem); + overflow: auto; } + html.theme--documenter-dark html.has-navbar-fixed-top-touch, + html.theme--documenter-dark body.has-navbar-fixed-top-touch { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom-touch, + html.theme--documenter-dark body.has-navbar-fixed-bottom-touch { + padding-bottom: 3.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar, + html.theme--documenter-dark .navbar-menu, + html.theme--documenter-dark .navbar-start, + html.theme--documenter-dark .navbar-end { + align-items: stretch; + display: flex; } + html.theme--documenter-dark .navbar { + min-height: 3.25rem; } + html.theme--documenter-dark .navbar.is-spaced { + padding: 1rem 2rem; } + html.theme--documenter-dark .navbar.is-spaced .navbar-start, + html.theme--documenter-dark .navbar.is-spaced .navbar-end { + align-items: center; } + html.theme--documenter-dark .navbar.is-spaced a.navbar-item, + html.theme--documenter-dark .navbar.is-spaced .navbar-link { + border-radius: 4px; } + html.theme--documenter-dark .navbar.is-transparent a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent a.navbar-item:hover, html.theme--documenter-dark .navbar.is-transparent a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-transparent .navbar-link:focus, + html.theme--documenter-dark .navbar.is-transparent .navbar-link:hover, + html.theme--documenter-dark .navbar.is-transparent .navbar-link.is-active { + background-color: transparent !important; } + html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { + background-color: transparent !important; } + html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #2ad7e6; } + html.theme--documenter-dark .navbar-burger { + display: none; } + html.theme--documenter-dark .navbar-item, + html.theme--documenter-dark .navbar-link { + align-items: center; + display: flex; } + html.theme--documenter-dark .navbar-item { + display: flex; } + html.theme--documenter-dark .navbar-item.has-dropdown { + align-items: stretch; } + html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-link::after { + transform: rotate(135deg) translate(0.25em, -0.25em); } + html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-dropdown { + border-bottom: 2px solid #dbdbdb; + border-radius: 6px 6px 0 0; + border-top: none; + bottom: 100%; + box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); + top: auto; } + html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown { + display: block; } + .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { + opacity: 1; + pointer-events: auto; + transform: translateY(0); } + html.theme--documenter-dark .navbar-menu { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .navbar-start { + justify-content: flex-start; + margin-right: auto; } + html.theme--documenter-dark .navbar-end { + justify-content: flex-end; + margin-left: auto; } + html.theme--documenter-dark .navbar-dropdown { + background-color: white; + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 2px solid #dbdbdb; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); + display: none; + font-size: 0.875rem; + left: 0; + min-width: 100%; + position: absolute; + top: 100%; + z-index: 20; } + html.theme--documenter-dark .navbar-dropdown .navbar-item { + padding: 0.375rem 1rem; + white-space: nowrap; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item { + padding-right: 3rem; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #2ad7e6; } + .navbar.is-spaced html.theme--documenter-dark .navbar-dropdown, html.theme--documenter-dark .navbar-dropdown.is-boxed { + border-radius: 6px; + border-top: none; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + display: block; + opacity: 0; + pointer-events: none; + top: calc(100% + (-4px)); + transform: translateY(-5px); + transition-duration: 86ms; + transition-property: opacity, transform; } + html.theme--documenter-dark .navbar-dropdown.is-right { + left: auto; + right: 0; } + html.theme--documenter-dark .navbar-divider { + display: block; } + html.theme--documenter-dark .navbar > .container .navbar-brand, + html.theme--documenter-dark .container > .navbar .navbar-brand { + margin-left: -.75rem; } + html.theme--documenter-dark .navbar > .container .navbar-menu, + html.theme--documenter-dark .container > .navbar .navbar-menu { + margin-right: -.75rem; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop, html.theme--documenter-dark .navbar.is-fixed-top-desktop { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .navbar.is-fixed-top-desktop { + top: 0; } + html.theme--documenter-dark html.has-navbar-fixed-top-desktop, + html.theme--documenter-dark body.has-navbar-fixed-top-desktop { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop, + html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop { + padding-bottom: 3.25rem; } + html.theme--documenter-dark html.has-spaced-navbar-fixed-top, + html.theme--documenter-dark body.has-spaced-navbar-fixed-top { + padding-top: 5.25rem; } + html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom, + html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom { + padding-bottom: 5.25rem; } + html.theme--documenter-dark a.navbar-item.is-active, + html.theme--documenter-dark .navbar-link.is-active { + color: #0a0a0a; } + html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover), + html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover) { + background-color: transparent; } + html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #fafafa; } } + html.theme--documenter-dark .hero.is-fullheight-with-navbar { + min-height: calc(100vh - 3.25rem); } + html.theme--documenter-dark .pagination { + font-size: 1rem; + margin: -0.25rem; } + html.theme--documenter-dark .pagination.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination { + font-size: 0.75rem; } + html.theme--documenter-dark .pagination.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .pagination.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .pagination.is-rounded .pagination-previous, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, + html.theme--documenter-dark .pagination.is-rounded .pagination-next, + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { + padding-left: 1em; + padding-right: 1em; + border-radius: 290486px; } + html.theme--documenter-dark .pagination.is-rounded .pagination-link, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { + border-radius: 290486px; } + html.theme--documenter-dark .pagination, + html.theme--documenter-dark .pagination-list { + align-items: center; + display: flex; + justify-content: center; + text-align: center; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark .pagination-link, + html.theme--documenter-dark .pagination-ellipsis { + font-size: 1em; + justify-content: center; + margin: 0.25rem; + padding-left: 0.5em; + padding-right: 0.5em; + text-align: center; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark .pagination-link { + border-color: #dbdbdb; + color: #363636; + min-width: 2.25em; } + html.theme--documenter-dark .pagination-previous:hover, + html.theme--documenter-dark .pagination-next:hover, + html.theme--documenter-dark .pagination-link:hover { + border-color: #b5b5b5; + color: #97ebf3; } + html.theme--documenter-dark .pagination-previous:focus, + html.theme--documenter-dark .pagination-next:focus, + html.theme--documenter-dark .pagination-link:focus { + border-color: #3c5dcd; } + html.theme--documenter-dark .pagination-previous:active, + html.theme--documenter-dark .pagination-next:active, + html.theme--documenter-dark .pagination-link:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } + html.theme--documenter-dark .pagination-previous[disabled], + html.theme--documenter-dark .pagination-next[disabled], + html.theme--documenter-dark .pagination-link[disabled] { + background-color: #dbdbdb; + border-color: #dbdbdb; + box-shadow: none; + color: #7a7a7a; + opacity: 0.5; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next { + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + html.theme--documenter-dark .pagination-link.is-current { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .pagination-ellipsis { + color: #b5b5b5; + pointer-events: none; } + html.theme--documenter-dark .pagination-list { + flex-wrap: wrap; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .pagination { + flex-wrap: wrap; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .pagination-list li { + flex-grow: 1; + flex-shrink: 1; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .pagination-list { + flex-grow: 1; + flex-shrink: 1; + justify-content: flex-start; + order: 1; } + html.theme--documenter-dark .pagination-previous { + order: 2; } + html.theme--documenter-dark .pagination-next { + order: 3; } + html.theme--documenter-dark .pagination { + justify-content: space-between; } + html.theme--documenter-dark .pagination.is-centered .pagination-previous { + order: 1; } + html.theme--documenter-dark .pagination.is-centered .pagination-list { + justify-content: center; + order: 2; } + html.theme--documenter-dark .pagination.is-centered .pagination-next { + order: 3; } + html.theme--documenter-dark .pagination.is-right .pagination-previous { + order: 1; } + html.theme--documenter-dark .pagination.is-right .pagination-next { + order: 2; } + html.theme--documenter-dark .pagination.is-right .pagination-list { + justify-content: flex-end; + order: 3; } } + html.theme--documenter-dark .panel { + font-size: 1rem; } + html.theme--documenter-dark .panel:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .panel-heading, + html.theme--documenter-dark .panel-tabs, + html.theme--documenter-dark .panel-block { + border-bottom: 1px solid #dbdbdb; + border-left: 1px solid #dbdbdb; + border-right: 1px solid #dbdbdb; } + html.theme--documenter-dark .panel-heading:first-child, + html.theme--documenter-dark .panel-tabs:first-child, + html.theme--documenter-dark .panel-block:first-child { + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark .panel-heading { + background-color: whitesmoke; + border-radius: 4px 4px 0 0; + color: #cdc3e3; + font-size: 1.25em; + font-weight: 300; + line-height: 1.25; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .panel-tabs { + align-items: flex-end; + display: flex; + font-size: 0.875em; + justify-content: center; } + html.theme--documenter-dark .panel-tabs a { + border-bottom: 1px solid #dbdbdb; + margin-bottom: -1px; + padding: 0.5em; } + html.theme--documenter-dark .panel-tabs a.is-active { + border-bottom-color: #4a4a4a; + color: #363636; } + html.theme--documenter-dark .panel-list a { + color: #fbfbfb; } + html.theme--documenter-dark .panel-list a:hover { + color: #2ad7e6; } + html.theme--documenter-dark .panel-block { + align-items: center; + color: #cdc3e3; + display: flex; + justify-content: flex-start; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .panel-block input[type="checkbox"] { + margin-right: 0.75em; } + html.theme--documenter-dark .panel-block > .control { + flex-grow: 1; + flex-shrink: 1; + width: 100%; } + html.theme--documenter-dark .panel-block.is-wrapped { + flex-wrap: wrap; } + html.theme--documenter-dark .panel-block.is-active { + border-left-color: #2ad7e6; + color: #363636; } + html.theme--documenter-dark .panel-block.is-active .panel-icon { + color: #2ad7e6; } + html.theme--documenter-dark a.panel-block, + html.theme--documenter-dark label.panel-block { + cursor: pointer; } + html.theme--documenter-dark a.panel-block:hover, + html.theme--documenter-dark label.panel-block:hover { + background-color: whitesmoke; } + html.theme--documenter-dark .panel-icon { + display: inline-block; + font-size: 14px; + height: 1em; + line-height: 1em; + text-align: center; + vertical-align: top; + width: 1em; + color: #7a7a7a; + margin-right: 0.75em; } + html.theme--documenter-dark .panel-icon .fa { + font-size: inherit; + line-height: inherit; } + html.theme--documenter-dark .tabs { + -webkit-overflow-scrolling: touch; + align-items: stretch; + display: flex; + font-size: 1rem; + justify-content: space-between; + overflow: hidden; + overflow-x: auto; + white-space: nowrap; } + html.theme--documenter-dark .tabs a { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + color: #fbfbfb; + display: flex; + justify-content: center; + margin-bottom: -1px; + padding: 0.5em 1em; + vertical-align: top; } + html.theme--documenter-dark .tabs a:hover { + border-bottom-color: #cdc3e3; + color: #cdc3e3; } + html.theme--documenter-dark .tabs li { + display: block; } + html.theme--documenter-dark .tabs li.is-active a { + border-bottom-color: #2ad7e6; + color: #2ad7e6; } + html.theme--documenter-dark .tabs ul { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + display: flex; + flex-grow: 1; + flex-shrink: 0; + justify-content: flex-start; } + html.theme--documenter-dark .tabs ul.is-left { + padding-right: 0.75em; } + html.theme--documenter-dark .tabs ul.is-center { + flex: none; + justify-content: center; + padding-left: 0.75em; + padding-right: 0.75em; } + html.theme--documenter-dark .tabs ul.is-right { + justify-content: flex-end; + padding-left: 0.75em; } + html.theme--documenter-dark .tabs .icon:first-child { + margin-right: 0.5em; } + html.theme--documenter-dark .tabs .icon:last-child { + margin-left: 0.5em; } + html.theme--documenter-dark .tabs.is-centered ul { + justify-content: center; } + html.theme--documenter-dark .tabs.is-right ul { + justify-content: flex-end; } + html.theme--documenter-dark .tabs.is-boxed a { + border: 1px solid transparent; + border-radius: 4px 4px 0 0; } + html.theme--documenter-dark .tabs.is-boxed a:hover { + background-color: whitesmoke; + border-bottom-color: #dbdbdb; } + html.theme--documenter-dark .tabs.is-boxed li.is-active a { + background-color: white; + border-color: #dbdbdb; + border-bottom-color: transparent !important; } + html.theme--documenter-dark .tabs.is-fullwidth li { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .tabs.is-toggle a { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px; + margin-bottom: 0; + position: relative; } + html.theme--documenter-dark .tabs.is-toggle a:hover { + background-color: whitesmoke; + border-color: #b5b5b5; + z-index: 2; } + html.theme--documenter-dark .tabs.is-toggle li + li { + margin-left: -1px; } + html.theme--documenter-dark .tabs.is-toggle li:first-child a { + border-radius: 4px 0 0 4px; } + html.theme--documenter-dark .tabs.is-toggle li:last-child a { + border-radius: 0 4px 4px 0; } + html.theme--documenter-dark .tabs.is-toggle li.is-active a { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; + z-index: 1; } + html.theme--documenter-dark .tabs.is-toggle ul { + border-bottom: none; } + html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:first-child a { + border-bottom-left-radius: 290486px; + border-top-left-radius: 290486px; + padding-left: 1.25em; } + html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:last-child a { + border-bottom-right-radius: 290486px; + border-top-right-radius: 290486px; + padding-right: 1.25em; } + html.theme--documenter-dark .tabs.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.tabs { + font-size: 0.75rem; } + html.theme--documenter-dark .tabs.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .tabs.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .column { + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + padding: 0.75rem; } + .columns.is-mobile > html.theme--documenter-dark .column.is-narrow { + flex: none; } + .columns.is-mobile > html.theme--documenter-dark .column.is-full { + flex: none; + width: 100%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-three-quarters { + flex: none; + width: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-two-thirds { + flex: none; + width: 66.6666%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-half { + flex: none; + width: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-third { + flex: none; + width: 33.3333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-quarter { + flex: none; + width: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-fifth { + flex: none; + width: 20%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-two-fifths { + flex: none; + width: 40%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-three-fifths { + flex: none; + width: 60%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-four-fifths { + flex: none; + width: 80%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-quarters { + margin-left: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-thirds { + margin-left: 66.6666%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-half { + margin-left: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-third { + margin-left: 33.3333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-quarter { + margin-left: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-fifth { + margin-left: 20%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-fifths { + margin-left: 40%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-fifths { + margin-left: 60%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-four-fifths { + margin-left: 80%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-0 { + flex: none; + width: 0%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-0 { + margin-left: 0%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-1 { + flex: none; + width: 8.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-1 { + margin-left: 8.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-2 { + flex: none; + width: 16.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-2 { + margin-left: 16.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-3 { + flex: none; + width: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-3 { + margin-left: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-4 { + flex: none; + width: 33.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-4 { + margin-left: 33.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-5 { + flex: none; + width: 41.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-5 { + margin-left: 41.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-6 { + flex: none; + width: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-6 { + margin-left: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-7 { + flex: none; + width: 58.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-7 { + margin-left: 58.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-8 { + flex: none; + width: 66.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-8 { + margin-left: 66.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-9 { + flex: none; + width: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-9 { + margin-left: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-10 { + flex: none; + width: 83.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-10 { + margin-left: 83.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-11 { + flex: none; + width: 91.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-11 { + margin-left: 91.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-12 { + flex: none; + width: 100%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-12 { + margin-left: 100%; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .column.is-narrow-mobile { + flex: none; } + html.theme--documenter-dark .column.is-full-mobile { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-mobile { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-mobile { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-mobile { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-mobile { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-mobile { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-mobile { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-mobile { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-mobile { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-mobile { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-mobile { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-mobile { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-mobile { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-mobile { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-mobile { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-mobile { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-mobile { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-mobile { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-mobile { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-mobile { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-mobile { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-mobile { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-mobile { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-mobile { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-mobile { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-mobile { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-mobile { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-mobile { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-mobile { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-mobile { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-mobile { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-mobile { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-mobile { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-mobile { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-mobile { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-mobile { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-mobile { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-mobile { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-mobile { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-mobile { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-mobile { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-mobile { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-mobile { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-mobile { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-mobile { + margin-left: 100%; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .column.is-narrow, html.theme--documenter-dark .column.is-narrow-tablet { + flex: none; } + html.theme--documenter-dark .column.is-full, html.theme--documenter-dark .column.is-full-tablet { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters, html.theme--documenter-dark .column.is-three-quarters-tablet { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds, html.theme--documenter-dark .column.is-two-thirds-tablet { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half, html.theme--documenter-dark .column.is-half-tablet { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third, html.theme--documenter-dark .column.is-one-third-tablet { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter, html.theme--documenter-dark .column.is-one-quarter-tablet { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth, html.theme--documenter-dark .column.is-one-fifth-tablet { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths, html.theme--documenter-dark .column.is-two-fifths-tablet { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths, html.theme--documenter-dark .column.is-three-fifths-tablet { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths, html.theme--documenter-dark .column.is-four-fifths-tablet { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters, html.theme--documenter-dark .column.is-offset-three-quarters-tablet { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds, html.theme--documenter-dark .column.is-offset-two-thirds-tablet { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half, html.theme--documenter-dark .column.is-offset-half-tablet { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third, html.theme--documenter-dark .column.is-offset-one-third-tablet { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter, html.theme--documenter-dark .column.is-offset-one-quarter-tablet { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth, html.theme--documenter-dark .column.is-offset-one-fifth-tablet { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths, html.theme--documenter-dark .column.is-offset-two-fifths-tablet { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths, html.theme--documenter-dark .column.is-offset-three-fifths-tablet { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths, html.theme--documenter-dark .column.is-offset-four-fifths-tablet { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0, html.theme--documenter-dark .column.is-0-tablet { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0, html.theme--documenter-dark .column.is-offset-0-tablet { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1, html.theme--documenter-dark .column.is-1-tablet { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1, html.theme--documenter-dark .column.is-offset-1-tablet { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2, html.theme--documenter-dark .column.is-2-tablet { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2, html.theme--documenter-dark .column.is-offset-2-tablet { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3, html.theme--documenter-dark .column.is-3-tablet { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3, html.theme--documenter-dark .column.is-offset-3-tablet { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4, html.theme--documenter-dark .column.is-4-tablet { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4, html.theme--documenter-dark .column.is-offset-4-tablet { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5, html.theme--documenter-dark .column.is-5-tablet { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5, html.theme--documenter-dark .column.is-offset-5-tablet { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6, html.theme--documenter-dark .column.is-6-tablet { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6, html.theme--documenter-dark .column.is-offset-6-tablet { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7, html.theme--documenter-dark .column.is-7-tablet { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7, html.theme--documenter-dark .column.is-offset-7-tablet { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8, html.theme--documenter-dark .column.is-8-tablet { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8, html.theme--documenter-dark .column.is-offset-8-tablet { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9, html.theme--documenter-dark .column.is-9-tablet { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9, html.theme--documenter-dark .column.is-offset-9-tablet { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10, html.theme--documenter-dark .column.is-10-tablet { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10, html.theme--documenter-dark .column.is-offset-10-tablet { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11, html.theme--documenter-dark .column.is-11-tablet { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11, html.theme--documenter-dark .column.is-offset-11-tablet { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12, html.theme--documenter-dark .column.is-12-tablet { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12, html.theme--documenter-dark .column.is-offset-12-tablet { + margin-left: 100%; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .column.is-narrow-touch { + flex: none; } + html.theme--documenter-dark .column.is-full-touch { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-touch { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-touch { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-touch { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-touch { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-touch { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-touch { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-touch { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-touch { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-touch { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-touch { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-touch { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-touch { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-touch { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-touch { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-touch { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-touch { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-touch { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-touch { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-touch { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-touch { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-touch { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-touch { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-touch { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-touch { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-touch { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-touch { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-touch { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-touch { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-touch { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-touch { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-touch { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-touch { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-touch { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-touch { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-touch { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-touch { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-touch { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-touch { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-touch { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-touch { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-touch { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-touch { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-touch { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-touch { + margin-left: 100%; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .column.is-narrow-desktop { + flex: none; } + html.theme--documenter-dark .column.is-full-desktop { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-desktop { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-desktop { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-desktop { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-desktop { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-desktop { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-desktop { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-desktop { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-desktop { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-desktop { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-desktop { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-desktop { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-desktop { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-desktop { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-desktop { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-desktop { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-desktop { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-desktop { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-desktop { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-desktop { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-desktop { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-desktop { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-desktop { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-desktop { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-desktop { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-desktop { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-desktop { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-desktop { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-desktop { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-desktop { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-desktop { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-desktop { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-desktop { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-desktop { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-desktop { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-desktop { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-desktop { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-desktop { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-desktop { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-desktop { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-desktop { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-desktop { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-desktop { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-desktop { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-desktop { + margin-left: 100%; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .column.is-narrow-widescreen { + flex: none; } + html.theme--documenter-dark .column.is-full-widescreen { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-widescreen { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-widescreen { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-widescreen { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-widescreen { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-widescreen { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-widescreen { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-widescreen { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-widescreen { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-widescreen { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-widescreen { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-widescreen { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-widescreen { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-widescreen { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-widescreen { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-widescreen { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-widescreen { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-widescreen { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-widescreen { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-widescreen { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-widescreen { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-widescreen { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-widescreen { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-widescreen { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-widescreen { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-widescreen { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-widescreen { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-widescreen { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-widescreen { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-widescreen { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-widescreen { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-widescreen { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-widescreen { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-widescreen { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-widescreen { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-widescreen { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-widescreen { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-widescreen { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-widescreen { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-widescreen { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-widescreen { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-widescreen { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-widescreen { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-widescreen { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-widescreen { + margin-left: 100%; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .column.is-narrow-fullhd { + flex: none; } + html.theme--documenter-dark .column.is-full-fullhd { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-fullhd { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-fullhd { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-fullhd { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-fullhd { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-fullhd { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-fullhd { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-fullhd { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-fullhd { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-fullhd { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-fullhd { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-fullhd { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-fullhd { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-fullhd { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-fullhd { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-fullhd { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-fullhd { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-fullhd { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-fullhd { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-fullhd { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-fullhd { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-fullhd { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-fullhd { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-fullhd { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-fullhd { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-fullhd { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-fullhd { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-fullhd { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-fullhd { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-fullhd { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-fullhd { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-fullhd { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-fullhd { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-fullhd { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-fullhd { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-fullhd { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-fullhd { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-fullhd { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-fullhd { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-fullhd { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-fullhd { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-fullhd { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-fullhd { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-fullhd { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-fullhd { + margin-left: 100%; } } + html.theme--documenter-dark .columns { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + html.theme--documenter-dark .columns:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .columns:not(:last-child) { + margin-bottom: calc(1.5rem - 0.75rem); } + html.theme--documenter-dark .columns.is-centered { + justify-content: center; } + html.theme--documenter-dark .columns.is-gapless { + margin-left: 0; + margin-right: 0; + margin-top: 0; } + html.theme--documenter-dark .columns.is-gapless > .column { + margin: 0; + padding: 0 !important; } + html.theme--documenter-dark .columns.is-gapless:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .columns.is-gapless:last-child { + margin-bottom: 0; } + html.theme--documenter-dark .columns.is-mobile { + display: flex; } + html.theme--documenter-dark .columns.is-multiline { + flex-wrap: wrap; } + html.theme--documenter-dark .columns.is-vcentered { + align-items: center; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns:not(.is-desktop) { + display: flex; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-desktop { + display: flex; } } + html.theme--documenter-dark .columns.is-variable { + --columnGap: 0.75rem; + margin-left: calc(-1 * var(--columnGap)); + margin-right: calc(-1 * var(--columnGap)); } + html.theme--documenter-dark .columns.is-variable .column { + padding-left: var(--columnGap); + padding-right: var(--columnGap); } + html.theme--documenter-dark .columns.is-variable.is-0 { + --columnGap: 0rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-0-mobile { + --columnGap: 0rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-0-tablet { + --columnGap: 0rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-0-tablet-only { + --columnGap: 0rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-0-touch { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-0-desktop { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-0-desktop-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-0-widescreen { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-0-widescreen-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-0-fullhd { + --columnGap: 0rem; } } + html.theme--documenter-dark .columns.is-variable.is-1 { + --columnGap: 0.25rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-1-mobile { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-1-tablet { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-1-tablet-only { + --columnGap: 0.25rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-1-touch { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-1-desktop { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-1-desktop-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-1-widescreen { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-1-widescreen-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-1-fullhd { + --columnGap: 0.25rem; } } + html.theme--documenter-dark .columns.is-variable.is-2 { + --columnGap: 0.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-2-mobile { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-2-tablet { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-2-tablet-only { + --columnGap: 0.5rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-2-touch { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-2-desktop { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-2-desktop-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-2-widescreen { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-2-widescreen-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-2-fullhd { + --columnGap: 0.5rem; } } + html.theme--documenter-dark .columns.is-variable.is-3 { + --columnGap: 0.75rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-3-mobile { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-3-tablet { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-3-tablet-only { + --columnGap: 0.75rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-3-touch { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-3-desktop { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-3-desktop-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-3-widescreen { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-3-widescreen-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-3-fullhd { + --columnGap: 0.75rem; } } + html.theme--documenter-dark .columns.is-variable.is-4 { + --columnGap: 1rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-4-mobile { + --columnGap: 1rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-4-tablet { + --columnGap: 1rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-4-tablet-only { + --columnGap: 1rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-4-touch { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-4-desktop { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-4-desktop-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-4-widescreen { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-4-widescreen-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-4-fullhd { + --columnGap: 1rem; } } + html.theme--documenter-dark .columns.is-variable.is-5 { + --columnGap: 1.25rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-5-mobile { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-5-tablet { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-5-tablet-only { + --columnGap: 1.25rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-5-touch { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-5-desktop { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-5-desktop-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-5-widescreen { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-5-widescreen-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-5-fullhd { + --columnGap: 1.25rem; } } + html.theme--documenter-dark .columns.is-variable.is-6 { + --columnGap: 1.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-6-mobile { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-6-tablet { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-6-tablet-only { + --columnGap: 1.5rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-6-touch { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-6-desktop { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-6-desktop-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-6-widescreen { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-6-widescreen-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-6-fullhd { + --columnGap: 1.5rem; } } + html.theme--documenter-dark .columns.is-variable.is-7 { + --columnGap: 1.75rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-7-mobile { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-7-tablet { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-7-tablet-only { + --columnGap: 1.75rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-7-touch { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-7-desktop { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-7-desktop-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-7-widescreen { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-7-fullhd { + --columnGap: 1.75rem; } } + html.theme--documenter-dark .columns.is-variable.is-8 { + --columnGap: 2rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-8-mobile { + --columnGap: 2rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-8-tablet { + --columnGap: 2rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-8-tablet-only { + --columnGap: 2rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-8-touch { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-8-desktop { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-8-desktop-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-8-widescreen { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-8-widescreen-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-8-fullhd { + --columnGap: 2rem; } } + html.theme--documenter-dark .tile { + align-items: stretch; + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + min-height: min-content; } + html.theme--documenter-dark .tile.is-ancestor { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + html.theme--documenter-dark .tile.is-ancestor:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .tile.is-ancestor:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .tile.is-child { + margin: 0 !important; } + html.theme--documenter-dark .tile.is-parent { + padding: 0.75rem; } + html.theme--documenter-dark .tile.is-vertical { + flex-direction: column; } + html.theme--documenter-dark .tile.is-vertical > .tile.is-child:not(:last-child) { + margin-bottom: 1.5rem !important; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .tile:not(.is-child) { + display: flex; } + html.theme--documenter-dark .tile.is-1 { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .tile.is-2 { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .tile.is-3 { + flex: none; + width: 25%; } + html.theme--documenter-dark .tile.is-4 { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .tile.is-5 { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .tile.is-6 { + flex: none; + width: 50%; } + html.theme--documenter-dark .tile.is-7 { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .tile.is-8 { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .tile.is-9 { + flex: none; + width: 75%; } + html.theme--documenter-dark .tile.is-10 { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .tile.is-11 { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .tile.is-12 { + flex: none; + width: 100%; } } + html.theme--documenter-dark .hero { + align-items: stretch; + display: flex; + flex-direction: column; + justify-content: space-between; } + html.theme--documenter-dark .hero .navbar { + background: none; } + html.theme--documenter-dark .hero .tabs ul { + border-bottom: none; } + html.theme--documenter-dark .hero.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-white strong { + color: inherit; } + html.theme--documenter-dark .hero.is-white .title { + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .subtitle { + color: rgba(10, 10, 10, 0.9); } + html.theme--documenter-dark .hero.is-white .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-white .subtitle strong { + color: #0a0a0a; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-white .navbar-menu { + background-color: white; } } + html.theme--documenter-dark .hero.is-white .navbar-item, + html.theme--documenter-dark .hero.is-white .navbar-link { + color: rgba(10, 10, 10, 0.7); } + html.theme--documenter-dark .hero.is-white a.navbar-item:hover, html.theme--documenter-dark .hero.is-white a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-white .navbar-link:hover, + html.theme--documenter-dark .hero.is-white .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .tabs a { + color: #0a0a0a; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-white .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-white .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a { + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a:hover { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .hero.is-white.is-bold { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-white.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } + html.theme--documenter-dark .hero.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-black strong { + color: inherit; } + html.theme--documenter-dark .hero.is-black .title { + color: white; } + html.theme--documenter-dark .hero.is-black .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-black .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-black .subtitle strong { + color: white; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-black .navbar-menu { + background-color: #0a0a0a; } } + html.theme--documenter-dark .hero.is-black .navbar-item, + html.theme--documenter-dark .hero.is-black .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-black a.navbar-item:hover, html.theme--documenter-dark .hero.is-black a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-black .navbar-link:hover, + html.theme--documenter-dark .hero.is-black .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .hero.is-black .tabs a { + color: white; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-black .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-black .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a { + color: white; } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a:hover { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-black.is-bold { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-black.is-bold .navbar-menu { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } + html.theme--documenter-dark .hero.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-light strong { + color: inherit; } + html.theme--documenter-dark .hero.is-light .title { + color: #363636; } + html.theme--documenter-dark .hero.is-light .subtitle { + color: rgba(54, 54, 54, 0.9); } + html.theme--documenter-dark .hero.is-light .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-light .subtitle strong { + color: #363636; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-light .navbar-menu { + background-color: whitesmoke; } } + html.theme--documenter-dark .hero.is-light .navbar-item, + html.theme--documenter-dark .hero.is-light .navbar-link { + color: rgba(54, 54, 54, 0.7); } + html.theme--documenter-dark .hero.is-light a.navbar-item:hover, html.theme--documenter-dark .hero.is-light a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-light .navbar-link:hover, + html.theme--documenter-dark .hero.is-light .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .hero.is-light .tabs a { + color: #363636; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-light .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-light .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a { + color: #363636; } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a:hover { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-light.is-bold { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-light.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } } + html.theme--documenter-dark .hero.is-dark, html.theme--documenter-dark .content kbd.hero { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-dark strong, + html.theme--documenter-dark .content kbd.hero strong { + color: inherit; } + html.theme--documenter-dark .hero.is-dark .title, html.theme--documenter-dark .content kbd.hero .title { + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .subtitle, html.theme--documenter-dark .content kbd.hero .subtitle { + color: rgba(245, 245, 245, 0.9); } + html.theme--documenter-dark .hero.is-dark .subtitle a:not(.button), html.theme--documenter-dark .content kbd.hero .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-dark .subtitle strong, + html.theme--documenter-dark .content kbd.hero .subtitle strong { + color: whitesmoke; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-dark .navbar-menu, html.theme--documenter-dark .content kbd.hero .navbar-menu { + background-color: #363636; } } + html.theme--documenter-dark .hero.is-dark .navbar-item, html.theme--documenter-dark .content kbd.hero .navbar-item, + html.theme--documenter-dark .hero.is-dark .navbar-link, + html.theme--documenter-dark .content kbd.hero .navbar-link { + color: rgba(245, 245, 245, 0.7); } + html.theme--documenter-dark .hero.is-dark a.navbar-item:hover, html.theme--documenter-dark .content kbd.hero a.navbar-item:hover, html.theme--documenter-dark .hero.is-dark a.navbar-item.is-active, html.theme--documenter-dark .content kbd.hero a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-dark .navbar-link:hover, + html.theme--documenter-dark .content kbd.hero .navbar-link:hover, + html.theme--documenter-dark .hero.is-dark .navbar-link.is-active, + html.theme--documenter-dark .content kbd.hero .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .tabs a, html.theme--documenter-dark .content kbd.hero .tabs a { + color: whitesmoke; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-dark .tabs a:hover, html.theme--documenter-dark .content kbd.hero .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-dark .tabs li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a { + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a:hover { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .hero.is-dark.is-bold, html.theme--documenter-dark .content kbd.hero.is-bold { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-dark.is-bold .navbar-menu, html.theme--documenter-dark .content kbd.hero.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } } + html.theme--documenter-dark .hero.is-primary, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-primary strong, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink strong { + color: inherit; } + html.theme--documenter-dark .hero.is-primary .title, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .title { + color: #fff; } + html.theme--documenter-dark .hero.is-primary .subtitle, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-primary .subtitle a:not(.button), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-primary .subtitle strong, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-primary .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-menu { + background-color: #4eb5de; } } + html.theme--documenter-dark .hero.is-primary .navbar-item, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-item, + html.theme--documenter-dark .hero.is-primary .navbar-link, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-primary a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, html.theme--documenter-dark .hero.is-primary a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-primary .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, + html.theme--documenter-dark .hero.is-primary .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .hero.is-primary .tabs a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-primary .tabs a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-primary .tabs li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .hero.is-primary.is-bold, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-primary.is-bold .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } } + html.theme--documenter-dark .hero.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-link strong { + color: inherit; } + html.theme--documenter-dark .hero.is-link .title { + color: #fff; } + html.theme--documenter-dark .hero.is-link .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-link .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-link .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-link .navbar-menu { + background-color: #2ad7e6; } } + html.theme--documenter-dark .hero.is-link .navbar-item, + html.theme--documenter-dark .hero.is-link .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-link a.navbar-item:hover, html.theme--documenter-dark .hero.is-link a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-link .navbar-link:hover, + html.theme--documenter-dark .hero.is-link .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .hero.is-link .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-link .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-link .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .hero.is-link.is-bold { + background-image: linear-gradient(141deg, #0cd0bf 0%, #2ad7e6 71%, #3bc2ee 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-link.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #0cd0bf 0%, #2ad7e6 71%, #3bc2ee 100%); } } + html.theme--documenter-dark .hero.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-info strong { + color: inherit; } + html.theme--documenter-dark .hero.is-info .title { + color: #fff; } + html.theme--documenter-dark .hero.is-info .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-info .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-info .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-info .navbar-menu { + background-color: #3489da; } } + html.theme--documenter-dark .hero.is-info .navbar-item, + html.theme--documenter-dark .hero.is-info .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-info a.navbar-item:hover, html.theme--documenter-dark .hero.is-info a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-info .navbar-link:hover, + html.theme--documenter-dark .hero.is-info .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .hero.is-info .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-info .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-info .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #3489da; } + html.theme--documenter-dark .hero.is-info.is-bold { + background-image: linear-gradient(141deg, #178cc4 0%, #3489da 71%, #447be3 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-info.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #178cc4 0%, #3489da 71%, #447be3 100%); } } + html.theme--documenter-dark .hero.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-success strong { + color: inherit; } + html.theme--documenter-dark .hero.is-success .title { + color: #fff; } + html.theme--documenter-dark .hero.is-success .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-success .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-success .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-success .navbar-menu { + background-color: #259a12; } } + html.theme--documenter-dark .hero.is-success .navbar-item, + html.theme--documenter-dark .hero.is-success .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-success a.navbar-item:hover, html.theme--documenter-dark .hero.is-success a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-success .navbar-link:hover, + html.theme--documenter-dark .hero.is-success .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .hero.is-success .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-success .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-success .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #259a12; } + html.theme--documenter-dark .hero.is-success.is-bold { + background-image: linear-gradient(141deg, #287207 0%, #259a12 71%, #10b614 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-success.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #287207 0%, #259a12 71%, #10b614 100%); } } + html.theme--documenter-dark .hero.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-warning strong { + color: inherit; } + html.theme--documenter-dark .hero.is-warning .title { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .subtitle { + color: rgba(0, 0, 0, 0.9); } + html.theme--documenter-dark .hero.is-warning .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-warning .subtitle strong { + color: rgba(0, 0, 0, 0.7); } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-warning .navbar-menu { + background-color: #f4c72f; } } + html.theme--documenter-dark .hero.is-warning .navbar-item, + html.theme--documenter-dark .hero.is-warning .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning a.navbar-item:hover, html.theme--documenter-dark .hero.is-warning a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-warning .navbar-link:hover, + html.theme--documenter-dark .hero.is-warning .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .tabs a { + color: rgba(0, 0, 0, 0.7); + opacity: 0.9; } + html.theme--documenter-dark .hero.is-warning .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-warning .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a:hover { + background-color: rgba(0, 0, 0, 0.7); + border-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .hero.is-warning.is-bold { + background-image: linear-gradient(141deg, #f09100 0%, #f4c72f 71%, #faef42 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-warning.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #f09100 0%, #f4c72f 71%, #faef42 100%); } } + html.theme--documenter-dark .hero.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-danger strong { + color: inherit; } + html.theme--documenter-dark .hero.is-danger .title { + color: #fff; } + html.theme--documenter-dark .hero.is-danger .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-danger .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-danger .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-danger .navbar-menu { + background-color: #cb3c33; } } + html.theme--documenter-dark .hero.is-danger .navbar-item, + html.theme--documenter-dark .hero.is-danger .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-danger a.navbar-item:hover, html.theme--documenter-dark .hero.is-danger a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-danger .navbar-link:hover, + html.theme--documenter-dark .hero.is-danger .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .hero.is-danger .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-danger .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-danger .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .hero.is-danger.is-bold { + background-image: linear-gradient(141deg, #ac1f2e 0%, #cb3c33 71%, #d66341 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-danger.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #ac1f2e 0%, #cb3c33 71%, #d66341 100%); } } + html.theme--documenter-dark .hero.is-small .hero-body, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.hero .hero-body { + padding-bottom: 1.5rem; + padding-top: 1.5rem; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero.is-medium .hero-body { + padding-bottom: 9rem; + padding-top: 9rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero.is-large .hero-body { + padding-bottom: 18rem; + padding-top: 18rem; } } + html.theme--documenter-dark .hero.is-halfheight .hero-body, html.theme--documenter-dark .hero.is-fullheight .hero-body, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body { + align-items: center; + display: flex; } + html.theme--documenter-dark .hero.is-halfheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body > .container { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .hero.is-halfheight { + min-height: 50vh; } + html.theme--documenter-dark .hero.is-fullheight { + min-height: 100vh; } + html.theme--documenter-dark .hero-video { + overflow: hidden; } + html.theme--documenter-dark .hero-video video { + left: 50%; + min-height: 100%; + min-width: 100%; + position: absolute; + top: 50%; + transform: translate3d(-50%, -50%, 0); } + html.theme--documenter-dark .hero-video.is-transparent { + opacity: 0.3; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero-video { + display: none; } } + html.theme--documenter-dark .hero-buttons { + margin-top: 1.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero-buttons .button { + display: flex; } + html.theme--documenter-dark .hero-buttons .button:not(:last-child) { + margin-bottom: 0.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero-buttons { + display: flex; + justify-content: center; } + html.theme--documenter-dark .hero-buttons .button:not(:last-child) { + margin-right: 1.5rem; } } + html.theme--documenter-dark .hero-head, + html.theme--documenter-dark .hero-foot { + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .hero-body { + flex-grow: 1; + flex-shrink: 0; + padding: 3rem 1.5rem; } + html.theme--documenter-dark .section { + padding: 3rem 1.5rem; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .section.is-medium { + padding: 9rem 1.5rem; } + html.theme--documenter-dark .section.is-large { + padding: 18rem 1.5rem; } } + html.theme--documenter-dark .footer { + background-color: #fafafa; + padding: 3rem 1.5rem 6rem; } + html.theme--documenter-dark h1 .docs-heading-anchor, html.theme--documenter-dark h1 .docs-heading-anchor:hover, html.theme--documenter-dark h1 .docs-heading-anchor:visited, html.theme--documenter-dark h2 .docs-heading-anchor, html.theme--documenter-dark h2 .docs-heading-anchor:hover, html.theme--documenter-dark h2 .docs-heading-anchor:visited, html.theme--documenter-dark h3 .docs-heading-anchor, html.theme--documenter-dark h3 .docs-heading-anchor:hover, html.theme--documenter-dark h3 .docs-heading-anchor:visited, html.theme--documenter-dark h4 .docs-heading-anchor, html.theme--documenter-dark h4 .docs-heading-anchor:hover, html.theme--documenter-dark h4 .docs-heading-anchor:visited, html.theme--documenter-dark h5 .docs-heading-anchor, html.theme--documenter-dark h5 .docs-heading-anchor:hover, html.theme--documenter-dark h5 .docs-heading-anchor:visited, html.theme--documenter-dark h6 .docs-heading-anchor, html.theme--documenter-dark h6 .docs-heading-anchor:hover, html.theme--documenter-dark h6 .docs-heading-anchor:visited { + color: #cdc3e3; } + html.theme--documenter-dark h1 .docs-heading-anchor-permalink, html.theme--documenter-dark h2 .docs-heading-anchor-permalink, html.theme--documenter-dark h3 .docs-heading-anchor-permalink, html.theme--documenter-dark h4 .docs-heading-anchor-permalink, html.theme--documenter-dark h5 .docs-heading-anchor-permalink, html.theme--documenter-dark h6 .docs-heading-anchor-permalink { + visibility: hidden; + vertical-align: middle; + margin-left: 0.5em; + font-size: 0.7rem; } + html.theme--documenter-dark h1 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h2 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h3 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h4 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h5 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h6 .docs-heading-anchor-permalink::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f0c1"; } + html.theme--documenter-dark h1:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h2:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h3:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h4:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h5:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h6:hover .docs-heading-anchor-permalink { + visibility: visible; } + html.theme--documenter-dark .docs-light-only { + display: none !important; } + html.theme--documenter-dark pre { + position: relative; + overflow: hidden; } + html.theme--documenter-dark pre code, html.theme--documenter-dark pre code.hljs { + padding: 0 0.75rem !important; + overflow: auto; + display: block; } + html.theme--documenter-dark pre code:first-of-type, html.theme--documenter-dark pre code.hljs:first-of-type { + padding-top: 0.5rem !important; } + html.theme--documenter-dark pre code:last-of-type, html.theme--documenter-dark pre code.hljs:last-of-type { + padding-bottom: 0.5rem !important; } + html.theme--documenter-dark pre .copy-button { + opacity: 0.2; + transition: opacity 0.2s; + position: absolute; + right: 0em; + top: 0em; + padding: 0.5em; + width: 2.5em; + height: 2.5em; + background: transparent; + border: none; + font-family: "Font Awesome 5 Free"; + color: #fbfbfb; + cursor: pointer; + text-align: center; } + html.theme--documenter-dark pre .copy-button:focus, html.theme--documenter-dark pre .copy-button:hover { + opacity: 1; + background: rgba(251, 251, 251, 0.1); + color: #2ad7e6; } + html.theme--documenter-dark pre .copy-button.success { + color: #259a12; + opacity: 1; } + html.theme--documenter-dark pre .copy-button.error { + color: #cb3c33; + opacity: 1; } + html.theme--documenter-dark pre:hover .copy-button { + opacity: 1; } + html.theme--documenter-dark .admonition { + background-color: #28282b; + border-style: solid; + border-width: 1px; + border-color: #ba3f1f; + border-radius: 4px; + font-size: 1rem; } + html.theme--documenter-dark .admonition strong { + color: currentColor; } + html.theme--documenter-dark .admonition.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.admonition { + font-size: 0.75rem; } + html.theme--documenter-dark .admonition.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .admonition.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .admonition.is-default { + background-color: #28282b; + border-color: #ba3f1f; } + html.theme--documenter-dark .admonition.is-default > .admonition-header { + background-color: #ba3f1f; } + html.theme--documenter-dark .admonition.is-info { + background-color: #28282b; + border-color: #28c; } + html.theme--documenter-dark .admonition.is-info > .admonition-header { + background-color: #28c; } + html.theme--documenter-dark .admonition.is-success { + background-color: #28282b; + border-color: #42ac68; } + html.theme--documenter-dark .admonition.is-success > .admonition-header { + background-color: #42ac68; } + html.theme--documenter-dark .admonition.is-warning { + background-color: #28282b; + border-color: #a88b17; } + html.theme--documenter-dark .admonition.is-warning > .admonition-header { + background-color: #a88b17; } + html.theme--documenter-dark .admonition.is-danger { + background-color: #28282b; + border-color: #c7524c; } + html.theme--documenter-dark .admonition.is-danger > .admonition-header { + background-color: #c7524c; } + html.theme--documenter-dark .admonition.is-compat { + background-color: #28282b; + border-color: #00a1b7; } + html.theme--documenter-dark .admonition.is-compat > .admonition-header { + background-color: #00a1b7; } + html.theme--documenter-dark .admonition-header { + background-color: #ba3f1f; + align-items: center; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.5rem 0.75rem; + position: relative; } + html.theme--documenter-dark .admonition-header:before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + margin-right: 0.75rem; + content: "\f06a"; } + html.theme--documenter-dark .admonition-body { + color: #fbfbfb; + padding: 0.5rem 0.75rem; } + html.theme--documenter-dark .admonition-body pre { + background-color: #312550; } + html.theme--documenter-dark .admonition-body code { + background-color: #312550; } + html.theme--documenter-dark .docstring { + margin-bottom: 1em; + background-color: transparent; + border: 1px solid #dbdbdb; + box-shadow: 3px 3px 4px #444444; + max-width: 100%; } + html.theme--documenter-dark .docstring > header { + display: flex; + flex-grow: 1; + align-items: stretch; + padding: 0.5rem 0.75rem; + background-color: #28282b; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + box-shadow: none; + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .docstring > header code { + background-color: transparent; } + html.theme--documenter-dark .docstring > header .docstring-binding { + margin-right: 0.3em; } + html.theme--documenter-dark .docstring > header .docstring-category { + margin-left: 0.3em; } + html.theme--documenter-dark .docstring > section { + position: relative; + padding: 0.75rem 0.75rem; + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .docstring > section:last-child { + border-bottom: none; } + html.theme--documenter-dark .docstring > section > a.docs-sourcelink { + transition: opacity 0.3s; + opacity: 0; + position: absolute; + right: 0.375rem; + bottom: 0.375rem; } + html.theme--documenter-dark .docstring > section > a.docs-sourcelink:focus { + opacity: 1 !important; } + html.theme--documenter-dark .docstring:hover > section > a.docs-sourcelink { + opacity: 0.2; } + html.theme--documenter-dark .docstring:focus-within > section > a.docs-sourcelink { + opacity: 0.2; } + html.theme--documenter-dark .docstring > section:hover a.docs-sourcelink { + opacity: 1; } + html.theme--documenter-dark .documenter-example-output { + background-color: #1e1e20; } + html.theme--documenter-dark .outdated-warning-overlay { + position: fixed; + top: 0; + left: 0; + right: 0; + box-shadow: 0 0 10px rgba(0, 0, 0, 0.3); + z-index: 999; + background-color: #28282b; + border-bottom: 3px solid #c7524c; + padding: 10px 35px; + text-align: center; + font-size: 15px; } + html.theme--documenter-dark .outdated-warning-overlay .outdated-warning-closer { + position: absolute; + top: calc(50% - 10px); + right: 18px; + cursor: pointer; + width: 12px; } + html.theme--documenter-dark .outdated-warning-overlay a { + color: #2ad7e6; } + html.theme--documenter-dark .outdated-warning-overlay a:hover { + color: #97ebf3; } + html.theme--documenter-dark .content pre { + border: 1px solid #dbdbdb; } + html.theme--documenter-dark .content code { + font-weight: inherit; } + html.theme--documenter-dark .content a code { + color: #2ad7e6; } + html.theme--documenter-dark .content h1 code, html.theme--documenter-dark .content h2 code, html.theme--documenter-dark .content h3 code, html.theme--documenter-dark .content h4 code, html.theme--documenter-dark .content h5 code, html.theme--documenter-dark .content h6 code { + color: #cdc3e3; } + html.theme--documenter-dark .content table { + display: block; + width: initial; + max-width: 100%; + overflow-x: auto; } + html.theme--documenter-dark .content blockquote > ul:first-child, html.theme--documenter-dark .content blockquote > ol:first-child, html.theme--documenter-dark .content .admonition-body > ul:first-child, html.theme--documenter-dark .content .admonition-body > ol:first-child { + margin-top: 0; } + html.theme--documenter-dark pre, html.theme--documenter-dark code { + font-variant-ligatures: no-contextual; } + html.theme--documenter-dark .breadcrumb a.is-disabled { + cursor: default; + pointer-events: none; } + html.theme--documenter-dark .breadcrumb a.is-disabled, html.theme--documenter-dark .breadcrumb a.is-disabled:hover { + color: #cdc3e3; } + html.theme--documenter-dark .hljs { + background: initial !important; } + html.theme--documenter-dark .katex .katex-mathml { + top: 0; + right: 0; } + html.theme--documenter-dark .katex-display, html.theme--documenter-dark mjx-container, html.theme--documenter-dark .MathJax_Display { + margin: 0.5em 0 !important; } + html.theme--documenter-dark html { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; } + html.theme--documenter-dark li.no-marker { + list-style: none; } + html.theme--documenter-dark #documenter .docs-main > article { + overflow-wrap: break-word; } + html.theme--documenter-dark #documenter .docs-main > article .math-container { + overflow-x: auto; + overflow-y: hidden; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-main { + max-width: 52rem; + margin-left: 20rem; + padding-right: 1rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main { + width: 100%; } + html.theme--documenter-dark #documenter .docs-main > article { + max-width: 52rem; + margin-left: auto; + margin-right: auto; + margin-bottom: 1rem; + padding: 0 1rem; } + html.theme--documenter-dark #documenter .docs-main > header, html.theme--documenter-dark #documenter .docs-main > nav { + max-width: 100%; + width: 100%; + margin: 0; } } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar { + background-color: #1e1e20; + border-bottom: 1px solid #dbdbdb; + z-index: 2; + min-height: 4rem; + margin-bottom: 1rem; + display: flex; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .breadcrumb { + flex-grow: 1; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right { + display: flex; + white-space: nowrap; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-icon, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + display: inline-block; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label { + padding: 0; + margin-left: 0.3em; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button { + margin: auto 0 auto 1rem; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + font-size: 1.5rem; + margin: auto 0 auto 1rem; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar > * { + margin: auto 0; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main header.docs-navbar { + position: sticky; + top: 0; + padding: 0 1rem; + /* For Headroom.js */ + transition-property: top, box-shadow; + -webkit-transition-property: top, box-shadow; + /* Safari */ + transition-duration: 0.3s; + -webkit-transition-duration: 0.3s; + /* Safari */ } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--not-top { + box-shadow: 0.2rem 0rem 0.4rem #bbb; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { + top: -4.5rem; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } } + html.theme--documenter-dark #documenter .docs-main section.footnotes { + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-main section.footnotes li .tag:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .content kbd:first-child, html.theme--documenter-dark .content #documenter .docs-main section.footnotes li kbd:first-child { + margin-right: 1em; + margin-bottom: 0.4em; } + html.theme--documenter-dark #documenter .docs-main .docs-footer { + display: flex; + flex-wrap: wrap; + margin-left: 0; + margin-right: 0; + border-top: 1px solid #dbdbdb; + padding-top: 1rem; + padding-bottom: 1rem; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main .docs-footer { + padding-left: 1rem; + padding-right: 1rem; } } + html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage, html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-prevpage { + flex-grow: 1; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage { + text-align: right; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .flexbox-break { + flex-basis: 100%; + height: 0; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .footer-message { + font-size: 0.8em; + margin: 0.5em auto 0 auto; + text-align: center; } + html.theme--documenter-dark #documenter .docs-sidebar { + display: flex; + flex-direction: column; + color: #fbfbfb; + background-color: #503c82; + border-right: 1px solid #dbdbdb; + padding: 0; + flex: 0 0 18rem; + z-index: 5; + font-size: 1rem; + position: fixed; + left: -18rem; + width: 18rem; + height: 100%; + transition: left 0.3s; + /* Setting up a nicer theme style for the scrollbar */ } + html.theme--documenter-dark #documenter .docs-sidebar.visible { + left: 0; + box-shadow: 0.4rem 0rem 0.8rem #bbb; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar.visible { + box-shadow: none; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar { + left: 0; + top: 0; } } + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo { + margin-top: 1rem; + padding: 0 1rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { + max-height: 6rem; + margin: auto; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name { + flex-shrink: 0; + font-size: 1.5rem; + font-weight: 700; + text-align: center; + white-space: nowrap; + overflow: hidden; + padding: 0.5rem 0; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name .docs-autofit { + max-width: 16.2rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a, html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a:hover { + color: #fbfbfb; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector { + border-top: 1px solid #dbdbdb; + display: none; + padding: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector.visible { + display: flex; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { + flex-grow: 1; + user-select: none; + border-top: 1px solid #dbdbdb; + padding-bottom: 1.5rem; + /* Managing collapsible submenus */ } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li > .tocitem { + font-weight: bold; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li li { + font-size: 0.95rem; + margin-left: 1em; + border-left: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input.collapse-toggle { + display: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.collapsed { + display: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed { + display: block; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem { + display: flex; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label { + flex-grow: 2; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron { + display: inline-block; + font-style: normal; + font-variant: normal; + text-rendering: auto; + line-height: 1; + font-size: 0.75rem; + margin-left: 1rem; + margin-top: auto; + margin-bottom: auto; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f054"; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before { + content: "\f078"; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem { + display: block; + padding: 0.5rem 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem:hover { + color: #fbfbfb; + background: #503c82; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem:hover { + color: #fbfbfb; + background-color: #3c2d60; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active { + border-top: 1px solid #dbdbdb; + border-bottom: 1px solid #dbdbdb; + background-color: #1e1e20; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover { + background-color: #1e1e20; + color: #fff; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover { + background-color: #3f2f66; + color: #fff; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child { + border-top: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal { + margin: 0 0.5rem 0.5rem; + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal li { + font-size: 0.85rem; + border-left: none; + margin-left: 0; + margin-top: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem { + width: 100%; + padding: 0; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before { + content: "⚬"; + margin-right: 0.4em; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search { + margin: auto; + margin-top: 0.5rem; + margin-bottom: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + width: 14.4rem; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar { + width: .3rem; + background: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #3f2f66; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover { + background: #2e224a; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-sidebar { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar { + width: .3rem; + background: none; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #3f2f66; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover { + background: #2e224a; } } + html.theme--documenter-dark #documenter .docs-main #documenter-search-info { + margin-bottom: 1rem; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results { + list-style-type: circle; + list-style-position: outside; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results li { + margin-left: 2rem; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results .docs-highlight { + background-color: yellow; } + html.theme--documenter-dark { + background-color: #1e1e20; + font-size: 16px; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + html.theme--documenter-dark #documenter .docs-sidebar { + border-right: none; + box-shadow: 0.24rem 0rem 0.4rem #444444; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + color: #fff; + background-color: #3f2f66; + border-color: #2e224a; + margin-top: 1.0rem; + margin-bottom: 1.0rem; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::placeholder { + color: #fff; } + html.theme--documenter-dark .hljs { + background: #2b2b2b; + color: #f8f8f2; } + html.theme--documenter-dark .hljs-comment, + html.theme--documenter-dark .hljs-quote { + color: #d4d0ab; } + html.theme--documenter-dark .hljs-variable, + html.theme--documenter-dark .hljs-template-variable, + html.theme--documenter-dark .hljs-tag, + html.theme--documenter-dark .hljs-name, + html.theme--documenter-dark .hljs-selector-id, + html.theme--documenter-dark .hljs-selector-class, + html.theme--documenter-dark .hljs-regexp, + html.theme--documenter-dark .hljs-deletion { + color: #ffa07a; } + html.theme--documenter-dark .hljs-number, + html.theme--documenter-dark .hljs-built_in, + html.theme--documenter-dark .hljs-literal, + html.theme--documenter-dark .hljs-type, + html.theme--documenter-dark .hljs-params, + html.theme--documenter-dark .hljs-meta, + html.theme--documenter-dark .hljs-link { + color: #f5ab35; } + html.theme--documenter-dark .hljs-attribute { + color: #ffd700; } + html.theme--documenter-dark .hljs-string, + html.theme--documenter-dark .hljs-symbol, + html.theme--documenter-dark .hljs-bullet, + html.theme--documenter-dark .hljs-addition { + color: #abe338; } + html.theme--documenter-dark .hljs-title, + html.theme--documenter-dark .hljs-section { + color: #00e0e0; } + html.theme--documenter-dark .hljs-keyword, + html.theme--documenter-dark .hljs-selector-tag { + color: #dcc6e0; } + html.theme--documenter-dark .hljs-emphasis { + font-style: italic; } + html.theme--documenter-dark .hljs-strong { + font-weight: bold; } + @media screen and (-ms-high-contrast: active) { + html.theme--documenter-dark .hljs-addition, + html.theme--documenter-dark .hljs-attribute, + html.theme--documenter-dark .hljs-built_in, + html.theme--documenter-dark .hljs-bullet, + html.theme--documenter-dark .hljs-comment, + html.theme--documenter-dark .hljs-link, + html.theme--documenter-dark .hljs-literal, + html.theme--documenter-dark .hljs-meta, + html.theme--documenter-dark .hljs-number, + html.theme--documenter-dark .hljs-params, + html.theme--documenter-dark .hljs-string, + html.theme--documenter-dark .hljs-symbol, + html.theme--documenter-dark .hljs-type, + html.theme--documenter-dark .hljs-quote { + color: highlight; } + html.theme--documenter-dark .hljs-keyword, + html.theme--documenter-dark .hljs-selector-tag { + font-weight: bold; } } + html.theme--documenter-dark .hljs-subst { + color: #f8f8f2; } diff --git a/previews/PR31/assets/themes/documenter-light.css b/previews/PR31/assets/themes/documenter-light.css new file mode 100644 index 00000000..e2c74638 --- /dev/null +++ b/previews/PR31/assets/themes/documenter-light.css @@ -0,0 +1,7750 @@ +@charset "UTF-8"; +/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */ +@keyframes spinAround { + from { + transform: rotate(0deg); } + to { + transform: rotate(359deg); } } + +.tabs, .pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis, .breadcrumb, .file, .button, .is-unselectable, .modal-close, .delete { + -webkit-touch-callout: none; + -webkit-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; } + +.navbar-link:not(.is-arrowless)::after, .select:not(.is-multiple):not(.is-loading)::after { + border: 3px solid transparent; + border-radius: 2px; + border-right: 0; + border-top: 0; + content: " "; + display: block; + height: 0.625em; + margin-top: -0.4375em; + pointer-events: none; + position: absolute; + top: 50%; + transform: rotate(-45deg); + transform-origin: center; + width: 0.625em; } + +.admonition:not(:last-child), .tabs:not(:last-child), .message:not(:last-child), .list:not(:last-child), .level:not(:last-child), .breadcrumb:not(:last-child), .highlight:not(:last-child), .block:not(:last-child), .title:not(:last-child), +.subtitle:not(:last-child), .table-container:not(:last-child), .table:not(:last-child), .progress:not(:last-child), .notification:not(:last-child), .content:not(:last-child), .box:not(:last-child) { + margin-bottom: 1.5rem; } + +.modal-close, .delete { + -moz-appearance: none; + -webkit-appearance: none; + background-color: rgba(10, 10, 10, 0.2); + border: none; + border-radius: 290486px; + cursor: pointer; + pointer-events: auto; + display: inline-block; + flex-grow: 0; + flex-shrink: 0; + font-size: 0; + height: 20px; + max-height: 20px; + max-width: 20px; + min-height: 20px; + min-width: 20px; + outline: none; + position: relative; + vertical-align: top; + width: 20px; } + .modal-close::before, .delete::before, .modal-close::after, .delete::after { + background-color: white; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + .modal-close::before, .delete::before { + height: 2px; + width: 50%; } + .modal-close::after, .delete::after { + height: 50%; + width: 2px; } + .modal-close:hover, .delete:hover, .modal-close:focus, .delete:focus { + background-color: rgba(10, 10, 10, 0.3); } + .modal-close:active, .delete:active { + background-color: rgba(10, 10, 10, 0.4); } + .is-small.modal-close, #documenter .docs-sidebar form.docs-search > input.modal-close, .is-small.delete, #documenter .docs-sidebar form.docs-search > input.delete { + height: 16px; + max-height: 16px; + max-width: 16px; + min-height: 16px; + min-width: 16px; + width: 16px; } + .is-medium.modal-close, .is-medium.delete { + height: 24px; + max-height: 24px; + max-width: 24px; + min-height: 24px; + min-width: 24px; + width: 24px; } + .is-large.modal-close, .is-large.delete { + height: 32px; + max-height: 32px; + max-width: 32px; + min-height: 32px; + min-width: 32px; + width: 32px; } + +.control.is-loading::after, .select.is-loading::after, .loader, .button.is-loading::after { + animation: spinAround 500ms infinite linear; + border: 2px solid #dbdbdb; + border-radius: 290486px; + border-right-color: transparent; + border-top-color: transparent; + content: ""; + display: block; + height: 1em; + position: relative; + width: 1em; } + +.hero-video, .modal-background, .modal, .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img, +.image.is-square .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img, +.image.is-1by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img, +.image.is-5by4 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img, +.image.is-4by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img, +.image.is-3by2 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img, +.image.is-5by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img, +.image.is-16by9 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img, +.image.is-2by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img, +.image.is-3by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img, +.image.is-4by5 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img, +.image.is-3by4 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img, +.image.is-2by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img, +.image.is-3by5 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img, +.image.is-9by16 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img, +.image.is-1by2 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img, +.image.is-1by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, .is-overlay { + bottom: 0; + left: 0; + position: absolute; + right: 0; + top: 0; } + +.pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis, .file-cta, +.file-name, .select select, .textarea, .input, #documenter .docs-sidebar form.docs-search > input, .button { + -moz-appearance: none; + -webkit-appearance: none; + align-items: center; + border: 1px solid transparent; + border-radius: 4px; + box-shadow: none; + display: inline-flex; + font-size: 1rem; + height: 2.25em; + justify-content: flex-start; + line-height: 1.5; + padding-bottom: calc(0.375em - 1px); + padding-left: calc(0.625em - 1px); + padding-right: calc(0.625em - 1px); + padding-top: calc(0.375em - 1px); + position: relative; + vertical-align: top; } + .pagination-previous:focus, + .pagination-next:focus, + .pagination-link:focus, + .pagination-ellipsis:focus, .file-cta:focus, + .file-name:focus, .select select:focus, .textarea:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .button:focus, .is-focused.pagination-previous, + .is-focused.pagination-next, + .is-focused.pagination-link, + .is-focused.pagination-ellipsis, .is-focused.file-cta, + .is-focused.file-name, .select select.is-focused, .is-focused.textarea, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-focused.button, .pagination-previous:active, + .pagination-next:active, + .pagination-link:active, + .pagination-ellipsis:active, .file-cta:active, + .file-name:active, .select select:active, .textarea:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .button:active, .is-active.pagination-previous, + .is-active.pagination-next, + .is-active.pagination-link, + .is-active.pagination-ellipsis, .is-active.file-cta, + .is-active.file-name, .select select.is-active, .is-active.textarea, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .is-active.button { + outline: none; } + .pagination-previous[disabled], + .pagination-next[disabled], + .pagination-link[disabled], + .pagination-ellipsis[disabled], .file-cta[disabled], + .file-name[disabled], .select select[disabled], .textarea[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], .button[disabled], fieldset[disabled] .pagination-previous, + fieldset[disabled] .pagination-next, + fieldset[disabled] .pagination-link, + fieldset[disabled] .pagination-ellipsis, fieldset[disabled] .file-cta, + fieldset[disabled] .file-name, fieldset[disabled] .select select, .select fieldset[disabled] select, fieldset[disabled] .textarea, fieldset[disabled] .input, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input, fieldset[disabled] .button { + cursor: not-allowed; } + +/*! minireset.css v0.0.4 | MIT License | github.com/jgthms/minireset.css */ +html, +body, +p, +ol, +ul, +li, +dl, +dt, +dd, +blockquote, +figure, +fieldset, +legend, +textarea, +pre, +iframe, +hr, +h1, +h2, +h3, +h4, +h5, +h6 { + margin: 0; + padding: 0; } + +h1, +h2, +h3, +h4, +h5, +h6 { + font-size: 100%; + font-weight: normal; } + +ul { + list-style: none; } + +button, +input, +select, +textarea { + margin: 0; } + +html { + box-sizing: border-box; } + +*, *::before, *::after { + box-sizing: inherit; } + +img, +embed, +iframe, +object, +video { + height: auto; + max-width: 100%; } + +audio { + max-width: 100%; } + +iframe { + border: 0; } + +table { + border-collapse: collapse; + border-spacing: 0; } + +td, +th { + padding: 0; } + td:not([align]), + th:not([align]) { + text-align: left; } + +html { + background-color: #fff; + font-size: 16px; + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + +article, +aside, +figure, +footer, +header, +hgroup, +section { + display: block; } + +body, +button, +input, +select, +textarea { + font-family: "Montserrat", sans-serif; } + +code, +pre { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; + font-family: "Source Code Pro", monospace; } + +body { + color: #202020; + font-size: 1em; + font-weight: 400; + line-height: 1.5; } + +a { + color: #149eaa; + cursor: pointer; + text-decoration: none; } + a strong { + color: currentColor; } + a:hover { + color: #107c85; } + +code { + background-color: #ebe8f4; + color: #000000; + font-size: 0.875em; + font-weight: normal; + padding: 0.1em; } + +hr { + background-color: whitesmoke; + border: none; + display: block; + height: 2px; + margin: 1.5rem 0; } + +img { + height: auto; + max-width: 100%; } + +input[type="checkbox"], +input[type="radio"] { + vertical-align: baseline; } + +small { + font-size: 0.875em; } + +span { + font-style: inherit; + font-weight: inherit; } + +strong { + color: #654ca3; + font-weight: 700; } + +fieldset { + border: none; } + +pre { + -webkit-overflow-scrolling: touch; + background-color: #ebe8f4; + color: #202020; + font-size: 0.875em; + overflow-x: auto; + padding: 1.25rem 1.5rem; + white-space: pre; + word-wrap: normal; } + pre code { + background-color: transparent; + color: currentColor; + font-size: 1em; + padding: 0; } + +table td, +table th { + vertical-align: top; } + table td:not([align]), + table th:not([align]) { + text-align: left; } + +table th { + color: #654ca3; } + +.is-clearfix::after { + clear: both; + content: " "; + display: table; } + +.is-pulled-left { + float: left !important; } + +.is-pulled-right { + float: right !important; } + +.is-clipped { + overflow: hidden !important; } + +.is-size-1 { + font-size: 3rem !important; } + +.is-size-2 { + font-size: 2.5rem !important; } + +.is-size-3 { + font-size: 2rem !important; } + +.is-size-4 { + font-size: 1.5rem !important; } + +.is-size-5 { + font-size: 1.25rem !important; } + +.is-size-6 { + font-size: 1rem !important; } + +.is-size-7, .docstring > section > a.docs-sourcelink { + font-size: 0.75rem !important; } + +@media screen and (max-width: 768px) { + .is-size-1-mobile { + font-size: 3rem !important; } + .is-size-2-mobile { + font-size: 2.5rem !important; } + .is-size-3-mobile { + font-size: 2rem !important; } + .is-size-4-mobile { + font-size: 1.5rem !important; } + .is-size-5-mobile { + font-size: 1.25rem !important; } + .is-size-6-mobile { + font-size: 1rem !important; } + .is-size-7-mobile { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 769px), print { + .is-size-1-tablet { + font-size: 3rem !important; } + .is-size-2-tablet { + font-size: 2.5rem !important; } + .is-size-3-tablet { + font-size: 2rem !important; } + .is-size-4-tablet { + font-size: 1.5rem !important; } + .is-size-5-tablet { + font-size: 1.25rem !important; } + .is-size-6-tablet { + font-size: 1rem !important; } + .is-size-7-tablet { + font-size: 0.75rem !important; } } + +@media screen and (max-width: 1055px) { + .is-size-1-touch { + font-size: 3rem !important; } + .is-size-2-touch { + font-size: 2.5rem !important; } + .is-size-3-touch { + font-size: 2rem !important; } + .is-size-4-touch { + font-size: 1.5rem !important; } + .is-size-5-touch { + font-size: 1.25rem !important; } + .is-size-6-touch { + font-size: 1rem !important; } + .is-size-7-touch { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1056px) { + .is-size-1-desktop { + font-size: 3rem !important; } + .is-size-2-desktop { + font-size: 2.5rem !important; } + .is-size-3-desktop { + font-size: 2rem !important; } + .is-size-4-desktop { + font-size: 1.5rem !important; } + .is-size-5-desktop { + font-size: 1.25rem !important; } + .is-size-6-desktop { + font-size: 1rem !important; } + .is-size-7-desktop { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1216px) { + .is-size-1-widescreen { + font-size: 3rem !important; } + .is-size-2-widescreen { + font-size: 2.5rem !important; } + .is-size-3-widescreen { + font-size: 2rem !important; } + .is-size-4-widescreen { + font-size: 1.5rem !important; } + .is-size-5-widescreen { + font-size: 1.25rem !important; } + .is-size-6-widescreen { + font-size: 1rem !important; } + .is-size-7-widescreen { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1408px) { + .is-size-1-fullhd { + font-size: 3rem !important; } + .is-size-2-fullhd { + font-size: 2.5rem !important; } + .is-size-3-fullhd { + font-size: 2rem !important; } + .is-size-4-fullhd { + font-size: 1.5rem !important; } + .is-size-5-fullhd { + font-size: 1.25rem !important; } + .is-size-6-fullhd { + font-size: 1rem !important; } + .is-size-7-fullhd { + font-size: 0.75rem !important; } } + +.has-text-centered { + text-align: center !important; } + +.has-text-justified { + text-align: justify !important; } + +.has-text-left { + text-align: left !important; } + +.has-text-right { + text-align: right !important; } + +@media screen and (max-width: 768px) { + .has-text-centered-mobile { + text-align: center !important; } } + +@media screen and (min-width: 769px), print { + .has-text-centered-tablet { + text-align: center !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-centered-tablet-only { + text-align: center !important; } } + +@media screen and (max-width: 1055px) { + .has-text-centered-touch { + text-align: center !important; } } + +@media screen and (min-width: 1056px) { + .has-text-centered-desktop { + text-align: center !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-centered-desktop-only { + text-align: center !important; } } + +@media screen and (min-width: 1216px) { + .has-text-centered-widescreen { + text-align: center !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-centered-widescreen-only { + text-align: center !important; } } + +@media screen and (min-width: 1408px) { + .has-text-centered-fullhd { + text-align: center !important; } } + +@media screen and (max-width: 768px) { + .has-text-justified-mobile { + text-align: justify !important; } } + +@media screen and (min-width: 769px), print { + .has-text-justified-tablet { + text-align: justify !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-justified-tablet-only { + text-align: justify !important; } } + +@media screen and (max-width: 1055px) { + .has-text-justified-touch { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) { + .has-text-justified-desktop { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-justified-desktop-only { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) { + .has-text-justified-widescreen { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-justified-widescreen-only { + text-align: justify !important; } } + +@media screen and (min-width: 1408px) { + .has-text-justified-fullhd { + text-align: justify !important; } } + +@media screen and (max-width: 768px) { + .has-text-left-mobile { + text-align: left !important; } } + +@media screen and (min-width: 769px), print { + .has-text-left-tablet { + text-align: left !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-left-tablet-only { + text-align: left !important; } } + +@media screen and (max-width: 1055px) { + .has-text-left-touch { + text-align: left !important; } } + +@media screen and (min-width: 1056px) { + .has-text-left-desktop { + text-align: left !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-left-desktop-only { + text-align: left !important; } } + +@media screen and (min-width: 1216px) { + .has-text-left-widescreen { + text-align: left !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-left-widescreen-only { + text-align: left !important; } } + +@media screen and (min-width: 1408px) { + .has-text-left-fullhd { + text-align: left !important; } } + +@media screen and (max-width: 768px) { + .has-text-right-mobile { + text-align: right !important; } } + +@media screen and (min-width: 769px), print { + .has-text-right-tablet { + text-align: right !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-right-tablet-only { + text-align: right !important; } } + +@media screen and (max-width: 1055px) { + .has-text-right-touch { + text-align: right !important; } } + +@media screen and (min-width: 1056px) { + .has-text-right-desktop { + text-align: right !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-right-desktop-only { + text-align: right !important; } } + +@media screen and (min-width: 1216px) { + .has-text-right-widescreen { + text-align: right !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-right-widescreen-only { + text-align: right !important; } } + +@media screen and (min-width: 1408px) { + .has-text-right-fullhd { + text-align: right !important; } } + +.is-capitalized { + text-transform: capitalize !important; } + +.is-lowercase { + text-transform: lowercase !important; } + +.is-uppercase { + text-transform: uppercase !important; } + +.is-italic { + font-style: italic !important; } + +.has-text-white { + color: white !important; } + +a.has-text-white:hover, a.has-text-white:focus { + color: #e6e6e6 !important; } + +.has-background-white { + background-color: white !important; } + +.has-text-black { + color: #0a0a0a !important; } + +a.has-text-black:hover, a.has-text-black:focus { + color: black !important; } + +.has-background-black { + background-color: #0a0a0a !important; } + +.has-text-light { + color: whitesmoke !important; } + +a.has-text-light:hover, a.has-text-light:focus { + color: #dbdbdb !important; } + +.has-background-light { + background-color: whitesmoke !important; } + +.has-text-dark { + color: #363636 !important; } + +a.has-text-dark:hover, a.has-text-dark:focus { + color: #1c1c1c !important; } + +.has-background-dark { + background-color: #363636 !important; } + +.has-text-primary { + color: #4eb5de !important; } + +a.has-text-primary:hover, a.has-text-primary:focus { + color: #27a1d2 !important; } + +.has-background-primary { + background-color: #4eb5de !important; } + +.has-text-link { + color: #149eaa !important; } + +a.has-text-link:hover, a.has-text-link:focus { + color: #0f747c !important; } + +.has-background-link { + background-color: #149eaa !important; } + +.has-text-info { + color: #209cee !important; } + +a.has-text-info:hover, a.has-text-info:focus { + color: #1081cb !important; } + +.has-background-info { + background-color: #209cee !important; } + +.has-text-success { + color: #22c35b !important; } + +a.has-text-success:hover, a.has-text-success:focus { + color: #1a9847 !important; } + +.has-background-success { + background-color: #22c35b !important; } + +.has-text-warning { + color: #ffdd57 !important; } + +a.has-text-warning:hover, a.has-text-warning:focus { + color: #ffd324 !important; } + +.has-background-warning { + background-color: #ffdd57 !important; } + +.has-text-danger { + color: #da0b00 !important; } + +a.has-text-danger:hover, a.has-text-danger:focus { + color: #a70800 !important; } + +.has-background-danger { + background-color: #da0b00 !important; } + +.has-text-black-bis { + color: #121212 !important; } + +.has-background-black-bis { + background-color: #121212 !important; } + +.has-text-black-ter { + color: #242424 !important; } + +.has-background-black-ter { + background-color: #242424 !important; } + +.has-text-grey-darker { + color: #363636 !important; } + +.has-background-grey-darker { + background-color: #363636 !important; } + +.has-text-grey-dark { + color: #4a4a4a !important; } + +.has-background-grey-dark { + background-color: #4a4a4a !important; } + +.has-text-grey { + color: #6b6b6b !important; } + +.has-background-grey { + background-color: #6b6b6b !important; } + +.has-text-grey-light { + color: #b5b5b5 !important; } + +.has-background-grey-light { + background-color: #b5b5b5 !important; } + +.has-text-grey-lighter { + color: #dbdbdb !important; } + +.has-background-grey-lighter { + background-color: #dbdbdb !important; } + +.has-text-white-ter { + color: whitesmoke !important; } + +.has-background-white-ter { + background-color: whitesmoke !important; } + +.has-text-white-bis { + color: #fafafa !important; } + +.has-background-white-bis { + background-color: #fafafa !important; } + +.has-text-weight-light { + font-weight: 300 !important; } + +.has-text-weight-normal { + font-weight: 400 !important; } + +.has-text-weight-medium { + font-weight: 500 !important; } + +.has-text-weight-semibold { + font-weight: 600 !important; } + +.has-text-weight-bold { + font-weight: 700 !important; } + +.is-family-primary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-secondary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-sans-serif { + font-family: "Montserrat", sans-serif !important; } + +.is-family-monospace { + font-family: "Source Code Pro", monospace !important; } + +.is-family-code { + font-family: "Source Code Pro", monospace !important; } + +.is-block { + display: block !important; } + +@media screen and (max-width: 768px) { + .is-block-mobile { + display: block !important; } } + +@media screen and (min-width: 769px), print { + .is-block-tablet { + display: block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-block-tablet-only { + display: block !important; } } + +@media screen and (max-width: 1055px) { + .is-block-touch { + display: block !important; } } + +@media screen and (min-width: 1056px) { + .is-block-desktop { + display: block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-block-desktop-only { + display: block !important; } } + +@media screen and (min-width: 1216px) { + .is-block-widescreen { + display: block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-block-widescreen-only { + display: block !important; } } + +@media screen and (min-width: 1408px) { + .is-block-fullhd { + display: block !important; } } + +.is-flex { + display: flex !important; } + +@media screen and (max-width: 768px) { + .is-flex-mobile { + display: flex !important; } } + +@media screen and (min-width: 769px), print { + .is-flex-tablet { + display: flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-flex-tablet-only { + display: flex !important; } } + +@media screen and (max-width: 1055px) { + .is-flex-touch { + display: flex !important; } } + +@media screen and (min-width: 1056px) { + .is-flex-desktop { + display: flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-flex-desktop-only { + display: flex !important; } } + +@media screen and (min-width: 1216px) { + .is-flex-widescreen { + display: flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-flex-widescreen-only { + display: flex !important; } } + +@media screen and (min-width: 1408px) { + .is-flex-fullhd { + display: flex !important; } } + +.is-inline { + display: inline !important; } + +@media screen and (max-width: 768px) { + .is-inline-mobile { + display: inline !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-tablet { + display: inline !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-tablet-only { + display: inline !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-touch { + display: inline !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-desktop { + display: inline !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-desktop-only { + display: inline !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-widescreen { + display: inline !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-widescreen-only { + display: inline !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-fullhd { + display: inline !important; } } + +.is-inline-block { + display: inline-block !important; } + +@media screen and (max-width: 768px) { + .is-inline-block-mobile { + display: inline-block !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-block-tablet { + display: inline-block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-block-tablet-only { + display: inline-block !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-block-touch { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-block-desktop { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-block-desktop-only { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-block-widescreen { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-block-widescreen-only { + display: inline-block !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-block-fullhd { + display: inline-block !important; } } + +.is-inline-flex { + display: inline-flex !important; } + +@media screen and (max-width: 768px) { + .is-inline-flex-mobile { + display: inline-flex !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-flex-tablet { + display: inline-flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-flex-tablet-only { + display: inline-flex !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-flex-touch { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-flex-desktop { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-flex-desktop-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-flex-widescreen { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-flex-widescreen-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-flex-fullhd { + display: inline-flex !important; } } + +.is-hidden { + display: none !important; } + +.is-sr-only { + border: none !important; + clip: rect(0, 0, 0, 0) !important; + height: 0.01em !important; + overflow: hidden !important; + padding: 0 !important; + position: absolute !important; + white-space: nowrap !important; + width: 0.01em !important; } + +@media screen and (max-width: 768px) { + .is-hidden-mobile { + display: none !important; } } + +@media screen and (min-width: 769px), print { + .is-hidden-tablet { + display: none !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-hidden-tablet-only { + display: none !important; } } + +@media screen and (max-width: 1055px) { + .is-hidden-touch { + display: none !important; } } + +@media screen and (min-width: 1056px) { + .is-hidden-desktop { + display: none !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-hidden-desktop-only { + display: none !important; } } + +@media screen and (min-width: 1216px) { + .is-hidden-widescreen { + display: none !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-hidden-widescreen-only { + display: none !important; } } + +@media screen and (min-width: 1408px) { + .is-hidden-fullhd { + display: none !important; } } + +.is-invisible { + visibility: hidden !important; } + +@media screen and (max-width: 768px) { + .is-invisible-mobile { + visibility: hidden !important; } } + +@media screen and (min-width: 769px), print { + .is-invisible-tablet { + visibility: hidden !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-invisible-tablet-only { + visibility: hidden !important; } } + +@media screen and (max-width: 1055px) { + .is-invisible-touch { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) { + .is-invisible-desktop { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-invisible-desktop-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) { + .is-invisible-widescreen { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-invisible-widescreen-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1408px) { + .is-invisible-fullhd { + visibility: hidden !important; } } + +.is-marginless { + margin: 0 !important; } + +.is-paddingless { + padding: 0 !important; } + +.is-radiusless { + border-radius: 0 !important; } + +.is-shadowless { + box-shadow: none !important; } + +.is-relative { + position: relative !important; } + +.box { + background-color: white; + border-radius: 6px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #202020; + display: block; + padding: 1.25rem; } + +a.box:hover, a.box:focus { + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #149eaa; } + +a.box:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #149eaa; } + +.button { + background-color: white; + border-color: #dbdbdb; + border-width: 1px; + color: #363636; + cursor: pointer; + justify-content: center; + padding-bottom: calc(0.375em - 1px); + padding-left: 0.75em; + padding-right: 0.75em; + padding-top: calc(0.375em - 1px); + text-align: center; + white-space: nowrap; } + .button strong { + color: inherit; } + .button .icon, .button .icon.is-small, .button #documenter .docs-sidebar form.docs-search > input.icon, #documenter .docs-sidebar .button form.docs-search > input.icon, .button .icon.is-medium, .button .icon.is-large { + height: 1.5em; + width: 1.5em; } + .button .icon:first-child:not(:last-child) { + margin-left: calc(-0.375em - 1px); + margin-right: 0.1875em; } + .button .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: calc(-0.375em - 1px); } + .button .icon:first-child:last-child { + margin-left: calc(-0.375em - 1px); + margin-right: calc(-0.375em - 1px); } + .button:hover, .button.is-hovered { + border-color: #b5b5b5; + color: #107c85; } + .button:focus, .button.is-focused { + border-color: #3c5dcd; + color: #363636; } + .button:focus:not(:active), .button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .button:active, .button.is-active { + border-color: #4a4a4a; + color: #363636; } + .button.is-text { + background-color: transparent; + border-color: transparent; + color: #202020; + text-decoration: underline; } + .button.is-text:hover, .button.is-text.is-hovered, .button.is-text:focus, .button.is-text.is-focused { + background-color: whitesmoke; + color: #654ca3; } + .button.is-text:active, .button.is-text.is-active { + background-color: #e8e8e8; + color: #654ca3; } + .button.is-text[disabled], fieldset[disabled] .button.is-text { + background-color: transparent; + border-color: transparent; + box-shadow: none; } + .button.is-white { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + .button.is-white:hover, .button.is-white.is-hovered { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + .button.is-white:focus, .button.is-white.is-focused { + border-color: transparent; + color: #0a0a0a; } + .button.is-white:focus:not(:active), .button.is-white.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .button.is-white:active, .button.is-white.is-active { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + .button.is-white[disabled], fieldset[disabled] .button.is-white { + background-color: white; + border-color: transparent; + box-shadow: none; } + .button.is-white.is-inverted { + background-color: #0a0a0a; + color: white; } + .button.is-white.is-inverted:hover, .button.is-white.is-inverted.is-hovered { + background-color: black; } + .button.is-white.is-inverted[disabled], fieldset[disabled] .button.is-white.is-inverted { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; + color: white; } + .button.is-white.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + .button.is-white.is-outlined:hover, .button.is-white.is-outlined.is-hovered, .button.is-white.is-outlined:focus, .button.is-white.is-outlined.is-focused { + background-color: white; + border-color: white; + color: #0a0a0a; } + .button.is-white.is-outlined.is-loading::after { + border-color: transparent transparent white white !important; } + .button.is-white.is-outlined.is-loading:hover::after, .button.is-white.is-outlined.is-loading.is-hovered::after, .button.is-white.is-outlined.is-loading:focus::after, .button.is-white.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-white.is-outlined[disabled], fieldset[disabled] .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + .button.is-white.is-inverted.is-outlined:hover, .button.is-white.is-inverted.is-outlined.is-hovered, .button.is-white.is-inverted.is-outlined:focus, .button.is-white.is-inverted.is-outlined.is-focused { + background-color: #0a0a0a; + color: white; } + .button.is-white.is-inverted.is-outlined.is-loading:hover::after, .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-white.is-inverted.is-outlined.is-loading:focus::after, .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + .button.is-white.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + .button.is-black:hover, .button.is-black.is-hovered { + background-color: #040404; + border-color: transparent; + color: white; } + .button.is-black:focus, .button.is-black.is-focused { + border-color: transparent; + color: white; } + .button.is-black:focus:not(:active), .button.is-black.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .button.is-black:active, .button.is-black.is-active { + background-color: black; + border-color: transparent; + color: white; } + .button.is-black[disabled], fieldset[disabled] .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; } + .button.is-black.is-inverted { + background-color: white; + color: #0a0a0a; } + .button.is-black.is-inverted:hover, .button.is-black.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-black.is-inverted[disabled], fieldset[disabled] .button.is-black.is-inverted { + background-color: white; + border-color: transparent; + box-shadow: none; + color: #0a0a0a; } + .button.is-black.is-loading::after { + border-color: transparent transparent white white !important; } + .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + .button.is-black.is-outlined:hover, .button.is-black.is-outlined.is-hovered, .button.is-black.is-outlined:focus, .button.is-black.is-outlined.is-focused { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .button.is-black.is-outlined.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-black.is-outlined.is-loading:hover::after, .button.is-black.is-outlined.is-loading.is-hovered::after, .button.is-black.is-outlined.is-loading:focus::after, .button.is-black.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + .button.is-black.is-outlined[disabled], fieldset[disabled] .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + .button.is-black.is-inverted.is-outlined:hover, .button.is-black.is-inverted.is-outlined.is-hovered, .button.is-black.is-inverted.is-outlined:focus, .button.is-black.is-inverted.is-outlined.is-focused { + background-color: white; + color: #0a0a0a; } + .button.is-black.is-inverted.is-outlined.is-loading:hover::after, .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-black.is-inverted.is-outlined.is-loading:focus::after, .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + .button.is-light { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + .button.is-light:hover, .button.is-light.is-hovered { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + .button.is-light:focus, .button.is-light.is-focused { + border-color: transparent; + color: #363636; } + .button.is-light:focus:not(:active), .button.is-light.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .button.is-light:active, .button.is-light.is-active { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + .button.is-light[disabled], fieldset[disabled] .button.is-light { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; } + .button.is-light.is-inverted { + background-color: #363636; + color: whitesmoke; } + .button.is-light.is-inverted:hover, .button.is-light.is-inverted.is-hovered { + background-color: #292929; } + .button.is-light.is-inverted[disabled], fieldset[disabled] .button.is-light.is-inverted { + background-color: #363636; + border-color: transparent; + box-shadow: none; + color: whitesmoke; } + .button.is-light.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + .button.is-light.is-outlined:hover, .button.is-light.is-outlined.is-hovered, .button.is-light.is-outlined:focus, .button.is-light.is-outlined.is-focused { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .button.is-light.is-outlined.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-light.is-outlined.is-loading:hover::after, .button.is-light.is-outlined.is-loading.is-hovered::after, .button.is-light.is-outlined.is-loading:focus::after, .button.is-light.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-light.is-outlined[disabled], fieldset[disabled] .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + .button.is-light.is-inverted.is-outlined:hover, .button.is-light.is-inverted.is-outlined.is-hovered, .button.is-light.is-inverted.is-outlined:focus, .button.is-light.is-inverted.is-outlined.is-focused { + background-color: #363636; + color: whitesmoke; } + .button.is-light.is-inverted.is-outlined.is-loading:hover::after, .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-light.is-inverted.is-outlined.is-loading:focus::after, .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + .button.is-dark, .content kbd.button { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + .button.is-dark:hover, .content kbd.button:hover, .button.is-dark.is-hovered, .content kbd.button.is-hovered { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + .button.is-dark:focus, .content kbd.button:focus, .button.is-dark.is-focused, .content kbd.button.is-focused { + border-color: transparent; + color: whitesmoke; } + .button.is-dark:focus:not(:active), .content kbd.button:focus:not(:active), .button.is-dark.is-focused:not(:active), .content kbd.button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .button.is-dark:active, .content kbd.button:active, .button.is-dark.is-active, .content kbd.button.is-active { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + .button.is-dark[disabled], .content kbd.button[disabled], fieldset[disabled] .button.is-dark, fieldset[disabled] .content kbd.button, .content fieldset[disabled] kbd.button { + background-color: #363636; + border-color: transparent; + box-shadow: none; } + .button.is-dark.is-inverted, .content kbd.button.is-inverted { + background-color: whitesmoke; + color: #363636; } + .button.is-dark.is-inverted:hover, .content kbd.button.is-inverted:hover, .button.is-dark.is-inverted.is-hovered, .content kbd.button.is-inverted.is-hovered { + background-color: #e8e8e8; } + .button.is-dark.is-inverted[disabled], .content kbd.button.is-inverted[disabled], fieldset[disabled] .button.is-dark.is-inverted, fieldset[disabled] .content kbd.button.is-inverted, .content fieldset[disabled] kbd.button.is-inverted { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; + color: #363636; } + .button.is-dark.is-loading::after, .content kbd.button.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-dark.is-outlined, .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + .button.is-dark.is-outlined:hover, .content kbd.button.is-outlined:hover, .button.is-dark.is-outlined.is-hovered, .content kbd.button.is-outlined.is-hovered, .button.is-dark.is-outlined:focus, .content kbd.button.is-outlined:focus, .button.is-dark.is-outlined.is-focused, .content kbd.button.is-outlined.is-focused { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .button.is-dark.is-outlined.is-loading::after, .content kbd.button.is-outlined.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-dark.is-outlined.is-loading:hover::after, .content kbd.button.is-outlined.is-loading:hover::after, .button.is-dark.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-outlined.is-loading:focus::after, .content kbd.button.is-outlined.is-loading:focus::after, .button.is-dark.is-outlined.is-loading.is-focused::after, .content kbd.button.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-dark.is-outlined[disabled], .content kbd.button.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-outlined, fieldset[disabled] .content kbd.button.is-outlined, .content fieldset[disabled] kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + .button.is-dark.is-inverted.is-outlined, .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + .button.is-dark.is-inverted.is-outlined:hover, .content kbd.button.is-inverted.is-outlined:hover, .button.is-dark.is-inverted.is-outlined.is-hovered, .content kbd.button.is-inverted.is-outlined.is-hovered, .button.is-dark.is-inverted.is-outlined:focus, .content kbd.button.is-inverted.is-outlined:focus, .button.is-dark.is-inverted.is-outlined.is-focused, .content kbd.button.is-inverted.is-outlined.is-focused { + background-color: whitesmoke; + color: #363636; } + .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-dark.is-inverted.is-outlined[disabled], .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-inverted.is-outlined, fieldset[disabled] .content kbd.button.is-inverted.is-outlined, .content fieldset[disabled] kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + .button.is-primary, .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + .button.is-primary:hover, .docstring > section > a.button.docs-sourcelink:hover, .button.is-primary.is-hovered, .docstring > section > a.button.is-hovered.docs-sourcelink { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + .button.is-primary:focus, .docstring > section > a.button.docs-sourcelink:focus, .button.is-primary.is-focused, .docstring > section > a.button.is-focused.docs-sourcelink { + border-color: transparent; + color: #fff; } + .button.is-primary:focus:not(:active), .docstring > section > a.button.docs-sourcelink:focus:not(:active), .button.is-primary.is-focused:not(:active), .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .button.is-primary:active, .docstring > section > a.button.docs-sourcelink:active, .button.is-primary.is-active, .docstring > section > a.button.is-active.docs-sourcelink { + background-color: #39acda; + border-color: transparent; + color: #fff; } + .button.is-primary[disabled], .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary, fieldset[disabled] .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + box-shadow: none; } + .button.is-primary.is-inverted, .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + .button.is-primary.is-inverted:hover, .docstring > section > a.button.is-inverted.docs-sourcelink:hover, .button.is-primary.is-inverted.is-hovered, .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { + background-color: #f2f2f2; } + .button.is-primary.is-inverted[disabled], .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted, fieldset[disabled] .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #4eb5de; } + .button.is-primary.is-loading::after, .docstring > section > a.button.is-loading.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-primary.is-outlined, .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + color: #4eb5de; } + .button.is-primary.is-outlined:hover, .docstring > section > a.button.is-outlined.docs-sourcelink:hover, .button.is-primary.is-outlined.is-hovered, .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-outlined:focus, .docstring > section > a.button.is-outlined.docs-sourcelink:focus, .button.is-primary.is-outlined.is-focused, .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + .button.is-primary.is-outlined.is-loading::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + .button.is-primary.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-primary.is-outlined[disabled], .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-outlined, fieldset[disabled] .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + box-shadow: none; + color: #4eb5de; } + .button.is-primary.is-inverted.is-outlined, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-primary.is-inverted.is-outlined:hover, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, .button.is-primary.is-inverted.is-outlined.is-hovered, .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-inverted.is-outlined:focus, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, .button.is-primary.is-inverted.is-outlined.is-focused, .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + .button.is-primary.is-inverted.is-outlined[disabled], .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted.is-outlined, fieldset[disabled] .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-link { + background-color: #149eaa; + border-color: transparent; + color: #fff; } + .button.is-link:hover, .button.is-link.is-hovered { + background-color: #13939f; + border-color: transparent; + color: #fff; } + .button.is-link:focus, .button.is-link.is-focused { + border-color: transparent; + color: #fff; } + .button.is-link:focus:not(:active), .button.is-link.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .button.is-link:active, .button.is-link.is-active { + background-color: #118993; + border-color: transparent; + color: #fff; } + .button.is-link[disabled], fieldset[disabled] .button.is-link { + background-color: #149eaa; + border-color: transparent; + box-shadow: none; } + .button.is-link.is-inverted { + background-color: #fff; + color: #149eaa; } + .button.is-link.is-inverted:hover, .button.is-link.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-link.is-inverted[disabled], fieldset[disabled] .button.is-link.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #149eaa; } + .button.is-link.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-link.is-outlined { + background-color: transparent; + border-color: #149eaa; + color: #149eaa; } + .button.is-link.is-outlined:hover, .button.is-link.is-outlined.is-hovered, .button.is-link.is-outlined:focus, .button.is-link.is-outlined.is-focused { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + .button.is-link.is-outlined.is-loading::after { + border-color: transparent transparent #149eaa #149eaa !important; } + .button.is-link.is-outlined.is-loading:hover::after, .button.is-link.is-outlined.is-loading.is-hovered::after, .button.is-link.is-outlined.is-loading:focus::after, .button.is-link.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-link.is-outlined[disabled], fieldset[disabled] .button.is-link.is-outlined { + background-color: transparent; + border-color: #149eaa; + box-shadow: none; + color: #149eaa; } + .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-link.is-inverted.is-outlined:hover, .button.is-link.is-inverted.is-outlined.is-hovered, .button.is-link.is-inverted.is-outlined:focus, .button.is-link.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #149eaa; } + .button.is-link.is-inverted.is-outlined.is-loading:hover::after, .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-link.is-inverted.is-outlined.is-loading:focus::after, .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #149eaa #149eaa !important; } + .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-info { + background-color: #209cee; + border-color: transparent; + color: #fff; } + .button.is-info:hover, .button.is-info.is-hovered { + background-color: #1497ed; + border-color: transparent; + color: #fff; } + .button.is-info:focus, .button.is-info.is-focused { + border-color: transparent; + color: #fff; } + .button.is-info:focus:not(:active), .button.is-info.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .button.is-info:active, .button.is-info.is-active { + background-color: #1190e3; + border-color: transparent; + color: #fff; } + .button.is-info[disabled], fieldset[disabled] .button.is-info { + background-color: #209cee; + border-color: transparent; + box-shadow: none; } + .button.is-info.is-inverted { + background-color: #fff; + color: #209cee; } + .button.is-info.is-inverted:hover, .button.is-info.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-info.is-inverted[disabled], fieldset[disabled] .button.is-info.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #209cee; } + .button.is-info.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-info.is-outlined { + background-color: transparent; + border-color: #209cee; + color: #209cee; } + .button.is-info.is-outlined:hover, .button.is-info.is-outlined.is-hovered, .button.is-info.is-outlined:focus, .button.is-info.is-outlined.is-focused { + background-color: #209cee; + border-color: #209cee; + color: #fff; } + .button.is-info.is-outlined.is-loading::after { + border-color: transparent transparent #209cee #209cee !important; } + .button.is-info.is-outlined.is-loading:hover::after, .button.is-info.is-outlined.is-loading.is-hovered::after, .button.is-info.is-outlined.is-loading:focus::after, .button.is-info.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-info.is-outlined[disabled], fieldset[disabled] .button.is-info.is-outlined { + background-color: transparent; + border-color: #209cee; + box-shadow: none; + color: #209cee; } + .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-info.is-inverted.is-outlined:hover, .button.is-info.is-inverted.is-outlined.is-hovered, .button.is-info.is-inverted.is-outlined:focus, .button.is-info.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #209cee; } + .button.is-info.is-inverted.is-outlined.is-loading:hover::after, .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-info.is-inverted.is-outlined.is-loading:focus::after, .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #209cee #209cee !important; } + .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-success { + background-color: #22c35b; + border-color: transparent; + color: #fff; } + .button.is-success:hover, .button.is-success.is-hovered { + background-color: #20b856; + border-color: transparent; + color: #fff; } + .button.is-success:focus, .button.is-success.is-focused { + border-color: transparent; + color: #fff; } + .button.is-success:focus:not(:active), .button.is-success.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .button.is-success:active, .button.is-success.is-active { + background-color: #1ead51; + border-color: transparent; + color: #fff; } + .button.is-success[disabled], fieldset[disabled] .button.is-success { + background-color: #22c35b; + border-color: transparent; + box-shadow: none; } + .button.is-success.is-inverted { + background-color: #fff; + color: #22c35b; } + .button.is-success.is-inverted:hover, .button.is-success.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-success.is-inverted[disabled], fieldset[disabled] .button.is-success.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #22c35b; } + .button.is-success.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-success.is-outlined { + background-color: transparent; + border-color: #22c35b; + color: #22c35b; } + .button.is-success.is-outlined:hover, .button.is-success.is-outlined.is-hovered, .button.is-success.is-outlined:focus, .button.is-success.is-outlined.is-focused { + background-color: #22c35b; + border-color: #22c35b; + color: #fff; } + .button.is-success.is-outlined.is-loading::after { + border-color: transparent transparent #22c35b #22c35b !important; } + .button.is-success.is-outlined.is-loading:hover::after, .button.is-success.is-outlined.is-loading.is-hovered::after, .button.is-success.is-outlined.is-loading:focus::after, .button.is-success.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-success.is-outlined[disabled], fieldset[disabled] .button.is-success.is-outlined { + background-color: transparent; + border-color: #22c35b; + box-shadow: none; + color: #22c35b; } + .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-success.is-inverted.is-outlined:hover, .button.is-success.is-inverted.is-outlined.is-hovered, .button.is-success.is-inverted.is-outlined:focus, .button.is-success.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #22c35b; } + .button.is-success.is-inverted.is-outlined.is-loading:hover::after, .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-success.is-inverted.is-outlined.is-loading:focus::after, .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #22c35b #22c35b !important; } + .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-warning { + background-color: #ffdd57; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:hover, .button.is-warning.is-hovered { + background-color: #ffda4a; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:focus, .button.is-warning.is-focused { + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:focus:not(:active), .button.is-warning.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .button.is-warning:active, .button.is-warning.is-active { + background-color: #ffd83e; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning[disabled], fieldset[disabled] .button.is-warning { + background-color: #ffdd57; + border-color: transparent; + box-shadow: none; } + .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .button.is-warning.is-inverted:hover, .button.is-warning.is-inverted.is-hovered { + background-color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-inverted[disabled], fieldset[disabled] .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + border-color: transparent; + box-shadow: none; + color: #ffdd57; } + .button.is-warning.is-loading::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + .button.is-warning.is-outlined { + background-color: transparent; + border-color: #ffdd57; + color: #ffdd57; } + .button.is-warning.is-outlined:hover, .button.is-warning.is-outlined.is-hovered, .button.is-warning.is-outlined:focus, .button.is-warning.is-outlined.is-focused { + background-color: #ffdd57; + border-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-outlined.is-loading::after { + border-color: transparent transparent #ffdd57 #ffdd57 !important; } + .button.is-warning.is-outlined.is-loading:hover::after, .button.is-warning.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-outlined.is-loading:focus::after, .button.is-warning.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + .button.is-warning.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-outlined { + background-color: transparent; + border-color: #ffdd57; + box-shadow: none; + color: #ffdd57; } + .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-inverted.is-outlined:hover, .button.is-warning.is-inverted.is-outlined.is-hovered, .button.is-warning.is-inverted.is-outlined:focus, .button.is-warning.is-inverted.is-outlined.is-focused { + background-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #ffdd57 #ffdd57 !important; } + .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + box-shadow: none; + color: rgba(0, 0, 0, 0.7); } + .button.is-danger { + background-color: #da0b00; + border-color: transparent; + color: #fff; } + .button.is-danger:hover, .button.is-danger.is-hovered { + background-color: #cd0a00; + border-color: transparent; + color: #fff; } + .button.is-danger:focus, .button.is-danger.is-focused { + border-color: transparent; + color: #fff; } + .button.is-danger:focus:not(:active), .button.is-danger.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .button.is-danger:active, .button.is-danger.is-active { + background-color: #c10a00; + border-color: transparent; + color: #fff; } + .button.is-danger[disabled], fieldset[disabled] .button.is-danger { + background-color: #da0b00; + border-color: transparent; + box-shadow: none; } + .button.is-danger.is-inverted { + background-color: #fff; + color: #da0b00; } + .button.is-danger.is-inverted:hover, .button.is-danger.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-danger.is-inverted[disabled], fieldset[disabled] .button.is-danger.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #da0b00; } + .button.is-danger.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-danger.is-outlined { + background-color: transparent; + border-color: #da0b00; + color: #da0b00; } + .button.is-danger.is-outlined:hover, .button.is-danger.is-outlined.is-hovered, .button.is-danger.is-outlined:focus, .button.is-danger.is-outlined.is-focused { + background-color: #da0b00; + border-color: #da0b00; + color: #fff; } + .button.is-danger.is-outlined.is-loading::after { + border-color: transparent transparent #da0b00 #da0b00 !important; } + .button.is-danger.is-outlined.is-loading:hover::after, .button.is-danger.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-outlined.is-loading:focus::after, .button.is-danger.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-danger.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-outlined { + background-color: transparent; + border-color: #da0b00; + box-shadow: none; + color: #da0b00; } + .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-danger.is-inverted.is-outlined:hover, .button.is-danger.is-inverted.is-outlined.is-hovered, .button.is-danger.is-inverted.is-outlined:focus, .button.is-danger.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #da0b00; } + .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #da0b00 #da0b00 !important; } + .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-small, #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 2px; + font-size: 0.75rem; } + .button.is-normal { + font-size: 1rem; } + .button.is-medium { + font-size: 1.25rem; } + .button.is-large { + font-size: 1.5rem; } + .button[disabled], fieldset[disabled] .button { + background-color: white; + border-color: #dbdbdb; + box-shadow: none; + opacity: 0.5; } + .button.is-fullwidth { + display: flex; + width: 100%; } + .button.is-loading { + color: transparent !important; + pointer-events: none; } + .button.is-loading::after { + position: absolute; + left: calc(50% - (1em / 2)); + top: calc(50% - (1em / 2)); + position: absolute !important; } + .button.is-static { + background-color: whitesmoke; + border-color: #dbdbdb; + color: #6b6b6b; + box-shadow: none; + pointer-events: none; } + .button.is-rounded, #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + +.buttons { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .buttons .button { + margin-bottom: 0.5rem; } + .buttons .button:not(:last-child):not(.is-fullwidth) { + margin-right: 0.5rem; } + .buttons:last-child { + margin-bottom: -0.5rem; } + .buttons:not(:last-child) { + margin-bottom: 1rem; } + .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { + border-radius: 2px; + font-size: 0.75rem; } + .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { + font-size: 1.25rem; } + .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { + font-size: 1.5rem; } + .buttons.has-addons .button:not(:first-child) { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .buttons.has-addons .button:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; + margin-right: -1px; } + .buttons.has-addons .button:last-child { + margin-right: 0; } + .buttons.has-addons .button:hover, .buttons.has-addons .button.is-hovered { + z-index: 2; } + .buttons.has-addons .button:focus, .buttons.has-addons .button.is-focused, .buttons.has-addons .button:active, .buttons.has-addons .button.is-active, .buttons.has-addons .button.is-selected { + z-index: 3; } + .buttons.has-addons .button:focus:hover, .buttons.has-addons .button.is-focused:hover, .buttons.has-addons .button:active:hover, .buttons.has-addons .button.is-active:hover, .buttons.has-addons .button.is-selected:hover { + z-index: 4; } + .buttons.has-addons .button.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .buttons.is-centered { + justify-content: center; } + .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + .buttons.is-right { + justify-content: flex-end; } + .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + +.container { + flex-grow: 1; + margin: 0 auto; + position: relative; + width: auto; } + @media screen and (min-width: 1056px) { + .container { + max-width: 992px; } + .container.is-fluid { + margin-left: 32px; + margin-right: 32px; + max-width: none; } } + @media screen and (max-width: 1215px) { + .container.is-widescreen { + max-width: 1152px; } } + @media screen and (max-width: 1407px) { + .container.is-fullhd { + max-width: 1344px; } } + @media screen and (min-width: 1216px) { + .container { + max-width: 1152px; } } + @media screen and (min-width: 1408px) { + .container { + max-width: 1344px; } } +.content li + li { + margin-top: 0.25em; } + +.content p:not(:last-child), +.content dl:not(:last-child), +.content ol:not(:last-child), +.content ul:not(:last-child), +.content blockquote:not(:last-child), +.content pre:not(:last-child), +.content table:not(:last-child) { + margin-bottom: 1em; } + +.content h1, +.content h2, +.content h3, +.content h4, +.content h5, +.content h6 { + color: #654ca3; + font-weight: 600; + line-height: 1.125; } + +.content h1 { + font-size: 2em; + margin-bottom: 0.5em; } + .content h1:not(:first-child) { + margin-top: 1em; } + +.content h2 { + font-size: 1.75em; + margin-bottom: 0.5714em; } + .content h2:not(:first-child) { + margin-top: 1.1428em; } + +.content h3 { + font-size: 1.5em; + margin-bottom: 0.6666em; } + .content h3:not(:first-child) { + margin-top: 1.3333em; } + +.content h4 { + font-size: 1.25em; + margin-bottom: 0.8em; } + +.content h5 { + font-size: 1.125em; + margin-bottom: 0.8888em; } + +.content h6 { + font-size: 1em; + margin-bottom: 1em; } + +.content blockquote { + background-color: whitesmoke; + border-left: 5px solid #dbdbdb; + padding: 1.25em 1.5em; } + +.content ol { + list-style-position: outside; + margin-left: 2em; + margin-top: 1em; } + .content ol:not([type]) { + list-style-type: decimal; } + .content ol.is-lower-alpha:not([type]) { + list-style-type: lower-alpha; } + .content ol.is-lower-roman:not([type]) { + list-style-type: lower-roman; } + .content ol.is-upper-alpha:not([type]) { + list-style-type: upper-alpha; } + .content ol.is-upper-roman:not([type]) { + list-style-type: upper-roman; } + +.content ul { + list-style: disc outside; + margin-left: 2em; + margin-top: 1em; } + .content ul ul { + list-style-type: circle; + margin-top: 0.5em; } + .content ul ul ul { + list-style-type: square; } + +.content dd { + margin-left: 2em; } + +.content figure { + margin-left: 2em; + margin-right: 2em; + text-align: center; } + .content figure:not(:first-child) { + margin-top: 2em; } + .content figure:not(:last-child) { + margin-bottom: 2em; } + .content figure img { + display: inline-block; } + .content figure figcaption { + font-style: italic; } + +.content pre { + -webkit-overflow-scrolling: touch; + overflow-x: auto; + padding: 0; + white-space: pre; + word-wrap: normal; } + +.content sup, +.content sub { + font-size: 75%; } + +.content table { + width: 100%; } + .content table td, + .content table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + .content table th { + color: #654ca3; } + .content table th:not([align]) { + text-align: left; } + .content table thead td, + .content table thead th { + border-width: 0 0 2px; + color: #654ca3; } + .content table tfoot td, + .content table tfoot th { + border-width: 2px 0 0; + color: #654ca3; } + .content table tbody tr:last-child td, + .content table tbody tr:last-child th { + border-bottom-width: 0; } + +.content .tabs li + li { + margin-top: 0; } + +.content.is-small, #documenter .docs-sidebar form.docs-search > input.content { + font-size: 0.75rem; } + +.content.is-medium { + font-size: 1.25rem; } + +.content.is-large { + font-size: 1.5rem; } + +.icon { + align-items: center; + display: inline-flex; + justify-content: center; + height: 1.5rem; + width: 1.5rem; } + .icon.is-small, #documenter .docs-sidebar form.docs-search > input.icon { + height: 1rem; + width: 1rem; } + .icon.is-medium { + height: 2rem; + width: 2rem; } + .icon.is-large { + height: 3rem; + width: 3rem; } + +.image, #documenter .docs-sidebar .docs-logo > img { + display: block; + position: relative; } + .image img, #documenter .docs-sidebar .docs-logo > img img { + display: block; + height: auto; + width: 100%; } + .image img.is-rounded, #documenter .docs-sidebar .docs-logo > img img.is-rounded { + border-radius: 290486px; } + .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img, + .image.is-square .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img, + .image.is-1by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img, + .image.is-5by4 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img, + .image.is-4by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img, + .image.is-3by2 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img, + .image.is-5by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img, + .image.is-16by9 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img, + .image.is-2by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img, + .image.is-3by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img, + .image.is-4by5 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img, + .image.is-3by4 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img, + .image.is-2by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img, + .image.is-3by5 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img, + .image.is-9by16 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img, + .image.is-1by2 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img, + .image.is-1by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { + height: 100%; + width: 100%; } + .image.is-square, #documenter .docs-sidebar .docs-logo > img.is-square, .image.is-1by1, #documenter .docs-sidebar .docs-logo > img.is-1by1 { + padding-top: 100%; } + .image.is-5by4, #documenter .docs-sidebar .docs-logo > img.is-5by4 { + padding-top: 80%; } + .image.is-4by3, #documenter .docs-sidebar .docs-logo > img.is-4by3 { + padding-top: 75%; } + .image.is-3by2, #documenter .docs-sidebar .docs-logo > img.is-3by2 { + padding-top: 66.6666%; } + .image.is-5by3, #documenter .docs-sidebar .docs-logo > img.is-5by3 { + padding-top: 60%; } + .image.is-16by9, #documenter .docs-sidebar .docs-logo > img.is-16by9 { + padding-top: 56.25%; } + .image.is-2by1, #documenter .docs-sidebar .docs-logo > img.is-2by1 { + padding-top: 50%; } + .image.is-3by1, #documenter .docs-sidebar .docs-logo > img.is-3by1 { + padding-top: 33.3333%; } + .image.is-4by5, #documenter .docs-sidebar .docs-logo > img.is-4by5 { + padding-top: 125%; } + .image.is-3by4, #documenter .docs-sidebar .docs-logo > img.is-3by4 { + padding-top: 133.3333%; } + .image.is-2by3, #documenter .docs-sidebar .docs-logo > img.is-2by3 { + padding-top: 150%; } + .image.is-3by5, #documenter .docs-sidebar .docs-logo > img.is-3by5 { + padding-top: 166.6666%; } + .image.is-9by16, #documenter .docs-sidebar .docs-logo > img.is-9by16 { + padding-top: 177.7777%; } + .image.is-1by2, #documenter .docs-sidebar .docs-logo > img.is-1by2 { + padding-top: 200%; } + .image.is-1by3, #documenter .docs-sidebar .docs-logo > img.is-1by3 { + padding-top: 300%; } + .image.is-16x16, #documenter .docs-sidebar .docs-logo > img.is-16x16 { + height: 16px; + width: 16px; } + .image.is-24x24, #documenter .docs-sidebar .docs-logo > img.is-24x24 { + height: 24px; + width: 24px; } + .image.is-32x32, #documenter .docs-sidebar .docs-logo > img.is-32x32 { + height: 32px; + width: 32px; } + .image.is-48x48, #documenter .docs-sidebar .docs-logo > img.is-48x48 { + height: 48px; + width: 48px; } + .image.is-64x64, #documenter .docs-sidebar .docs-logo > img.is-64x64 { + height: 64px; + width: 64px; } + .image.is-96x96, #documenter .docs-sidebar .docs-logo > img.is-96x96 { + height: 96px; + width: 96px; } + .image.is-128x128, #documenter .docs-sidebar .docs-logo > img.is-128x128 { + height: 128px; + width: 128px; } + +.notification { + background-color: whitesmoke; + border-radius: 4px; + padding: 1.25rem 2.5rem 1.25rem 1.5rem; + position: relative; } + .notification a:not(.button):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + .notification strong { + color: currentColor; } + .notification code, + .notification pre { + background: white; } + .notification pre code { + background: transparent; } + .notification > .delete { + position: absolute; + right: 0.5rem; + top: 0.5rem; } + .notification .title, + .notification .subtitle, + .notification .content { + color: currentColor; } + .notification.is-white { + background-color: white; + color: #0a0a0a; } + .notification.is-black { + background-color: #0a0a0a; + color: white; } + .notification.is-light { + background-color: whitesmoke; + color: #363636; } + .notification.is-dark, .content kbd.notification { + background-color: #363636; + color: whitesmoke; } + .notification.is-primary, .docstring > section > a.notification.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .notification.is-link { + background-color: #149eaa; + color: #fff; } + .notification.is-info { + background-color: #209cee; + color: #fff; } + .notification.is-success { + background-color: #22c35b; + color: #fff; } + .notification.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .notification.is-danger { + background-color: #da0b00; + color: #fff; } + +.progress { + -moz-appearance: none; + -webkit-appearance: none; + border: none; + border-radius: 290486px; + display: block; + height: 1rem; + overflow: hidden; + padding: 0; + width: 100%; } + .progress::-webkit-progress-bar { + background-color: #dbdbdb; } + .progress::-webkit-progress-value { + background-color: #202020; } + .progress::-moz-progress-bar { + background-color: #202020; } + .progress::-ms-fill { + background-color: #202020; + border: none; } + .progress.is-white::-webkit-progress-value { + background-color: white; } + .progress.is-white::-moz-progress-bar { + background-color: white; } + .progress.is-white::-ms-fill { + background-color: white; } + .progress.is-white:indeterminate { + background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); } + .progress.is-black::-webkit-progress-value { + background-color: #0a0a0a; } + .progress.is-black::-moz-progress-bar { + background-color: #0a0a0a; } + .progress.is-black::-ms-fill { + background-color: #0a0a0a; } + .progress.is-black:indeterminate { + background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); } + .progress.is-light::-webkit-progress-value { + background-color: whitesmoke; } + .progress.is-light::-moz-progress-bar { + background-color: whitesmoke; } + .progress.is-light::-ms-fill { + background-color: whitesmoke; } + .progress.is-light:indeterminate { + background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); } + .progress.is-dark::-webkit-progress-value, .content kbd.progress::-webkit-progress-value { + background-color: #363636; } + .progress.is-dark::-moz-progress-bar, .content kbd.progress::-moz-progress-bar { + background-color: #363636; } + .progress.is-dark::-ms-fill, .content kbd.progress::-ms-fill { + background-color: #363636; } + .progress.is-dark:indeterminate, .content kbd.progress:indeterminate { + background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); } + .progress.is-primary::-webkit-progress-value, .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { + background-color: #4eb5de; } + .progress.is-primary::-moz-progress-bar, .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { + background-color: #4eb5de; } + .progress.is-primary::-ms-fill, .docstring > section > a.progress.docs-sourcelink::-ms-fill { + background-color: #4eb5de; } + .progress.is-primary:indeterminate, .docstring > section > a.progress.docs-sourcelink:indeterminate { + background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); } + .progress.is-link::-webkit-progress-value { + background-color: #149eaa; } + .progress.is-link::-moz-progress-bar { + background-color: #149eaa; } + .progress.is-link::-ms-fill { + background-color: #149eaa; } + .progress.is-link:indeterminate { + background-image: linear-gradient(to right, #149eaa 30%, #dbdbdb 30%); } + .progress.is-info::-webkit-progress-value { + background-color: #209cee; } + .progress.is-info::-moz-progress-bar { + background-color: #209cee; } + .progress.is-info::-ms-fill { + background-color: #209cee; } + .progress.is-info:indeterminate { + background-image: linear-gradient(to right, #209cee 30%, #dbdbdb 30%); } + .progress.is-success::-webkit-progress-value { + background-color: #22c35b; } + .progress.is-success::-moz-progress-bar { + background-color: #22c35b; } + .progress.is-success::-ms-fill { + background-color: #22c35b; } + .progress.is-success:indeterminate { + background-image: linear-gradient(to right, #22c35b 30%, #dbdbdb 30%); } + .progress.is-warning::-webkit-progress-value { + background-color: #ffdd57; } + .progress.is-warning::-moz-progress-bar { + background-color: #ffdd57; } + .progress.is-warning::-ms-fill { + background-color: #ffdd57; } + .progress.is-warning:indeterminate { + background-image: linear-gradient(to right, #ffdd57 30%, #dbdbdb 30%); } + .progress.is-danger::-webkit-progress-value { + background-color: #da0b00; } + .progress.is-danger::-moz-progress-bar { + background-color: #da0b00; } + .progress.is-danger::-ms-fill { + background-color: #da0b00; } + .progress.is-danger:indeterminate { + background-image: linear-gradient(to right, #da0b00 30%, #dbdbdb 30%); } + .progress:indeterminate { + animation-duration: 1.5s; + animation-iteration-count: infinite; + animation-name: moveIndeterminate; + animation-timing-function: linear; + background-color: #dbdbdb; + background-image: linear-gradient(to right, #202020 30%, #dbdbdb 30%); + background-position: top left; + background-repeat: no-repeat; + background-size: 150% 150%; } + .progress:indeterminate::-webkit-progress-bar { + background-color: transparent; } + .progress:indeterminate::-moz-progress-bar { + background-color: transparent; } + .progress.is-small, #documenter .docs-sidebar form.docs-search > input.progress { + height: 0.75rem; } + .progress.is-medium { + height: 1.25rem; } + .progress.is-large { + height: 1.5rem; } + +@keyframes moveIndeterminate { + from { + background-position: 200% 0; } + to { + background-position: -200% 0; } } + +.table { + background-color: white; + color: #363636; } + .table td, + .table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + .table td.is-white, + .table th.is-white { + background-color: white; + border-color: white; + color: #0a0a0a; } + .table td.is-black, + .table th.is-black { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .table td.is-light, + .table th.is-light { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .table td.is-dark, + .table th.is-dark { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .table td.is-primary, + .table th.is-primary { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + .table td.is-link, + .table th.is-link { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + .table td.is-info, + .table th.is-info { + background-color: #209cee; + border-color: #209cee; + color: #fff; } + .table td.is-success, + .table th.is-success { + background-color: #22c35b; + border-color: #22c35b; + color: #fff; } + .table td.is-warning, + .table th.is-warning { + background-color: #ffdd57; + border-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .table td.is-danger, + .table th.is-danger { + background-color: #da0b00; + border-color: #da0b00; + color: #fff; } + .table td.is-narrow, + .table th.is-narrow { + white-space: nowrap; + width: 1%; } + .table td.is-selected, + .table th.is-selected { + background-color: #4eb5de; + color: #fff; } + .table td.is-selected a, + .table td.is-selected strong, + .table th.is-selected a, + .table th.is-selected strong { + color: currentColor; } + .table th { + color: #654ca3; } + .table th:not([align]) { + text-align: left; } + .table tr.is-selected { + background-color: #4eb5de; + color: #fff; } + .table tr.is-selected a, + .table tr.is-selected strong { + color: currentColor; } + .table tr.is-selected td, + .table tr.is-selected th { + border-color: #fff; + color: currentColor; } + .table thead { + background-color: transparent; } + .table thead td, + .table thead th { + border-width: 0 0 2px; + color: #654ca3; } + .table tfoot { + background-color: transparent; } + .table tfoot td, + .table tfoot th { + border-width: 2px 0 0; + color: #654ca3; } + .table tbody { + background-color: transparent; } + .table tbody tr:last-child td, + .table tbody tr:last-child th { + border-bottom-width: 0; } + .table.is-bordered td, + .table.is-bordered th { + border-width: 1px; } + .table.is-bordered tr:last-child td, + .table.is-bordered tr:last-child th { + border-bottom-width: 1px; } + .table.is-fullwidth { + width: 100%; } + .table.is-hoverable tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { + background-color: whitesmoke; } + .table.is-narrow td, + .table.is-narrow th { + padding: 0.25em 0.5em; } + .table.is-striped tbody tr:not(.is-selected):nth-child(even) { + background-color: #fafafa; } + +.table-container { + -webkit-overflow-scrolling: touch; + overflow: auto; + overflow-y: hidden; + max-width: 100%; } + +.tags { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .tags .tag, .tags .content kbd, .content .tags kbd, .tags .docstring > section > a.docs-sourcelink { + margin-bottom: 0.5rem; } + .tags .tag:not(:last-child), .tags .content kbd:not(:last-child), .content .tags kbd:not(:last-child), .tags .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0.5rem; } + .tags:last-child { + margin-bottom: -0.5rem; } + .tags:not(:last-child) { + margin-bottom: 1rem; } + .tags.are-medium .tag:not(.is-normal):not(.is-large), .tags.are-medium .content kbd:not(.is-normal):not(.is-large), .content .tags.are-medium kbd:not(.is-normal):not(.is-large), .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { + font-size: 1rem; } + .tags.are-large .tag:not(.is-normal):not(.is-medium), .tags.are-large .content kbd:not(.is-normal):not(.is-medium), .content .tags.are-large kbd:not(.is-normal):not(.is-medium), .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { + font-size: 1.25rem; } + .tags.is-centered { + justify-content: center; } + .tags.is-centered .tag, .tags.is-centered .content kbd, .content .tags.is-centered kbd, .tags.is-centered .docstring > section > a.docs-sourcelink { + margin-right: 0.25rem; + margin-left: 0.25rem; } + .tags.is-right { + justify-content: flex-end; } + .tags.is-right .tag:not(:first-child), .tags.is-right .content kbd:not(:first-child), .content .tags.is-right kbd:not(:first-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0.5rem; } + .tags.is-right .tag:not(:last-child), .tags.is-right .content kbd:not(:last-child), .content .tags.is-right kbd:not(:last-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0; } + .tags.has-addons .tag, .tags.has-addons .content kbd, .content .tags.has-addons kbd, .tags.has-addons .docstring > section > a.docs-sourcelink { + margin-right: 0; } + .tags.has-addons .tag:not(:first-child), .tags.has-addons .content kbd:not(:first-child), .content .tags.has-addons kbd:not(:first-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0; + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .tags.has-addons .tag:not(:last-child), .tags.has-addons .content kbd:not(:last-child), .content .tags.has-addons kbd:not(:last-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + +.tag:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink:not(body) { + align-items: center; + background-color: whitesmoke; + border-radius: 4px; + color: #202020; + display: inline-flex; + font-size: 0.75rem; + height: 2em; + justify-content: center; + line-height: 1.5; + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + .tag:not(body) .delete, .content kbd:not(body) .delete, .docstring > section > a.docs-sourcelink:not(body) .delete { + margin-left: 0.25rem; + margin-right: -0.375rem; } + .tag.is-white:not(body), .content kbd.is-white:not(body), .docstring > section > a.docs-sourcelink.is-white:not(body) { + background-color: white; + color: #0a0a0a; } + .tag.is-black:not(body), .content kbd.is-black:not(body), .docstring > section > a.docs-sourcelink.is-black:not(body) { + background-color: #0a0a0a; + color: white; } + .tag.is-light:not(body), .content kbd.is-light:not(body), .docstring > section > a.docs-sourcelink.is-light:not(body) { + background-color: whitesmoke; + color: #363636; } + .tag.is-dark:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink.is-dark:not(body), .content .docstring > section > kbd:not(body) { + background-color: #363636; + color: whitesmoke; } + .tag.is-primary:not(body), .content kbd.is-primary:not(body), .docstring > section > a.docs-sourcelink:not(body) { + background-color: #4eb5de; + color: #fff; } + .tag.is-link:not(body), .content kbd.is-link:not(body), .docstring > section > a.docs-sourcelink.is-link:not(body) { + background-color: #149eaa; + color: #fff; } + .tag.is-info:not(body), .content kbd.is-info:not(body), .docstring > section > a.docs-sourcelink.is-info:not(body) { + background-color: #209cee; + color: #fff; } + .tag.is-success:not(body), .content kbd.is-success:not(body), .docstring > section > a.docs-sourcelink.is-success:not(body) { + background-color: #22c35b; + color: #fff; } + .tag.is-warning:not(body), .content kbd.is-warning:not(body), .docstring > section > a.docs-sourcelink.is-warning:not(body) { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .tag.is-danger:not(body), .content kbd.is-danger:not(body), .docstring > section > a.docs-sourcelink.is-danger:not(body) { + background-color: #da0b00; + color: #fff; } + .tag.is-normal:not(body), .content kbd.is-normal:not(body), .docstring > section > a.docs-sourcelink.is-normal:not(body) { + font-size: 0.75rem; } + .tag.is-medium:not(body), .content kbd.is-medium:not(body), .docstring > section > a.docs-sourcelink.is-medium:not(body) { + font-size: 1rem; } + .tag.is-large:not(body), .content kbd.is-large:not(body), .docstring > section > a.docs-sourcelink.is-large:not(body) { + font-size: 1.25rem; } + .tag:not(body) .icon:first-child:not(:last-child), .content kbd:not(body) .icon:first-child:not(:last-child), .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { + margin-left: -0.375em; + margin-right: 0.1875em; } + .tag:not(body) .icon:last-child:not(:first-child), .content kbd:not(body) .icon:last-child:not(:first-child), .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: -0.375em; } + .tag:not(body) .icon:first-child:last-child, .content kbd:not(body) .icon:first-child:last-child, .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { + margin-left: -0.375em; + margin-right: -0.375em; } + .tag.is-delete:not(body), .content kbd.is-delete:not(body), .docstring > section > a.docs-sourcelink.is-delete:not(body) { + margin-left: 1px; + padding: 0; + position: relative; + width: 2em; } + .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + background-color: currentColor; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { + height: 1px; + width: 50%; } + .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + height: 50%; + width: 1px; } + .tag.is-delete:not(body):hover, .content kbd.is-delete:not(body):hover, .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, .tag.is-delete:not(body):focus, .content kbd.is-delete:not(body):focus, .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { + background-color: #e8e8e8; } + .tag.is-delete:not(body):active, .content kbd.is-delete:not(body):active, .docstring > section > a.docs-sourcelink.is-delete:not(body):active { + background-color: #dbdbdb; } + .tag.is-rounded:not(body), #documenter .docs-sidebar form.docs-search > input:not(body), .content kbd.is-rounded:not(body), #documenter .docs-sidebar .content form.docs-search > input:not(body), .docstring > section > a.docs-sourcelink.is-rounded:not(body) { + border-radius: 290486px; } + +a.tag:hover, .docstring > section > a.docs-sourcelink:hover { + text-decoration: underline; } + +.title, +.subtitle { + word-break: break-word; } + .title em, + .title span, + .subtitle em, + .subtitle span { + font-weight: inherit; } + .title sub, + .subtitle sub { + font-size: 0.75em; } + .title sup, + .subtitle sup { + font-size: 0.75em; } + .title .tag, .title .content kbd, .content .title kbd, .title .docstring > section > a.docs-sourcelink, + .subtitle .tag, + .subtitle .content kbd, + .content .subtitle kbd, + .subtitle .docstring > section > a.docs-sourcelink { + vertical-align: middle; } + +.title { + color: #363636; + font-size: 2rem; + font-weight: 600; + line-height: 1.125; } + .title strong { + color: inherit; + font-weight: inherit; } + .title + .highlight { + margin-top: -0.75rem; } + .title:not(.is-spaced) + .subtitle { + margin-top: -1.25rem; } + .title.is-1 { + font-size: 3rem; } + .title.is-2 { + font-size: 2.5rem; } + .title.is-3 { + font-size: 2rem; } + .title.is-4 { + font-size: 1.5rem; } + .title.is-5 { + font-size: 1.25rem; } + .title.is-6 { + font-size: 1rem; } + .title.is-7 { + font-size: 0.75rem; } + +.subtitle { + color: #4a4a4a; + font-size: 1.25rem; + font-weight: 400; + line-height: 1.25; } + .subtitle strong { + color: #363636; + font-weight: 600; } + .subtitle:not(.is-spaced) + .title { + margin-top: -1.25rem; } + .subtitle.is-1 { + font-size: 3rem; } + .subtitle.is-2 { + font-size: 2.5rem; } + .subtitle.is-3 { + font-size: 2rem; } + .subtitle.is-4 { + font-size: 1.5rem; } + .subtitle.is-5 { + font-size: 1.25rem; } + .subtitle.is-6 { + font-size: 1rem; } + .subtitle.is-7 { + font-size: 0.75rem; } + +.heading { + display: block; + font-size: 11px; + letter-spacing: 1px; + margin-bottom: 5px; + text-transform: uppercase; } + +.highlight { + font-weight: 400; + max-width: 100%; + overflow: hidden; + padding: 0; } + .highlight pre { + overflow: auto; + max-width: 100%; } + +.number { + align-items: center; + background-color: whitesmoke; + border-radius: 290486px; + display: inline-flex; + font-size: 1.25rem; + height: 2em; + justify-content: center; + margin-right: 1.5rem; + min-width: 2.5em; + padding: 0.25rem 0.5rem; + text-align: center; + vertical-align: top; } + +.select select, .textarea, .input, #documenter .docs-sidebar form.docs-search > input { + background-color: white; + border-color: #dbdbdb; + border-radius: 4px; + color: #363636; } + .select select::-moz-placeholder, .textarea::-moz-placeholder, .input::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select::-webkit-input-placeholder, .textarea::-webkit-input-placeholder, .input::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:-moz-placeholder, .textarea:-moz-placeholder, .input:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:-ms-input-placeholder, .textarea:-ms-input-placeholder, .input:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:hover, .textarea:hover, .input:hover, #documenter .docs-sidebar form.docs-search > input:hover, .select select.is-hovered, .is-hovered.textarea, .is-hovered.input, #documenter .docs-sidebar form.docs-search > input.is-hovered { + border-color: #149eaa; } + .select select:focus, .textarea:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .select select.is-focused, .is-focused.textarea, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .select select:active, .textarea:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .select select.is-active, .is-active.textarea, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + border-color: #fff; + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .select select[disabled], .textarea[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] .select select, .select fieldset[disabled] select, fieldset[disabled] .textarea, fieldset[disabled] .input, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input { + background-color: whitesmoke; + border-color: whitesmoke; + box-shadow: none; + color: #6b6b6b; } + .select select[disabled]::-moz-placeholder, .textarea[disabled]::-moz-placeholder, .input[disabled]::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] .select select::-moz-placeholder, .select fieldset[disabled] select::-moz-placeholder, fieldset[disabled] .textarea::-moz-placeholder, fieldset[disabled] .input::-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-moz-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]::-webkit-input-placeholder, .textarea[disabled]::-webkit-input-placeholder, .input[disabled]::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] .select select::-webkit-input-placeholder, .select fieldset[disabled] select::-webkit-input-placeholder, fieldset[disabled] .textarea::-webkit-input-placeholder, fieldset[disabled] .input::-webkit-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-webkit-input-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]:-moz-placeholder, .textarea[disabled]:-moz-placeholder, .input[disabled]:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] .select select:-moz-placeholder, .select fieldset[disabled] select:-moz-placeholder, fieldset[disabled] .textarea:-moz-placeholder, fieldset[disabled] .input:-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-moz-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]:-ms-input-placeholder, .textarea[disabled]:-ms-input-placeholder, .input[disabled]:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] .select select:-ms-input-placeholder, .select fieldset[disabled] select:-ms-input-placeholder, fieldset[disabled] .textarea:-ms-input-placeholder, fieldset[disabled] .input:-ms-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-ms-input-placeholder { + color: rgba(107, 107, 107, 0.3); } + +.textarea, .input, #documenter .docs-sidebar form.docs-search > input { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); + max-width: 100%; + width: 100%; } + .textarea[readonly], .input[readonly], #documenter .docs-sidebar form.docs-search > input[readonly] { + box-shadow: none; } + .is-white.textarea, .is-white.input, #documenter .docs-sidebar form.docs-search > input.is-white { + border-color: white; } + .is-white.textarea:focus, .is-white.input:focus, #documenter .docs-sidebar form.docs-search > input.is-white:focus, .is-white.is-focused.textarea, .is-white.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-white.textarea:active, .is-white.input:active, #documenter .docs-sidebar form.docs-search > input.is-white:active, .is-white.is-active.textarea, .is-white.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .is-black.textarea, .is-black.input, #documenter .docs-sidebar form.docs-search > input.is-black { + border-color: #0a0a0a; } + .is-black.textarea:focus, .is-black.input:focus, #documenter .docs-sidebar form.docs-search > input.is-black:focus, .is-black.is-focused.textarea, .is-black.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-black.textarea:active, .is-black.input:active, #documenter .docs-sidebar form.docs-search > input.is-black:active, .is-black.is-active.textarea, .is-black.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .is-light.textarea, .is-light.input, #documenter .docs-sidebar form.docs-search > input.is-light { + border-color: whitesmoke; } + .is-light.textarea:focus, .is-light.input:focus, #documenter .docs-sidebar form.docs-search > input.is-light:focus, .is-light.is-focused.textarea, .is-light.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-light.textarea:active, .is-light.input:active, #documenter .docs-sidebar form.docs-search > input.is-light:active, .is-light.is-active.textarea, .is-light.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .is-dark.textarea, .content kbd.textarea, .is-dark.input, #documenter .docs-sidebar form.docs-search > input.is-dark, .content kbd.input { + border-color: #363636; } + .is-dark.textarea:focus, .content kbd.textarea:focus, .is-dark.input:focus, #documenter .docs-sidebar form.docs-search > input.is-dark:focus, .content kbd.input:focus, .is-dark.is-focused.textarea, .content kbd.is-focused.textarea, .is-dark.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .content kbd.is-focused.input, #documenter .docs-sidebar .content form.docs-search > input.is-focused, .is-dark.textarea:active, .content kbd.textarea:active, .is-dark.input:active, #documenter .docs-sidebar form.docs-search > input.is-dark:active, .content kbd.input:active, .is-dark.is-active.textarea, .content kbd.is-active.textarea, .is-dark.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .content kbd.is-active.input, #documenter .docs-sidebar .content form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .is-primary.textarea, .docstring > section > a.textarea.docs-sourcelink, .is-primary.input, #documenter .docs-sidebar form.docs-search > input.is-primary, .docstring > section > a.input.docs-sourcelink { + border-color: #4eb5de; } + .is-primary.textarea:focus, .docstring > section > a.textarea.docs-sourcelink:focus, .is-primary.input:focus, #documenter .docs-sidebar form.docs-search > input.is-primary:focus, .docstring > section > a.input.docs-sourcelink:focus, .is-primary.is-focused.textarea, .docstring > section > a.is-focused.textarea.docs-sourcelink, .is-primary.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .docstring > section > a.is-focused.input.docs-sourcelink, .is-primary.textarea:active, .docstring > section > a.textarea.docs-sourcelink:active, .is-primary.input:active, #documenter .docs-sidebar form.docs-search > input.is-primary:active, .docstring > section > a.input.docs-sourcelink:active, .is-primary.is-active.textarea, .docstring > section > a.is-active.textarea.docs-sourcelink, .is-primary.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .docstring > section > a.is-active.input.docs-sourcelink { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .is-link.textarea, .is-link.input, #documenter .docs-sidebar form.docs-search > input.is-link { + border-color: #149eaa; } + .is-link.textarea:focus, .is-link.input:focus, #documenter .docs-sidebar form.docs-search > input.is-link:focus, .is-link.is-focused.textarea, .is-link.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-link.textarea:active, .is-link.input:active, #documenter .docs-sidebar form.docs-search > input.is-link:active, .is-link.is-active.textarea, .is-link.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .is-info.textarea, .is-info.input, #documenter .docs-sidebar form.docs-search > input.is-info { + border-color: #209cee; } + .is-info.textarea:focus, .is-info.input:focus, #documenter .docs-sidebar form.docs-search > input.is-info:focus, .is-info.is-focused.textarea, .is-info.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-info.textarea:active, .is-info.input:active, #documenter .docs-sidebar form.docs-search > input.is-info:active, .is-info.is-active.textarea, .is-info.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .is-success.textarea, .is-success.input, #documenter .docs-sidebar form.docs-search > input.is-success { + border-color: #22c35b; } + .is-success.textarea:focus, .is-success.input:focus, #documenter .docs-sidebar form.docs-search > input.is-success:focus, .is-success.is-focused.textarea, .is-success.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-success.textarea:active, .is-success.input:active, #documenter .docs-sidebar form.docs-search > input.is-success:active, .is-success.is-active.textarea, .is-success.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .is-warning.textarea, .is-warning.input, #documenter .docs-sidebar form.docs-search > input.is-warning { + border-color: #ffdd57; } + .is-warning.textarea:focus, .is-warning.input:focus, #documenter .docs-sidebar form.docs-search > input.is-warning:focus, .is-warning.is-focused.textarea, .is-warning.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-warning.textarea:active, .is-warning.input:active, #documenter .docs-sidebar form.docs-search > input.is-warning:active, .is-warning.is-active.textarea, .is-warning.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .is-danger.textarea, .is-danger.input, #documenter .docs-sidebar form.docs-search > input.is-danger { + border-color: #da0b00; } + .is-danger.textarea:focus, .is-danger.input:focus, #documenter .docs-sidebar form.docs-search > input.is-danger:focus, .is-danger.is-focused.textarea, .is-danger.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-danger.textarea:active, .is-danger.input:active, #documenter .docs-sidebar form.docs-search > input.is-danger:active, .is-danger.is-active.textarea, .is-danger.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .is-small.textarea, .is-small.input, #documenter .docs-sidebar form.docs-search > input { + border-radius: 2px; + font-size: 0.75rem; } + .is-medium.textarea, .is-medium.input, #documenter .docs-sidebar form.docs-search > input.is-medium { + font-size: 1.25rem; } + .is-large.textarea, .is-large.input, #documenter .docs-sidebar form.docs-search > input.is-large { + font-size: 1.5rem; } + .is-fullwidth.textarea, .is-fullwidth.input, #documenter .docs-sidebar form.docs-search > input.is-fullwidth { + display: block; + width: 100%; } + .is-inline.textarea, .is-inline.input, #documenter .docs-sidebar form.docs-search > input.is-inline { + display: inline; + width: auto; } + +.input.is-rounded, #documenter .docs-sidebar form.docs-search > input { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + +.input.is-static, #documenter .docs-sidebar form.docs-search > input.is-static { + background-color: transparent; + border-color: transparent; + box-shadow: none; + padding-left: 0; + padding-right: 0; } + +.textarea { + display: block; + max-width: 100%; + min-width: 100%; + padding: 0.625em; + resize: vertical; } + .textarea:not([rows]) { + max-height: 600px; + min-height: 120px; } + .textarea[rows] { + height: initial; } + .textarea.has-fixed-size { + resize: none; } + +.radio, .checkbox { + cursor: pointer; + display: inline-block; + line-height: 1.25; + position: relative; } + .radio input, .checkbox input { + cursor: pointer; } + .radio:hover, .checkbox:hover { + color: #363636; } + .radio[disabled], .checkbox[disabled], fieldset[disabled] .radio, fieldset[disabled] .checkbox { + color: #6b6b6b; + cursor: not-allowed; } + +.radio + .radio { + margin-left: 0.5em; } + +.select { + display: inline-block; + max-width: 100%; + position: relative; + vertical-align: top; } + .select:not(.is-multiple) { + height: 2.25em; } + .select:not(.is-multiple):not(.is-loading)::after { + border-color: #149eaa; + right: 1.125em; + z-index: 4; } + .select.is-rounded select, #documenter .docs-sidebar form.docs-search > input.select select { + border-radius: 290486px; + padding-left: 1em; } + .select select { + cursor: pointer; + display: block; + font-size: 1em; + max-width: 100%; + outline: none; } + .select select::-ms-expand { + display: none; } + .select select[disabled]:hover, fieldset[disabled] .select select:hover { + border-color: whitesmoke; } + .select select:not([multiple]) { + padding-right: 2.5em; } + .select select[multiple] { + height: auto; + padding: 0; } + .select select[multiple] option { + padding: 0.5em 1em; } + .select:not(.is-multiple):not(.is-loading):hover::after { + border-color: #363636; } + .select.is-white:not(:hover)::after { + border-color: white; } + .select.is-white select { + border-color: white; } + .select.is-white select:hover, .select.is-white select.is-hovered { + border-color: #f2f2f2; } + .select.is-white select:focus, .select.is-white select.is-focused, .select.is-white select:active, .select.is-white select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .select.is-black:not(:hover)::after { + border-color: #0a0a0a; } + .select.is-black select { + border-color: #0a0a0a; } + .select.is-black select:hover, .select.is-black select.is-hovered { + border-color: black; } + .select.is-black select:focus, .select.is-black select.is-focused, .select.is-black select:active, .select.is-black select.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .select.is-light:not(:hover)::after { + border-color: whitesmoke; } + .select.is-light select { + border-color: whitesmoke; } + .select.is-light select:hover, .select.is-light select.is-hovered { + border-color: #e8e8e8; } + .select.is-light select:focus, .select.is-light select.is-focused, .select.is-light select:active, .select.is-light select.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .select.is-dark:not(:hover)::after, .content kbd.select:not(:hover)::after { + border-color: #363636; } + .select.is-dark select, .content kbd.select select { + border-color: #363636; } + .select.is-dark select:hover, .content kbd.select select:hover, .select.is-dark select.is-hovered, .content kbd.select select.is-hovered { + border-color: #292929; } + .select.is-dark select:focus, .content kbd.select select:focus, .select.is-dark select.is-focused, .content kbd.select select.is-focused, .select.is-dark select:active, .content kbd.select select:active, .select.is-dark select.is-active, .content kbd.select select.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .select.is-primary:not(:hover)::after, .docstring > section > a.select.docs-sourcelink:not(:hover)::after { + border-color: #4eb5de; } + .select.is-primary select, .docstring > section > a.select.docs-sourcelink select { + border-color: #4eb5de; } + .select.is-primary select:hover, .docstring > section > a.select.docs-sourcelink select:hover, .select.is-primary select.is-hovered, .docstring > section > a.select.docs-sourcelink select.is-hovered { + border-color: #39acda; } + .select.is-primary select:focus, .docstring > section > a.select.docs-sourcelink select:focus, .select.is-primary select.is-focused, .docstring > section > a.select.docs-sourcelink select.is-focused, .select.is-primary select:active, .docstring > section > a.select.docs-sourcelink select:active, .select.is-primary select.is-active, .docstring > section > a.select.docs-sourcelink select.is-active { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .select.is-link:not(:hover)::after { + border-color: #149eaa; } + .select.is-link select { + border-color: #149eaa; } + .select.is-link select:hover, .select.is-link select.is-hovered { + border-color: #118993; } + .select.is-link select:focus, .select.is-link select.is-focused, .select.is-link select:active, .select.is-link select.is-active { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .select.is-info:not(:hover)::after { + border-color: #209cee; } + .select.is-info select { + border-color: #209cee; } + .select.is-info select:hover, .select.is-info select.is-hovered { + border-color: #1190e3; } + .select.is-info select:focus, .select.is-info select.is-focused, .select.is-info select:active, .select.is-info select.is-active { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .select.is-success:not(:hover)::after { + border-color: #22c35b; } + .select.is-success select { + border-color: #22c35b; } + .select.is-success select:hover, .select.is-success select.is-hovered { + border-color: #1ead51; } + .select.is-success select:focus, .select.is-success select.is-focused, .select.is-success select:active, .select.is-success select.is-active { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .select.is-warning:not(:hover)::after { + border-color: #ffdd57; } + .select.is-warning select { + border-color: #ffdd57; } + .select.is-warning select:hover, .select.is-warning select.is-hovered { + border-color: #ffd83e; } + .select.is-warning select:focus, .select.is-warning select.is-focused, .select.is-warning select:active, .select.is-warning select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .select.is-danger:not(:hover)::after { + border-color: #da0b00; } + .select.is-danger select { + border-color: #da0b00; } + .select.is-danger select:hover, .select.is-danger select.is-hovered { + border-color: #c10a00; } + .select.is-danger select:focus, .select.is-danger select.is-focused, .select.is-danger select:active, .select.is-danger select.is-active { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .select.is-small, #documenter .docs-sidebar form.docs-search > input.select { + border-radius: 2px; + font-size: 0.75rem; } + .select.is-medium { + font-size: 1.25rem; } + .select.is-large { + font-size: 1.5rem; } + .select.is-disabled::after { + border-color: #6b6b6b; } + .select.is-fullwidth { + width: 100%; } + .select.is-fullwidth select { + width: 100%; } + .select.is-loading::after { + margin-top: 0; + position: absolute; + right: 0.625em; + top: 0.625em; + transform: none; } + .select.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + .select.is-loading.is-medium:after { + font-size: 1.25rem; } + .select.is-loading.is-large:after { + font-size: 1.5rem; } + +.file { + align-items: stretch; + display: flex; + justify-content: flex-start; + position: relative; } + .file.is-white .file-cta { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + .file.is-white:hover .file-cta, .file.is-white.is-hovered .file-cta { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + .file.is-white:focus .file-cta, .file.is-white.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); + color: #0a0a0a; } + .file.is-white:active .file-cta, .file.is-white.is-active .file-cta { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + .file.is-black .file-cta { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + .file.is-black:hover .file-cta, .file.is-black.is-hovered .file-cta { + background-color: #040404; + border-color: transparent; + color: white; } + .file.is-black:focus .file-cta, .file.is-black.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); + color: white; } + .file.is-black:active .file-cta, .file.is-black.is-active .file-cta { + background-color: black; + border-color: transparent; + color: white; } + .file.is-light .file-cta { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + .file.is-light:hover .file-cta, .file.is-light.is-hovered .file-cta { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + .file.is-light:focus .file-cta, .file.is-light.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25); + color: #363636; } + .file.is-light:active .file-cta, .file.is-light.is-active .file-cta { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + .file.is-dark .file-cta, .content kbd.file .file-cta { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + .file.is-dark:hover .file-cta, .content kbd.file:hover .file-cta, .file.is-dark.is-hovered .file-cta, .content kbd.file.is-hovered .file-cta { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + .file.is-dark:focus .file-cta, .content kbd.file:focus .file-cta, .file.is-dark.is-focused .file-cta, .content kbd.file.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25); + color: whitesmoke; } + .file.is-dark:active .file-cta, .content kbd.file:active .file-cta, .file.is-dark.is-active .file-cta, .content kbd.file.is-active .file-cta { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + .file.is-primary .file-cta, .docstring > section > a.file.docs-sourcelink .file-cta { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + .file.is-primary:hover .file-cta, .docstring > section > a.file.docs-sourcelink:hover .file-cta, .file.is-primary.is-hovered .file-cta, .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + .file.is-primary:focus .file-cta, .docstring > section > a.file.docs-sourcelink:focus .file-cta, .file.is-primary.is-focused .file-cta, .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25); + color: #fff; } + .file.is-primary:active .file-cta, .docstring > section > a.file.docs-sourcelink:active .file-cta, .file.is-primary.is-active .file-cta, .docstring > section > a.file.is-active.docs-sourcelink .file-cta { + background-color: #39acda; + border-color: transparent; + color: #fff; } + .file.is-link .file-cta { + background-color: #149eaa; + border-color: transparent; + color: #fff; } + .file.is-link:hover .file-cta, .file.is-link.is-hovered .file-cta { + background-color: #13939f; + border-color: transparent; + color: #fff; } + .file.is-link:focus .file-cta, .file.is-link.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(20, 158, 170, 0.25); + color: #fff; } + .file.is-link:active .file-cta, .file.is-link.is-active .file-cta { + background-color: #118993; + border-color: transparent; + color: #fff; } + .file.is-info .file-cta { + background-color: #209cee; + border-color: transparent; + color: #fff; } + .file.is-info:hover .file-cta, .file.is-info.is-hovered .file-cta { + background-color: #1497ed; + border-color: transparent; + color: #fff; } + .file.is-info:focus .file-cta, .file.is-info.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(32, 156, 238, 0.25); + color: #fff; } + .file.is-info:active .file-cta, .file.is-info.is-active .file-cta { + background-color: #1190e3; + border-color: transparent; + color: #fff; } + .file.is-success .file-cta { + background-color: #22c35b; + border-color: transparent; + color: #fff; } + .file.is-success:hover .file-cta, .file.is-success.is-hovered .file-cta { + background-color: #20b856; + border-color: transparent; + color: #fff; } + .file.is-success:focus .file-cta, .file.is-success.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(34, 195, 91, 0.25); + color: #fff; } + .file.is-success:active .file-cta, .file.is-success.is-active .file-cta { + background-color: #1ead51; + border-color: transparent; + color: #fff; } + .file.is-warning .file-cta { + background-color: #ffdd57; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:hover .file-cta, .file.is-warning.is-hovered .file-cta { + background-color: #ffda4a; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:focus .file-cta, .file.is-warning.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 221, 87, 0.25); + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:active .file-cta, .file.is-warning.is-active .file-cta { + background-color: #ffd83e; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-danger .file-cta { + background-color: #da0b00; + border-color: transparent; + color: #fff; } + .file.is-danger:hover .file-cta, .file.is-danger.is-hovered .file-cta { + background-color: #cd0a00; + border-color: transparent; + color: #fff; } + .file.is-danger:focus .file-cta, .file.is-danger.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(218, 11, 0, 0.25); + color: #fff; } + .file.is-danger:active .file-cta, .file.is-danger.is-active .file-cta { + background-color: #c10a00; + border-color: transparent; + color: #fff; } + .file.is-small, #documenter .docs-sidebar form.docs-search > input.file { + font-size: 0.75rem; } + .file.is-medium { + font-size: 1.25rem; } + .file.is-medium .file-icon .fa { + font-size: 21px; } + .file.is-large { + font-size: 1.5rem; } + .file.is-large .file-icon .fa { + font-size: 28px; } + .file.has-name .file-cta { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + .file.has-name .file-name { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .file.has-name.is-empty .file-cta { + border-radius: 4px; } + .file.has-name.is-empty .file-name { + display: none; } + .file.is-boxed .file-label { + flex-direction: column; } + .file.is-boxed .file-cta { + flex-direction: column; + height: auto; + padding: 1em 3em; } + .file.is-boxed .file-name { + border-width: 0 1px 1px; } + .file.is-boxed .file-icon { + height: 1.5em; + width: 1.5em; } + .file.is-boxed .file-icon .fa { + font-size: 21px; } + .file.is-boxed.is-small .file-icon .fa, #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { + font-size: 14px; } + .file.is-boxed.is-medium .file-icon .fa { + font-size: 28px; } + .file.is-boxed.is-large .file-icon .fa { + font-size: 35px; } + .file.is-boxed.has-name .file-cta { + border-radius: 4px 4px 0 0; } + .file.is-boxed.has-name .file-name { + border-radius: 0 0 4px 4px; + border-width: 0 1px 1px; } + .file.is-centered { + justify-content: center; } + .file.is-fullwidth .file-label { + width: 100%; } + .file.is-fullwidth .file-name { + flex-grow: 1; + max-width: none; } + .file.is-right { + justify-content: flex-end; } + .file.is-right .file-cta { + border-radius: 0 4px 4px 0; } + .file.is-right .file-name { + border-radius: 4px 0 0 4px; + border-width: 1px 0 1px 1px; + order: -1; } + +.file-label { + align-items: stretch; + display: flex; + cursor: pointer; + justify-content: flex-start; + overflow: hidden; + position: relative; } + .file-label:hover .file-cta { + background-color: #eeeeee; + color: #363636; } + .file-label:hover .file-name { + border-color: #d5d5d5; } + .file-label:active .file-cta { + background-color: #e8e8e8; + color: #363636; } + .file-label:active .file-name { + border-color: #cfcfcf; } + +.file-input { + height: 100%; + left: 0; + opacity: 0; + outline: none; + position: absolute; + top: 0; + width: 100%; } + +.file-cta, +.file-name { + border-color: #dbdbdb; + border-radius: 4px; + font-size: 1em; + padding-left: 1em; + padding-right: 1em; + white-space: nowrap; } + +.file-cta { + background-color: whitesmoke; + color: #4a4a4a; } + +.file-name { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px 1px 1px 0; + display: block; + max-width: 16em; + overflow: hidden; + text-align: left; + text-overflow: ellipsis; } + +.file-icon { + align-items: center; + display: flex; + height: 1em; + justify-content: center; + margin-right: 0.5em; + width: 1em; } + .file-icon .fa { + font-size: 14px; } + +.label { + color: #363636; + display: block; + font-size: 1rem; + font-weight: 700; } + .label:not(:last-child) { + margin-bottom: 0.5em; } + .label.is-small, #documenter .docs-sidebar form.docs-search > input.label { + font-size: 0.75rem; } + .label.is-medium { + font-size: 1.25rem; } + .label.is-large { + font-size: 1.5rem; } + +.help { + display: block; + font-size: 0.75rem; + margin-top: 0.25rem; } + .help.is-white { + color: white; } + .help.is-black { + color: #0a0a0a; } + .help.is-light { + color: whitesmoke; } + .help.is-dark, .content kbd.help { + color: #363636; } + .help.is-primary, .docstring > section > a.help.docs-sourcelink { + color: #4eb5de; } + .help.is-link { + color: #149eaa; } + .help.is-info { + color: #209cee; } + .help.is-success { + color: #22c35b; } + .help.is-warning { + color: #ffdd57; } + .help.is-danger { + color: #da0b00; } + +.field:not(:last-child) { + margin-bottom: 0.75rem; } + +.field.has-addons { + display: flex; + justify-content: flex-start; } + .field.has-addons .control:not(:last-child) { + margin-right: -1px; } + .field.has-addons .control:not(:first-child):not(:last-child) .button, + .field.has-addons .control:not(:first-child):not(:last-child) .input, + .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, + .field.has-addons .control:not(:first-child):not(:last-child) .select select { + border-radius: 0; } + .field.has-addons .control:first-child:not(:only-child) .button, + .field.has-addons .control:first-child:not(:only-child) .input, + .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, + .field.has-addons .control:first-child:not(:only-child) .select select { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + .field.has-addons .control:last-child:not(:only-child) .button, + .field.has-addons .control:last-child:not(:only-child) .input, + .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, + .field.has-addons .control:last-child:not(:only-child) .select select { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .field.has-addons .control .button:not([disabled]):hover, .field.has-addons .control .button.is-hovered:not([disabled]), + .field.has-addons .control .input:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, + .field.has-addons .control .input.is-hovered:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), + .field.has-addons .control .select select:not([disabled]):hover, + .field.has-addons .control .select select.is-hovered:not([disabled]) { + z-index: 2; } + .field.has-addons .control .button:not([disabled]):focus, .field.has-addons .control .button.is-focused:not([disabled]), .field.has-addons .control .button:not([disabled]):active, .field.has-addons .control .button.is-active:not([disabled]), + .field.has-addons .control .input:not([disabled]):focus, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, + .field.has-addons .control .input.is-focused:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), + .field.has-addons .control .input:not([disabled]):active, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, + .field.has-addons .control .input.is-active:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), + .field.has-addons .control .select select:not([disabled]):focus, + .field.has-addons .control .select select.is-focused:not([disabled]), + .field.has-addons .control .select select:not([disabled]):active, + .field.has-addons .control .select select.is-active:not([disabled]) { + z-index: 3; } + .field.has-addons .control .button:not([disabled]):focus:hover, .field.has-addons .control .button.is-focused:not([disabled]):hover, .field.has-addons .control .button:not([disabled]):active:hover, .field.has-addons .control .button.is-active:not([disabled]):hover, + .field.has-addons .control .input:not([disabled]):focus:hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, + .field.has-addons .control .input.is-focused:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, + .field.has-addons .control .input:not([disabled]):active:hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, + .field.has-addons .control .input.is-active:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, + .field.has-addons .control .select select:not([disabled]):focus:hover, + .field.has-addons .control .select select.is-focused:not([disabled]):hover, + .field.has-addons .control .select select:not([disabled]):active:hover, + .field.has-addons .control .select select.is-active:not([disabled]):hover { + z-index: 4; } + .field.has-addons .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .field.has-addons.has-addons-centered { + justify-content: center; } + .field.has-addons.has-addons-right { + justify-content: flex-end; } + .field.has-addons.has-addons-fullwidth .control { + flex-grow: 1; + flex-shrink: 0; } + +.field.is-grouped { + display: flex; + justify-content: flex-start; } + .field.is-grouped > .control { + flex-shrink: 0; } + .field.is-grouped > .control:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + .field.is-grouped > .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .field.is-grouped.is-grouped-centered { + justify-content: center; } + .field.is-grouped.is-grouped-right { + justify-content: flex-end; } + .field.is-grouped.is-grouped-multiline { + flex-wrap: wrap; } + .field.is-grouped.is-grouped-multiline > .control:last-child, .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { + margin-bottom: 0.75rem; } + .field.is-grouped.is-grouped-multiline:last-child { + margin-bottom: -0.75rem; } + .field.is-grouped.is-grouped-multiline:not(:last-child) { + margin-bottom: 0; } + +@media screen and (min-width: 769px), print { + .field.is-horizontal { + display: flex; } } + +.field-label .label { + font-size: inherit; } + +@media screen and (max-width: 768px) { + .field-label { + margin-bottom: 0.5rem; } } + +@media screen and (min-width: 769px), print { + .field-label { + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + margin-right: 1.5rem; + text-align: right; } + .field-label.is-small, #documenter .docs-sidebar form.docs-search > input.field-label { + font-size: 0.75rem; + padding-top: 0.375em; } + .field-label.is-normal { + padding-top: 0.375em; } + .field-label.is-medium { + font-size: 1.25rem; + padding-top: 0.375em; } + .field-label.is-large { + font-size: 1.5rem; + padding-top: 0.375em; } } + +.field-body .field .field { + margin-bottom: 0; } + +@media screen and (min-width: 769px), print { + .field-body { + display: flex; + flex-basis: 0; + flex-grow: 5; + flex-shrink: 1; } + .field-body .field { + margin-bottom: 0; } + .field-body > .field { + flex-shrink: 1; } + .field-body > .field:not(.is-narrow) { + flex-grow: 1; } + .field-body > .field:not(:last-child) { + margin-right: 0.75rem; } } + +.control { + box-sizing: border-box; + clear: both; + font-size: 1rem; + position: relative; + text-align: left; } + .control.has-icons-left .input:focus ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, + .control.has-icons-left .select:focus ~ .icon, .control.has-icons-right .input:focus ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, + .control.has-icons-right .select:focus ~ .icon { + color: #6b6b6b; } + .control.has-icons-left .input.is-small ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, + .control.has-icons-left .select.is-small ~ .icon, .control.has-icons-right .input.is-small ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, + .control.has-icons-right .select.is-small ~ .icon { + font-size: 0.75rem; } + .control.has-icons-left .input.is-medium ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, + .control.has-icons-left .select.is-medium ~ .icon, .control.has-icons-right .input.is-medium ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, + .control.has-icons-right .select.is-medium ~ .icon { + font-size: 1.25rem; } + .control.has-icons-left .input.is-large ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, + .control.has-icons-left .select.is-large ~ .icon, .control.has-icons-right .input.is-large ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, + .control.has-icons-right .select.is-large ~ .icon { + font-size: 1.5rem; } + .control.has-icons-left .icon, .control.has-icons-right .icon { + color: #dbdbdb; + height: 2.25em; + pointer-events: none; + position: absolute; + top: 0; + width: 2.25em; + z-index: 4; } + .control.has-icons-left .input, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, + .control.has-icons-left .select select { + padding-left: 2.25em; } + .control.has-icons-left .icon.is-left { + left: 0; } + .control.has-icons-right .input, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, + .control.has-icons-right .select select { + padding-right: 2.25em; } + .control.has-icons-right .icon.is-right { + right: 0; } + .control.is-loading::after { + position: absolute !important; + right: 0.625em; + top: 0.625em; + z-index: 4; } + .control.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + .control.is-loading.is-medium:after { + font-size: 1.25rem; } + .control.is-loading.is-large:after { + font-size: 1.5rem; } + +.breadcrumb { + font-size: 1rem; + white-space: nowrap; } + .breadcrumb a { + align-items: center; + color: #149eaa; + display: flex; + justify-content: center; + padding: 0 0.75em; } + .breadcrumb a:hover { + color: #107c85; } + .breadcrumb li { + align-items: center; + display: flex; } + .breadcrumb li:first-child a { + padding-left: 0; } + .breadcrumb li.is-active a { + color: #654ca3; + cursor: default; + pointer-events: none; } + .breadcrumb li + li::before { + color: #b5b5b5; + content: "\0002f"; } + .breadcrumb ul, + .breadcrumb ol { + align-items: flex-start; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .breadcrumb .icon:first-child { + margin-right: 0.5em; } + .breadcrumb .icon:last-child { + margin-left: 0.5em; } + .breadcrumb.is-centered ol, + .breadcrumb.is-centered ul { + justify-content: center; } + .breadcrumb.is-right ol, + .breadcrumb.is-right ul { + justify-content: flex-end; } + .breadcrumb.is-small, #documenter .docs-sidebar form.docs-search > input.breadcrumb { + font-size: 0.75rem; } + .breadcrumb.is-medium { + font-size: 1.25rem; } + .breadcrumb.is-large { + font-size: 1.5rem; } + .breadcrumb.has-arrow-separator li + li::before { + content: "\02192"; } + .breadcrumb.has-bullet-separator li + li::before { + content: "\02022"; } + .breadcrumb.has-dot-separator li + li::before { + content: "\000b7"; } + .breadcrumb.has-succeeds-separator li + li::before { + content: "\0227B"; } + +.card { + background-color: white; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #202020; + max-width: 100%; + position: relative; } + +.card-header { + background-color: transparent; + align-items: stretch; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + display: flex; } + +.card-header-title { + align-items: center; + color: #654ca3; + display: flex; + flex-grow: 1; + font-weight: 700; + padding: 0.75rem; } + .card-header-title.is-centered { + justify-content: center; } + +.card-header-icon { + align-items: center; + cursor: pointer; + display: flex; + justify-content: center; + padding: 0.75rem; } + +.card-image { + display: block; + position: relative; } + +.card-content { + background-color: transparent; + padding: 1.5rem; } + +.card-footer { + background-color: transparent; + border-top: 1px solid #dbdbdb; + align-items: stretch; + display: flex; } + +.card-footer-item { + align-items: center; + display: flex; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + justify-content: center; + padding: 0.75rem; } + .card-footer-item:not(:last-child) { + border-right: 1px solid #dbdbdb; } + +.card .media:not(:last-child) { + margin-bottom: 1.5rem; } + +.dropdown { + display: inline-flex; + position: relative; + vertical-align: top; } + .dropdown.is-active .dropdown-menu, .dropdown.is-hoverable:hover .dropdown-menu { + display: block; } + .dropdown.is-right .dropdown-menu { + left: auto; + right: 0; } + .dropdown.is-up .dropdown-menu { + bottom: 100%; + padding-bottom: 4px; + padding-top: initial; + top: auto; } + +.dropdown-menu { + display: none; + left: 0; + min-width: 12rem; + padding-top: 4px; + position: absolute; + top: 100%; + z-index: 20; } + +.dropdown-content { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + +.dropdown-item { + color: #4a4a4a; + display: block; + font-size: 0.875rem; + line-height: 1.5; + padding: 0.375rem 1rem; + position: relative; } + +a.dropdown-item, +button.dropdown-item { + padding-right: 3rem; + text-align: left; + white-space: nowrap; + width: 100%; } + a.dropdown-item:hover, + button.dropdown-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + a.dropdown-item.is-active, + button.dropdown-item.is-active { + background-color: #149eaa; + color: #fff; } + +.dropdown-divider { + background-color: #dbdbdb; + border: none; + display: block; + height: 1px; + margin: 0.5rem 0; } + +.level { + align-items: center; + justify-content: space-between; } + .level code { + border-radius: 4px; } + .level img { + display: inline-block; + vertical-align: top; } + .level.is-mobile { + display: flex; } + .level.is-mobile .level-left, + .level.is-mobile .level-right { + display: flex; } + .level.is-mobile .level-left + .level-right { + margin-top: 0; } + .level.is-mobile .level-item:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + .level.is-mobile .level-item:not(.is-narrow) { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + .level { + display: flex; } + .level > .level-item:not(.is-narrow) { + flex-grow: 1; } } +.level-item { + align-items: center; + display: flex; + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; + justify-content: center; } + .level-item .title, + .level-item .subtitle { + margin-bottom: 0; } + @media screen and (max-width: 768px) { + .level-item:not(:last-child) { + margin-bottom: 0.75rem; } } +.level-left, +.level-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + .level-left .level-item.is-flexible, + .level-right .level-item.is-flexible { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + .level-left .level-item:not(:last-child), + .level-right .level-item:not(:last-child) { + margin-right: 0.75rem; } } +.level-left { + align-items: center; + justify-content: flex-start; } + @media screen and (max-width: 768px) { + .level-left + .level-right { + margin-top: 1.5rem; } } + @media screen and (min-width: 769px), print { + .level-left { + display: flex; } } +.level-right { + align-items: center; + justify-content: flex-end; } + @media screen and (min-width: 769px), print { + .level-right { + display: flex; } } +.list { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } + +.list-item { + display: block; + padding: 0.5em 1em; } + .list-item:not(a) { + color: #202020; } + .list-item:first-child { + border-top-left-radius: 4px; + border-top-right-radius: 4px; } + .list-item:last-child { + border-bottom-left-radius: 4px; + border-bottom-right-radius: 4px; } + .list-item:not(:last-child) { + border-bottom: 1px solid #dbdbdb; } + .list-item.is-active { + background-color: #149eaa; + color: #fff; } + +a.list-item { + background-color: whitesmoke; + cursor: pointer; } + +.media { + align-items: flex-start; + display: flex; + text-align: left; } + .media .content:not(:last-child) { + margin-bottom: 0.75rem; } + .media .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + display: flex; + padding-top: 0.75rem; } + .media .media .content:not(:last-child), + .media .media .control:not(:last-child) { + margin-bottom: 0.5rem; } + .media .media .media { + padding-top: 0.5rem; } + .media .media .media + .media { + margin-top: 0.5rem; } + .media + .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + margin-top: 1rem; + padding-top: 1rem; } + .media.is-large + .media { + margin-top: 1.5rem; + padding-top: 1.5rem; } + +.media-left, +.media-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + +.media-left { + margin-right: 1rem; } + +.media-right { + margin-left: 1rem; } + +.media-content { + flex-basis: auto; + flex-grow: 1; + flex-shrink: 1; + text-align: left; } + +@media screen and (max-width: 768px) { + .media-content { + overflow-x: auto; } } + +.menu { + font-size: 1rem; } + .menu.is-small, #documenter .docs-sidebar form.docs-search > input.menu { + font-size: 0.75rem; } + .menu.is-medium { + font-size: 1.25rem; } + .menu.is-large { + font-size: 1.5rem; } + +.menu-list { + line-height: 1.25; } + .menu-list a { + border-radius: 2px; + color: #202020; + display: block; + padding: 0.5em 0.75em; } + .menu-list a:hover { + background-color: whitesmoke; + color: #654ca3; } + .menu-list a.is-active { + background-color: #149eaa; + color: #fff; } + .menu-list li ul { + border-left: 1px solid #dbdbdb; + margin: 0.75em; + padding-left: 0.75em; } + +.menu-label { + color: #6b6b6b; + font-size: 0.75em; + letter-spacing: 0.1em; + text-transform: uppercase; } + .menu-label:not(:first-child) { + margin-top: 1em; } + .menu-label:not(:last-child) { + margin-bottom: 1em; } + +.message { + background-color: whitesmoke; + border-radius: 4px; + font-size: 1rem; } + .message strong { + color: currentColor; } + .message a:not(.button):not(.tag):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + .message.is-small, #documenter .docs-sidebar form.docs-search > input.message { + font-size: 0.75rem; } + .message.is-medium { + font-size: 1.25rem; } + .message.is-large { + font-size: 1.5rem; } + .message.is-white { + background-color: white; } + .message.is-white .message-header { + background-color: white; + color: #0a0a0a; } + .message.is-white .message-body { + border-color: white; + color: #4d4d4d; } + .message.is-black { + background-color: #fafafa; } + .message.is-black .message-header { + background-color: #0a0a0a; + color: white; } + .message.is-black .message-body { + border-color: #0a0a0a; + color: #090909; } + .message.is-light { + background-color: #fafafa; } + .message.is-light .message-header { + background-color: whitesmoke; + color: #363636; } + .message.is-light .message-body { + border-color: whitesmoke; + color: #505050; } + .message.is-dark, .content kbd.message { + background-color: #fafafa; } + .message.is-dark .message-header, .content kbd.message .message-header { + background-color: #363636; + color: whitesmoke; } + .message.is-dark .message-body, .content kbd.message .message-body { + border-color: #363636; + color: #2a2a2a; } + .message.is-primary, .docstring > section > a.message.docs-sourcelink { + background-color: #f6fbfd; } + .message.is-primary .message-header, .docstring > section > a.message.docs-sourcelink .message-header { + background-color: #4eb5de; + color: #fff; } + .message.is-primary .message-body, .docstring > section > a.message.docs-sourcelink .message-body { + border-color: #4eb5de; + color: #1f556a; } + .message.is-link { + background-color: #f6fdfe; } + .message.is-link .message-header { + background-color: #149eaa; + color: #fff; } + .message.is-link .message-body { + border-color: #149eaa; + color: #0b393d; } + .message.is-info { + background-color: #f6fbfe; } + .message.is-info .message-header { + background-color: #209cee; + color: #fff; } + .message.is-info .message-body { + border-color: #209cee; + color: #12537d; } + .message.is-success { + background-color: #f6fdf9; } + .message.is-success .message-header { + background-color: #22c35b; + color: #fff; } + .message.is-success .message-body { + border-color: #22c35b; + color: #0f361d; } + .message.is-warning { + background-color: #fffdf5; } + .message.is-warning .message-header { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .message.is-warning .message-body { + border-color: #ffdd57; + color: #3c3108; } + .message.is-danger { + background-color: #fff5f5; } + .message.is-danger .message-header { + background-color: #da0b00; + color: #fff; } + .message.is-danger .message-body { + border-color: #da0b00; + color: #9b0c04; } + +.message-header { + align-items: center; + background-color: #202020; + border-radius: 4px 4px 0 0; + color: #fff; + display: flex; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.75em 1em; + position: relative; } + .message-header .delete { + flex-grow: 0; + flex-shrink: 0; + margin-left: 0.75em; } + .message-header + .message-body { + border-width: 0; + border-top-left-radius: 0; + border-top-right-radius: 0; } + +.message-body { + border-color: #dbdbdb; + border-radius: 4px; + border-style: solid; + border-width: 0 0 0 4px; + color: #202020; + padding: 1.25em 1.5em; } + .message-body code, + .message-body pre { + background-color: white; } + .message-body pre code { + background-color: transparent; } + +.modal { + align-items: center; + display: none; + flex-direction: column; + justify-content: center; + overflow: hidden; + position: fixed; + z-index: 40; } + .modal.is-active { + display: flex; } + +.modal-background { + background-color: rgba(10, 10, 10, 0.86); } + +.modal-content, +.modal-card { + margin: 0 20px; + max-height: calc(100vh - 160px); + overflow: auto; + position: relative; + width: 100%; } + @media screen and (min-width: 769px), print { + .modal-content, + .modal-card { + margin: 0 auto; + max-height: calc(100vh - 40px); + width: 640px; } } +.modal-close { + background: none; + height: 40px; + position: fixed; + right: 20px; + top: 20px; + width: 40px; } + +.modal-card { + display: flex; + flex-direction: column; + max-height: calc(100vh - 40px); + overflow: hidden; + -ms-overflow-y: visible; } + +.modal-card-head, +.modal-card-foot { + align-items: center; + background-color: whitesmoke; + display: flex; + flex-shrink: 0; + justify-content: flex-start; + padding: 20px; + position: relative; } + +.modal-card-head { + border-bottom: 1px solid #dbdbdb; + border-top-left-radius: 6px; + border-top-right-radius: 6px; } + +.modal-card-title { + color: #654ca3; + flex-grow: 1; + flex-shrink: 0; + font-size: 1.5rem; + line-height: 1; } + +.modal-card-foot { + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 1px solid #dbdbdb; } + .modal-card-foot .button:not(:last-child) { + margin-right: 0.5em; } + +.modal-card-body { + -webkit-overflow-scrolling: touch; + background-color: white; + flex-grow: 1; + flex-shrink: 1; + overflow: auto; + padding: 20px; } + +.navbar { + background-color: white; + min-height: 3.25rem; + position: relative; + z-index: 30; } + .navbar.is-white { + background-color: white; + color: #0a0a0a; } + .navbar.is-white .navbar-brand > .navbar-item, + .navbar.is-white .navbar-brand .navbar-link { + color: #0a0a0a; } + .navbar.is-white .navbar-brand > a.navbar-item:focus, .navbar.is-white .navbar-brand > a.navbar-item:hover, .navbar.is-white .navbar-brand > a.navbar-item.is-active, + .navbar.is-white .navbar-brand .navbar-link:focus, + .navbar.is-white .navbar-brand .navbar-link:hover, + .navbar.is-white .navbar-brand .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-brand .navbar-link::after { + border-color: #0a0a0a; } + .navbar.is-white .navbar-burger { + color: #0a0a0a; } + @media screen and (min-width: 1056px) { + .navbar.is-white .navbar-start > .navbar-item, + .navbar.is-white .navbar-start .navbar-link, + .navbar.is-white .navbar-end > .navbar-item, + .navbar.is-white .navbar-end .navbar-link { + color: #0a0a0a; } + .navbar.is-white .navbar-start > a.navbar-item:focus, .navbar.is-white .navbar-start > a.navbar-item:hover, .navbar.is-white .navbar-start > a.navbar-item.is-active, + .navbar.is-white .navbar-start .navbar-link:focus, + .navbar.is-white .navbar-start .navbar-link:hover, + .navbar.is-white .navbar-start .navbar-link.is-active, + .navbar.is-white .navbar-end > a.navbar-item:focus, + .navbar.is-white .navbar-end > a.navbar-item:hover, + .navbar.is-white .navbar-end > a.navbar-item.is-active, + .navbar.is-white .navbar-end .navbar-link:focus, + .navbar.is-white .navbar-end .navbar-link:hover, + .navbar.is-white .navbar-end .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-start .navbar-link::after, + .navbar.is-white .navbar-end .navbar-link::after { + border-color: #0a0a0a; } + .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-dropdown a.navbar-item.is-active { + background-color: white; + color: #0a0a0a; } } + .navbar.is-black { + background-color: #0a0a0a; + color: white; } + .navbar.is-black .navbar-brand > .navbar-item, + .navbar.is-black .navbar-brand .navbar-link { + color: white; } + .navbar.is-black .navbar-brand > a.navbar-item:focus, .navbar.is-black .navbar-brand > a.navbar-item:hover, .navbar.is-black .navbar-brand > a.navbar-item.is-active, + .navbar.is-black .navbar-brand .navbar-link:focus, + .navbar.is-black .navbar-brand .navbar-link:hover, + .navbar.is-black .navbar-brand .navbar-link.is-active { + background-color: black; + color: white; } + .navbar.is-black .navbar-brand .navbar-link::after { + border-color: white; } + .navbar.is-black .navbar-burger { + color: white; } + @media screen and (min-width: 1056px) { + .navbar.is-black .navbar-start > .navbar-item, + .navbar.is-black .navbar-start .navbar-link, + .navbar.is-black .navbar-end > .navbar-item, + .navbar.is-black .navbar-end .navbar-link { + color: white; } + .navbar.is-black .navbar-start > a.navbar-item:focus, .navbar.is-black .navbar-start > a.navbar-item:hover, .navbar.is-black .navbar-start > a.navbar-item.is-active, + .navbar.is-black .navbar-start .navbar-link:focus, + .navbar.is-black .navbar-start .navbar-link:hover, + .navbar.is-black .navbar-start .navbar-link.is-active, + .navbar.is-black .navbar-end > a.navbar-item:focus, + .navbar.is-black .navbar-end > a.navbar-item:hover, + .navbar.is-black .navbar-end > a.navbar-item.is-active, + .navbar.is-black .navbar-end .navbar-link:focus, + .navbar.is-black .navbar-end .navbar-link:hover, + .navbar.is-black .navbar-end .navbar-link.is-active { + background-color: black; + color: white; } + .navbar.is-black .navbar-start .navbar-link::after, + .navbar.is-black .navbar-end .navbar-link::after { + border-color: white; } + .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { + background-color: black; + color: white; } + .navbar.is-black .navbar-dropdown a.navbar-item.is-active { + background-color: #0a0a0a; + color: white; } } + .navbar.is-light { + background-color: whitesmoke; + color: #363636; } + .navbar.is-light .navbar-brand > .navbar-item, + .navbar.is-light .navbar-brand .navbar-link { + color: #363636; } + .navbar.is-light .navbar-brand > a.navbar-item:focus, .navbar.is-light .navbar-brand > a.navbar-item:hover, .navbar.is-light .navbar-brand > a.navbar-item.is-active, + .navbar.is-light .navbar-brand .navbar-link:focus, + .navbar.is-light .navbar-brand .navbar-link:hover, + .navbar.is-light .navbar-brand .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-brand .navbar-link::after { + border-color: #363636; } + .navbar.is-light .navbar-burger { + color: #363636; } + @media screen and (min-width: 1056px) { + .navbar.is-light .navbar-start > .navbar-item, + .navbar.is-light .navbar-start .navbar-link, + .navbar.is-light .navbar-end > .navbar-item, + .navbar.is-light .navbar-end .navbar-link { + color: #363636; } + .navbar.is-light .navbar-start > a.navbar-item:focus, .navbar.is-light .navbar-start > a.navbar-item:hover, .navbar.is-light .navbar-start > a.navbar-item.is-active, + .navbar.is-light .navbar-start .navbar-link:focus, + .navbar.is-light .navbar-start .navbar-link:hover, + .navbar.is-light .navbar-start .navbar-link.is-active, + .navbar.is-light .navbar-end > a.navbar-item:focus, + .navbar.is-light .navbar-end > a.navbar-item:hover, + .navbar.is-light .navbar-end > a.navbar-item.is-active, + .navbar.is-light .navbar-end .navbar-link:focus, + .navbar.is-light .navbar-end .navbar-link:hover, + .navbar.is-light .navbar-end .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-start .navbar-link::after, + .navbar.is-light .navbar-end .navbar-link::after { + border-color: #363636; } + .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #363636; } } + .navbar.is-dark, .content kbd.navbar { + background-color: #363636; + color: whitesmoke; } + .navbar.is-dark .navbar-brand > .navbar-item, .content kbd.navbar .navbar-brand > .navbar-item, + .navbar.is-dark .navbar-brand .navbar-link, + .content kbd.navbar .navbar-brand .navbar-link { + color: whitesmoke; } + .navbar.is-dark .navbar-brand > a.navbar-item:focus, .content kbd.navbar .navbar-brand > a.navbar-item:focus, .navbar.is-dark .navbar-brand > a.navbar-item:hover, .content kbd.navbar .navbar-brand > a.navbar-item:hover, .navbar.is-dark .navbar-brand > a.navbar-item.is-active, .content kbd.navbar .navbar-brand > a.navbar-item.is-active, + .navbar.is-dark .navbar-brand .navbar-link:focus, + .content kbd.navbar .navbar-brand .navbar-link:focus, + .navbar.is-dark .navbar-brand .navbar-link:hover, + .content kbd.navbar .navbar-brand .navbar-link:hover, + .navbar.is-dark .navbar-brand .navbar-link.is-active, + .content kbd.navbar .navbar-brand .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-brand .navbar-link::after, .content kbd.navbar .navbar-brand .navbar-link::after { + border-color: whitesmoke; } + .navbar.is-dark .navbar-burger, .content kbd.navbar .navbar-burger { + color: whitesmoke; } + @media screen and (min-width: 1056px) { + .navbar.is-dark .navbar-start > .navbar-item, .content kbd.navbar .navbar-start > .navbar-item, + .navbar.is-dark .navbar-start .navbar-link, + .content kbd.navbar .navbar-start .navbar-link, + .navbar.is-dark .navbar-end > .navbar-item, + .content kbd.navbar .navbar-end > .navbar-item, + .navbar.is-dark .navbar-end .navbar-link, + .content kbd.navbar .navbar-end .navbar-link { + color: whitesmoke; } + .navbar.is-dark .navbar-start > a.navbar-item:focus, .content kbd.navbar .navbar-start > a.navbar-item:focus, .navbar.is-dark .navbar-start > a.navbar-item:hover, .content kbd.navbar .navbar-start > a.navbar-item:hover, .navbar.is-dark .navbar-start > a.navbar-item.is-active, .content kbd.navbar .navbar-start > a.navbar-item.is-active, + .navbar.is-dark .navbar-start .navbar-link:focus, + .content kbd.navbar .navbar-start .navbar-link:focus, + .navbar.is-dark .navbar-start .navbar-link:hover, + .content kbd.navbar .navbar-start .navbar-link:hover, + .navbar.is-dark .navbar-start .navbar-link.is-active, + .content kbd.navbar .navbar-start .navbar-link.is-active, + .navbar.is-dark .navbar-end > a.navbar-item:focus, + .content kbd.navbar .navbar-end > a.navbar-item:focus, + .navbar.is-dark .navbar-end > a.navbar-item:hover, + .content kbd.navbar .navbar-end > a.navbar-item:hover, + .navbar.is-dark .navbar-end > a.navbar-item.is-active, + .content kbd.navbar .navbar-end > a.navbar-item.is-active, + .navbar.is-dark .navbar-end .navbar-link:focus, + .content kbd.navbar .navbar-end .navbar-link:focus, + .navbar.is-dark .navbar-end .navbar-link:hover, + .content kbd.navbar .navbar-end .navbar-link:hover, + .navbar.is-dark .navbar-end .navbar-link.is-active, + .content kbd.navbar .navbar-end .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-start .navbar-link::after, .content kbd.navbar .navbar-start .navbar-link::after, + .navbar.is-dark .navbar-end .navbar-link::after, + .content kbd.navbar .navbar-end .navbar-link::after { + border-color: whitesmoke; } + .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, + .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, + .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { + background-color: #363636; + color: whitesmoke; } } + .navbar.is-primary, .docstring > section > a.navbar.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .navbar.is-primary .navbar-brand > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, + .navbar.is-primary .navbar-brand .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-primary .navbar-brand > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, .navbar.is-primary .navbar-brand > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, .navbar.is-primary .navbar-brand > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, + .navbar.is-primary .navbar-brand .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, + .navbar.is-primary .navbar-brand .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, + .navbar.is-primary .navbar-brand .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-brand .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-primary .navbar-burger, .docstring > section > a.navbar.docs-sourcelink .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-primary .navbar-start > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, + .navbar.is-primary .navbar-start .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, + .navbar.is-primary .navbar-end > .navbar-item, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, + .navbar.is-primary .navbar-end .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { + color: #fff; } + .navbar.is-primary .navbar-start > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, .navbar.is-primary .navbar-start > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, .navbar.is-primary .navbar-start > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, + .navbar.is-primary .navbar-start .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, + .navbar.is-primary .navbar-start .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, + .navbar.is-primary .navbar-start .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, + .navbar.is-primary .navbar-end > a.navbar-item:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, + .navbar.is-primary .navbar-end > a.navbar-item:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, + .navbar.is-primary .navbar-end > a.navbar-item.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, + .navbar.is-primary .navbar-end .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, + .navbar.is-primary .navbar-end .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, + .navbar.is-primary .navbar-end .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-start .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, + .navbar.is-primary .navbar-end .navbar-link::after, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { + background-color: #4eb5de; + color: #fff; } } + .navbar.is-link { + background-color: #149eaa; + color: #fff; } + .navbar.is-link .navbar-brand > .navbar-item, + .navbar.is-link .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-link .navbar-brand > a.navbar-item:focus, .navbar.is-link .navbar-brand > a.navbar-item:hover, .navbar.is-link .navbar-brand > a.navbar-item.is-active, + .navbar.is-link .navbar-brand .navbar-link:focus, + .navbar.is-link .navbar-brand .navbar-link:hover, + .navbar.is-link .navbar-brand .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-link .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-link .navbar-start > .navbar-item, + .navbar.is-link .navbar-start .navbar-link, + .navbar.is-link .navbar-end > .navbar-item, + .navbar.is-link .navbar-end .navbar-link { + color: #fff; } + .navbar.is-link .navbar-start > a.navbar-item:focus, .navbar.is-link .navbar-start > a.navbar-item:hover, .navbar.is-link .navbar-start > a.navbar-item.is-active, + .navbar.is-link .navbar-start .navbar-link:focus, + .navbar.is-link .navbar-start .navbar-link:hover, + .navbar.is-link .navbar-start .navbar-link.is-active, + .navbar.is-link .navbar-end > a.navbar-item:focus, + .navbar.is-link .navbar-end > a.navbar-item:hover, + .navbar.is-link .navbar-end > a.navbar-item.is-active, + .navbar.is-link .navbar-end .navbar-link:focus, + .navbar.is-link .navbar-end .navbar-link:hover, + .navbar.is-link .navbar-end .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-start .navbar-link::after, + .navbar.is-link .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-dropdown a.navbar-item.is-active { + background-color: #149eaa; + color: #fff; } } + .navbar.is-info { + background-color: #209cee; + color: #fff; } + .navbar.is-info .navbar-brand > .navbar-item, + .navbar.is-info .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-info .navbar-brand > a.navbar-item:focus, .navbar.is-info .navbar-brand > a.navbar-item:hover, .navbar.is-info .navbar-brand > a.navbar-item.is-active, + .navbar.is-info .navbar-brand .navbar-link:focus, + .navbar.is-info .navbar-brand .navbar-link:hover, + .navbar.is-info .navbar-brand .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-info .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-info .navbar-start > .navbar-item, + .navbar.is-info .navbar-start .navbar-link, + .navbar.is-info .navbar-end > .navbar-item, + .navbar.is-info .navbar-end .navbar-link { + color: #fff; } + .navbar.is-info .navbar-start > a.navbar-item:focus, .navbar.is-info .navbar-start > a.navbar-item:hover, .navbar.is-info .navbar-start > a.navbar-item.is-active, + .navbar.is-info .navbar-start .navbar-link:focus, + .navbar.is-info .navbar-start .navbar-link:hover, + .navbar.is-info .navbar-start .navbar-link.is-active, + .navbar.is-info .navbar-end > a.navbar-item:focus, + .navbar.is-info .navbar-end > a.navbar-item:hover, + .navbar.is-info .navbar-end > a.navbar-item.is-active, + .navbar.is-info .navbar-end .navbar-link:focus, + .navbar.is-info .navbar-end .navbar-link:hover, + .navbar.is-info .navbar-end .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-start .navbar-link::after, + .navbar.is-info .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-dropdown a.navbar-item.is-active { + background-color: #209cee; + color: #fff; } } + .navbar.is-success { + background-color: #22c35b; + color: #fff; } + .navbar.is-success .navbar-brand > .navbar-item, + .navbar.is-success .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-success .navbar-brand > a.navbar-item:focus, .navbar.is-success .navbar-brand > a.navbar-item:hover, .navbar.is-success .navbar-brand > a.navbar-item.is-active, + .navbar.is-success .navbar-brand .navbar-link:focus, + .navbar.is-success .navbar-brand .navbar-link:hover, + .navbar.is-success .navbar-brand .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-success .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-success .navbar-start > .navbar-item, + .navbar.is-success .navbar-start .navbar-link, + .navbar.is-success .navbar-end > .navbar-item, + .navbar.is-success .navbar-end .navbar-link { + color: #fff; } + .navbar.is-success .navbar-start > a.navbar-item:focus, .navbar.is-success .navbar-start > a.navbar-item:hover, .navbar.is-success .navbar-start > a.navbar-item.is-active, + .navbar.is-success .navbar-start .navbar-link:focus, + .navbar.is-success .navbar-start .navbar-link:hover, + .navbar.is-success .navbar-start .navbar-link.is-active, + .navbar.is-success .navbar-end > a.navbar-item:focus, + .navbar.is-success .navbar-end > a.navbar-item:hover, + .navbar.is-success .navbar-end > a.navbar-item.is-active, + .navbar.is-success .navbar-end .navbar-link:focus, + .navbar.is-success .navbar-end .navbar-link:hover, + .navbar.is-success .navbar-end .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-start .navbar-link::after, + .navbar.is-success .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-dropdown a.navbar-item.is-active { + background-color: #22c35b; + color: #fff; } } + .navbar.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand > .navbar-item, + .navbar.is-warning .navbar-brand .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand > a.navbar-item:focus, .navbar.is-warning .navbar-brand > a.navbar-item:hover, .navbar.is-warning .navbar-brand > a.navbar-item.is-active, + .navbar.is-warning .navbar-brand .navbar-link:focus, + .navbar.is-warning .navbar-brand .navbar-link:hover, + .navbar.is-warning .navbar-brand .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-burger { + color: rgba(0, 0, 0, 0.7); } + @media screen and (min-width: 1056px) { + .navbar.is-warning .navbar-start > .navbar-item, + .navbar.is-warning .navbar-start .navbar-link, + .navbar.is-warning .navbar-end > .navbar-item, + .navbar.is-warning .navbar-end .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-start > a.navbar-item:focus, .navbar.is-warning .navbar-start > a.navbar-item:hover, .navbar.is-warning .navbar-start > a.navbar-item.is-active, + .navbar.is-warning .navbar-start .navbar-link:focus, + .navbar.is-warning .navbar-start .navbar-link:hover, + .navbar.is-warning .navbar-start .navbar-link.is-active, + .navbar.is-warning .navbar-end > a.navbar-item:focus, + .navbar.is-warning .navbar-end > a.navbar-item:hover, + .navbar.is-warning .navbar-end > a.navbar-item.is-active, + .navbar.is-warning .navbar-end .navbar-link:focus, + .navbar.is-warning .navbar-end .navbar-link:hover, + .navbar.is-warning .navbar-end .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-start .navbar-link::after, + .navbar.is-warning .navbar-end .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } } + .navbar.is-danger { + background-color: #da0b00; + color: #fff; } + .navbar.is-danger .navbar-brand > .navbar-item, + .navbar.is-danger .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-danger .navbar-brand > a.navbar-item:focus, .navbar.is-danger .navbar-brand > a.navbar-item:hover, .navbar.is-danger .navbar-brand > a.navbar-item.is-active, + .navbar.is-danger .navbar-brand .navbar-link:focus, + .navbar.is-danger .navbar-brand .navbar-link:hover, + .navbar.is-danger .navbar-brand .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-danger .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-danger .navbar-start > .navbar-item, + .navbar.is-danger .navbar-start .navbar-link, + .navbar.is-danger .navbar-end > .navbar-item, + .navbar.is-danger .navbar-end .navbar-link { + color: #fff; } + .navbar.is-danger .navbar-start > a.navbar-item:focus, .navbar.is-danger .navbar-start > a.navbar-item:hover, .navbar.is-danger .navbar-start > a.navbar-item.is-active, + .navbar.is-danger .navbar-start .navbar-link:focus, + .navbar.is-danger .navbar-start .navbar-link:hover, + .navbar.is-danger .navbar-start .navbar-link.is-active, + .navbar.is-danger .navbar-end > a.navbar-item:focus, + .navbar.is-danger .navbar-end > a.navbar-item:hover, + .navbar.is-danger .navbar-end > a.navbar-item.is-active, + .navbar.is-danger .navbar-end .navbar-link:focus, + .navbar.is-danger .navbar-end .navbar-link:hover, + .navbar.is-danger .navbar-end .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-start .navbar-link::after, + .navbar.is-danger .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { + background-color: #da0b00; + color: #fff; } } + .navbar > .container { + align-items: stretch; + display: flex; + min-height: 3.25rem; + width: 100%; } + .navbar.has-shadow { + box-shadow: 0 2px 0 0 whitesmoke; } + .navbar.is-fixed-bottom, .navbar.is-fixed-top { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom { + bottom: 0; } + .navbar.is-fixed-bottom.has-shadow { + box-shadow: 0 -2px 0 0 whitesmoke; } + .navbar.is-fixed-top { + top: 0; } + +html.has-navbar-fixed-top, +body.has-navbar-fixed-top { + padding-top: 3.25rem; } + +html.has-navbar-fixed-bottom, +body.has-navbar-fixed-bottom { + padding-bottom: 3.25rem; } + +.navbar-brand, +.navbar-tabs { + align-items: stretch; + display: flex; + flex-shrink: 0; + min-height: 3.25rem; } + +.navbar-brand a.navbar-item:focus, .navbar-brand a.navbar-item:hover { + background-color: transparent; } + +.navbar-tabs { + -webkit-overflow-scrolling: touch; + max-width: 100vw; + overflow-x: auto; + overflow-y: hidden; } + +.navbar-burger { + color: #4a4a4a; + cursor: pointer; + display: block; + height: 3.25rem; + position: relative; + width: 3.25rem; + margin-left: auto; } + .navbar-burger span { + background-color: currentColor; + display: block; + height: 1px; + left: calc(50% - 8px); + position: absolute; + transform-origin: center; + transition-duration: 86ms; + transition-property: background-color, opacity, transform; + transition-timing-function: ease-out; + width: 16px; } + .navbar-burger span:nth-child(1) { + top: calc(50% - 6px); } + .navbar-burger span:nth-child(2) { + top: calc(50% - 1px); } + .navbar-burger span:nth-child(3) { + top: calc(50% + 4px); } + .navbar-burger:hover { + background-color: rgba(0, 0, 0, 0.05); } + .navbar-burger.is-active span:nth-child(1) { + transform: translateY(5px) rotate(45deg); } + .navbar-burger.is-active span:nth-child(2) { + opacity: 0; } + .navbar-burger.is-active span:nth-child(3) { + transform: translateY(-5px) rotate(-45deg); } + +.navbar-menu { + display: none; } + +.navbar-item, +.navbar-link { + color: #4a4a4a; + display: block; + line-height: 1.5; + padding: 0.5rem 0.75rem; + position: relative; } + .navbar-item .icon:only-child, + .navbar-link .icon:only-child { + margin-left: -0.25rem; + margin-right: -0.25rem; } + +a.navbar-item, +.navbar-link { + cursor: pointer; } + a.navbar-item:focus, a.navbar-item:focus-within, a.navbar-item:hover, a.navbar-item.is-active, + .navbar-link:focus, + .navbar-link:focus-within, + .navbar-link:hover, + .navbar-link.is-active { + background-color: #fafafa; + color: #149eaa; } + +.navbar-item { + display: block; + flex-grow: 0; + flex-shrink: 0; } + .navbar-item img { + max-height: 1.75rem; } + .navbar-item.has-dropdown { + padding: 0; } + .navbar-item.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .navbar-item.is-tab { + border-bottom: 1px solid transparent; + min-height: 3.25rem; + padding-bottom: calc(0.5rem - 1px); } + .navbar-item.is-tab:focus, .navbar-item.is-tab:hover { + background-color: transparent; + border-bottom-color: #149eaa; } + .navbar-item.is-tab.is-active { + background-color: transparent; + border-bottom-color: #149eaa; + border-bottom-style: solid; + border-bottom-width: 3px; + color: #149eaa; + padding-bottom: calc(0.5rem - 3px); } + +.navbar-content { + flex-grow: 1; + flex-shrink: 1; } + +.navbar-link:not(.is-arrowless) { + padding-right: 2.5em; } + .navbar-link:not(.is-arrowless)::after { + border-color: #149eaa; + margin-top: -0.375em; + right: 1.125em; } + +.navbar-dropdown { + font-size: 0.875rem; + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + .navbar-dropdown .navbar-item { + padding-left: 1.5rem; + padding-right: 1.5rem; } + +.navbar-divider { + background-color: whitesmoke; + border: none; + display: none; + height: 2px; + margin: 0.5rem 0; } + +@media screen and (max-width: 1055px) { + .navbar > .container { + display: block; } + .navbar-brand .navbar-item, + .navbar-tabs .navbar-item { + align-items: center; + display: flex; } + .navbar-link::after { + display: none; } + .navbar-menu { + background-color: white; + box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); + padding: 0.5rem 0; } + .navbar-menu.is-active { + display: block; } + .navbar.is-fixed-bottom-touch, .navbar.is-fixed-top-touch { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom-touch { + bottom: 0; } + .navbar.is-fixed-bottom-touch.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + .navbar.is-fixed-top-touch { + top: 0; } + .navbar.is-fixed-top .navbar-menu, .navbar.is-fixed-top-touch .navbar-menu { + -webkit-overflow-scrolling: touch; + max-height: calc(100vh - 3.25rem); + overflow: auto; } + html.has-navbar-fixed-top-touch, + body.has-navbar-fixed-top-touch { + padding-top: 3.25rem; } + html.has-navbar-fixed-bottom-touch, + body.has-navbar-fixed-bottom-touch { + padding-bottom: 3.25rem; } } + +@media screen and (min-width: 1056px) { + .navbar, + .navbar-menu, + .navbar-start, + .navbar-end { + align-items: stretch; + display: flex; } + .navbar { + min-height: 3.25rem; } + .navbar.is-spaced { + padding: 1rem 2rem; } + .navbar.is-spaced .navbar-start, + .navbar.is-spaced .navbar-end { + align-items: center; } + .navbar.is-spaced a.navbar-item, + .navbar.is-spaced .navbar-link { + border-radius: 4px; } + .navbar.is-transparent a.navbar-item:focus, .navbar.is-transparent a.navbar-item:hover, .navbar.is-transparent a.navbar-item.is-active, + .navbar.is-transparent .navbar-link:focus, + .navbar.is-transparent .navbar-link:hover, + .navbar.is-transparent .navbar-link.is-active { + background-color: transparent !important; } + .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { + background-color: transparent !important; } + .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #149eaa; } + .navbar-burger { + display: none; } + .navbar-item, + .navbar-link { + align-items: center; + display: flex; } + .navbar-item { + display: flex; } + .navbar-item.has-dropdown { + align-items: stretch; } + .navbar-item.has-dropdown-up .navbar-link::after { + transform: rotate(135deg) translate(0.25em, -0.25em); } + .navbar-item.has-dropdown-up .navbar-dropdown { + border-bottom: 2px solid #dbdbdb; + border-radius: 6px 6px 0 0; + border-top: none; + bottom: 100%; + box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); + top: auto; } + .navbar-item.is-active .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown { + display: block; } + .navbar.is-spaced .navbar-item.is-active .navbar-dropdown, .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:hover .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { + opacity: 1; + pointer-events: auto; + transform: translateY(0); } + .navbar-menu { + flex-grow: 1; + flex-shrink: 0; } + .navbar-start { + justify-content: flex-start; + margin-right: auto; } + .navbar-end { + justify-content: flex-end; + margin-left: auto; } + .navbar-dropdown { + background-color: white; + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 2px solid #dbdbdb; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); + display: none; + font-size: 0.875rem; + left: 0; + min-width: 100%; + position: absolute; + top: 100%; + z-index: 20; } + .navbar-dropdown .navbar-item { + padding: 0.375rem 1rem; + white-space: nowrap; } + .navbar-dropdown a.navbar-item { + padding-right: 3rem; } + .navbar-dropdown a.navbar-item:focus, .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #149eaa; } + .navbar.is-spaced .navbar-dropdown, .navbar-dropdown.is-boxed { + border-radius: 6px; + border-top: none; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + display: block; + opacity: 0; + pointer-events: none; + top: calc(100% + (-4px)); + transform: translateY(-5px); + transition-duration: 86ms; + transition-property: opacity, transform; } + .navbar-dropdown.is-right { + left: auto; + right: 0; } + .navbar-divider { + display: block; } + .navbar > .container .navbar-brand, + .container > .navbar .navbar-brand { + margin-left: -.75rem; } + .navbar > .container .navbar-menu, + .container > .navbar .navbar-menu { + margin-right: -.75rem; } + .navbar.is-fixed-bottom-desktop, .navbar.is-fixed-top-desktop { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom-desktop { + bottom: 0; } + .navbar.is-fixed-bottom-desktop.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + .navbar.is-fixed-top-desktop { + top: 0; } + html.has-navbar-fixed-top-desktop, + body.has-navbar-fixed-top-desktop { + padding-top: 3.25rem; } + html.has-navbar-fixed-bottom-desktop, + body.has-navbar-fixed-bottom-desktop { + padding-bottom: 3.25rem; } + html.has-spaced-navbar-fixed-top, + body.has-spaced-navbar-fixed-top { + padding-top: 5.25rem; } + html.has-spaced-navbar-fixed-bottom, + body.has-spaced-navbar-fixed-bottom { + padding-bottom: 5.25rem; } + a.navbar-item.is-active, + .navbar-link.is-active { + color: #0a0a0a; } + a.navbar-item.is-active:not(:focus):not(:hover), + .navbar-link.is-active:not(:focus):not(:hover) { + background-color: transparent; } + .navbar-item.has-dropdown:focus .navbar-link, .navbar-item.has-dropdown:hover .navbar-link, .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #fafafa; } } + +.hero.is-fullheight-with-navbar { + min-height: calc(100vh - 3.25rem); } + +.pagination { + font-size: 1rem; + margin: -0.25rem; } + .pagination.is-small, #documenter .docs-sidebar form.docs-search > input.pagination { + font-size: 0.75rem; } + .pagination.is-medium { + font-size: 1.25rem; } + .pagination.is-large { + font-size: 1.5rem; } + .pagination.is-rounded .pagination-previous, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, + .pagination.is-rounded .pagination-next, + #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { + padding-left: 1em; + padding-right: 1em; + border-radius: 290486px; } + .pagination.is-rounded .pagination-link, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { + border-radius: 290486px; } + +.pagination, +.pagination-list { + align-items: center; + display: flex; + justify-content: center; + text-align: center; } + +.pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis { + font-size: 1em; + justify-content: center; + margin: 0.25rem; + padding-left: 0.5em; + padding-right: 0.5em; + text-align: center; } + +.pagination-previous, +.pagination-next, +.pagination-link { + border-color: #dbdbdb; + color: #363636; + min-width: 2.25em; } + .pagination-previous:hover, + .pagination-next:hover, + .pagination-link:hover { + border-color: #b5b5b5; + color: #107c85; } + .pagination-previous:focus, + .pagination-next:focus, + .pagination-link:focus { + border-color: #3c5dcd; } + .pagination-previous:active, + .pagination-next:active, + .pagination-link:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } + .pagination-previous[disabled], + .pagination-next[disabled], + .pagination-link[disabled] { + background-color: #dbdbdb; + border-color: #dbdbdb; + box-shadow: none; + color: #6b6b6b; + opacity: 0.5; } + +.pagination-previous, +.pagination-next { + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + +.pagination-link.is-current { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + +.pagination-ellipsis { + color: #b5b5b5; + pointer-events: none; } + +.pagination-list { + flex-wrap: wrap; } + +@media screen and (max-width: 768px) { + .pagination { + flex-wrap: wrap; } + .pagination-previous, + .pagination-next { + flex-grow: 1; + flex-shrink: 1; } + .pagination-list li { + flex-grow: 1; + flex-shrink: 1; } } + +@media screen and (min-width: 769px), print { + .pagination-list { + flex-grow: 1; + flex-shrink: 1; + justify-content: flex-start; + order: 1; } + .pagination-previous { + order: 2; } + .pagination-next { + order: 3; } + .pagination { + justify-content: space-between; } + .pagination.is-centered .pagination-previous { + order: 1; } + .pagination.is-centered .pagination-list { + justify-content: center; + order: 2; } + .pagination.is-centered .pagination-next { + order: 3; } + .pagination.is-right .pagination-previous { + order: 1; } + .pagination.is-right .pagination-next { + order: 2; } + .pagination.is-right .pagination-list { + justify-content: flex-end; + order: 3; } } + +.panel { + font-size: 1rem; } + .panel:not(:last-child) { + margin-bottom: 1.5rem; } + +.panel-heading, +.panel-tabs, +.panel-block { + border-bottom: 1px solid #dbdbdb; + border-left: 1px solid #dbdbdb; + border-right: 1px solid #dbdbdb; } + .panel-heading:first-child, + .panel-tabs:first-child, + .panel-block:first-child { + border-top: 1px solid #dbdbdb; } + +.panel-heading { + background-color: whitesmoke; + border-radius: 4px 4px 0 0; + color: #654ca3; + font-size: 1.25em; + font-weight: 300; + line-height: 1.25; + padding: 0.5em 0.75em; } + +.panel-tabs { + align-items: flex-end; + display: flex; + font-size: 0.875em; + justify-content: center; } + .panel-tabs a { + border-bottom: 1px solid #dbdbdb; + margin-bottom: -1px; + padding: 0.5em; } + .panel-tabs a.is-active { + border-bottom-color: #4a4a4a; + color: #363636; } + +.panel-list a { + color: #202020; } + .panel-list a:hover { + color: #149eaa; } + +.panel-block { + align-items: center; + color: #654ca3; + display: flex; + justify-content: flex-start; + padding: 0.5em 0.75em; } + .panel-block input[type="checkbox"] { + margin-right: 0.75em; } + .panel-block > .control { + flex-grow: 1; + flex-shrink: 1; + width: 100%; } + .panel-block.is-wrapped { + flex-wrap: wrap; } + .panel-block.is-active { + border-left-color: #149eaa; + color: #363636; } + .panel-block.is-active .panel-icon { + color: #149eaa; } + +a.panel-block, +label.panel-block { + cursor: pointer; } + a.panel-block:hover, + label.panel-block:hover { + background-color: whitesmoke; } + +.panel-icon { + display: inline-block; + font-size: 14px; + height: 1em; + line-height: 1em; + text-align: center; + vertical-align: top; + width: 1em; + color: #6b6b6b; + margin-right: 0.75em; } + .panel-icon .fa { + font-size: inherit; + line-height: inherit; } + +.tabs { + -webkit-overflow-scrolling: touch; + align-items: stretch; + display: flex; + font-size: 1rem; + justify-content: space-between; + overflow: hidden; + overflow-x: auto; + white-space: nowrap; } + .tabs a { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + color: #202020; + display: flex; + justify-content: center; + margin-bottom: -1px; + padding: 0.5em 1em; + vertical-align: top; } + .tabs a:hover { + border-bottom-color: #654ca3; + color: #654ca3; } + .tabs li { + display: block; } + .tabs li.is-active a { + border-bottom-color: #149eaa; + color: #149eaa; } + .tabs ul { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + display: flex; + flex-grow: 1; + flex-shrink: 0; + justify-content: flex-start; } + .tabs ul.is-left { + padding-right: 0.75em; } + .tabs ul.is-center { + flex: none; + justify-content: center; + padding-left: 0.75em; + padding-right: 0.75em; } + .tabs ul.is-right { + justify-content: flex-end; + padding-left: 0.75em; } + .tabs .icon:first-child { + margin-right: 0.5em; } + .tabs .icon:last-child { + margin-left: 0.5em; } + .tabs.is-centered ul { + justify-content: center; } + .tabs.is-right ul { + justify-content: flex-end; } + .tabs.is-boxed a { + border: 1px solid transparent; + border-radius: 4px 4px 0 0; } + .tabs.is-boxed a:hover { + background-color: whitesmoke; + border-bottom-color: #dbdbdb; } + .tabs.is-boxed li.is-active a { + background-color: white; + border-color: #dbdbdb; + border-bottom-color: transparent !important; } + .tabs.is-fullwidth li { + flex-grow: 1; + flex-shrink: 0; } + .tabs.is-toggle a { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px; + margin-bottom: 0; + position: relative; } + .tabs.is-toggle a:hover { + background-color: whitesmoke; + border-color: #b5b5b5; + z-index: 2; } + .tabs.is-toggle li + li { + margin-left: -1px; } + .tabs.is-toggle li:first-child a { + border-radius: 4px 0 0 4px; } + .tabs.is-toggle li:last-child a { + border-radius: 0 4px 4px 0; } + .tabs.is-toggle li.is-active a { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; + z-index: 1; } + .tabs.is-toggle ul { + border-bottom: none; } + .tabs.is-toggle.is-toggle-rounded li:first-child a { + border-bottom-left-radius: 290486px; + border-top-left-radius: 290486px; + padding-left: 1.25em; } + .tabs.is-toggle.is-toggle-rounded li:last-child a { + border-bottom-right-radius: 290486px; + border-top-right-radius: 290486px; + padding-right: 1.25em; } + .tabs.is-small, #documenter .docs-sidebar form.docs-search > input.tabs { + font-size: 0.75rem; } + .tabs.is-medium { + font-size: 1.25rem; } + .tabs.is-large { + font-size: 1.5rem; } + +.column { + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + padding: 0.75rem; } + .columns.is-mobile > .column.is-narrow { + flex: none; } + .columns.is-mobile > .column.is-full { + flex: none; + width: 100%; } + .columns.is-mobile > .column.is-three-quarters { + flex: none; + width: 75%; } + .columns.is-mobile > .column.is-two-thirds { + flex: none; + width: 66.6666%; } + .columns.is-mobile > .column.is-half { + flex: none; + width: 50%; } + .columns.is-mobile > .column.is-one-third { + flex: none; + width: 33.3333%; } + .columns.is-mobile > .column.is-one-quarter { + flex: none; + width: 25%; } + .columns.is-mobile > .column.is-one-fifth { + flex: none; + width: 20%; } + .columns.is-mobile > .column.is-two-fifths { + flex: none; + width: 40%; } + .columns.is-mobile > .column.is-three-fifths { + flex: none; + width: 60%; } + .columns.is-mobile > .column.is-four-fifths { + flex: none; + width: 80%; } + .columns.is-mobile > .column.is-offset-three-quarters { + margin-left: 75%; } + .columns.is-mobile > .column.is-offset-two-thirds { + margin-left: 66.6666%; } + .columns.is-mobile > .column.is-offset-half { + margin-left: 50%; } + .columns.is-mobile > .column.is-offset-one-third { + margin-left: 33.3333%; } + .columns.is-mobile > .column.is-offset-one-quarter { + margin-left: 25%; } + .columns.is-mobile > .column.is-offset-one-fifth { + margin-left: 20%; } + .columns.is-mobile > .column.is-offset-two-fifths { + margin-left: 40%; } + .columns.is-mobile > .column.is-offset-three-fifths { + margin-left: 60%; } + .columns.is-mobile > .column.is-offset-four-fifths { + margin-left: 80%; } + .columns.is-mobile > .column.is-0 { + flex: none; + width: 0%; } + .columns.is-mobile > .column.is-offset-0 { + margin-left: 0%; } + .columns.is-mobile > .column.is-1 { + flex: none; + width: 8.3333333333%; } + .columns.is-mobile > .column.is-offset-1 { + margin-left: 8.3333333333%; } + .columns.is-mobile > .column.is-2 { + flex: none; + width: 16.6666666667%; } + .columns.is-mobile > .column.is-offset-2 { + margin-left: 16.6666666667%; } + .columns.is-mobile > .column.is-3 { + flex: none; + width: 25%; } + .columns.is-mobile > .column.is-offset-3 { + margin-left: 25%; } + .columns.is-mobile > .column.is-4 { + flex: none; + width: 33.3333333333%; } + .columns.is-mobile > .column.is-offset-4 { + margin-left: 33.3333333333%; } + .columns.is-mobile > .column.is-5 { + flex: none; + width: 41.6666666667%; } + .columns.is-mobile > .column.is-offset-5 { + margin-left: 41.6666666667%; } + .columns.is-mobile > .column.is-6 { + flex: none; + width: 50%; } + .columns.is-mobile > .column.is-offset-6 { + margin-left: 50%; } + .columns.is-mobile > .column.is-7 { + flex: none; + width: 58.3333333333%; } + .columns.is-mobile > .column.is-offset-7 { + margin-left: 58.3333333333%; } + .columns.is-mobile > .column.is-8 { + flex: none; + width: 66.6666666667%; } + .columns.is-mobile > .column.is-offset-8 { + margin-left: 66.6666666667%; } + .columns.is-mobile > .column.is-9 { + flex: none; + width: 75%; } + .columns.is-mobile > .column.is-offset-9 { + margin-left: 75%; } + .columns.is-mobile > .column.is-10 { + flex: none; + width: 83.3333333333%; } + .columns.is-mobile > .column.is-offset-10 { + margin-left: 83.3333333333%; } + .columns.is-mobile > .column.is-11 { + flex: none; + width: 91.6666666667%; } + .columns.is-mobile > .column.is-offset-11 { + margin-left: 91.6666666667%; } + .columns.is-mobile > .column.is-12 { + flex: none; + width: 100%; } + .columns.is-mobile > .column.is-offset-12 { + margin-left: 100%; } + @media screen and (max-width: 768px) { + .column.is-narrow-mobile { + flex: none; } + .column.is-full-mobile { + flex: none; + width: 100%; } + .column.is-three-quarters-mobile { + flex: none; + width: 75%; } + .column.is-two-thirds-mobile { + flex: none; + width: 66.6666%; } + .column.is-half-mobile { + flex: none; + width: 50%; } + .column.is-one-third-mobile { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-mobile { + flex: none; + width: 25%; } + .column.is-one-fifth-mobile { + flex: none; + width: 20%; } + .column.is-two-fifths-mobile { + flex: none; + width: 40%; } + .column.is-three-fifths-mobile { + flex: none; + width: 60%; } + .column.is-four-fifths-mobile { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-mobile { + margin-left: 75%; } + .column.is-offset-two-thirds-mobile { + margin-left: 66.6666%; } + .column.is-offset-half-mobile { + margin-left: 50%; } + .column.is-offset-one-third-mobile { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-mobile { + margin-left: 25%; } + .column.is-offset-one-fifth-mobile { + margin-left: 20%; } + .column.is-offset-two-fifths-mobile { + margin-left: 40%; } + .column.is-offset-three-fifths-mobile { + margin-left: 60%; } + .column.is-offset-four-fifths-mobile { + margin-left: 80%; } + .column.is-0-mobile { + flex: none; + width: 0%; } + .column.is-offset-0-mobile { + margin-left: 0%; } + .column.is-1-mobile { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-mobile { + margin-left: 8.3333333333%; } + .column.is-2-mobile { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-mobile { + margin-left: 16.6666666667%; } + .column.is-3-mobile { + flex: none; + width: 25%; } + .column.is-offset-3-mobile { + margin-left: 25%; } + .column.is-4-mobile { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-mobile { + margin-left: 33.3333333333%; } + .column.is-5-mobile { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-mobile { + margin-left: 41.6666666667%; } + .column.is-6-mobile { + flex: none; + width: 50%; } + .column.is-offset-6-mobile { + margin-left: 50%; } + .column.is-7-mobile { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-mobile { + margin-left: 58.3333333333%; } + .column.is-8-mobile { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-mobile { + margin-left: 66.6666666667%; } + .column.is-9-mobile { + flex: none; + width: 75%; } + .column.is-offset-9-mobile { + margin-left: 75%; } + .column.is-10-mobile { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-mobile { + margin-left: 83.3333333333%; } + .column.is-11-mobile { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-mobile { + margin-left: 91.6666666667%; } + .column.is-12-mobile { + flex: none; + width: 100%; } + .column.is-offset-12-mobile { + margin-left: 100%; } } + @media screen and (min-width: 769px), print { + .column.is-narrow, .column.is-narrow-tablet { + flex: none; } + .column.is-full, .column.is-full-tablet { + flex: none; + width: 100%; } + .column.is-three-quarters, .column.is-three-quarters-tablet { + flex: none; + width: 75%; } + .column.is-two-thirds, .column.is-two-thirds-tablet { + flex: none; + width: 66.6666%; } + .column.is-half, .column.is-half-tablet { + flex: none; + width: 50%; } + .column.is-one-third, .column.is-one-third-tablet { + flex: none; + width: 33.3333%; } + .column.is-one-quarter, .column.is-one-quarter-tablet { + flex: none; + width: 25%; } + .column.is-one-fifth, .column.is-one-fifth-tablet { + flex: none; + width: 20%; } + .column.is-two-fifths, .column.is-two-fifths-tablet { + flex: none; + width: 40%; } + .column.is-three-fifths, .column.is-three-fifths-tablet { + flex: none; + width: 60%; } + .column.is-four-fifths, .column.is-four-fifths-tablet { + flex: none; + width: 80%; } + .column.is-offset-three-quarters, .column.is-offset-three-quarters-tablet { + margin-left: 75%; } + .column.is-offset-two-thirds, .column.is-offset-two-thirds-tablet { + margin-left: 66.6666%; } + .column.is-offset-half, .column.is-offset-half-tablet { + margin-left: 50%; } + .column.is-offset-one-third, .column.is-offset-one-third-tablet { + margin-left: 33.3333%; } + .column.is-offset-one-quarter, .column.is-offset-one-quarter-tablet { + margin-left: 25%; } + .column.is-offset-one-fifth, .column.is-offset-one-fifth-tablet { + margin-left: 20%; } + .column.is-offset-two-fifths, .column.is-offset-two-fifths-tablet { + margin-left: 40%; } + .column.is-offset-three-fifths, .column.is-offset-three-fifths-tablet { + margin-left: 60%; } + .column.is-offset-four-fifths, .column.is-offset-four-fifths-tablet { + margin-left: 80%; } + .column.is-0, .column.is-0-tablet { + flex: none; + width: 0%; } + .column.is-offset-0, .column.is-offset-0-tablet { + margin-left: 0%; } + .column.is-1, .column.is-1-tablet { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1, .column.is-offset-1-tablet { + margin-left: 8.3333333333%; } + .column.is-2, .column.is-2-tablet { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2, .column.is-offset-2-tablet { + margin-left: 16.6666666667%; } + .column.is-3, .column.is-3-tablet { + flex: none; + width: 25%; } + .column.is-offset-3, .column.is-offset-3-tablet { + margin-left: 25%; } + .column.is-4, .column.is-4-tablet { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4, .column.is-offset-4-tablet { + margin-left: 33.3333333333%; } + .column.is-5, .column.is-5-tablet { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5, .column.is-offset-5-tablet { + margin-left: 41.6666666667%; } + .column.is-6, .column.is-6-tablet { + flex: none; + width: 50%; } + .column.is-offset-6, .column.is-offset-6-tablet { + margin-left: 50%; } + .column.is-7, .column.is-7-tablet { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7, .column.is-offset-7-tablet { + margin-left: 58.3333333333%; } + .column.is-8, .column.is-8-tablet { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8, .column.is-offset-8-tablet { + margin-left: 66.6666666667%; } + .column.is-9, .column.is-9-tablet { + flex: none; + width: 75%; } + .column.is-offset-9, .column.is-offset-9-tablet { + margin-left: 75%; } + .column.is-10, .column.is-10-tablet { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10, .column.is-offset-10-tablet { + margin-left: 83.3333333333%; } + .column.is-11, .column.is-11-tablet { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11, .column.is-offset-11-tablet { + margin-left: 91.6666666667%; } + .column.is-12, .column.is-12-tablet { + flex: none; + width: 100%; } + .column.is-offset-12, .column.is-offset-12-tablet { + margin-left: 100%; } } + @media screen and (max-width: 1055px) { + .column.is-narrow-touch { + flex: none; } + .column.is-full-touch { + flex: none; + width: 100%; } + .column.is-three-quarters-touch { + flex: none; + width: 75%; } + .column.is-two-thirds-touch { + flex: none; + width: 66.6666%; } + .column.is-half-touch { + flex: none; + width: 50%; } + .column.is-one-third-touch { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-touch { + flex: none; + width: 25%; } + .column.is-one-fifth-touch { + flex: none; + width: 20%; } + .column.is-two-fifths-touch { + flex: none; + width: 40%; } + .column.is-three-fifths-touch { + flex: none; + width: 60%; } + .column.is-four-fifths-touch { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-touch { + margin-left: 75%; } + .column.is-offset-two-thirds-touch { + margin-left: 66.6666%; } + .column.is-offset-half-touch { + margin-left: 50%; } + .column.is-offset-one-third-touch { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-touch { + margin-left: 25%; } + .column.is-offset-one-fifth-touch { + margin-left: 20%; } + .column.is-offset-two-fifths-touch { + margin-left: 40%; } + .column.is-offset-three-fifths-touch { + margin-left: 60%; } + .column.is-offset-four-fifths-touch { + margin-left: 80%; } + .column.is-0-touch { + flex: none; + width: 0%; } + .column.is-offset-0-touch { + margin-left: 0%; } + .column.is-1-touch { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-touch { + margin-left: 8.3333333333%; } + .column.is-2-touch { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-touch { + margin-left: 16.6666666667%; } + .column.is-3-touch { + flex: none; + width: 25%; } + .column.is-offset-3-touch { + margin-left: 25%; } + .column.is-4-touch { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-touch { + margin-left: 33.3333333333%; } + .column.is-5-touch { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-touch { + margin-left: 41.6666666667%; } + .column.is-6-touch { + flex: none; + width: 50%; } + .column.is-offset-6-touch { + margin-left: 50%; } + .column.is-7-touch { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-touch { + margin-left: 58.3333333333%; } + .column.is-8-touch { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-touch { + margin-left: 66.6666666667%; } + .column.is-9-touch { + flex: none; + width: 75%; } + .column.is-offset-9-touch { + margin-left: 75%; } + .column.is-10-touch { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-touch { + margin-left: 83.3333333333%; } + .column.is-11-touch { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-touch { + margin-left: 91.6666666667%; } + .column.is-12-touch { + flex: none; + width: 100%; } + .column.is-offset-12-touch { + margin-left: 100%; } } + @media screen and (min-width: 1056px) { + .column.is-narrow-desktop { + flex: none; } + .column.is-full-desktop { + flex: none; + width: 100%; } + .column.is-three-quarters-desktop { + flex: none; + width: 75%; } + .column.is-two-thirds-desktop { + flex: none; + width: 66.6666%; } + .column.is-half-desktop { + flex: none; + width: 50%; } + .column.is-one-third-desktop { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-desktop { + flex: none; + width: 25%; } + .column.is-one-fifth-desktop { + flex: none; + width: 20%; } + .column.is-two-fifths-desktop { + flex: none; + width: 40%; } + .column.is-three-fifths-desktop { + flex: none; + width: 60%; } + .column.is-four-fifths-desktop { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-desktop { + margin-left: 75%; } + .column.is-offset-two-thirds-desktop { + margin-left: 66.6666%; } + .column.is-offset-half-desktop { + margin-left: 50%; } + .column.is-offset-one-third-desktop { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-desktop { + margin-left: 25%; } + .column.is-offset-one-fifth-desktop { + margin-left: 20%; } + .column.is-offset-two-fifths-desktop { + margin-left: 40%; } + .column.is-offset-three-fifths-desktop { + margin-left: 60%; } + .column.is-offset-four-fifths-desktop { + margin-left: 80%; } + .column.is-0-desktop { + flex: none; + width: 0%; } + .column.is-offset-0-desktop { + margin-left: 0%; } + .column.is-1-desktop { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-desktop { + margin-left: 8.3333333333%; } + .column.is-2-desktop { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-desktop { + margin-left: 16.6666666667%; } + .column.is-3-desktop { + flex: none; + width: 25%; } + .column.is-offset-3-desktop { + margin-left: 25%; } + .column.is-4-desktop { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-desktop { + margin-left: 33.3333333333%; } + .column.is-5-desktop { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-desktop { + margin-left: 41.6666666667%; } + .column.is-6-desktop { + flex: none; + width: 50%; } + .column.is-offset-6-desktop { + margin-left: 50%; } + .column.is-7-desktop { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-desktop { + margin-left: 58.3333333333%; } + .column.is-8-desktop { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-desktop { + margin-left: 66.6666666667%; } + .column.is-9-desktop { + flex: none; + width: 75%; } + .column.is-offset-9-desktop { + margin-left: 75%; } + .column.is-10-desktop { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-desktop { + margin-left: 83.3333333333%; } + .column.is-11-desktop { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-desktop { + margin-left: 91.6666666667%; } + .column.is-12-desktop { + flex: none; + width: 100%; } + .column.is-offset-12-desktop { + margin-left: 100%; } } + @media screen and (min-width: 1216px) { + .column.is-narrow-widescreen { + flex: none; } + .column.is-full-widescreen { + flex: none; + width: 100%; } + .column.is-three-quarters-widescreen { + flex: none; + width: 75%; } + .column.is-two-thirds-widescreen { + flex: none; + width: 66.6666%; } + .column.is-half-widescreen { + flex: none; + width: 50%; } + .column.is-one-third-widescreen { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-widescreen { + flex: none; + width: 25%; } + .column.is-one-fifth-widescreen { + flex: none; + width: 20%; } + .column.is-two-fifths-widescreen { + flex: none; + width: 40%; } + .column.is-three-fifths-widescreen { + flex: none; + width: 60%; } + .column.is-four-fifths-widescreen { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-widescreen { + margin-left: 75%; } + .column.is-offset-two-thirds-widescreen { + margin-left: 66.6666%; } + .column.is-offset-half-widescreen { + margin-left: 50%; } + .column.is-offset-one-third-widescreen { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-widescreen { + margin-left: 25%; } + .column.is-offset-one-fifth-widescreen { + margin-left: 20%; } + .column.is-offset-two-fifths-widescreen { + margin-left: 40%; } + .column.is-offset-three-fifths-widescreen { + margin-left: 60%; } + .column.is-offset-four-fifths-widescreen { + margin-left: 80%; } + .column.is-0-widescreen { + flex: none; + width: 0%; } + .column.is-offset-0-widescreen { + margin-left: 0%; } + .column.is-1-widescreen { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-widescreen { + margin-left: 8.3333333333%; } + .column.is-2-widescreen { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-widescreen { + margin-left: 16.6666666667%; } + .column.is-3-widescreen { + flex: none; + width: 25%; } + .column.is-offset-3-widescreen { + margin-left: 25%; } + .column.is-4-widescreen { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-widescreen { + margin-left: 33.3333333333%; } + .column.is-5-widescreen { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-widescreen { + margin-left: 41.6666666667%; } + .column.is-6-widescreen { + flex: none; + width: 50%; } + .column.is-offset-6-widescreen { + margin-left: 50%; } + .column.is-7-widescreen { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-widescreen { + margin-left: 58.3333333333%; } + .column.is-8-widescreen { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-widescreen { + margin-left: 66.6666666667%; } + .column.is-9-widescreen { + flex: none; + width: 75%; } + .column.is-offset-9-widescreen { + margin-left: 75%; } + .column.is-10-widescreen { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-widescreen { + margin-left: 83.3333333333%; } + .column.is-11-widescreen { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-widescreen { + margin-left: 91.6666666667%; } + .column.is-12-widescreen { + flex: none; + width: 100%; } + .column.is-offset-12-widescreen { + margin-left: 100%; } } + @media screen and (min-width: 1408px) { + .column.is-narrow-fullhd { + flex: none; } + .column.is-full-fullhd { + flex: none; + width: 100%; } + .column.is-three-quarters-fullhd { + flex: none; + width: 75%; } + .column.is-two-thirds-fullhd { + flex: none; + width: 66.6666%; } + .column.is-half-fullhd { + flex: none; + width: 50%; } + .column.is-one-third-fullhd { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-fullhd { + flex: none; + width: 25%; } + .column.is-one-fifth-fullhd { + flex: none; + width: 20%; } + .column.is-two-fifths-fullhd { + flex: none; + width: 40%; } + .column.is-three-fifths-fullhd { + flex: none; + width: 60%; } + .column.is-four-fifths-fullhd { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-fullhd { + margin-left: 75%; } + .column.is-offset-two-thirds-fullhd { + margin-left: 66.6666%; } + .column.is-offset-half-fullhd { + margin-left: 50%; } + .column.is-offset-one-third-fullhd { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-fullhd { + margin-left: 25%; } + .column.is-offset-one-fifth-fullhd { + margin-left: 20%; } + .column.is-offset-two-fifths-fullhd { + margin-left: 40%; } + .column.is-offset-three-fifths-fullhd { + margin-left: 60%; } + .column.is-offset-four-fifths-fullhd { + margin-left: 80%; } + .column.is-0-fullhd { + flex: none; + width: 0%; } + .column.is-offset-0-fullhd { + margin-left: 0%; } + .column.is-1-fullhd { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-fullhd { + margin-left: 8.3333333333%; } + .column.is-2-fullhd { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-fullhd { + margin-left: 16.6666666667%; } + .column.is-3-fullhd { + flex: none; + width: 25%; } + .column.is-offset-3-fullhd { + margin-left: 25%; } + .column.is-4-fullhd { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-fullhd { + margin-left: 33.3333333333%; } + .column.is-5-fullhd { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-fullhd { + margin-left: 41.6666666667%; } + .column.is-6-fullhd { + flex: none; + width: 50%; } + .column.is-offset-6-fullhd { + margin-left: 50%; } + .column.is-7-fullhd { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-fullhd { + margin-left: 58.3333333333%; } + .column.is-8-fullhd { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-fullhd { + margin-left: 66.6666666667%; } + .column.is-9-fullhd { + flex: none; + width: 75%; } + .column.is-offset-9-fullhd { + margin-left: 75%; } + .column.is-10-fullhd { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-fullhd { + margin-left: 83.3333333333%; } + .column.is-11-fullhd { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-fullhd { + margin-left: 91.6666666667%; } + .column.is-12-fullhd { + flex: none; + width: 100%; } + .column.is-offset-12-fullhd { + margin-left: 100%; } } +.columns { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + .columns:last-child { + margin-bottom: -0.75rem; } + .columns:not(:last-child) { + margin-bottom: calc(1.5rem - 0.75rem); } + .columns.is-centered { + justify-content: center; } + .columns.is-gapless { + margin-left: 0; + margin-right: 0; + margin-top: 0; } + .columns.is-gapless > .column { + margin: 0; + padding: 0 !important; } + .columns.is-gapless:not(:last-child) { + margin-bottom: 1.5rem; } + .columns.is-gapless:last-child { + margin-bottom: 0; } + .columns.is-mobile { + display: flex; } + .columns.is-multiline { + flex-wrap: wrap; } + .columns.is-vcentered { + align-items: center; } + @media screen and (min-width: 769px), print { + .columns:not(.is-desktop) { + display: flex; } } + @media screen and (min-width: 1056px) { + .columns.is-desktop { + display: flex; } } +.columns.is-variable { + --columnGap: 0.75rem; + margin-left: calc(-1 * var(--columnGap)); + margin-right: calc(-1 * var(--columnGap)); } + .columns.is-variable .column { + padding-left: var(--columnGap); + padding-right: var(--columnGap); } + .columns.is-variable.is-0 { + --columnGap: 0rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-0-mobile { + --columnGap: 0rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-0-tablet { + --columnGap: 0rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-0-tablet-only { + --columnGap: 0rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-0-touch { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-0-desktop { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-0-desktop-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-0-widescreen { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-0-widescreen-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-0-fullhd { + --columnGap: 0rem; } } + .columns.is-variable.is-1 { + --columnGap: 0.25rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-1-mobile { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-1-tablet { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-1-tablet-only { + --columnGap: 0.25rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-1-touch { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-1-desktop { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-1-desktop-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-1-widescreen { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-1-widescreen-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-1-fullhd { + --columnGap: 0.25rem; } } + .columns.is-variable.is-2 { + --columnGap: 0.5rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-2-mobile { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-2-tablet { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-2-tablet-only { + --columnGap: 0.5rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-2-touch { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-2-desktop { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-2-desktop-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-2-widescreen { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-2-widescreen-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-2-fullhd { + --columnGap: 0.5rem; } } + .columns.is-variable.is-3 { + --columnGap: 0.75rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-3-mobile { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-3-tablet { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-3-tablet-only { + --columnGap: 0.75rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-3-touch { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-3-desktop { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-3-desktop-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-3-widescreen { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-3-widescreen-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-3-fullhd { + --columnGap: 0.75rem; } } + .columns.is-variable.is-4 { + --columnGap: 1rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-4-mobile { + --columnGap: 1rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-4-tablet { + --columnGap: 1rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-4-tablet-only { + --columnGap: 1rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-4-touch { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-4-desktop { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-4-desktop-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-4-widescreen { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-4-widescreen-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-4-fullhd { + --columnGap: 1rem; } } + .columns.is-variable.is-5 { + --columnGap: 1.25rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-5-mobile { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-5-tablet { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-5-tablet-only { + --columnGap: 1.25rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-5-touch { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-5-desktop { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-5-desktop-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-5-widescreen { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-5-widescreen-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-5-fullhd { + --columnGap: 1.25rem; } } + .columns.is-variable.is-6 { + --columnGap: 1.5rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-6-mobile { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-6-tablet { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-6-tablet-only { + --columnGap: 1.5rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-6-touch { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-6-desktop { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-6-desktop-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-6-widescreen { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-6-widescreen-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-6-fullhd { + --columnGap: 1.5rem; } } + .columns.is-variable.is-7 { + --columnGap: 1.75rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-7-mobile { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-7-tablet { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-7-tablet-only { + --columnGap: 1.75rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-7-touch { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-7-desktop { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-7-desktop-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-7-widescreen { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-7-widescreen-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-7-fullhd { + --columnGap: 1.75rem; } } + .columns.is-variable.is-8 { + --columnGap: 2rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-8-mobile { + --columnGap: 2rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-8-tablet { + --columnGap: 2rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-8-tablet-only { + --columnGap: 2rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-8-touch { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-8-desktop { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-8-desktop-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-8-widescreen { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-8-widescreen-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-8-fullhd { + --columnGap: 2rem; } } +.tile { + align-items: stretch; + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + min-height: min-content; } + .tile.is-ancestor { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + .tile.is-ancestor:last-child { + margin-bottom: -0.75rem; } + .tile.is-ancestor:not(:last-child) { + margin-bottom: 0.75rem; } + .tile.is-child { + margin: 0 !important; } + .tile.is-parent { + padding: 0.75rem; } + .tile.is-vertical { + flex-direction: column; } + .tile.is-vertical > .tile.is-child:not(:last-child) { + margin-bottom: 1.5rem !important; } + @media screen and (min-width: 769px), print { + .tile:not(.is-child) { + display: flex; } + .tile.is-1 { + flex: none; + width: 8.3333333333%; } + .tile.is-2 { + flex: none; + width: 16.6666666667%; } + .tile.is-3 { + flex: none; + width: 25%; } + .tile.is-4 { + flex: none; + width: 33.3333333333%; } + .tile.is-5 { + flex: none; + width: 41.6666666667%; } + .tile.is-6 { + flex: none; + width: 50%; } + .tile.is-7 { + flex: none; + width: 58.3333333333%; } + .tile.is-8 { + flex: none; + width: 66.6666666667%; } + .tile.is-9 { + flex: none; + width: 75%; } + .tile.is-10 { + flex: none; + width: 83.3333333333%; } + .tile.is-11 { + flex: none; + width: 91.6666666667%; } + .tile.is-12 { + flex: none; + width: 100%; } } +.hero { + align-items: stretch; + display: flex; + flex-direction: column; + justify-content: space-between; } + .hero .navbar { + background: none; } + .hero .tabs ul { + border-bottom: none; } + .hero.is-white { + background-color: white; + color: #0a0a0a; } + .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-white strong { + color: inherit; } + .hero.is-white .title { + color: #0a0a0a; } + .hero.is-white .subtitle { + color: rgba(10, 10, 10, 0.9); } + .hero.is-white .subtitle a:not(.button), + .hero.is-white .subtitle strong { + color: #0a0a0a; } + @media screen and (max-width: 1055px) { + .hero.is-white .navbar-menu { + background-color: white; } } + .hero.is-white .navbar-item, + .hero.is-white .navbar-link { + color: rgba(10, 10, 10, 0.7); } + .hero.is-white a.navbar-item:hover, .hero.is-white a.navbar-item.is-active, + .hero.is-white .navbar-link:hover, + .hero.is-white .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .hero.is-white .tabs a { + color: #0a0a0a; + opacity: 0.9; } + .hero.is-white .tabs a:hover { + opacity: 1; } + .hero.is-white .tabs li.is-active a { + opacity: 1; } + .hero.is-white .tabs.is-boxed a, .hero.is-white .tabs.is-toggle a { + color: #0a0a0a; } + .hero.is-white .tabs.is-boxed a:hover, .hero.is-white .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-white .tabs.is-boxed li.is-active a, .hero.is-white .tabs.is-boxed li.is-active a:hover, .hero.is-white .tabs.is-toggle li.is-active a, .hero.is-white .tabs.is-toggle li.is-active a:hover { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .hero.is-white.is-bold { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } + @media screen and (max-width: 768px) { + .hero.is-white.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } + .hero.is-black { + background-color: #0a0a0a; + color: white; } + .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-black strong { + color: inherit; } + .hero.is-black .title { + color: white; } + .hero.is-black .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-black .subtitle a:not(.button), + .hero.is-black .subtitle strong { + color: white; } + @media screen and (max-width: 1055px) { + .hero.is-black .navbar-menu { + background-color: #0a0a0a; } } + .hero.is-black .navbar-item, + .hero.is-black .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-black a.navbar-item:hover, .hero.is-black a.navbar-item.is-active, + .hero.is-black .navbar-link:hover, + .hero.is-black .navbar-link.is-active { + background-color: black; + color: white; } + .hero.is-black .tabs a { + color: white; + opacity: 0.9; } + .hero.is-black .tabs a:hover { + opacity: 1; } + .hero.is-black .tabs li.is-active a { + opacity: 1; } + .hero.is-black .tabs.is-boxed a, .hero.is-black .tabs.is-toggle a { + color: white; } + .hero.is-black .tabs.is-boxed a:hover, .hero.is-black .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-black .tabs.is-boxed li.is-active a, .hero.is-black .tabs.is-boxed li.is-active a:hover, .hero.is-black .tabs.is-toggle li.is-active a, .hero.is-black .tabs.is-toggle li.is-active a:hover { + background-color: white; + border-color: white; + color: #0a0a0a; } + .hero.is-black.is-bold { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } + @media screen and (max-width: 768px) { + .hero.is-black.is-bold .navbar-menu { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } + .hero.is-light { + background-color: whitesmoke; + color: #363636; } + .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-light strong { + color: inherit; } + .hero.is-light .title { + color: #363636; } + .hero.is-light .subtitle { + color: rgba(54, 54, 54, 0.9); } + .hero.is-light .subtitle a:not(.button), + .hero.is-light .subtitle strong { + color: #363636; } + @media screen and (max-width: 1055px) { + .hero.is-light .navbar-menu { + background-color: whitesmoke; } } + .hero.is-light .navbar-item, + .hero.is-light .navbar-link { + color: rgba(54, 54, 54, 0.7); } + .hero.is-light a.navbar-item:hover, .hero.is-light a.navbar-item.is-active, + .hero.is-light .navbar-link:hover, + .hero.is-light .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .hero.is-light .tabs a { + color: #363636; + opacity: 0.9; } + .hero.is-light .tabs a:hover { + opacity: 1; } + .hero.is-light .tabs li.is-active a { + opacity: 1; } + .hero.is-light .tabs.is-boxed a, .hero.is-light .tabs.is-toggle a { + color: #363636; } + .hero.is-light .tabs.is-boxed a:hover, .hero.is-light .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-light .tabs.is-boxed li.is-active a, .hero.is-light .tabs.is-boxed li.is-active a:hover, .hero.is-light .tabs.is-toggle li.is-active a, .hero.is-light .tabs.is-toggle li.is-active a:hover { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .hero.is-light.is-bold { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } + @media screen and (max-width: 768px) { + .hero.is-light.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } } + .hero.is-dark, .content kbd.hero { + background-color: #363636; + color: whitesmoke; } + .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-dark strong, + .content kbd.hero strong { + color: inherit; } + .hero.is-dark .title, .content kbd.hero .title { + color: whitesmoke; } + .hero.is-dark .subtitle, .content kbd.hero .subtitle { + color: rgba(245, 245, 245, 0.9); } + .hero.is-dark .subtitle a:not(.button), .content kbd.hero .subtitle a:not(.button), + .hero.is-dark .subtitle strong, + .content kbd.hero .subtitle strong { + color: whitesmoke; } + @media screen and (max-width: 1055px) { + .hero.is-dark .navbar-menu, .content kbd.hero .navbar-menu { + background-color: #363636; } } + .hero.is-dark .navbar-item, .content kbd.hero .navbar-item, + .hero.is-dark .navbar-link, + .content kbd.hero .navbar-link { + color: rgba(245, 245, 245, 0.7); } + .hero.is-dark a.navbar-item:hover, .content kbd.hero a.navbar-item:hover, .hero.is-dark a.navbar-item.is-active, .content kbd.hero a.navbar-item.is-active, + .hero.is-dark .navbar-link:hover, + .content kbd.hero .navbar-link:hover, + .hero.is-dark .navbar-link.is-active, + .content kbd.hero .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .hero.is-dark .tabs a, .content kbd.hero .tabs a { + color: whitesmoke; + opacity: 0.9; } + .hero.is-dark .tabs a:hover, .content kbd.hero .tabs a:hover { + opacity: 1; } + .hero.is-dark .tabs li.is-active a, .content kbd.hero .tabs li.is-active a { + opacity: 1; } + .hero.is-dark .tabs.is-boxed a, .content kbd.hero .tabs.is-boxed a, .hero.is-dark .tabs.is-toggle a, .content kbd.hero .tabs.is-toggle a { + color: whitesmoke; } + .hero.is-dark .tabs.is-boxed a:hover, .content kbd.hero .tabs.is-boxed a:hover, .hero.is-dark .tabs.is-toggle a:hover, .content kbd.hero .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-dark .tabs.is-boxed li.is-active a, .content kbd.hero .tabs.is-boxed li.is-active a, .hero.is-dark .tabs.is-boxed li.is-active a:hover, .hero.is-dark .tabs.is-toggle li.is-active a, .content kbd.hero .tabs.is-toggle li.is-active a, .hero.is-dark .tabs.is-toggle li.is-active a:hover { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .hero.is-dark.is-bold, .content kbd.hero.is-bold { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } + @media screen and (max-width: 768px) { + .hero.is-dark.is-bold .navbar-menu, .content kbd.hero.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } } + .hero.is-primary, .docstring > section > a.hero.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-primary strong, + .docstring > section > a.hero.docs-sourcelink strong { + color: inherit; } + .hero.is-primary .title, .docstring > section > a.hero.docs-sourcelink .title { + color: #fff; } + .hero.is-primary .subtitle, .docstring > section > a.hero.docs-sourcelink .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-primary .subtitle a:not(.button), .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), + .hero.is-primary .subtitle strong, + .docstring > section > a.hero.docs-sourcelink .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-primary .navbar-menu, .docstring > section > a.hero.docs-sourcelink .navbar-menu { + background-color: #4eb5de; } } + .hero.is-primary .navbar-item, .docstring > section > a.hero.docs-sourcelink .navbar-item, + .hero.is-primary .navbar-link, + .docstring > section > a.hero.docs-sourcelink .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-primary a.navbar-item:hover, .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, .hero.is-primary a.navbar-item.is-active, .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, + .hero.is-primary .navbar-link:hover, + .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, + .hero.is-primary .navbar-link.is-active, + .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .hero.is-primary .tabs a, .docstring > section > a.hero.docs-sourcelink .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-primary .tabs a:hover, .docstring > section > a.hero.docs-sourcelink .tabs a:hover { + opacity: 1; } + .hero.is-primary .tabs li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { + opacity: 1; } + .hero.is-primary .tabs.is-boxed a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, .hero.is-primary .tabs.is-toggle a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { + color: #fff; } + .hero.is-primary .tabs.is-boxed a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, .hero.is-primary .tabs.is-toggle a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-primary .tabs.is-boxed li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, .hero.is-primary .tabs.is-boxed li.is-active a:hover, .hero.is-primary .tabs.is-toggle li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, .hero.is-primary .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #4eb5de; } + .hero.is-primary.is-bold, .docstring > section > a.hero.is-bold.docs-sourcelink { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } + @media screen and (max-width: 768px) { + .hero.is-primary.is-bold .navbar-menu, .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } } + .hero.is-link { + background-color: #149eaa; + color: #fff; } + .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-link strong { + color: inherit; } + .hero.is-link .title { + color: #fff; } + .hero.is-link .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-link .subtitle a:not(.button), + .hero.is-link .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-link .navbar-menu { + background-color: #149eaa; } } + .hero.is-link .navbar-item, + .hero.is-link .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-link a.navbar-item:hover, .hero.is-link a.navbar-item.is-active, + .hero.is-link .navbar-link:hover, + .hero.is-link .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .hero.is-link .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-link .tabs a:hover { + opacity: 1; } + .hero.is-link .tabs li.is-active a { + opacity: 1; } + .hero.is-link .tabs.is-boxed a, .hero.is-link .tabs.is-toggle a { + color: #fff; } + .hero.is-link .tabs.is-boxed a:hover, .hero.is-link .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-link .tabs.is-boxed li.is-active a, .hero.is-link .tabs.is-boxed li.is-active a:hover, .hero.is-link .tabs.is-toggle li.is-active a, .hero.is-link .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #149eaa; } + .hero.is-link.is-bold { + background-image: linear-gradient(141deg, #088379 0%, #149eaa 71%, #119ac6 100%); } + @media screen and (max-width: 768px) { + .hero.is-link.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #088379 0%, #149eaa 71%, #119ac6 100%); } } + .hero.is-info { + background-color: #209cee; + color: #fff; } + .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-info strong { + color: inherit; } + .hero.is-info .title { + color: #fff; } + .hero.is-info .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-info .subtitle a:not(.button), + .hero.is-info .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-info .navbar-menu { + background-color: #209cee; } } + .hero.is-info .navbar-item, + .hero.is-info .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-info a.navbar-item:hover, .hero.is-info a.navbar-item.is-active, + .hero.is-info .navbar-link:hover, + .hero.is-info .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .hero.is-info .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-info .tabs a:hover { + opacity: 1; } + .hero.is-info .tabs li.is-active a { + opacity: 1; } + .hero.is-info .tabs.is-boxed a, .hero.is-info .tabs.is-toggle a { + color: #fff; } + .hero.is-info .tabs.is-boxed a:hover, .hero.is-info .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-info .tabs.is-boxed li.is-active a, .hero.is-info .tabs.is-boxed li.is-active a:hover, .hero.is-info .tabs.is-toggle li.is-active a, .hero.is-info .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #209cee; } + .hero.is-info.is-bold { + background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } + @media screen and (max-width: 768px) { + .hero.is-info.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } } + .hero.is-success { + background-color: #22c35b; + color: #fff; } + .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-success strong { + color: inherit; } + .hero.is-success .title { + color: #fff; } + .hero.is-success .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-success .subtitle a:not(.button), + .hero.is-success .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-success .navbar-menu { + background-color: #22c35b; } } + .hero.is-success .navbar-item, + .hero.is-success .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-success a.navbar-item:hover, .hero.is-success a.navbar-item.is-active, + .hero.is-success .navbar-link:hover, + .hero.is-success .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .hero.is-success .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-success .tabs a:hover { + opacity: 1; } + .hero.is-success .tabs li.is-active a { + opacity: 1; } + .hero.is-success .tabs.is-boxed a, .hero.is-success .tabs.is-toggle a { + color: #fff; } + .hero.is-success .tabs.is-boxed a:hover, .hero.is-success .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-success .tabs.is-boxed li.is-active a, .hero.is-success .tabs.is-boxed li.is-active a:hover, .hero.is-success .tabs.is-toggle li.is-active a, .hero.is-success .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #22c35b; } + .hero.is-success.is-bold { + background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } + @media screen and (max-width: 768px) { + .hero.is-success.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } } + .hero.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-warning strong { + color: inherit; } + .hero.is-warning .title { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .subtitle { + color: rgba(0, 0, 0, 0.9); } + .hero.is-warning .subtitle a:not(.button), + .hero.is-warning .subtitle strong { + color: rgba(0, 0, 0, 0.7); } + @media screen and (max-width: 1055px) { + .hero.is-warning .navbar-menu { + background-color: #ffdd57; } } + .hero.is-warning .navbar-item, + .hero.is-warning .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning a.navbar-item:hover, .hero.is-warning a.navbar-item.is-active, + .hero.is-warning .navbar-link:hover, + .hero.is-warning .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .tabs a { + color: rgba(0, 0, 0, 0.7); + opacity: 0.9; } + .hero.is-warning .tabs a:hover { + opacity: 1; } + .hero.is-warning .tabs li.is-active a { + opacity: 1; } + .hero.is-warning .tabs.is-boxed a, .hero.is-warning .tabs.is-toggle a { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .tabs.is-boxed a:hover, .hero.is-warning .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-warning .tabs.is-boxed li.is-active a, .hero.is-warning .tabs.is-boxed li.is-active a:hover, .hero.is-warning .tabs.is-toggle li.is-active a, .hero.is-warning .tabs.is-toggle li.is-active a:hover { + background-color: rgba(0, 0, 0, 0.7); + border-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .hero.is-warning.is-bold { + background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } + @media screen and (max-width: 768px) { + .hero.is-warning.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } } + .hero.is-danger { + background-color: #da0b00; + color: #fff; } + .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-danger strong { + color: inherit; } + .hero.is-danger .title { + color: #fff; } + .hero.is-danger .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-danger .subtitle a:not(.button), + .hero.is-danger .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-danger .navbar-menu { + background-color: #da0b00; } } + .hero.is-danger .navbar-item, + .hero.is-danger .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-danger a.navbar-item:hover, .hero.is-danger a.navbar-item.is-active, + .hero.is-danger .navbar-link:hover, + .hero.is-danger .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .hero.is-danger .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-danger .tabs a:hover { + opacity: 1; } + .hero.is-danger .tabs li.is-active a { + opacity: 1; } + .hero.is-danger .tabs.is-boxed a, .hero.is-danger .tabs.is-toggle a { + color: #fff; } + .hero.is-danger .tabs.is-boxed a:hover, .hero.is-danger .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-danger .tabs.is-boxed li.is-active a, .hero.is-danger .tabs.is-boxed li.is-active a:hover, .hero.is-danger .tabs.is-toggle li.is-active a, .hero.is-danger .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #da0b00; } + .hero.is-danger.is-bold { + background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } + @media screen and (max-width: 768px) { + .hero.is-danger.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } } + .hero.is-small .hero-body, #documenter .docs-sidebar form.docs-search > input.hero .hero-body { + padding-bottom: 1.5rem; + padding-top: 1.5rem; } + @media screen and (min-width: 769px), print { + .hero.is-medium .hero-body { + padding-bottom: 9rem; + padding-top: 9rem; } } + @media screen and (min-width: 769px), print { + .hero.is-large .hero-body { + padding-bottom: 18rem; + padding-top: 18rem; } } + .hero.is-halfheight .hero-body, .hero.is-fullheight .hero-body, .hero.is-fullheight-with-navbar .hero-body { + align-items: center; + display: flex; } + .hero.is-halfheight .hero-body > .container, .hero.is-fullheight .hero-body > .container, .hero.is-fullheight-with-navbar .hero-body > .container { + flex-grow: 1; + flex-shrink: 1; } + .hero.is-halfheight { + min-height: 50vh; } + .hero.is-fullheight { + min-height: 100vh; } + +.hero-video { + overflow: hidden; } + .hero-video video { + left: 50%; + min-height: 100%; + min-width: 100%; + position: absolute; + top: 50%; + transform: translate3d(-50%, -50%, 0); } + .hero-video.is-transparent { + opacity: 0.3; } + @media screen and (max-width: 768px) { + .hero-video { + display: none; } } +.hero-buttons { + margin-top: 1.5rem; } + @media screen and (max-width: 768px) { + .hero-buttons .button { + display: flex; } + .hero-buttons .button:not(:last-child) { + margin-bottom: 0.75rem; } } + @media screen and (min-width: 769px), print { + .hero-buttons { + display: flex; + justify-content: center; } + .hero-buttons .button:not(:last-child) { + margin-right: 1.5rem; } } +.hero-head, +.hero-foot { + flex-grow: 0; + flex-shrink: 0; } + +.hero-body { + flex-grow: 1; + flex-shrink: 0; + padding: 3rem 1.5rem; } + +.section { + padding: 3rem 1.5rem; } + @media screen and (min-width: 1056px) { + .section.is-medium { + padding: 9rem 1.5rem; } + .section.is-large { + padding: 18rem 1.5rem; } } +.footer { + background-color: #fafafa; + padding: 3rem 1.5rem 6rem; } + +h1 .docs-heading-anchor, h1 .docs-heading-anchor:hover, h1 .docs-heading-anchor:visited, h2 .docs-heading-anchor, h2 .docs-heading-anchor:hover, h2 .docs-heading-anchor:visited, h3 .docs-heading-anchor, h3 .docs-heading-anchor:hover, h3 .docs-heading-anchor:visited, h4 .docs-heading-anchor, h4 .docs-heading-anchor:hover, h4 .docs-heading-anchor:visited, h5 .docs-heading-anchor, h5 .docs-heading-anchor:hover, h5 .docs-heading-anchor:visited, h6 .docs-heading-anchor, h6 .docs-heading-anchor:hover, h6 .docs-heading-anchor:visited { + color: #654ca3; } + +h1 .docs-heading-anchor-permalink, h2 .docs-heading-anchor-permalink, h3 .docs-heading-anchor-permalink, h4 .docs-heading-anchor-permalink, h5 .docs-heading-anchor-permalink, h6 .docs-heading-anchor-permalink { + visibility: hidden; + vertical-align: middle; + margin-left: 0.5em; + font-size: 0.7rem; } + h1 .docs-heading-anchor-permalink::before, h2 .docs-heading-anchor-permalink::before, h3 .docs-heading-anchor-permalink::before, h4 .docs-heading-anchor-permalink::before, h5 .docs-heading-anchor-permalink::before, h6 .docs-heading-anchor-permalink::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f0c1"; } + +h1:hover .docs-heading-anchor-permalink, h2:hover .docs-heading-anchor-permalink, h3:hover .docs-heading-anchor-permalink, h4:hover .docs-heading-anchor-permalink, h5:hover .docs-heading-anchor-permalink, h6:hover .docs-heading-anchor-permalink { + visibility: visible; } + +.docs-dark-only { + display: none !important; } + +pre { + position: relative; + overflow: hidden; } + pre code, pre code.hljs { + padding: 0 0.75rem !important; + overflow: auto; + display: block; } + pre code:first-of-type, pre code.hljs:first-of-type { + padding-top: 0.5rem !important; } + pre code:last-of-type, pre code.hljs:last-of-type { + padding-bottom: 0.5rem !important; } + pre .copy-button { + opacity: 0.2; + transition: opacity 0.2s; + position: absolute; + right: 0em; + top: 0em; + padding: 0.5em; + width: 2.5em; + height: 2.5em; + background: transparent; + border: none; + font-family: "Font Awesome 5 Free"; + color: #202020; + cursor: pointer; + text-align: center; } + pre .copy-button:focus, pre .copy-button:hover { + opacity: 1; + background: rgba(32, 32, 32, 0.1); + color: #149eaa; } + pre .copy-button.success { + color: #259a12; + opacity: 1; } + pre .copy-button.error { + color: #cb3c33; + opacity: 1; } + pre:hover .copy-button { + opacity: 1; } + +.admonition { + background-color: #b5b5b5; + border-style: solid; + border-width: 1px; + border-color: #363636; + border-radius: 4px; + font-size: 1rem; } + .admonition strong { + color: currentColor; } + .admonition.is-small, #documenter .docs-sidebar form.docs-search > input.admonition { + font-size: 0.75rem; } + .admonition.is-medium { + font-size: 1.25rem; } + .admonition.is-large { + font-size: 1.5rem; } + .admonition.is-default { + background-color: #b5b5b5; + border-color: #363636; } + .admonition.is-default > .admonition-header { + background-color: #363636; + color: #fff; } + .admonition.is-default > .admonition-body { + color: #fff; } + .admonition.is-info { + background-color: #def0fc; + border-color: #209cee; } + .admonition.is-info > .admonition-header { + background-color: #209cee; + color: #fff; } + .admonition.is-info > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-success { + background-color: #bdf4d1; + border-color: #22c35b; } + .admonition.is-success > .admonition-header { + background-color: #22c35b; + color: #fff; } + .admonition.is-success > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-warning { + background-color: #fff3c5; + border-color: #ffdd57; } + .admonition.is-warning > .admonition-header { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .admonition.is-warning > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-danger { + background-color: #ffaba7; + border-color: #da0b00; } + .admonition.is-danger > .admonition-header { + background-color: #da0b00; + color: #fff; } + .admonition.is-danger > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-compat { + background-color: #bdeff5; + border-color: #1db5c9; } + .admonition.is-compat > .admonition-header { + background-color: #1db5c9; + color: #fff; } + .admonition.is-compat > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + +.admonition-header { + color: #fff; + background-color: #363636; + align-items: center; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.5rem 0.75rem; + position: relative; } + .admonition-header:before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + margin-right: 0.75rem; + content: "\f06a"; } + +.admonition-body { + color: #202020; + padding: 0.5rem 0.75rem; } + .admonition-body pre { + background-color: #ebe8f4; } + .admonition-body code { + background-color: #ebe8f4; } + +.docstring { + margin-bottom: 1em; + background-color: transparent; + border: 1px solid #dbdbdb; + box-shadow: 2px 2px 3px rgba(10, 10, 10, 0.1); + max-width: 100%; } + .docstring > header { + display: flex; + flex-grow: 1; + align-items: stretch; + padding: 0.5rem 0.75rem; + background-color: #f7f7f7; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + box-shadow: none; + border-bottom: 1px solid #dbdbdb; } + .docstring > header code { + background-color: transparent; } + .docstring > header .docstring-binding { + margin-right: 0.3em; } + .docstring > header .docstring-category { + margin-left: 0.3em; } + .docstring > section { + position: relative; + padding: 0.75rem 0.75rem; + border-bottom: 1px solid #dbdbdb; } + .docstring > section:last-child { + border-bottom: none; } + .docstring > section > a.docs-sourcelink { + transition: opacity 0.3s; + opacity: 0; + position: absolute; + right: 0.375rem; + bottom: 0.375rem; } + .docstring > section > a.docs-sourcelink:focus { + opacity: 1 !important; } + .docstring:hover > section > a.docs-sourcelink { + opacity: 0.2; } + .docstring:focus-within > section > a.docs-sourcelink { + opacity: 0.2; } + .docstring > section:hover a.docs-sourcelink { + opacity: 1; } + +.documenter-example-output { + background-color: #fff; } + +.outdated-warning-overlay { + position: fixed; + top: 0; + left: 0; + right: 0; + box-shadow: 0 0 10px rgba(0, 0, 0, 0.3); + z-index: 999; + background-color: #ffaba7; + color: rgba(0, 0, 0, 0.7); + border-bottom: 3px solid #da0b00; + padding: 10px 35px; + text-align: center; + font-size: 15px; } + .outdated-warning-overlay .outdated-warning-closer { + position: absolute; + top: calc(50% - 10px); + right: 18px; + cursor: pointer; + width: 12px; } + .outdated-warning-overlay a { + color: #149eaa; } + .outdated-warning-overlay a:hover { + color: #107c85; } + +.content pre { + border: 1px solid #dbdbdb; } + +.content code { + font-weight: inherit; } + +.content a code { + color: #149eaa; } + +.content h1 code, .content h2 code, .content h3 code, .content h4 code, .content h5 code, .content h6 code { + color: #654ca3; } + +.content table { + display: block; + width: initial; + max-width: 100%; + overflow-x: auto; } + +.content blockquote > ul:first-child, .content blockquote > ol:first-child, .content .admonition-body > ul:first-child, .content .admonition-body > ol:first-child { + margin-top: 0; } + +pre, code { + font-variant-ligatures: no-contextual; } + +.breadcrumb a.is-disabled { + cursor: default; + pointer-events: none; } + .breadcrumb a.is-disabled, .breadcrumb a.is-disabled:hover { + color: #654ca3; } + +.hljs { + background: initial !important; } + +.katex .katex-mathml { + top: 0; + right: 0; } + +.katex-display, mjx-container, .MathJax_Display { + margin: 0.5em 0 !important; } + +html { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; } + +li.no-marker { + list-style: none; } + +/* This file contain the overall layout. + * + * The main container is
          that is identified by id #documenter. + */ +#documenter .docs-main > article { + overflow-wrap: break-word; } + #documenter .docs-main > article .math-container { + overflow-x: auto; + overflow-y: hidden; } + +@media screen and (min-width: 1056px) { + #documenter .docs-main { + max-width: 52rem; + margin-left: 20rem; + padding-right: 1rem; } } + +@media screen and (max-width: 1055px) { + #documenter .docs-main { + width: 100%; } + #documenter .docs-main > article { + max-width: 52rem; + margin-left: auto; + margin-right: auto; + margin-bottom: 1rem; + padding: 0 1rem; } + #documenter .docs-main > header, #documenter .docs-main > nav { + max-width: 100%; + width: 100%; + margin: 0; } } + +#documenter .docs-main header.docs-navbar { + background-color: #fff; + border-bottom: 1px solid #dbdbdb; + z-index: 2; + min-height: 4rem; + margin-bottom: 1rem; + display: flex; } + #documenter .docs-main header.docs-navbar .breadcrumb { + flex-grow: 1; } + #documenter .docs-main header.docs-navbar .docs-right { + display: flex; + white-space: nowrap; } + #documenter .docs-main header.docs-navbar .docs-right .docs-icon, #documenter .docs-main header.docs-navbar .docs-right .docs-label, #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + display: inline-block; } + #documenter .docs-main header.docs-navbar .docs-right .docs-label { + padding: 0; + margin-left: 0.3em; } + #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button { + margin: auto 0 auto 1rem; } + #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + font-size: 1.5rem; + margin: auto 0 auto 1rem; } + #documenter .docs-main header.docs-navbar > * { + margin: auto 0; } + @media screen and (max-width: 1055px) { + #documenter .docs-main header.docs-navbar { + position: sticky; + top: 0; + padding: 0 1rem; + /* For Headroom.js */ + transition-property: top, box-shadow; + -webkit-transition-property: top, box-shadow; + /* Safari */ + transition-duration: 0.3s; + -webkit-transition-duration: 0.3s; + /* Safari */ } + #documenter .docs-main header.docs-navbar.headroom--not-top { + box-shadow: 0.2rem 0rem 0.4rem #bbb; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } + #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { + top: -4.5rem; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } } +#documenter .docs-main section.footnotes { + border-top: 1px solid #dbdbdb; } + #documenter .docs-main section.footnotes li .tag:first-child, #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, #documenter .docs-main section.footnotes li .content kbd:first-child, .content #documenter .docs-main section.footnotes li kbd:first-child { + margin-right: 1em; + margin-bottom: 0.4em; } + +#documenter .docs-main .docs-footer { + display: flex; + flex-wrap: wrap; + margin-left: 0; + margin-right: 0; + border-top: 1px solid #dbdbdb; + padding-top: 1rem; + padding-bottom: 1rem; } + @media screen and (max-width: 1055px) { + #documenter .docs-main .docs-footer { + padding-left: 1rem; + padding-right: 1rem; } } + #documenter .docs-main .docs-footer .docs-footer-nextpage, #documenter .docs-main .docs-footer .docs-footer-prevpage { + flex-grow: 1; } + #documenter .docs-main .docs-footer .docs-footer-nextpage { + text-align: right; } + #documenter .docs-main .docs-footer .flexbox-break { + flex-basis: 100%; + height: 0; } + #documenter .docs-main .docs-footer .footer-message { + font-size: 0.8em; + margin: 0.5em auto 0 auto; + text-align: center; } + +#documenter .docs-sidebar { + display: flex; + flex-direction: column; + color: #fff; + background-color: #654ca3; + border-right: 1px solid #dbdbdb; + padding: 0; + flex: 0 0 18rem; + z-index: 5; + font-size: 1em; + position: fixed; + left: -18rem; + width: 18rem; + height: 100%; + transition: left 0.3s; + /* Setting up a nicer theme style for the scrollbar */ } + #documenter .docs-sidebar.visible { + left: 0; + box-shadow: 0.4rem 0rem 0.8rem #bbb; } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar.visible { + box-shadow: none; } } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar { + left: 0; + top: 0; } } + #documenter .docs-sidebar .docs-logo { + margin-top: 1rem; + padding: 0 1rem; } + #documenter .docs-sidebar .docs-logo > img { + max-height: 6rem; + margin: auto; } + #documenter .docs-sidebar .docs-package-name { + flex-shrink: 0; + font-size: 1.5rem; + font-weight: 700; + text-align: center; + white-space: nowrap; + overflow: hidden; + padding: 0.5rem 0; } + #documenter .docs-sidebar .docs-package-name .docs-autofit { + max-width: 16.2rem; } + #documenter .docs-sidebar .docs-package-name a, #documenter .docs-sidebar .docs-package-name a:hover { + color: #fff; } + #documenter .docs-sidebar .docs-version-selector { + border-top: 1px solid #dbdbdb; + display: none; + padding: 0.5rem; } + #documenter .docs-sidebar .docs-version-selector.visible { + display: flex; } + #documenter .docs-sidebar ul.docs-menu { + flex-grow: 1; + user-select: none; + border-top: 1px solid #dbdbdb; + padding-bottom: 1.5rem; + /* Managing collapsible submenus */ } + #documenter .docs-sidebar ul.docs-menu > li > .tocitem { + font-weight: bold; } + #documenter .docs-sidebar ul.docs-menu > li li { + font-size: 0.95em; + margin-left: 1em; + border-left: 1px solid #dbdbdb; } + #documenter .docs-sidebar ul.docs-menu input.collapse-toggle { + display: none; } + #documenter .docs-sidebar ul.docs-menu ul.collapsed { + display: none; } + #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed { + display: block; } + #documenter .docs-sidebar ul.docs-menu label.tocitem { + display: flex; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label { + flex-grow: 2; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron { + display: inline-block; + font-style: normal; + font-variant: normal; + text-rendering: auto; + line-height: 1; + font-size: 0.75em; + margin-left: 1rem; + margin-top: auto; + margin-bottom: auto; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f054"; } + #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before { + content: "\f078"; } + #documenter .docs-sidebar ul.docs-menu .tocitem { + display: block; + padding: 0.5rem 0.5rem; } + #documenter .docs-sidebar ul.docs-menu .tocitem, #documenter .docs-sidebar ul.docs-menu .tocitem:hover { + color: #fff; + background: #654ca3; } + #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, #documenter .docs-sidebar ul.docs-menu label.tocitem:hover { + color: #fff; + background-color: #4b3979; } + #documenter .docs-sidebar ul.docs-menu li.is-active { + border-top: 1px solid #dbdbdb; + border-bottom: 1px solid #dbdbdb; + background-color: #fff; } + #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover { + background-color: #fff; + color: #202020; } + #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover { + background-color: #ddd7ec; + color: #202020; } + #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child { + border-top: none; } + #documenter .docs-sidebar ul.docs-menu ul.internal { + margin: 0 0.5rem 0.5rem; + border-top: 1px solid #dbdbdb; } + #documenter .docs-sidebar ul.docs-menu ul.internal li { + font-size: 0.85em; + border-left: none; + margin-left: 0; + margin-top: 0.5rem; } + #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem { + width: 100%; + padding: 0; } + #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before { + content: "⚬"; + margin-right: 0.4em; } + #documenter .docs-sidebar form.docs-search { + margin: auto; + margin-top: 0.5rem; + margin-bottom: 0.5rem; } + #documenter .docs-sidebar form.docs-search > input { + width: 14.4rem; } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar ul.docs-menu { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar { + width: .3rem; + background: none; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #543f87; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover { + background: #43326b; } } + @media screen and (max-width: 1055px) { + #documenter .docs-sidebar { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + #documenter .docs-sidebar::-webkit-scrollbar { + width: .3rem; + background: none; } + #documenter .docs-sidebar::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #543f87; } + #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover { + background: #43326b; } } +#documenter .docs-main #documenter-search-info { + margin-bottom: 1rem; } + +#documenter .docs-main #documenter-search-results { + list-style-type: circle; + list-style-position: outside; } + #documenter .docs-main #documenter-search-results li { + margin-left: 2rem; 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Gets put into the tag.. +function set_theme_from_local_storage() { + // Intialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if(window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the browser supports user color preference + var darkPreference = false; + // Check if the users preference is for dark color scheme + if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { + darkPreference = true; + } + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; var disabled = []; var darkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if(themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); + // Check if the theme is primary dark theme + var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null); + // If ss is for dark theme then set the value of darkTheme to the name of the theme + if(isDarkTheme) darkTheme = themename; + // If we find a matching theme (and it's not the default), we'll set active to non-null + if(themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if(themename !== theme) disabled.push(ss); + } + if(active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + theme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + else if(darkTheme !== null && darkPreference === true) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + darkTheme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + if (ss.ownerNode.getAttribute("data-theme-name") !== darkTheme) { + ss.disabled = true; + } + }); + } +} +set_theme_from_local_storage(); diff --git a/previews/PR31/assets/warner.js b/previews/PR31/assets/warner.js new file mode 100644 index 00000000..5531c885 --- /dev/null +++ b/previews/PR31/assets/warner.js @@ -0,0 +1,49 @@ +function maybeAddWarning () { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return + }; + + // Current version is not a version number, so we can't tell if it's the newest version. 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          Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/previews/PR31/index.html b/previews/PR31/index.html new file mode 100644 index 00000000..f62ecc7a --- /dev/null +++ b/previews/PR31/index.html @@ -0,0 +1,2 @@ + +TransitionIndicators.jl · TransitionIndicators.jl
          Edit on GitHub

          TransitionIndicators.jl

          TransitionIndicators.jl

          TransitionIndicators — Module

          TransitionIndicators.jl

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          A Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

          To install it, run import Pkg; Pkg.add("TransitionIndicators").

          All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

          source
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          If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

          Content

          Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionIndicators.jl sticks to the latter terminology and provides an interface that:

          • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
          • Makes the surrogate analysis to test for significance under the hub.
          • Can be easily extended by any user without touching the source code.
          • Reduces the programming overhead for any researcher willing to benchmark new methods.
          • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
          • Increases trustworthiness thanks to a large test suite.
          Similar projects

          An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

          Approaches

          Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system with continuous right-hand side approaches a bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionIndicators.jl is designed to allow these cutting-edge methods and foster the development of new ones.

          diff --git a/previews/PR31/search/index.html b/previews/PR31/search/index.html new file mode 100644 index 00000000..ef64991d --- /dev/null +++ b/previews/PR31/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionIndicators.jl

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            diff --git a/previews/PR31/search_index.js b/previews/PR31/search_index.js new file mode 100644 index 00000000..c2ed5816 --- /dev/null +++ b/previews/PR31/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionIndicators.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionIndicators.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"api/#Indicators-analysis","page":"API","title":"Indicators analysis","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"IndicatorsConfig\nSignificanceConfig\nindicators_analysis","category":"page"},{"location":"api/#TransitionIndicators.IndicatorsConfig","page":"API","title":"TransitionIndicators.IndicatorsConfig","text":"IndicatorsConfig(indicators...; window_kwargs...)\n\nA configuration for computing indicators from timeseries. Indicators are standard Julia functions that input an AbstractVector and output a real number. Any number of indicators can be given. Indicators typically used in the literature are listed in the documentation section Indicators.\n\nKeywords are propagated into WindowViewer to create a sliding window for estimating the indicators.\n\nAlong with SignificanceConfig it is given to indicators_analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.SignificanceConfig","page":"API","title":"TransitionIndicators.SignificanceConfig","text":"SignificanceConfig(change_metrics...; kwargs...)\n\nA configuration for estimating a significant change of indicators computed from timeseries. Along with IndicatorsConfig it is given to indicators_analysis.\n\nchange_metrics can be a single Julia function, in which case the same metric is applied over all indicators in IndicatorsConfig. change_metrics can also be many functions, each one for each indicator.\n\nKeyword arguments\n\nn_surrogates::Int = 10_000: how many surrogates to create.\nsurrogate_method::S = RandomFourier(): what method to use to create the surrogates. Any Surrogate subtype from TimeseriesSurrogates.jl is valid.\nrng::AbstractRNG = Random.default_rng()`: a random number generator for the surrogates. See the Julia manual for more.\nwv_indicator_width::Int = 100,\nwv_indicator_stride::Int = 5,\nwidth, stride = 20, 1: width and stride given to the WindowViewer of the indicator timeseries. Notice that here the default values are different.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.indicators_analysis","page":"API","title":"TransitionIndicators.indicators_analysis","text":"indicators_analysis(x, indicators::IndicatorsConfig, significance::SignificanceConfig)\n\nPerform an analysis of transition indicators for input timeseries x by specifying which indicators to use and with what sliding window (IndicatorsConfig), as well as how to measure significant changes in the indicators (SignificanceConfig).\n\nReturn the output as IndicatorsResults.\n\nThis function performs the analysis described in the documentation Example sections. It computes various indicators over sliding windows of x, and then computes change metrics of over sliding windows of the indicators. In parallel it does exactly the same computations for surrogates of x. The returned output contains all these computed timeseries and can be given to indicators_significance.\n\n\n\n\n\n","category":"function"},{"location":"api/#Indicators-significance","page":"API","title":"Indicators significance","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"indicators_significance\nSignificanceTest\nQuantile\nSigma\nsignificant","category":"page"},{"location":"api/#TransitionIndicators.indicators_significance","page":"API","title":"TransitionIndicators.indicators_significance","text":"indicators_significance(res::IndicatorsResults, q::SignificanceTest) → out\n\nGiven the output of indicators_analysis, estimate when the computed indicators have a statistically significant change, with \"significant\" defined by q, which is a subtype of SignificanceTest.\n\nThe output is returned as an n×m matrix with n the length of the time vector of the change metric timeseries, and m the number of change metrics (which is the same as the number of indicators). The values of the matrix are Booleans (true for significant).\n\nYou can use prod(out; dim = 2) for logical & product across indicators.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.Quantile","page":"API","title":"TransitionIndicators.Quantile","text":"Quantile(q = 0.99, dir::Symbol = :updown) <: SignificanceTest\n\nSignificance is claimed by comparing the real value v with the q-th quantile of the surrogate distribution. Three possibilities are provided depending on dir:\n\ndir = :updown: Significance is claimed if v is more than the q-th or is less than the 1-q-th quantile\ndir = :up: if v is more than q-th\ndir = :down: if v is less than 1-q-th\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.Sigma","page":"API","title":"TransitionIndicators.Sigma","text":"Sigma(n::Real = 3, dir::Symbol = :updown) <: SignificanceTest\n\nSignificance is claimed by comparing the real value v with the mean μ and standard deviation σ of the surrogate distribution. Three possibilities are provided depending on dir:\n\ndir = :updown: significance is claimed if v is more than μ + n*σ or less than μ - n*σ.\ndir = :up: if v is more than μ + n*σ\ndir = :down: if v is less than μ - n*σ\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.significant","page":"API","title":"TransitionIndicators.significant","text":"significant(v::Real, s_vals::AbstractVector, q::Significance) → true/false\n\nReturn true if the value v is significant when compared to distribution of surrogate values s_vals according to the criterion q (see SignificanceTest). If not significant, return false.\n\nIf given q::Real, then Quantile is used.\n\n\n\n\n\n","category":"function"},{"location":"api/#indicator_functions","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"ar1_whitenoise\nStatistics.mean(::Any)\nStatistics.var(::AbstractArray)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#TransitionIndicators.ar1_whitenoise","page":"API","title":"TransitionIndicators.ar1_whitenoise","text":"ar1_whitenoise(x) → ̂θ\n\nEstimate the AR1 regression coefficient θ of a vector time series x. Computation based on the analytic solution of the least-square parameter estimation:\n\n hattheta = dfracsum_i=2^n x_i x_i-1sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1)). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Change-metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"RidgeRegression\nkendalltau\nspearman","category":"page"},{"location":"api/#TransitionIndicators.RidgeRegression","page":"API","title":"TransitionIndicators.RidgeRegression","text":"RidgeRegression(t, width; lambda = 0.0) → rr\n\nInitialize a ridge regression for a time vector t, a sliding-window width and an optional regularizeation term lambda. The output rr can then be used as a function to perform the regression and extract the slope! If lambda = 0, linear regression is recovered (default case). For more information, visit: https://en.wikipedia.org/wiki/Ridge_regression.\n\nExamples\n\njulia> t = 0.0:1.0:100;\njulia> x = 2.3 .* t .+ 1.2;\njulia> rr = RidgeRegression(t);\njulia> rr(x)\n2.299999999999999\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.kendalltau","page":"API","title":"TransitionIndicators.kendalltau","text":"kendalltau(x)\n\nCompute the kendall-τ correlation coefficient of the time series x.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.spearman","page":"API","title":"TransitionIndicators.spearman","text":"spearman(x)\n\nCompute the spearman correlation coefficient of the time series x.\n\n\n\n\n\n","category":"function"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Significance-metrics","page":"API","title":"Significance metrics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"threshold_indicators\nmeasure_significance\nconfidence_interval\nnormalized_percentile","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionIndicators.WindowViewer","page":"API","title":"TransitionIndicators.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride as taken as length(x)÷100 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.windowmap","page":"API","title":"TransitionIndicators.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.windowmap!","page":"API","title":"TransitionIndicators.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"#TransitionIndicators.jl","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"(Image: TransitionIndicators.jl)","category":"page"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"TransitionIndicators","category":"page"},{"location":"#TransitionIndicators","page":"TransitionIndicators.jl","title":"TransitionIndicators","text":"TransitionIndicators.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\nTo install it, run import Pkg; Pkg.add(\"TransitionIndicators\").\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionIndicators.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionIndicators.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionIndicators.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system with continuous right-hand side approaches a bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionIndicators.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any pre-processing of raw data first such as detrending (not part of TransitionIndicators.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend or jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionIndicators.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionIndicators\nusing CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionIndicators.jl\nAny timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionIndicators.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\nt_indicator = windowmap(midpoint, tfluct; indicator_window...)\n\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\n\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a ridge regression","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 20, stride = 1)\nridgereg = RidgeRegression(t_indicator, change_window.width)\n\nt_change = windowmap(midpoint, t_indicator; change_window...)\nchange_l = windowmap(ridgereg, indicator_l; change_window...)\nchange_nl = windowmap(ridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionIndicators, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\nfig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))\nlines!(ax, tfluct, s .- 0.05; color = Cycled(3))\nax.title = \"real signal vs. surrogate(s)\"\n\n# compute and plot change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(ridgereg, indicator_s; change_window...)\n\nax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = \"nonlin\")\nlines!(ax, t_change, change_s; color = Cycled(3), label = \"surrogate\")\naxislegend()\nax.title = \"change metric\"\n\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test. We calculate the change metric for thousands of surrogates of the input timeseries, and then detect the points in time where the change metric timeseries exceeds a threshold (such as the 95-quantile) of the change metrics of the surrogates.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To visualize significant trends, we plot the bands giving the (-2 sigma 2 sigma) and (-3 sigma 3 sigma) intervals of the surrogate values, with sigma the standard-deviation of indicator slope across the surrogate timeseries:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig = Figure()\naxl = Axis(fig[1,1]; title = \"linear\")\naxnl = Axis(fig[1,2]; title = \"nonlinear\")\n\nfor (j, ax, x) in zip(1:2, (axl, axnl), (x_l_fluct, x_nl_fluct))\n\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n change_s_distr = zeros(n_surrogates, length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(ridgereg, indicator_s; change_window...)\n change_s_distr[i, :] .= change_s\n end\n\n mu = vec(mean(change_s_distr, dims = 1))\n sigma = vec(std(change_s_distr, dims = 1))\n\n # Plot (real signal) change metric and various confidence intervals\n orig_change = j == 1 ? change_l : change_nl\n lines!(ax, t_change, orig_change; color = Cycled(j))\n band!(ax, t_change, mu .- 2 .* sigma, mu .+ 2 .* sigma, color = (:red, 0.2) )\n band!(ax, t_change, mu .- 3 .* sigma, mu .+ 3 .* sigma, color = (:red, 0.1) )\nend\n\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, while the data generated by the linear model does not.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionIndicators.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionIndicators.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several different indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow as follows:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Create an instance of IndicatorsConfig, that dictates which indicators will be used, and over what sliding window.\nCreate an instance of SignificanceConfig, that dictates what change metrics, surrogate types, and sliding window will be used to quantify a significant change of the indicators.\nAlong with the input timeseries x these three are plugged into indicators_analysis.\nThe output, which is an IndicatorsResults, can be used to visualize the results, or given to indicators_significance to provide flags of the timepoints where there is a significant change of each indicator.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks apply this process, and visualize it, for the examples we used in the educational part of the tutorial.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"First we load, and do the necessary pre-processing, to get input data","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionIndicators, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_nl_fluct)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Then we decide what indicators and change metrices to use","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# these indicators are suitable for Critical Slowing Down\nindicators = [var, ar1_whitenoise]\nind_conf = IndicatorsConfig(indicators; width = 400)\n\n# use spearman correlation for both indicators\nchange_metric = spearman\nsig_conf = SignificanceConfig(change_metric; width = 20, n_surrogates = 1000)\n\n# perform the full analysis\nresult = indicators_analysis(x_nl_fluct, ind_conf, sig_conf)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"And lastly, obtain some flags for when there is a significant indicator change","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"sig = indicators_significance(result, 0.99)\n\n# Plot the original timeseries\nfig, ax = lines(tfluct, x_nl_fluct; label = \"input\")\n# Scatter the significance of each indicator\nfor i in size(sig, 2)\n signif_idxs = findall(sig[:, i])\n isempty(signif_idxs) && continue\n # get timepoints in real time\n tflags = tfluct[result.t_change[signif_idxs]]\n vlines!(ax, tflags; label = \"indicator $(indicators[i])\", color = Cycled(1+i))\nend\naxislegend()\nfig","category":"page"}] +} diff --git a/previews/PR31/siteinfo.js b/previews/PR31/siteinfo.js new file mode 100644 index 00000000..48dcbe84 --- /dev/null +++ b/previews/PR31/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR31"; diff --git a/previews/PR31/tutorial/index.html b/previews/PR31/tutorial/index.html new file mode 100644 index 00000000..def29b71 --- /dev/null +++ b/previews/PR31/tutorial/index.html @@ -0,0 +1,121 @@ + +Tutorial · TransitionIndicators.jl
            Edit on GitHub

            Tutorial

            Workflow

            Computing transition indicators consists of the following steps:

            1. Doing any pre-processing of raw data first such as detrending (not part of TransitionIndicators.jl). This yields the input timeseries.
            2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
            3. Computing the changes of the indicator by sliding a window over its timeseries.
            4. Generating many surrogates that preserve important statistical properties of the original timeseries.
            5. Performing step 2 and 3 for the surrogate timeseries.
            6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend or jump or anything else) when compared to the surrogate data.

            These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionIndicators.jl exports.

            Tutorial – Educational

            Raw input data

            Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

            \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

            with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

            using TransitionIndicators
+using CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig

            Preprocessing

            Not part of TransitionIndicators.jl

            Any timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionIndicators.jl and is the responsibility of the researcher.

            The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

            x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

            At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

            Detrending in Julia

            Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

            Indicator timeseries

            We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

            indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+t_indicator = windowmap(midpoint, tfluct; indicator_window...)
+
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

            The lines plotted above are the indicator timeseries.

            Change metric timeseries

            From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a ridge regression

            change_window = (width = 20, stride = 1)
+ridgereg = RidgeRegression(t_indicator, change_window.width)
+
+t_change = windowmap(midpoint, t_indicator; change_window...)
+change_l = windowmap(ridgereg, indicator_l; change_window...)
+change_nl = windowmap(ridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

            Timeseries surrogates

            As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

            In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionIndicators, so that you don't have to using both of them.

            To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

            # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))
+lines!(ax, tfluct, s .- 0.05; color = Cycled(3))
+ax.title = "real signal vs. surrogate(s)"
+
+# compute and plot change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(ridgereg, indicator_s; change_window...)
+
+ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin")
+lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate")
+axislegend()
+ax.title = "change metric"
+
+fig

            Quantifying significance

            To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test. We calculate the change metric for thousands of surrogates of the input timeseries, and then detect the points in time where the change metric timeseries exceeds a threshold (such as the 95-quantile) of the change metrics of the surrogates.

            To visualize significant trends, we plot the bands giving the $(-2 \, \sigma, 2 \, \sigma)$ and $(-3 \, \sigma, 3 \, \sigma)$ intervals of the surrogate values, with $\sigma$ the standard-deviation of indicator slope across the surrogate timeseries:

            n_surrogates = 1_000
+fig = Figure()
+axl = Axis(fig[1,1]; title = "linear")
+axnl = Axis(fig[1,2]; title = "nonlinear")
+
+for (j, ax, x) in zip(1:2, (axl, axnl), (x_l_fluct, x_nl_fluct))
+
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    change_s_distr =  zeros(n_surrogates, length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(ridgereg, indicator_s; change_window...)
+        change_s_distr[i, :] .= change_s
+    end
+
+    mu = vec(mean(change_s_distr, dims = 1))
+    sigma = vec(std(change_s_distr, dims = 1))
+
+    # Plot (real signal) change metric and various confidence intervals
+    orig_change = j == 1 ? change_l : change_nl
+    lines!(ax, t_change, orig_change; color = Cycled(j))
+    band!(ax, t_change, mu .- 2 .* sigma, mu .+ 2 .* sigma, color = (:red, 0.2) )
+    band!(ax, t_change, mu .- 3 .* sigma, mu .+ 3 .* sigma, color = (:red, 0.1) )
+end
+
+fig

            As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, while the data generated by the linear model does not.

            Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

            Tutorial – TransitionIndicators.jl

            TransitionIndicators.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several different indicators / change metrics in one go.

            The interface is simple, and directly parallelizes the Workflow as follows:

            1. Create an instance of IndicatorsConfig, that dictates which indicators will be used, and over what sliding window.
            2. Create an instance of SignificanceConfig, that dictates what change metrics, surrogate types, and sliding window will be used to quantify a significant change of the indicators.
            3. Along with the input timeseries x these three are plugged into indicators_analysis.
            4. The output, which is an IndicatorsResults, can be used to visualize the results, or given to indicators_significance to provide flags of the timepoints where there is a significant change of each indicator.

            The following blocks apply this process, and visualize it, for the examples we used in the educational part of the tutorial.

            First we load, and do the necessary pre-processing, to get input data

            using TransitionIndicators, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_nl_fluct)
+ax.title = "input timeseries"
+fig

            Then we decide what indicators and change metrices to use

            # these indicators are suitable for Critical Slowing Down
+indicators = [var, ar1_whitenoise]
+ind_conf = IndicatorsConfig(indicators; width = 400)
+
+# use spearman correlation for both indicators
+change_metric = spearman
+sig_conf = SignificanceConfig(change_metric; width = 20, n_surrogates = 1000)
+
+# perform the full analysis
+result = indicators_analysis(x_nl_fluct, ind_conf, sig_conf)
            IndicatorsResults
+ input timeseries: 2500-element Vector{Float64}
+ indicators:       Function[Statistics.var, TransitionIndicators.ar1_whitenoise]
+ indicator length: 2100
+ change metrics:   [TransitionIndicators.spearman]
+ surrogate:        RandomFourier(true)
+ surrogate #:      1000
+

            And lastly, obtain some flags for when there is a significant indicator change

            sig = indicators_significance(result, 0.99)
+
+# Plot the original timeseries
+fig, ax = lines(tfluct, x_nl_fluct; label = "input")
+# Scatter the significance of each indicator
+for i in size(sig, 2)
+    signif_idxs = findall(sig[:, i])
+    isempty(signif_idxs) && continue
+    # get timepoints in real time
+    tflags = tfluct[result.t_change[signif_idxs]]
+    vlines!(ax, tflags; label = "indicator $(indicators[i])", color = Cycled(1+i))
+end
+axislegend()
+fig
            diff --git a/previews/PR31/tutorial_literate.jl b/previews/PR31/tutorial_literate.jl new file mode 100644 index 00000000..7817d0f2 --- /dev/null +++ b/previews/PR31/tutorial_literate.jl @@ -0,0 +1,202 @@ +using TransitionIndicators, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_nlinear) +lines!(ax, t, x_linear) +ax.title = "raw data" +fig + +# +x_nl_fluct = diff(x_nlinear) +x_l_fluct = diff(x_linear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_nl_fluct) +ax.title = "input timeseries" +fig + +# +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +t_indicator = windowmap(midpoint, tfluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +# +change_window = (width = 20, stride = 1) +ridgereg = RidgeRegression(t_indicator, change_window.width) + +t_change = windowmap(midpoint, t_indicator; change_window...) +change_l = windowmap(ridgereg, indicator_l; change_window...) +change_nl = windowmap(ridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_nl) +# lines!(ax, t_change, change_l) +ax.title = "change metric timeseries" +fig + + +# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) +fig, ax = lines(tfluct, x_nl_fluct) +lines!(ax, tfluct, s .- 0.05; color = Cycled(3)) +ax.title = "real signal vs. surrogate(s)" + +# compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(ridgereg, indicator_s; change_window...) +fig, ax = lines(t_indicator, indicator_nl) +lines!(ax, t_indicator, indicator_s; color = Cycled(3)) +ax.ylabel = "indicator" +ax, = lines(fig[1,2], t_change, change_nl) +lines!(ax, t_change, change_s; color = Cycled(3)) +ax.ylabel = "change metric" +Label(fig[0, :], "real signal vs. surrogate(s)"; + tellheight = true, tellwidth = false, valign = :bottom, font = "TeX Gyre Heros Bold" +) +fig + + + + +lines!(ax, tfluct, s .- 0.05; color = Cycled(3)) +ax.title = "real signal vs. surrogate(s)" + + + +ax, = lines(fig[1,2], t_change, change_nl; label = "real") +lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate") +axislegend() +ax.title = "change metric" + +fig + +# %% + +n_surrogates = 1_000 +fig = Figure() +axnl = Axis(fig[1,1]; title = "nonlinear") +# axl = Axis(fig[1,2]; title = "linear") +axl = nothing + +for (j, ax, x) in zip(1:2, (axnl, axl), (x_nl_fluct, x_l_fluct)) + + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + change_s_distr = zeros(n_surrogates, length(change_s)) + + # Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(ridgereg, indicator_s; change_window...) + change_s_distr[i, :] .= change_s + end + + mu = vec(mean(change_s_distr, dims = 1)) + sigma = vec(std(change_s_distr, dims = 1)) + + # Plot (real signal) change metric and various confidence intervals + orig_change = j == 1 ? change_nl : change_l + lines!(ax, t_change, orig_change; color = Cycled(j)) + # band!(ax, t_change, mu .- 2 .* sigma, mu .+ 2 .* sigma, color = (:red, 0.2) ) + band!(ax, t_change, mu .- 3 .* sigma, mu .+ 3 .* sigma, color = (Main.COLORS[3], 0.2), + label = "±3σ") + axislegend(ax) + j == 1 && break +end + +fig + +# %% + +# these indicators are suitable for Critical Slowing Down +indicators = [var, ar1_whitenoise] +ind_conf = IndicatorsConfig(indicators; width = 400) + +# use spearman correlation for both indicators +change_metric = spearman +sig_conf = SignificanceConfig(change_metric; width = 20, n_surrogates = 1000) + +# perform the full analysis +result = indicators_analysis(x_nl_fluct, ind_conf, sig_conf) + +# And lastly, obtain some flags for when there is a significant indicator change +sig = indicators_significance(result, 0.99) + +# Plot the original timeseries +fig, ax = lines(tfluct, x_nl_fluct; label = "input") +# Scatter the significance of each indicator +for i in size(sig, 2) + signif_idxs = findall(sig[:, i]) + isempty(signif_idxs) && continue + # get timepoints in real time + tflags = tfluct[result.t_change[signif_idxs]] + vlines!(ax, tflags; label = "flags for $(indicators[i])", color = Cycled(3)) +end +axislegend() +fig + + + +# Tutorial short + +using TransitionIndicators, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +fig, ax = lines(t, x_nlinear;z) +ax.title = "original timeseries" +fig + +input = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(tfluct, input; color = Cycled(2)) +ax.title = "input timeseries" +fig + + + +# these indicators are suitable for Critical Slowing Down +indicators = [var, ar1_whitenoise] +ind_conf = IndicatorsConfig(indicators; + width = 400 +) +# use spearman correlation for both indicators +change_metric = spearman +sig_conf = SignificanceConfig(change_metric; + width = 20, n_surrogates = 10_000, + surrogate_method = RandomFourier(), +) + +# perform the full analysis +result = indicators_analysis(input, ind_conf, sig_conf) + +# And lastly, obtain some flags for when there +# is a significant indicator change +sig = indicators_significance(result, 0.99) + +sig + +# Plot the original timeseries +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2), label = "input") +# Scatter the significance of each indicator +for i in size(sig, 2) + signif_idxs = findall(sig[:, i]) + isempty(signif_idxs) && continue + # get timepoints in real time + tflags = tfluct[result.t_change[signif_idxs]] + vlines!(ax, tflags; label = "indicator $(indicators[i])", color = Cycled(2+i)) +end +axislegend() +fig + + diff --git a/previews/PR34/api/index.html b/previews/PR34/api/index.html new file mode 100644 index 00000000..414ff73f --- /dev/null +++ b/previews/PR34/api/index.html @@ -0,0 +1,11 @@ + +API · TransitionIndicators.jl
            Edit on GitHub

            API

            Load data

            Indicators analysis

            TransitionIndicators.precompute_metrics — Function
            precompute_metrics(metrics::Vector, t::AbstractVector)

            Precompute functions contained in metrics that can be precomputed based on the time vector t. Relies on abstract type PrecomputableFunction.

            The output f::Vector{Function} contains the ready-to-use metrics.

            source
            TransitionIndicators.IndicatorsConfig — Type
            IndicatorsConfig(t::AbstractVector, f::Function, indicators...; kwargs...)

            A configuration for computing indicators from timeseries with time t. Indicators are standard Julia functions that input an ::AbstractVector and output a ::Real. Any number of indicators can be given. Indicators typically used in the literature are listed in the documentation section Indicators.

            Keywords are propagated into WindowViewer to create a sliding window for estimating the indicators. The time vector resulting from the sliding window is obtained under the hood by:

            t_indicator = windowmap(f, t, kwargs...)

            Common choices for f are:

            • last: use x[k-width:k] to estimate the indicator at time step k.
            • midpoint: use x[k-width÷2:k+width÷2] to estimate the indicator at time step k.
            • first: use x[k:k+width] to estimate the indicator at time step k.

            Along with SignificanceConfig it is given to indicators_analysis.

            source
            TransitionIndicators.SignificanceConfig — Type
            SignificanceConfig(indconfig, f, change_metrics...; kwargs...)

            A configuration for estimating a significant change of indicators based on a sliding window and and indconfig::IndicatorsConfig. The time vector resulting from the sliding window is obtained under the hood by:

            t_change = windowmap(f, indconfig.t_indicator, kwargs...)

            Common choices for f are:

            • last: use x[k-width:k] to estimate the indicator change at time step k.
            • midpoint: use x[k-width÷2:k+width÷2] to estimate the indicator change

            at time step k.

            • first: use x[k:k+width] to estimate the indicator change at time step k.

            Along with IndicatorsConfig, SignificanceConfig is given to indicators_analysis.

            change_metrics can be a single Julia function, in which case the same metric is applied over all indicators in IndicatorsConfig. change_metrics can also be many functions, each one for each indicator.

            Keyword arguments

            • n_surrogates::Int = 10_000: how many surrogates to create.
            • surrogate_method::S = RandomFourier(): what method to use to create the surrogates. Any Surrogate subtype from TimeseriesSurrogates.jl is valid.
            • rng::AbstractRNG = Random.default_rng()`: a random number generator for the surrogates. See the Julia manual for more.
            • width::Int: width given to the WindowViewer of the indicator timeseries to estimate transient changes of the indicator.
            • stride::Int: stride given to the WindowViewer of the indicator timeseries to estimate transient changes of the indicator.
            • tail::Symbol: kind of tail test to do (one of :left, :right, :both).
            source
            TransitionIndicators.indicators_analysis — Function
            indicators_analysis(t, x, indicators::IndicatorsConfig, sigconfig::SignificanceConfig)

            Perform an analysis of transition indicators for input timeseries x with time vector t by specifying which indicators to use and with what sliding window (IndicatorsConfig), as well as how to measure significant changes in the indicators (SignificanceConfig). If t is not provided, it is assumed that t=eachindex(x).

            Return the output as IndicatorsResults.

            This function performs the analysis described in the documentation Example sections. It computes various indicators over sliding windows of x, and then computes change metrics of over sliding windows of the indicators. It does exactly the same computations for surrogates of x and use this result to check for significance of the change metrics by computing the p-value. The returned output contains all these computed timeseries.

            source
            TransitionIndicators.IndicatorsResults — Type
            IndicatorsResults

            A struct containing the output of indicators_analysis, which is the main computational part of TransitionIndicators.jl. It can be used for analysis and visualization purposes.

            It has the following fields:

            • x: the input timeseries.

            • t: the time vector of the input timeseries.

            • indicators::Vector{Function}: indicators used in the processing.

            • x_indicator, the indicator timeseries (matrix with each column one indicator).

            • t_indicator, the time vector of the indicator timeseries.

            • change_metrics::Vector{Function}: change metrics used in the processing.

            • x_change, the change metric timeseries (matrix with each column one change metric).

            • t_change, the time vector of the change metric timeseries.

            • pval, the p-value of the change metrics w.r.t. the surrogates. It is a 2-dimensional array, where first dimension = time, second dimension = change metric. I.e. pval[:, k] will give the time series of p-value of the k-th change metric.

            source

            Indicators

            Statistics.mean — Method
            mean(itr)

            Compute the mean of all elements in a collection.

            Note

            If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

            Examples

            julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
            Statistics.var — Method
            var(itr; corrected::Bool=true, mean=nothing[, dims])

            Compute the sample variance of collection itr.

            The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

            If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

            A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

            Note

            If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

            StatsBase.skewness — Function
            skewness(v, [wv::AbstractWeights], m=mean(v))

            Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

            StatsBase.kurtosis — Function
            kurtosis(v, [wv::AbstractWeights], m=mean(v))

            Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

            TransitionIndicators.ar1_whitenoise — Function
            ar1_whitenoise(x::AbstractVector)

            Return the AR1 regression coefficient θ of a time series x. Computation based on the analytic solution of the least-square parameter estimation:

            \[ \hat{\theta} = \dfrac{\sum_{i=2}^{n} x_i \, x_{i-1}}{\sum_{i=2}^{n} x_{i-1}^2}\]

            source
            TransitionIndicators.LowfreqPowerSpectrum — Type
            LowfreqPowerSpectrum(; q_lofreq = 0.1)

            Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

            lfps = precompute( LowfreqPowerSpectrum() )

            Keyword arguments:

            • q_lofreq: a number between 0 and 1 that characterises which portion of the

            frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

            source
            TransitionIndicators.PrecomputedLowfreqPowerSpectrum — Type
            PrecomputedLowfreqPowerSpectrum(x::AbstractVector)

            A struct containing all the precomputed fields to efficiently perform repetitive computation of the low-frequency power spectrum (LFPS), a number between 0 and 1 that characterizes the amount of power contained in the low frequencies of the power density spectrum of x. Once lfps::PrecomputedLowfreqPowerSpectrum is initialized, it can be used as a function to obtain the LFPS of x::AbstractVector by:

            lfps(x)
            source
            Missing docstring.

            Missing docstring for PermutationEntropy(). Check Documenter's build log for details.

            Change metrics

            Surrogates

            For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

            Sliding windows

            TransitionIndicators.WindowViewer — Type
            WindowViewer(x; width, stride)

            Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

            If not given, the keywords width, stride are taken as default_window_width(x) and 1.

            source
            TransitionIndicators.windowmap — Function
            windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

            A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

            source
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+ }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR34/assets/search.js b/previews/PR34/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR34/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
          • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR34/assets/themes/documenter-dark.css b/previews/PR34/assets/themes/documenter-dark.css new file mode 100644 index 00000000..aedf20e6 --- /dev/null +++ b/previews/PR34/assets/themes/documenter-dark.css @@ -0,0 +1,7396 @@ +@charset "UTF-8"; +/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */ +@keyframes spinAround { + from { + transform: rotate(0deg); } + to { + transform: rotate(359deg); } } + +html.theme--documenter-dark .tabs, html.theme--documenter-dark .pagination-previous, +html.theme--documenter-dark .pagination-next, +html.theme--documenter-dark .pagination-link, +html.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .breadcrumb, html.theme--documenter-dark .file, html.theme--documenter-dark .button, .is-unselectable, html.theme--documenter-dark .modal-close, html.theme--documenter-dark .delete { + -webkit-touch-callout: none; + -webkit-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; } + +html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after, html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after { + border: 3px solid transparent; + border-radius: 2px; + border-right: 0; + border-top: 0; + content: " "; + display: block; + height: 0.625em; + margin-top: -0.4375em; + pointer-events: none; + position: absolute; + top: 50%; + transform: rotate(-45deg); + transform-origin: center; + width: 0.625em; } + +html.theme--documenter-dark .admonition:not(:last-child), html.theme--documenter-dark .tabs:not(:last-child), html.theme--documenter-dark .message:not(:last-child), html.theme--documenter-dark .list:not(:last-child), html.theme--documenter-dark .level:not(:last-child), html.theme--documenter-dark .breadcrumb:not(:last-child), html.theme--documenter-dark .highlight:not(:last-child), html.theme--documenter-dark .block:not(:last-child), html.theme--documenter-dark .title:not(:last-child), +html.theme--documenter-dark .subtitle:not(:last-child), html.theme--documenter-dark .table-container:not(:last-child), html.theme--documenter-dark .table:not(:last-child), html.theme--documenter-dark .progress:not(:last-child), html.theme--documenter-dark .notification:not(:last-child), html.theme--documenter-dark .content:not(:last-child), html.theme--documenter-dark .box:not(:last-child) { + margin-bottom: 1.5rem; } + +html.theme--documenter-dark .modal-close, html.theme--documenter-dark .delete { + -moz-appearance: none; + -webkit-appearance: none; + background-color: rgba(10, 10, 10, 0.2); + border: none; + border-radius: 290486px; + cursor: pointer; + pointer-events: auto; + display: inline-block; + flex-grow: 0; + flex-shrink: 0; + font-size: 0; + height: 20px; + max-height: 20px; + max-width: 20px; + min-height: 20px; + min-width: 20px; + outline: none; + position: relative; + vertical-align: top; + width: 20px; } + html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::before, html.theme--documenter-dark .modal-close::after, html.theme--documenter-dark .delete::after { + background-color: white; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::before { + height: 2px; + width: 50%; } + html.theme--documenter-dark .modal-close::after, html.theme--documenter-dark .delete::after { + height: 50%; + width: 2px; } + html.theme--documenter-dark .modal-close:hover, html.theme--documenter-dark .delete:hover, html.theme--documenter-dark .modal-close:focus, html.theme--documenter-dark .delete:focus { + background-color: rgba(10, 10, 10, 0.3); } + html.theme--documenter-dark .modal-close:active, html.theme--documenter-dark .delete:active { + background-color: rgba(10, 10, 10, 0.4); } + html.theme--documenter-dark .is-small.modal-close, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.modal-close, html.theme--documenter-dark .is-small.delete, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.delete { + height: 16px; + max-height: 16px; + max-width: 16px; + min-height: 16px; + min-width: 16px; + width: 16px; } + html.theme--documenter-dark .is-medium.modal-close, html.theme--documenter-dark .is-medium.delete { + height: 24px; + max-height: 24px; + max-width: 24px; + min-height: 24px; + min-width: 24px; + width: 24px; } + html.theme--documenter-dark .is-large.modal-close, html.theme--documenter-dark .is-large.delete { + height: 32px; + max-height: 32px; + max-width: 32px; + min-height: 32px; + min-width: 32px; + width: 32px; } + +html.theme--documenter-dark .control.is-loading::after, html.theme--documenter-dark .select.is-loading::after, html.theme--documenter-dark .loader, html.theme--documenter-dark .button.is-loading::after { + animation: spinAround 500ms infinite linear; + border: 2px solid #dbdbdb; + border-radius: 290486px; + border-right-color: transparent; + border-top-color: transparent; + content: ""; + display: block; + height: 1em; + position: relative; + width: 1em; } + +html.theme--documenter-dark .hero-video, html.theme--documenter-dark .modal-background, html.theme--documenter-dark .modal, html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img, +html.theme--documenter-dark .image.is-square .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img, +html.theme--documenter-dark .image.is-1by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img, +html.theme--documenter-dark .image.is-5by4 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img, +html.theme--documenter-dark .image.is-4by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img, +html.theme--documenter-dark .image.is-3by2 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img, +html.theme--documenter-dark .image.is-5by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img, +html.theme--documenter-dark .image.is-16by9 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img, +html.theme--documenter-dark .image.is-2by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img, +html.theme--documenter-dark .image.is-3by1 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img, +html.theme--documenter-dark .image.is-4by5 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img, +html.theme--documenter-dark .image.is-3by4 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img, +html.theme--documenter-dark .image.is-2by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img, +html.theme--documenter-dark .image.is-3by5 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img, +html.theme--documenter-dark .image.is-9by16 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img, +html.theme--documenter-dark .image.is-1by2 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img, +html.theme--documenter-dark .image.is-1by3 .has-ratio, +html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, .is-overlay { + bottom: 0; + left: 0; + position: absolute; + right: 0; + top: 0; } + +html.theme--documenter-dark .pagination-previous, +html.theme--documenter-dark .pagination-next, +html.theme--documenter-dark .pagination-link, +html.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .file-cta, +html.theme--documenter-dark .file-name, html.theme--documenter-dark .select select, html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .button { + -moz-appearance: none; + -webkit-appearance: none; + align-items: center; + border: 1px solid transparent; + border-radius: 4px; + box-shadow: none; + display: inline-flex; + font-size: 1rem; + height: 2.25em; + justify-content: flex-start; + line-height: 1.5; + padding-bottom: calc(0.375em - 1px); + padding-left: calc(0.625em - 1px); + padding-right: calc(0.625em - 1px); + padding-top: calc(0.375em - 1px); + position: relative; + vertical-align: top; } + html.theme--documenter-dark .pagination-previous:focus, + html.theme--documenter-dark .pagination-next:focus, + html.theme--documenter-dark .pagination-link:focus, + html.theme--documenter-dark .pagination-ellipsis:focus, html.theme--documenter-dark .file-cta:focus, + html.theme--documenter-dark .file-name:focus, html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .button:focus, html.theme--documenter-dark .is-focused.pagination-previous, + html.theme--documenter-dark .is-focused.pagination-next, + html.theme--documenter-dark .is-focused.pagination-link, + html.theme--documenter-dark .is-focused.pagination-ellipsis, html.theme--documenter-dark .is-focused.file-cta, + html.theme--documenter-dark .is-focused.file-name, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-focused.button, html.theme--documenter-dark .pagination-previous:active, + html.theme--documenter-dark .pagination-next:active, + html.theme--documenter-dark .pagination-link:active, + html.theme--documenter-dark .pagination-ellipsis:active, html.theme--documenter-dark .file-cta:active, + html.theme--documenter-dark .file-name:active, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .button:active, html.theme--documenter-dark .is-active.pagination-previous, + html.theme--documenter-dark .is-active.pagination-next, + html.theme--documenter-dark .is-active.pagination-link, + html.theme--documenter-dark .is-active.pagination-ellipsis, html.theme--documenter-dark .is-active.file-cta, + html.theme--documenter-dark .is-active.file-name, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .is-active.button { + outline: none; } + html.theme--documenter-dark .pagination-previous[disabled], + html.theme--documenter-dark .pagination-next[disabled], + html.theme--documenter-dark .pagination-link[disabled], + html.theme--documenter-dark .pagination-ellipsis[disabled], html.theme--documenter-dark .file-cta[disabled], + html.theme--documenter-dark .file-name[disabled], html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], html.theme--documenter-dark .button[disabled], fieldset[disabled] html.theme--documenter-dark .pagination-previous, html.theme--documenter-dark fieldset[disabled] .pagination-previous, + fieldset[disabled] html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark fieldset[disabled] .pagination-next, + fieldset[disabled] html.theme--documenter-dark .pagination-link, + html.theme--documenter-dark fieldset[disabled] .pagination-link, + fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis, + html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis, fieldset[disabled] html.theme--documenter-dark .file-cta, html.theme--documenter-dark fieldset[disabled] .file-cta, + fieldset[disabled] html.theme--documenter-dark .file-name, + html.theme--documenter-dark fieldset[disabled] .file-name, fieldset[disabled] html.theme--documenter-dark .select select, fieldset[disabled] html.theme--documenter-dark .textarea, fieldset[disabled] html.theme--documenter-dark .input, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark fieldset[disabled] .select select, html.theme--documenter-dark .select fieldset[disabled] select, html.theme--documenter-dark fieldset[disabled] .textarea, html.theme--documenter-dark fieldset[disabled] .input, html.theme--documenter-dark fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search > input, fieldset[disabled] html.theme--documenter-dark .button, html.theme--documenter-dark fieldset[disabled] .button { + cursor: not-allowed; } + +/*! minireset.css v0.0.4 | MIT License | github.com/jgthms/minireset.css */ +html, +body, +p, +ol, +ul, +li, +dl, +dt, +dd, +blockquote, +figure, +fieldset, +legend, +textarea, +pre, +iframe, +hr, +h1, +h2, +h3, +h4, +h5, +h6 { + margin: 0; + padding: 0; } + +h1, +h2, +h3, +h4, +h5, +h6 { + font-size: 100%; + font-weight: normal; } + +ul { + list-style: none; } + +button, +input, +select, +textarea { + margin: 0; } + +html { + box-sizing: border-box; } + +*, *::before, *::after { + box-sizing: inherit; } + +img, +embed, +iframe, +object, +video { + height: auto; + max-width: 100%; } + +audio { + max-width: 100%; } + +iframe { + border: 0; } + +table { + border-collapse: collapse; + border-spacing: 0; } + +td, +th { + padding: 0; } + td:not([align]), + th:not([align]) { + text-align: left; } + +.is-clearfix::after { + clear: both; + content: " "; + display: table; } + +.is-pulled-left { + float: left !important; } + +.is-pulled-right { + float: right !important; } + +.is-clipped { + overflow: hidden !important; } + +.is-size-1 { + font-size: 3rem !important; } + +.is-size-2 { + font-size: 2.5rem !important; } + +.is-size-3 { + font-size: 2rem !important; } + +.is-size-4 { + font-size: 1.5rem !important; } + +.is-size-5 { + font-size: 1.25rem !important; } + +.is-size-6 { + font-size: 1rem !important; } + +.is-size-7, html.theme--documenter-dark .docstring > section > a.docs-sourcelink { + font-size: 0.75rem !important; } + +@media screen and (max-width: 768px) { + .is-size-1-mobile { + font-size: 3rem !important; } + .is-size-2-mobile { + font-size: 2.5rem !important; } + .is-size-3-mobile { + font-size: 2rem !important; } + .is-size-4-mobile { + font-size: 1.5rem !important; } + .is-size-5-mobile { + font-size: 1.25rem !important; } + .is-size-6-mobile { + font-size: 1rem !important; } + .is-size-7-mobile { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 769px), print { + .is-size-1-tablet { + font-size: 3rem !important; } + .is-size-2-tablet { + font-size: 2.5rem !important; } + .is-size-3-tablet { + font-size: 2rem !important; } + .is-size-4-tablet { + font-size: 1.5rem !important; } + .is-size-5-tablet { + font-size: 1.25rem !important; } + .is-size-6-tablet { + font-size: 1rem !important; } + .is-size-7-tablet { + font-size: 0.75rem !important; } } + +@media screen and (max-width: 1055px) { + .is-size-1-touch { + font-size: 3rem !important; } + .is-size-2-touch { + font-size: 2.5rem !important; } + .is-size-3-touch { + font-size: 2rem !important; } + .is-size-4-touch { + font-size: 1.5rem !important; } + .is-size-5-touch { + font-size: 1.25rem !important; } + .is-size-6-touch { + font-size: 1rem !important; } + .is-size-7-touch { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1056px) { + .is-size-1-desktop { + font-size: 3rem !important; } + .is-size-2-desktop { + font-size: 2.5rem !important; } + .is-size-3-desktop { + font-size: 2rem !important; } + .is-size-4-desktop { + font-size: 1.5rem !important; } + .is-size-5-desktop { + font-size: 1.25rem !important; } + .is-size-6-desktop { + font-size: 1rem !important; } + .is-size-7-desktop { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1216px) { + .is-size-1-widescreen { + font-size: 3rem !important; } + .is-size-2-widescreen { + font-size: 2.5rem !important; } + .is-size-3-widescreen { + font-size: 2rem !important; } + .is-size-4-widescreen { + font-size: 1.5rem !important; } + .is-size-5-widescreen { + font-size: 1.25rem !important; } + .is-size-6-widescreen { + font-size: 1rem !important; } + .is-size-7-widescreen { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1408px) { + .is-size-1-fullhd { + font-size: 3rem !important; } + .is-size-2-fullhd { + font-size: 2.5rem !important; } + .is-size-3-fullhd { + font-size: 2rem !important; } + .is-size-4-fullhd { + font-size: 1.5rem !important; } + .is-size-5-fullhd { + font-size: 1.25rem !important; } + .is-size-6-fullhd { + font-size: 1rem !important; } + .is-size-7-fullhd { + font-size: 0.75rem !important; } } + +.has-text-centered { + text-align: center !important; } + +.has-text-justified { + text-align: justify !important; } + +.has-text-left { + text-align: left !important; } + +.has-text-right { + text-align: right !important; } + +@media screen and (max-width: 768px) { + .has-text-centered-mobile { + text-align: center !important; } } + +@media screen and (min-width: 769px), print { + .has-text-centered-tablet { + text-align: center !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-centered-tablet-only { + text-align: center !important; } } + +@media screen and (max-width: 1055px) { + .has-text-centered-touch { + text-align: center !important; } } + +@media screen and (min-width: 1056px) { + .has-text-centered-desktop { + text-align: center !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-centered-desktop-only { + text-align: center !important; } } + +@media screen and (min-width: 1216px) { + .has-text-centered-widescreen { + text-align: center !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-centered-widescreen-only { + text-align: center !important; } } + +@media screen and (min-width: 1408px) { + .has-text-centered-fullhd { + text-align: center !important; } } + +@media screen and (max-width: 768px) { + .has-text-justified-mobile { + text-align: justify !important; } } + +@media screen and (min-width: 769px), print { + .has-text-justified-tablet { + text-align: justify !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-justified-tablet-only { + text-align: justify !important; } } + +@media screen and (max-width: 1055px) { + .has-text-justified-touch { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) { + .has-text-justified-desktop { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-justified-desktop-only { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) { + .has-text-justified-widescreen { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-justified-widescreen-only { + text-align: justify !important; } } + +@media screen and (min-width: 1408px) { + .has-text-justified-fullhd { + text-align: justify !important; } } + +@media screen and (max-width: 768px) { + .has-text-left-mobile { + text-align: left !important; } } + +@media screen and (min-width: 769px), print { + .has-text-left-tablet { + text-align: left !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-left-tablet-only { + text-align: left !important; } } + +@media screen and (max-width: 1055px) { + .has-text-left-touch { + text-align: left !important; } } + +@media screen and (min-width: 1056px) { + .has-text-left-desktop { + text-align: left !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-left-desktop-only { + text-align: left !important; } } + +@media screen and (min-width: 1216px) { + .has-text-left-widescreen { + text-align: left !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-left-widescreen-only { + text-align: left !important; } } + +@media screen and (min-width: 1408px) { + .has-text-left-fullhd { + text-align: left !important; } } + +@media screen and (max-width: 768px) { + .has-text-right-mobile { + text-align: right !important; } } + +@media screen and (min-width: 769px), print { + .has-text-right-tablet { + text-align: right !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-right-tablet-only { + text-align: right !important; } } + +@media screen and (max-width: 1055px) { + .has-text-right-touch { + text-align: right !important; } } + +@media screen and (min-width: 1056px) { + .has-text-right-desktop { + text-align: right !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-right-desktop-only { + text-align: right !important; } } + +@media screen and (min-width: 1216px) { + .has-text-right-widescreen { + text-align: right !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-right-widescreen-only { + text-align: right !important; } } + +@media screen and (min-width: 1408px) { + .has-text-right-fullhd { + text-align: right !important; } } + +.is-capitalized { + text-transform: capitalize !important; } + +.is-lowercase { + text-transform: lowercase !important; } + +.is-uppercase { + text-transform: uppercase !important; } + +.is-italic { + font-style: italic !important; } + +.has-text-white { + color: white !important; } + +a.has-text-white:hover, a.has-text-white:focus { + color: #e6e6e6 !important; } + +.has-background-white { + background-color: white !important; } + +.has-text-black { + color: #0a0a0a !important; } + +a.has-text-black:hover, a.has-text-black:focus { + color: black !important; } + +.has-background-black { + background-color: #0a0a0a !important; } + +.has-text-light { + color: whitesmoke !important; } + +a.has-text-light:hover, a.has-text-light:focus { + color: #dbdbdb !important; } + +.has-background-light { + background-color: whitesmoke !important; } + +.has-text-dark { + color: #363636 !important; } + +a.has-text-dark:hover, a.has-text-dark:focus { + color: #1c1c1c !important; } + +.has-background-dark { + background-color: #363636 !important; } + +.has-text-primary { + color: #4eb5de !important; } + +a.has-text-primary:hover, a.has-text-primary:focus { + color: #27a1d2 !important; } + +.has-background-primary { + background-color: #4eb5de !important; } + +.has-text-link { + color: #2ad7e6 !important; } + +a.has-text-link:hover, a.has-text-link:focus { + color: #17b7c5 !important; } + +.has-background-link { + background-color: #2ad7e6 !important; } + +.has-text-info { + color: #3489da !important; } + +a.has-text-info:hover, a.has-text-info:focus { + color: #226fb9 !important; } + +.has-background-info { + background-color: #3489da !important; } + +.has-text-success { + color: #259a12 !important; } + +a.has-text-success:hover, a.has-text-success:focus { + color: #1a6c0d !important; } + +.has-background-success { + background-color: #259a12 !important; } + 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+.has-background-grey { + background-color: #7a7a7a !important; } + +.has-text-grey-light { + color: #b5b5b5 !important; } + +.has-background-grey-light { + background-color: #b5b5b5 !important; } + +.has-text-grey-lighter { + color: #dbdbdb !important; } + +.has-background-grey-lighter { + background-color: #dbdbdb !important; } + +.has-text-white-ter { + color: whitesmoke !important; } + +.has-background-white-ter { + background-color: whitesmoke !important; } + +.has-text-white-bis { + color: #fafafa !important; } + +.has-background-white-bis { + background-color: #fafafa !important; } + +.has-text-weight-light { + font-weight: 300 !important; } + +.has-text-weight-normal { + font-weight: 400 !important; } + +.has-text-weight-medium { + font-weight: 500 !important; } + +.has-text-weight-semibold { + font-weight: 600 !important; } + +.has-text-weight-bold { + font-weight: 700 !important; } + +.is-family-primary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-secondary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-sans-serif { + font-family: "Montserrat", sans-serif !important; } + +.is-family-monospace { + font-family: "Source Code Pro", monospace !important; } + +.is-family-code { + font-family: "Source Code Pro", monospace !important; } + +.is-block { + display: block !important; } + +@media screen and (max-width: 768px) { + .is-block-mobile { + display: block !important; } } + +@media screen and (min-width: 769px), print { + .is-block-tablet { + display: block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-block-tablet-only { + display: block !important; } } + +@media screen and (max-width: 1055px) { + .is-block-touch { + display: block !important; } } + +@media screen and (min-width: 1056px) { + .is-block-desktop { + display: block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-block-desktop-only { + display: block !important; } } + +@media screen and (min-width: 1216px) { + .is-block-widescreen { + display: block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-block-widescreen-only { + display: block !important; } } + +@media screen and (min-width: 1408px) { + .is-block-fullhd { + display: block !important; } } + +.is-flex { + display: flex !important; } + +@media screen and (max-width: 768px) { + .is-flex-mobile { + display: flex !important; } } + +@media screen and (min-width: 769px), print { + .is-flex-tablet { + display: flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-flex-tablet-only { + display: flex !important; } } + +@media screen and (max-width: 1055px) { + .is-flex-touch { + display: flex !important; } } + +@media screen and (min-width: 1056px) { + .is-flex-desktop { + display: flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-flex-desktop-only { + display: flex !important; } } + +@media screen and (min-width: 1216px) { + .is-flex-widescreen { + display: flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-flex-widescreen-only { + display: flex !important; } } + +@media screen and (min-width: 1408px) { + .is-flex-fullhd { + display: flex !important; } } + +.is-inline { + display: inline !important; } + +@media screen and (max-width: 768px) { + .is-inline-mobile { + display: inline !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-tablet { + display: inline !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-tablet-only { + display: inline !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-touch { + display: inline !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-desktop { + display: inline !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-desktop-only { + display: inline !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-widescreen { + display: inline !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-widescreen-only { + display: inline !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-fullhd { + display: inline !important; } } + +.is-inline-block { + display: inline-block !important; } + +@media screen and (max-width: 768px) { + .is-inline-block-mobile { + display: inline-block !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-block-tablet { + display: inline-block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-block-tablet-only { + display: inline-block !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-block-touch { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-block-desktop { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-block-desktop-only { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-block-widescreen { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-block-widescreen-only { + display: inline-block !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-block-fullhd { + display: inline-block !important; } } + +.is-inline-flex { + display: inline-flex !important; } + +@media screen and (max-width: 768px) { + .is-inline-flex-mobile { + display: inline-flex !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-flex-tablet { + display: inline-flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-flex-tablet-only { + display: inline-flex !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-flex-touch { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-flex-desktop { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-flex-desktop-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-flex-widescreen { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-flex-widescreen-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-flex-fullhd { + display: inline-flex !important; } } + +.is-hidden { + display: none !important; } + +.is-sr-only { + border: none !important; + clip: rect(0, 0, 0, 0) !important; + height: 0.01em !important; + overflow: hidden !important; + padding: 0 !important; + position: absolute !important; + white-space: nowrap !important; + width: 0.01em !important; } + +@media screen and (max-width: 768px) { + .is-hidden-mobile { + display: none !important; } } + +@media screen and (min-width: 769px), print { + .is-hidden-tablet { + display: none !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-hidden-tablet-only { + display: none !important; } } + +@media screen and (max-width: 1055px) { + .is-hidden-touch { + display: none !important; } } + +@media screen and (min-width: 1056px) { + .is-hidden-desktop { + display: none !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-hidden-desktop-only { + display: none !important; } } + +@media screen and (min-width: 1216px) { + .is-hidden-widescreen { + display: none !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-hidden-widescreen-only { + display: none !important; } } + +@media screen and (min-width: 1408px) { + .is-hidden-fullhd { + display: none !important; } } + +.is-invisible { + visibility: hidden !important; } + +@media screen and (max-width: 768px) { + .is-invisible-mobile { + visibility: hidden !important; } } + +@media screen and (min-width: 769px), print { + .is-invisible-tablet { + visibility: hidden !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-invisible-tablet-only { + visibility: hidden !important; } } + +@media screen and (max-width: 1055px) { + .is-invisible-touch { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) { + .is-invisible-desktop { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-invisible-desktop-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) { + .is-invisible-widescreen { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-invisible-widescreen-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1408px) { + .is-invisible-fullhd { + visibility: hidden !important; } } + +.is-marginless { + margin: 0 !important; } + +.is-paddingless { + padding: 0 !important; } + +.is-radiusless { + border-radius: 0 !important; } + +.is-shadowless { + box-shadow: none !important; } + +.is-relative { + position: relative !important; } + +html.theme--documenter-dark { + /* This file contain the overall layout. + * + * The main container is
            that is identified by id #documenter. + */ + /*! + Theme: a11y-dark + Author: @ericwbailey + Maintainer: @ericwbailey + + Based on the Tomorrow Night Eighties theme: https://github.com/isagalaev/highlight.js/blob/master/src/styles/tomorrow-night-eighties.css +*/ + /* Comment */ + /* Red */ + /* Orange */ + /* Yellow */ + /* Green */ + /* Blue */ + /* Purple */ } + html.theme--documenter-dark html { + background-color: #1e1e20; + font-size: 16px; + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + html.theme--documenter-dark article, + html.theme--documenter-dark aside, + html.theme--documenter-dark figure, + html.theme--documenter-dark footer, + html.theme--documenter-dark header, + html.theme--documenter-dark hgroup, + html.theme--documenter-dark section { + display: block; } + html.theme--documenter-dark body, + html.theme--documenter-dark button, + html.theme--documenter-dark input, + html.theme--documenter-dark select, + html.theme--documenter-dark textarea { + font-family: "Montserrat", sans-serif; } + html.theme--documenter-dark code, + html.theme--documenter-dark pre { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; + font-family: "Source Code Pro", monospace; } + html.theme--documenter-dark body { + color: #fbfbfb; + font-size: 1em; + font-weight: 400; + line-height: 1.5; } + html.theme--documenter-dark a { + color: #2ad7e6; + cursor: pointer; + text-decoration: none; } + html.theme--documenter-dark a strong { + color: currentColor; } + html.theme--documenter-dark a:hover { + color: #97ebf3; } + html.theme--documenter-dark code { + background-color: #312550; + color: #fff; + font-size: 0.875em; + font-weight: normal; + padding: 0.1em; } + html.theme--documenter-dark hr { + background-color: whitesmoke; + border: none; + display: block; + height: 2px; + margin: 1.5rem 0; } + html.theme--documenter-dark img { + height: auto; + max-width: 100%; } + html.theme--documenter-dark input[type="checkbox"], + html.theme--documenter-dark input[type="radio"] { + vertical-align: baseline; } + html.theme--documenter-dark small { + font-size: 0.875em; } + html.theme--documenter-dark span { + font-style: inherit; + font-weight: inherit; } + html.theme--documenter-dark strong { + color: #cdc3e3; + font-weight: 700; } + html.theme--documenter-dark fieldset { + border: none; } + html.theme--documenter-dark pre { + -webkit-overflow-scrolling: touch; + background-color: #312550; + color: #fbfbfb; + font-size: 0.875em; + overflow-x: auto; + padding: 1.25rem 1.5rem; + white-space: pre; + word-wrap: normal; } + html.theme--documenter-dark pre code { + background-color: transparent; + color: currentColor; + font-size: 1em; + padding: 0; } + html.theme--documenter-dark table td, + html.theme--documenter-dark table th { + vertical-align: top; } + html.theme--documenter-dark table td:not([align]), + html.theme--documenter-dark table th:not([align]) { + text-align: left; } + html.theme--documenter-dark table th { + color: #cdc3e3; } + html.theme--documenter-dark .box { + background-color: white; + border-radius: 6px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #fbfbfb; + display: block; + padding: 1.25rem; } + html.theme--documenter-dark a.box:hover, html.theme--documenter-dark a.box:focus { + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #2ad7e6; } + html.theme--documenter-dark a.box:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #2ad7e6; } + html.theme--documenter-dark .button { + background-color: white; + border-color: #dbdbdb; + border-width: 1px; + color: #363636; + cursor: pointer; + justify-content: center; + padding-bottom: calc(0.375em - 1px); + padding-left: 0.75em; + padding-right: 0.75em; + padding-top: calc(0.375em - 1px); + text-align: center; + white-space: nowrap; } + html.theme--documenter-dark .button strong { + color: inherit; } + html.theme--documenter-dark .button .icon, html.theme--documenter-dark .button .icon.is-small, html.theme--documenter-dark .button #documenter .docs-sidebar form.docs-search > input.icon, html.theme--documenter-dark #documenter .docs-sidebar .button form.docs-search > input.icon, html.theme--documenter-dark .button .icon.is-medium, html.theme--documenter-dark .button .icon.is-large { + height: 1.5em; + width: 1.5em; } + html.theme--documenter-dark .button .icon:first-child:not(:last-child) { + margin-left: calc(-0.375em - 1px); + margin-right: 0.1875em; } + html.theme--documenter-dark .button .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: calc(-0.375em - 1px); } + html.theme--documenter-dark .button .icon:first-child:last-child { + margin-left: calc(-0.375em - 1px); + margin-right: calc(-0.375em - 1px); } + html.theme--documenter-dark .button:hover, html.theme--documenter-dark .button.is-hovered { + border-color: #b5b5b5; + color: #97ebf3; } + html.theme--documenter-dark .button:focus, html.theme--documenter-dark .button.is-focused { + border-color: #3c5dcd; + color: #363636; } + html.theme--documenter-dark .button:focus:not(:active), html.theme--documenter-dark .button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .button:active, html.theme--documenter-dark .button.is-active { + border-color: #4a4a4a; + color: #363636; } + html.theme--documenter-dark .button.is-text { + background-color: transparent; + border-color: transparent; + color: #fbfbfb; + text-decoration: underline; } + html.theme--documenter-dark .button.is-text:hover, html.theme--documenter-dark .button.is-text.is-hovered, html.theme--documenter-dark .button.is-text:focus, html.theme--documenter-dark .button.is-text.is-focused { + background-color: whitesmoke; + color: #cdc3e3; } + html.theme--documenter-dark .button.is-text:active, html.theme--documenter-dark .button.is-text.is-active { + background-color: #e8e8e8; + color: #cdc3e3; } + html.theme--documenter-dark .button.is-text[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-text { + background-color: transparent; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-white { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:hover, html.theme--documenter-dark .button.is-white.is-hovered { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:focus, html.theme--documenter-dark .button.is-white.is-focused { + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white:focus:not(:active), html.theme--documenter-dark .button.is-white.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .button.is-white:active, html.theme--documenter-dark .button.is-white.is-active { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white { + background-color: white; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-white.is-inverted { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-hovered { + background-color: black; } + html.theme--documenter-dark .button.is-white.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-white.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + html.theme--documenter-dark .button.is-white.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-outlined.is-focused { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-white.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:hover, html.theme--documenter-dark .button.is-black.is-hovered { + background-color: #040404; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:focus, html.theme--documenter-dark .button.is-black.is-focused { + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black:focus:not(:active), html.theme--documenter-dark .button.is-black.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .button.is-black:active, html.theme--documenter-dark .button.is-black.is-active { + background-color: black; + border-color: transparent; + color: white; } + html.theme--documenter-dark .button.is-black[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-black.is-inverted { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-black.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted { + background-color: white; + border-color: transparent; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-loading::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-outlined.is-focused { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + html.theme--documenter-dark .button.is-black.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + html.theme--documenter-dark .button.is-light { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:hover, html.theme--documenter-dark .button.is-light.is-hovered { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:focus, html.theme--documenter-dark .button.is-light.is-focused { + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light:focus:not(:active), html.theme--documenter-dark .button.is-light.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .button.is-light:active, html.theme--documenter-dark .button.is-light.is-active { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .button.is-light[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-light.is-inverted { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-hovered { + background-color: #292929; } + html.theme--documenter-dark .button.is-light.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted { + background-color: #363636; + border-color: transparent; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-outlined.is-focused { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-light.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark, html.theme--documenter-dark .content kbd.button { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:hover, html.theme--documenter-dark .content kbd.button:hover, html.theme--documenter-dark .button.is-dark.is-hovered, html.theme--documenter-dark .content kbd.button.is-hovered { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:focus, html.theme--documenter-dark .content kbd.button:focus, html.theme--documenter-dark .button.is-dark.is-focused, html.theme--documenter-dark .content kbd.button.is-focused { + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark:focus:not(:active), html.theme--documenter-dark .content kbd.button:focus:not(:active), html.theme--documenter-dark .button.is-dark.is-focused:not(:active), html.theme--documenter-dark .content kbd.button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .button.is-dark:active, html.theme--documenter-dark .content kbd.button:active, html.theme--documenter-dark .button.is-dark.is-active, html.theme--documenter-dark .content kbd.button.is-active { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark[disabled], html.theme--documenter-dark .content kbd.button[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark, fieldset[disabled] html.theme--documenter-dark .content kbd.button { + background-color: #363636; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-dark.is-inverted, html.theme--documenter-dark .content kbd.button.is-inverted { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted:hover, html.theme--documenter-dark .content kbd.button.is-inverted:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered { + background-color: #e8e8e8; } + html.theme--documenter-dark .button.is-dark.is-inverted[disabled], html.theme--documenter-dark .content kbd.button.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-loading::after, html.theme--documenter-dark .content kbd.button.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-dark.is-outlined, html.theme--documenter-dark .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-outlined.is-focused { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + html.theme--documenter-dark .button.is-dark.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + html.theme--documenter-dark .button.is-primary, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:hover, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-hovered.docs-sourcelink { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:focus, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary:focus:not(:active), html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus:not(:active), html.theme--documenter-dark .button.is-primary.is-focused:not(:active), html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .button.is-primary:active, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:active, html.theme--documenter-dark .button.is-primary.is-active, html.theme--documenter-dark .docstring > section > a.button.is-active.docs-sourcelink { + background-color: #39acda; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-primary[disabled], html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-primary.is-inverted, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-primary.is-inverted[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-loading.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-primary.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-primary.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + box-shadow: none; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-link { + background-color: #2ad7e6; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:hover, html.theme--documenter-dark .button.is-link.is-hovered { + background-color: #1ed5e5; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:focus, html.theme--documenter-dark .button.is-link.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link:focus:not(:active), html.theme--documenter-dark .button.is-link.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .button.is-link:active, html.theme--documenter-dark .button.is-link.is-active { + background-color: #1acddc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-link[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link { + background-color: #2ad7e6; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-link.is-inverted { + background-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-link.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-link.is-outlined { + background-color: transparent; + border-color: #2ad7e6; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-outlined.is-focused { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after { + border-color: transparent transparent #2ad7e6 #2ad7e6 !important; } + html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-link.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined { + background-color: transparent; + border-color: #2ad7e6; + box-shadow: none; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #2ad7e6 #2ad7e6 !important; } + html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-info { + background-color: #3489da; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:hover, html.theme--documenter-dark .button.is-info.is-hovered { + background-color: #2983d8; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:focus, html.theme--documenter-dark .button.is-info.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info:focus:not(:active), html.theme--documenter-dark .button.is-info.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .button.is-info:active, html.theme--documenter-dark .button.is-info.is-active { + background-color: #267ccf; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-info[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info { + background-color: #3489da; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-info.is-inverted { + background-color: #fff; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-info.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-info.is-outlined { + background-color: transparent; + border-color: #3489da; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-outlined.is-focused { + background-color: #3489da; + border-color: #3489da; + color: #fff; } + html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after { + border-color: transparent transparent #3489da #3489da !important; } + html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-info.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined { + background-color: transparent; + border-color: #3489da; + box-shadow: none; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #3489da; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #3489da #3489da !important; } + html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-success { + background-color: #259a12; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:hover, html.theme--documenter-dark .button.is-success.is-hovered { + background-color: #228f11; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:focus, html.theme--documenter-dark .button.is-success.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success:focus:not(:active), html.theme--documenter-dark .button.is-success.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .button.is-success:active, html.theme--documenter-dark .button.is-success.is-active { + background-color: #20830f; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-success[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success { + background-color: #259a12; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-success.is-inverted { + background-color: #fff; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-success.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-success.is-outlined { + background-color: transparent; + border-color: #259a12; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-outlined.is-focused { + background-color: #259a12; + border-color: #259a12; + color: #fff; } + html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after { + border-color: transparent transparent #259a12 #259a12 !important; } + html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-success.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined { + background-color: transparent; + border-color: #259a12; + box-shadow: none; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #259a12; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #259a12 #259a12 !important; } + html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-warning { + background-color: #f4c72f; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:hover, html.theme--documenter-dark .button.is-warning.is-hovered { + background-color: #f3c423; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:focus, html.theme--documenter-dark .button.is-warning.is-focused { + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning:focus:not(:active), html.theme--documenter-dark .button.is-warning.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .button.is-warning:active, html.theme--documenter-dark .button.is-warning.is-active { + background-color: #f3c017; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning { + background-color: #f4c72f; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered { + background-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + border-color: transparent; + box-shadow: none; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-loading::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + html.theme--documenter-dark .button.is-warning.is-outlined { + background-color: transparent; + border-color: #f4c72f; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-outlined.is-focused { + background-color: #f4c72f; + border-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after { + border-color: transparent transparent #f4c72f #f4c72f !important; } + html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + html.theme--documenter-dark .button.is-warning.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined { + background-color: transparent; + border-color: #f4c72f; + box-shadow: none; + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused { + background-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #f4c72f #f4c72f !important; } + html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + box-shadow: none; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .button.is-danger { + background-color: #cb3c33; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:hover, html.theme--documenter-dark .button.is-danger.is-hovered { + background-color: #c13930; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:focus, html.theme--documenter-dark .button.is-danger.is-focused { + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger:focus:not(:active), html.theme--documenter-dark .button.is-danger.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .button.is-danger:active, html.theme--documenter-dark .button.is-danger.is-active { + background-color: #b7362e; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .button.is-danger[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger { + background-color: #cb3c33; + border-color: transparent; + box-shadow: none; } + html.theme--documenter-dark .button.is-danger.is-inverted { + background-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered { + background-color: #f2f2f2; } + html.theme--documenter-dark .button.is-danger.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-danger.is-outlined { + background-color: transparent; + border-color: #cb3c33; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-outlined.is-focused { + background-color: #cb3c33; + border-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after { + border-color: transparent transparent #cb3c33 #cb3c33 !important; } + html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + html.theme--documenter-dark .button.is-danger.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined { + background-color: transparent; + border-color: #cb3c33; + box-shadow: none; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #cb3c33 #cb3c33 !important; } + html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + html.theme--documenter-dark .button.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .button.is-normal { + font-size: 1rem; } + html.theme--documenter-dark .button.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .button.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .button[disabled], fieldset[disabled] html.theme--documenter-dark .button { + background-color: white; + border-color: #dbdbdb; + box-shadow: none; + opacity: 0.5; } + html.theme--documenter-dark .button.is-fullwidth { + display: flex; + width: 100%; } + html.theme--documenter-dark .button.is-loading { + color: transparent !important; + pointer-events: none; } + html.theme--documenter-dark .button.is-loading::after { + position: absolute; + left: calc(50% - (1em / 2)); + top: calc(50% - (1em / 2)); + position: absolute !important; } + html.theme--documenter-dark .button.is-static { + background-color: whitesmoke; + border-color: #dbdbdb; + color: #7a7a7a; + box-shadow: none; + pointer-events: none; } + html.theme--documenter-dark .button.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + html.theme--documenter-dark .buttons { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .buttons .button { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth) { + margin-right: 0.5rem; } + html.theme--documenter-dark .buttons:last-child { + margin-bottom: -0.5rem; } + html.theme--documenter-dark .buttons:not(:last-child) { + margin-bottom: 1rem; } + html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { + font-size: 1.25rem; } + html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { + font-size: 1.5rem; } + html.theme--documenter-dark .buttons.has-addons .button:not(:first-child) { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .buttons.has-addons .button:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; + margin-right: -1px; } + html.theme--documenter-dark .buttons.has-addons .button:last-child { + margin-right: 0; } + html.theme--documenter-dark .buttons.has-addons .button:hover, html.theme--documenter-dark .buttons.has-addons .button.is-hovered { + z-index: 2; } + html.theme--documenter-dark .buttons.has-addons .button:focus, html.theme--documenter-dark .buttons.has-addons .button.is-focused, html.theme--documenter-dark .buttons.has-addons .button:active, html.theme--documenter-dark .buttons.has-addons .button.is-active, html.theme--documenter-dark .buttons.has-addons .button.is-selected { + z-index: 3; } + html.theme--documenter-dark .buttons.has-addons .button:focus:hover, html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover, html.theme--documenter-dark .buttons.has-addons .button:active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover { + z-index: 4; } + html.theme--documenter-dark .buttons.has-addons .button.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .buttons.is-centered { + justify-content: center; } + html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + html.theme--documenter-dark .buttons.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + html.theme--documenter-dark .container { + flex-grow: 1; + margin: 0 auto; + position: relative; + width: auto; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .container { + max-width: 992px; } + html.theme--documenter-dark .container.is-fluid { + margin-left: 32px; + margin-right: 32px; + max-width: none; } } + @media screen and (max-width: 1215px) { + html.theme--documenter-dark .container.is-widescreen { + max-width: 1152px; } } + @media screen and (max-width: 1407px) { + html.theme--documenter-dark .container.is-fullhd { + max-width: 1344px; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .container { + max-width: 1152px; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .container { + max-width: 1344px; } } + html.theme--documenter-dark .content li + li { + margin-top: 0.25em; } + html.theme--documenter-dark .content p:not(:last-child), + html.theme--documenter-dark .content dl:not(:last-child), + html.theme--documenter-dark .content ol:not(:last-child), + html.theme--documenter-dark .content ul:not(:last-child), + html.theme--documenter-dark .content blockquote:not(:last-child), + html.theme--documenter-dark .content pre:not(:last-child), + html.theme--documenter-dark .content table:not(:last-child) { + margin-bottom: 1em; } + html.theme--documenter-dark .content h1, + html.theme--documenter-dark .content h2, + html.theme--documenter-dark .content h3, + html.theme--documenter-dark .content h4, + html.theme--documenter-dark .content h5, + html.theme--documenter-dark .content h6 { + color: #cdc3e3; + font-weight: 600; + line-height: 1.125; } + html.theme--documenter-dark .content h1 { + font-size: 2em; + margin-bottom: 0.5em; } + html.theme--documenter-dark .content h1:not(:first-child) { + margin-top: 1em; } + html.theme--documenter-dark .content h2 { + font-size: 1.75em; + margin-bottom: 0.5714em; } + html.theme--documenter-dark .content h2:not(:first-child) { + margin-top: 1.1428em; } + html.theme--documenter-dark .content h3 { + font-size: 1.5em; + margin-bottom: 0.6666em; } + html.theme--documenter-dark .content h3:not(:first-child) { + margin-top: 1.3333em; } + html.theme--documenter-dark .content h4 { + font-size: 1.25em; + margin-bottom: 0.8em; } + html.theme--documenter-dark .content h5 { + font-size: 1.125em; + margin-bottom: 0.8888em; } + html.theme--documenter-dark .content h6 { + font-size: 1em; + margin-bottom: 1em; } + html.theme--documenter-dark .content blockquote { + background-color: whitesmoke; + border-left: 5px solid #dbdbdb; + padding: 1.25em 1.5em; } + html.theme--documenter-dark .content ol { + list-style-position: outside; + margin-left: 2em; + margin-top: 1em; } + html.theme--documenter-dark .content ol:not([type]) { + list-style-type: decimal; } + html.theme--documenter-dark .content ol.is-lower-alpha:not([type]) { + list-style-type: lower-alpha; } + html.theme--documenter-dark .content ol.is-lower-roman:not([type]) { + list-style-type: lower-roman; } + html.theme--documenter-dark .content ol.is-upper-alpha:not([type]) { + list-style-type: upper-alpha; } + html.theme--documenter-dark .content ol.is-upper-roman:not([type]) { + list-style-type: upper-roman; } + html.theme--documenter-dark .content ul { + list-style: disc outside; + margin-left: 2em; + margin-top: 1em; } + html.theme--documenter-dark .content ul ul { + list-style-type: circle; + margin-top: 0.5em; } + html.theme--documenter-dark .content ul ul ul { + list-style-type: square; } + html.theme--documenter-dark .content dd { + margin-left: 2em; } + html.theme--documenter-dark .content figure { + margin-left: 2em; + margin-right: 2em; + text-align: center; } + html.theme--documenter-dark .content figure:not(:first-child) { + margin-top: 2em; } + html.theme--documenter-dark .content figure:not(:last-child) { + margin-bottom: 2em; } + html.theme--documenter-dark .content figure img { + display: inline-block; } + html.theme--documenter-dark .content figure figcaption { + font-style: italic; } + html.theme--documenter-dark .content pre { + -webkit-overflow-scrolling: touch; + overflow-x: auto; + padding: 0; + white-space: pre; + word-wrap: normal; } + html.theme--documenter-dark .content sup, + html.theme--documenter-dark .content sub { + font-size: 75%; } + html.theme--documenter-dark .content table { + width: 100%; } + html.theme--documenter-dark .content table td, + html.theme--documenter-dark .content table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + html.theme--documenter-dark .content table th { + color: #cdc3e3; } + html.theme--documenter-dark .content table th:not([align]) { + text-align: left; } + html.theme--documenter-dark .content table thead td, + html.theme--documenter-dark .content table thead th { + border-width: 0 0 2px; + color: #cdc3e3; } + html.theme--documenter-dark .content table tfoot td, + html.theme--documenter-dark .content table tfoot th { + border-width: 2px 0 0; + color: #cdc3e3; } + html.theme--documenter-dark .content table tbody tr:last-child td, + html.theme--documenter-dark .content table tbody tr:last-child th { + border-bottom-width: 0; } + html.theme--documenter-dark .content .tabs li + li { + margin-top: 0; } + html.theme--documenter-dark .content.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.content { + font-size: 0.75rem; } + html.theme--documenter-dark .content.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .content.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .icon { + align-items: center; + display: inline-flex; + justify-content: center; + height: 1.5rem; + width: 1.5rem; } + html.theme--documenter-dark .icon.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.icon { + height: 1rem; + width: 1rem; } + html.theme--documenter-dark .icon.is-medium { + height: 2rem; + width: 2rem; } + html.theme--documenter-dark .icon.is-large { + height: 3rem; + width: 3rem; } + html.theme--documenter-dark .image, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { + display: block; + position: relative; } + html.theme--documenter-dark .image img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img { + display: block; + height: auto; + width: 100%; } + html.theme--documenter-dark .image img.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img.is-rounded { + border-radius: 290486px; } + html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img, + html.theme--documenter-dark .image.is-square .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img, + html.theme--documenter-dark .image.is-1by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img, + html.theme--documenter-dark .image.is-5by4 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img, + html.theme--documenter-dark .image.is-4by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img, + html.theme--documenter-dark .image.is-3by2 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img, + html.theme--documenter-dark .image.is-5by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img, + html.theme--documenter-dark .image.is-16by9 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img, + html.theme--documenter-dark .image.is-2by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img, + html.theme--documenter-dark .image.is-3by1 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img, + html.theme--documenter-dark .image.is-4by5 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img, + html.theme--documenter-dark .image.is-3by4 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img, + html.theme--documenter-dark .image.is-2by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img, + html.theme--documenter-dark .image.is-3by5 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img, + html.theme--documenter-dark .image.is-9by16 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img, + html.theme--documenter-dark .image.is-1by2 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img, + html.theme--documenter-dark .image.is-1by3 .has-ratio, + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { + height: 100%; + width: 100%; } + html.theme--documenter-dark .image.is-square, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square, html.theme--documenter-dark .image.is-1by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 { + padding-top: 100%; } + html.theme--documenter-dark .image.is-5by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 { + padding-top: 80%; } + html.theme--documenter-dark .image.is-4by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 { + padding-top: 75%; } + html.theme--documenter-dark .image.is-3by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 { + padding-top: 66.6666%; } + html.theme--documenter-dark .image.is-5by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 { + padding-top: 60%; } + html.theme--documenter-dark .image.is-16by9, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 { + padding-top: 56.25%; } + html.theme--documenter-dark .image.is-2by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 { + padding-top: 50%; } + html.theme--documenter-dark .image.is-3by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 { + padding-top: 33.3333%; } + html.theme--documenter-dark .image.is-4by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 { + padding-top: 125%; } + html.theme--documenter-dark .image.is-3by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 { + padding-top: 133.3333%; } + html.theme--documenter-dark .image.is-2by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 { + padding-top: 150%; } + html.theme--documenter-dark .image.is-3by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 { + padding-top: 166.6666%; } + html.theme--documenter-dark .image.is-9by16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 { + padding-top: 177.7777%; } + html.theme--documenter-dark .image.is-1by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 { + padding-top: 200%; } + html.theme--documenter-dark .image.is-1by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 { + padding-top: 300%; } + html.theme--documenter-dark .image.is-16x16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16x16 { + height: 16px; + width: 16px; } + html.theme--documenter-dark .image.is-24x24, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-24x24 { + height: 24px; + width: 24px; } + html.theme--documenter-dark .image.is-32x32, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-32x32 { + height: 32px; + width: 32px; } + html.theme--documenter-dark .image.is-48x48, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-48x48 { + height: 48px; + width: 48px; } + html.theme--documenter-dark .image.is-64x64, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-64x64 { + height: 64px; + width: 64px; } + html.theme--documenter-dark .image.is-96x96, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-96x96 { + height: 96px; + width: 96px; } + html.theme--documenter-dark .image.is-128x128, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-128x128 { + height: 128px; + width: 128px; } + html.theme--documenter-dark .notification { + background-color: whitesmoke; + border-radius: 4px; + padding: 1.25rem 2.5rem 1.25rem 1.5rem; + position: relative; } + html.theme--documenter-dark .notification a:not(.button):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + html.theme--documenter-dark .notification strong { + color: currentColor; } + html.theme--documenter-dark .notification code, + html.theme--documenter-dark .notification pre { + background: white; } + html.theme--documenter-dark .notification pre code { + background: transparent; } + html.theme--documenter-dark .notification > .delete { + position: absolute; + right: 0.5rem; + top: 0.5rem; } + html.theme--documenter-dark .notification .title, + html.theme--documenter-dark .notification .subtitle, + html.theme--documenter-dark .notification .content { + color: currentColor; } + html.theme--documenter-dark .notification.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .notification.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .notification.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .notification.is-dark, html.theme--documenter-dark .content kbd.notification { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .notification.is-primary, html.theme--documenter-dark .docstring > section > a.notification.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .notification.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .notification.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .notification.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .notification.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .notification.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .progress { + -moz-appearance: none; + -webkit-appearance: none; + border: none; + border-radius: 290486px; + display: block; + height: 1rem; + overflow: hidden; + padding: 0; + width: 100%; } + html.theme--documenter-dark .progress::-webkit-progress-bar { + background-color: #dbdbdb; } + html.theme--documenter-dark .progress::-webkit-progress-value { + background-color: #fbfbfb; } + html.theme--documenter-dark .progress::-moz-progress-bar { + background-color: #fbfbfb; } + html.theme--documenter-dark .progress::-ms-fill { + background-color: #fbfbfb; + border: none; } + html.theme--documenter-dark .progress.is-white::-webkit-progress-value { + background-color: white; } + html.theme--documenter-dark .progress.is-white::-moz-progress-bar { + background-color: white; } + html.theme--documenter-dark .progress.is-white::-ms-fill { + background-color: white; } + html.theme--documenter-dark .progress.is-white:indeterminate { + background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-black::-webkit-progress-value { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black::-moz-progress-bar { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black::-ms-fill { + background-color: #0a0a0a; } + html.theme--documenter-dark .progress.is-black:indeterminate { + background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-light::-webkit-progress-value { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light::-moz-progress-bar { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light::-ms-fill { + background-color: whitesmoke; } + html.theme--documenter-dark .progress.is-light:indeterminate { + background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-dark::-webkit-progress-value, html.theme--documenter-dark .content kbd.progress::-webkit-progress-value { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark::-moz-progress-bar, html.theme--documenter-dark .content kbd.progress::-moz-progress-bar { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark::-ms-fill, html.theme--documenter-dark .content kbd.progress::-ms-fill { + background-color: #363636; } + html.theme--documenter-dark .progress.is-dark:indeterminate, html.theme--documenter-dark .content kbd.progress:indeterminate { + background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-primary::-webkit-progress-value, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary::-moz-progress-bar, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary::-ms-fill, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-ms-fill { + background-color: #4eb5de; } + html.theme--documenter-dark .progress.is-primary:indeterminate, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink:indeterminate { + background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-link::-webkit-progress-value { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link::-moz-progress-bar { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link::-ms-fill { + background-color: #2ad7e6; } + html.theme--documenter-dark .progress.is-link:indeterminate { + background-image: linear-gradient(to right, #2ad7e6 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-info::-webkit-progress-value { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info::-moz-progress-bar { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info::-ms-fill { + background-color: #3489da; } + html.theme--documenter-dark .progress.is-info:indeterminate { + background-image: linear-gradient(to right, #3489da 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-success::-webkit-progress-value { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success::-moz-progress-bar { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success::-ms-fill { + background-color: #259a12; } + html.theme--documenter-dark .progress.is-success:indeterminate { + background-image: linear-gradient(to right, #259a12 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-warning::-webkit-progress-value { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning::-moz-progress-bar { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning::-ms-fill { + background-color: #f4c72f; } + html.theme--documenter-dark .progress.is-warning:indeterminate { + background-image: linear-gradient(to right, #f4c72f 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress.is-danger::-webkit-progress-value { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger::-moz-progress-bar { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger::-ms-fill { + background-color: #cb3c33; } + html.theme--documenter-dark .progress.is-danger:indeterminate { + background-image: linear-gradient(to right, #cb3c33 30%, #dbdbdb 30%); } + html.theme--documenter-dark .progress:indeterminate { + animation-duration: 1.5s; + animation-iteration-count: infinite; + animation-name: moveIndeterminate; + animation-timing-function: linear; + background-color: #dbdbdb; + background-image: linear-gradient(to right, #fbfbfb 30%, #dbdbdb 30%); + background-position: top left; + background-repeat: no-repeat; + background-size: 150% 150%; } + html.theme--documenter-dark .progress:indeterminate::-webkit-progress-bar { + background-color: transparent; } + html.theme--documenter-dark .progress:indeterminate::-moz-progress-bar { + background-color: transparent; } + html.theme--documenter-dark .progress.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.progress { + height: 0.75rem; } + html.theme--documenter-dark .progress.is-medium { + height: 1.25rem; } + html.theme--documenter-dark .progress.is-large { + height: 1.5rem; } + +@keyframes moveIndeterminate { + from { + background-position: 200% 0; } + to { + background-position: -200% 0; } } + html.theme--documenter-dark .table { + background-color: white; + color: #363636; } + html.theme--documenter-dark .table td, + html.theme--documenter-dark .table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + html.theme--documenter-dark .table td.is-white, + html.theme--documenter-dark .table th.is-white { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .table td.is-black, + html.theme--documenter-dark .table th.is-black { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .table td.is-light, + html.theme--documenter-dark .table th.is-light { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .table td.is-dark, + html.theme--documenter-dark .table th.is-dark { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .table td.is-primary, + html.theme--documenter-dark .table th.is-primary { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table td.is-link, + html.theme--documenter-dark .table th.is-link { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .table td.is-info, + html.theme--documenter-dark .table th.is-info { + background-color: #3489da; + border-color: #3489da; + color: #fff; } + html.theme--documenter-dark .table td.is-success, + html.theme--documenter-dark .table th.is-success { + background-color: #259a12; + border-color: #259a12; + color: #fff; } + html.theme--documenter-dark .table td.is-warning, + html.theme--documenter-dark .table th.is-warning { + background-color: #f4c72f; + border-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .table td.is-danger, + html.theme--documenter-dark .table th.is-danger { + background-color: #cb3c33; + border-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .table td.is-narrow, + html.theme--documenter-dark .table th.is-narrow { + white-space: nowrap; + width: 1%; } + html.theme--documenter-dark .table td.is-selected, + html.theme--documenter-dark .table th.is-selected { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table td.is-selected a, + html.theme--documenter-dark .table td.is-selected strong, + html.theme--documenter-dark .table th.is-selected a, + html.theme--documenter-dark .table th.is-selected strong { + color: currentColor; } + html.theme--documenter-dark .table th { + color: #cdc3e3; } + html.theme--documenter-dark .table th:not([align]) { + text-align: left; } + html.theme--documenter-dark .table tr.is-selected { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .table tr.is-selected a, + html.theme--documenter-dark .table tr.is-selected strong { + color: currentColor; } + html.theme--documenter-dark .table tr.is-selected td, + html.theme--documenter-dark .table tr.is-selected th { + border-color: #fff; + color: currentColor; } + html.theme--documenter-dark .table thead { + background-color: transparent; } + html.theme--documenter-dark .table thead td, + html.theme--documenter-dark .table thead th { + border-width: 0 0 2px; + color: #cdc3e3; } + html.theme--documenter-dark .table tfoot { + background-color: transparent; } + html.theme--documenter-dark .table tfoot td, + html.theme--documenter-dark .table tfoot th { + border-width: 2px 0 0; + color: #cdc3e3; } + html.theme--documenter-dark .table tbody { + background-color: transparent; } + html.theme--documenter-dark .table tbody tr:last-child td, + html.theme--documenter-dark .table tbody tr:last-child th { + border-bottom-width: 0; } + html.theme--documenter-dark .table.is-bordered td, + html.theme--documenter-dark .table.is-bordered th { + border-width: 1px; } + html.theme--documenter-dark .table.is-bordered tr:last-child td, + html.theme--documenter-dark .table.is-bordered tr:last-child th { + border-bottom-width: 1px; } + html.theme--documenter-dark .table.is-fullwidth { + width: 100%; } + html.theme--documenter-dark .table.is-hoverable tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { + background-color: whitesmoke; } + html.theme--documenter-dark .table.is-narrow td, + html.theme--documenter-dark .table.is-narrow th { + padding: 0.25em 0.5em; } + html.theme--documenter-dark .table.is-striped tbody tr:not(.is-selected):nth-child(even) { + background-color: #fafafa; } + html.theme--documenter-dark .table-container { + -webkit-overflow-scrolling: touch; + overflow: auto; + overflow-y: hidden; + max-width: 100%; } + html.theme--documenter-dark .tags { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .tags .tag, html.theme--documenter-dark .tags .content kbd, html.theme--documenter-dark .content .tags kbd, html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .tags .tag:not(:last-child), html.theme--documenter-dark .tags .content kbd:not(:last-child), html.theme--documenter-dark .content .tags kbd:not(:last-child), html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0.5rem; } + html.theme--documenter-dark .tags:last-child { + margin-bottom: -0.5rem; } + html.theme--documenter-dark .tags:not(:last-child) { + margin-bottom: 1rem; } + html.theme--documenter-dark .tags.are-medium .tag:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .content kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .content .tags.are-medium kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { + font-size: 1rem; } + html.theme--documenter-dark .tags.are-large .tag:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .content kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .content .tags.are-large kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { + font-size: 1.25rem; } + html.theme--documenter-dark .tags.is-centered { + justify-content: center; } + html.theme--documenter-dark .tags.is-centered .tag, html.theme--documenter-dark .tags.is-centered .content kbd, html.theme--documenter-dark .content .tags.is-centered kbd, html.theme--documenter-dark .tags.is-centered .docstring > section > a.docs-sourcelink { + margin-right: 0.25rem; + margin-left: 0.25rem; } + html.theme--documenter-dark .tags.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .tags.is-right .tag:not(:first-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:first-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0.5rem; } + html.theme--documenter-dark .tags.is-right .tag:not(:last-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:last-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0; } + html.theme--documenter-dark .tags.has-addons .tag, html.theme--documenter-dark .tags.has-addons .content kbd, html.theme--documenter-dark .content .tags.has-addons kbd, html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink { + margin-right: 0; } + html.theme--documenter-dark .tags.has-addons .tag:not(:first-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:first-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0; + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .tags.has-addons .tag:not(:last-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:last-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .tag:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { + align-items: center; + background-color: whitesmoke; + border-radius: 4px; + color: #fbfbfb; + display: inline-flex; + font-size: 0.75rem; + height: 2em; + justify-content: center; + line-height: 1.5; + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + html.theme--documenter-dark .tag:not(body) .delete, html.theme--documenter-dark .content kbd:not(body) .delete, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .delete { + margin-left: 0.25rem; + margin-right: -0.375rem; } + html.theme--documenter-dark .tag.is-white:not(body), html.theme--documenter-dark .content kbd.is-white:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-white:not(body) { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .tag.is-black:not(body), html.theme--documenter-dark .content kbd.is-black:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-black:not(body) { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .tag.is-light:not(body), html.theme--documenter-dark .content kbd.is-light:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-light:not(body) { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .tag.is-dark:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-dark:not(body), html.theme--documenter-dark .content .docstring > section > kbd:not(body) { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .tag.is-primary:not(body), html.theme--documenter-dark .content kbd.is-primary:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .tag.is-link:not(body), html.theme--documenter-dark .content kbd.is-link:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-link:not(body) { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .tag.is-info:not(body), html.theme--documenter-dark .content kbd.is-info:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-info:not(body) { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .tag.is-success:not(body), html.theme--documenter-dark .content kbd.is-success:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-success:not(body) { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .tag.is-warning:not(body), html.theme--documenter-dark .content kbd.is-warning:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-warning:not(body) { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .tag.is-danger:not(body), html.theme--documenter-dark .content kbd.is-danger:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-danger:not(body) { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .tag.is-normal:not(body), html.theme--documenter-dark .content kbd.is-normal:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-normal:not(body) { + font-size: 0.75rem; } + html.theme--documenter-dark .tag.is-medium:not(body), html.theme--documenter-dark .content kbd.is-medium:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-medium:not(body) { + font-size: 1rem; } + html.theme--documenter-dark .tag.is-large:not(body), html.theme--documenter-dark .content kbd.is-large:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-large:not(body) { + font-size: 1.25rem; } + html.theme--documenter-dark .tag:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .content kbd:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { + margin-left: -0.375em; + margin-right: 0.1875em; } + html.theme--documenter-dark .tag:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .content kbd:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: -0.375em; } + html.theme--documenter-dark .tag:not(body) .icon:first-child:last-child, html.theme--documenter-dark .content kbd:not(body) .icon:first-child:last-child, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { + margin-left: -0.375em; + margin-right: -0.375em; } + html.theme--documenter-dark .tag.is-delete:not(body), html.theme--documenter-dark .content kbd.is-delete:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body) { + margin-left: 1px; + padding: 0; + position: relative; + width: 2em; } + html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + background-color: currentColor; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { + height: 1px; + width: 50%; } + html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + height: 50%; + width: 1px; } + html.theme--documenter-dark .tag.is-delete:not(body):hover, html.theme--documenter-dark .content kbd.is-delete:not(body):hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, html.theme--documenter-dark .tag.is-delete:not(body):focus, html.theme--documenter-dark .content kbd.is-delete:not(body):focus, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { + background-color: #e8e8e8; } + html.theme--documenter-dark .tag.is-delete:not(body):active, html.theme--documenter-dark .content kbd.is-delete:not(body):active, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):active { + background-color: #dbdbdb; } + html.theme--documenter-dark .tag.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:not(body), html.theme--documenter-dark .content kbd.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-rounded:not(body) { + border-radius: 290486px; } + html.theme--documenter-dark a.tag:hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:hover { + text-decoration: underline; } + html.theme--documenter-dark .title, + html.theme--documenter-dark .subtitle { + word-break: break-word; } + html.theme--documenter-dark .title em, + html.theme--documenter-dark .title span, + html.theme--documenter-dark .subtitle em, + html.theme--documenter-dark .subtitle span { + font-weight: inherit; } + html.theme--documenter-dark .title sub, + html.theme--documenter-dark .subtitle sub { + font-size: 0.75em; } + html.theme--documenter-dark .title sup, + html.theme--documenter-dark .subtitle sup { + font-size: 0.75em; } + html.theme--documenter-dark .title .tag, html.theme--documenter-dark .title .content kbd, html.theme--documenter-dark .content .title kbd, html.theme--documenter-dark .title .docstring > section > a.docs-sourcelink, + html.theme--documenter-dark .subtitle .tag, + html.theme--documenter-dark .subtitle .content kbd, + html.theme--documenter-dark .content .subtitle kbd, + html.theme--documenter-dark .subtitle .docstring > section > a.docs-sourcelink { + vertical-align: middle; } + html.theme--documenter-dark .title { + color: #363636; + font-size: 2rem; + font-weight: 600; + line-height: 1.125; } + html.theme--documenter-dark .title strong { + color: inherit; + font-weight: inherit; } + html.theme--documenter-dark .title + .highlight { + margin-top: -0.75rem; } + html.theme--documenter-dark .title:not(.is-spaced) + .subtitle { + margin-top: -1.25rem; } + html.theme--documenter-dark .title.is-1 { + font-size: 3rem; } + html.theme--documenter-dark .title.is-2 { + font-size: 2.5rem; } + html.theme--documenter-dark .title.is-3 { + font-size: 2rem; } + html.theme--documenter-dark .title.is-4 { + font-size: 1.5rem; } + html.theme--documenter-dark .title.is-5 { + font-size: 1.25rem; } + html.theme--documenter-dark .title.is-6 { + font-size: 1rem; } + html.theme--documenter-dark .title.is-7 { + font-size: 0.75rem; } + html.theme--documenter-dark .subtitle { + color: #4a4a4a; + font-size: 1.25rem; + font-weight: 400; + line-height: 1.25; } + html.theme--documenter-dark .subtitle strong { + color: #363636; + font-weight: 600; } + html.theme--documenter-dark .subtitle:not(.is-spaced) + .title { + margin-top: -1.25rem; } + html.theme--documenter-dark .subtitle.is-1 { + font-size: 3rem; } + html.theme--documenter-dark .subtitle.is-2 { + font-size: 2.5rem; } + html.theme--documenter-dark .subtitle.is-3 { + font-size: 2rem; } + html.theme--documenter-dark .subtitle.is-4 { + font-size: 1.5rem; } + html.theme--documenter-dark .subtitle.is-5 { + font-size: 1.25rem; } + html.theme--documenter-dark .subtitle.is-6 { + font-size: 1rem; } + html.theme--documenter-dark .subtitle.is-7 { + font-size: 0.75rem; } + html.theme--documenter-dark .heading { + display: block; + font-size: 11px; + letter-spacing: 1px; + margin-bottom: 5px; + text-transform: uppercase; } + html.theme--documenter-dark .highlight { + font-weight: 400; + max-width: 100%; + overflow: hidden; + padding: 0; } + html.theme--documenter-dark .highlight pre { + overflow: auto; + max-width: 100%; } + html.theme--documenter-dark .number { + align-items: center; + background-color: whitesmoke; + border-radius: 290486px; + display: inline-flex; + font-size: 1.25rem; + height: 2em; + justify-content: center; + margin-right: 1.5rem; + min-width: 2.5em; + padding: 0.25rem 0.5rem; + text-align: center; + vertical-align: top; } + html.theme--documenter-dark .select select, html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + background-color: white; + border-color: #dbdbdb; + border-radius: 4px; + color: #363636; } + html.theme--documenter-dark .select select::-moz-placeholder, html.theme--documenter-dark .textarea::-moz-placeholder, html.theme--documenter-dark .input::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select::-webkit-input-placeholder, html.theme--documenter-dark .textarea::-webkit-input-placeholder, html.theme--documenter-dark .input::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:-moz-placeholder, html.theme--documenter-dark .textarea:-moz-placeholder, html.theme--documenter-dark .input:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:-ms-input-placeholder, html.theme--documenter-dark .textarea:-ms-input-placeholder, html.theme--documenter-dark .input:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + html.theme--documenter-dark .select select:hover, html.theme--documenter-dark .textarea:hover, html.theme--documenter-dark .input:hover, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:hover, html.theme--documenter-dark .select select.is-hovered, html.theme--documenter-dark .is-hovered.textarea, html.theme--documenter-dark .is-hovered.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-hovered { + border-color: #149eaa; } + html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + border-color: #fff; + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] html.theme--documenter-dark .select select, fieldset[disabled] html.theme--documenter-dark .textarea, fieldset[disabled] html.theme--documenter-dark .input, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + background-color: whitesmoke; + border-color: whitesmoke; + box-shadow: none; + color: #7a7a7a; } + html.theme--documenter-dark .select select[disabled]::-moz-placeholder, html.theme--documenter-dark .textarea[disabled]::-moz-placeholder, html.theme--documenter-dark .input[disabled]::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .textarea[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .input[disabled]::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]:-moz-placeholder, html.theme--documenter-dark .textarea[disabled]:-moz-placeholder, html.theme--documenter-dark .input[disabled]:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .select select[disabled]:-ms-input-placeholder, html.theme--documenter-dark .textarea[disabled]:-ms-input-placeholder, html.theme--documenter-dark .input[disabled]:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(122, 122, 122, 0.3); } + html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); + max-width: 100%; + width: 100%; } + html.theme--documenter-dark .textarea[readonly], html.theme--documenter-dark .input[readonly], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[readonly] { + box-shadow: none; } + html.theme--documenter-dark .is-white.textarea, html.theme--documenter-dark .is-white.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white { + border-color: white; } + html.theme--documenter-dark .is-white.textarea:focus, html.theme--documenter-dark .is-white.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:focus, html.theme--documenter-dark .is-white.is-focused.textarea, html.theme--documenter-dark .is-white.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-white.textarea:active, html.theme--documenter-dark .is-white.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:active, html.theme--documenter-dark .is-white.is-active.textarea, html.theme--documenter-dark .is-white.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .is-black.textarea, html.theme--documenter-dark .is-black.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black { + border-color: #0a0a0a; } + html.theme--documenter-dark .is-black.textarea:focus, html.theme--documenter-dark .is-black.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:focus, html.theme--documenter-dark .is-black.is-focused.textarea, html.theme--documenter-dark .is-black.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-black.textarea:active, html.theme--documenter-dark .is-black.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:active, html.theme--documenter-dark .is-black.is-active.textarea, html.theme--documenter-dark .is-black.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .is-light.textarea, html.theme--documenter-dark .is-light.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light { + border-color: whitesmoke; } + html.theme--documenter-dark .is-light.textarea:focus, html.theme--documenter-dark .is-light.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:focus, html.theme--documenter-dark .is-light.is-focused.textarea, html.theme--documenter-dark .is-light.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-light.textarea:active, html.theme--documenter-dark .is-light.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:active, html.theme--documenter-dark .is-light.is-active.textarea, html.theme--documenter-dark .is-light.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .is-dark.textarea, html.theme--documenter-dark .content kbd.textarea, html.theme--documenter-dark .is-dark.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark, html.theme--documenter-dark .content kbd.input { + border-color: #363636; } + html.theme--documenter-dark .is-dark.textarea:focus, html.theme--documenter-dark .content kbd.textarea:focus, html.theme--documenter-dark .is-dark.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:focus, html.theme--documenter-dark .content kbd.input:focus, html.theme--documenter-dark .is-dark.is-focused.textarea, html.theme--documenter-dark .content kbd.is-focused.textarea, html.theme--documenter-dark .is-dark.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .content kbd.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-focused, html.theme--documenter-dark .is-dark.textarea:active, html.theme--documenter-dark .content kbd.textarea:active, html.theme--documenter-dark .is-dark.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:active, html.theme--documenter-dark .content kbd.input:active, html.theme--documenter-dark .is-dark.is-active.textarea, html.theme--documenter-dark .content kbd.is-active.textarea, html.theme--documenter-dark .is-dark.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .content kbd.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .is-primary.textarea, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink { + border-color: #4eb5de; } + html.theme--documenter-dark .is-primary.textarea:focus, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:focus, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.is-focused.textarea, html.theme--documenter-dark .docstring > section > a.is-focused.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .docstring > section > a.is-focused.input.docs-sourcelink, html.theme--documenter-dark .is-primary.textarea:active, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:active, html.theme--documenter-dark .is-primary.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:active, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:active, html.theme--documenter-dark .is-primary.is-active.textarea, html.theme--documenter-dark .docstring > section > a.is-active.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .docstring > section > a.is-active.input.docs-sourcelink { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .is-link.textarea, html.theme--documenter-dark .is-link.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link { + border-color: #2ad7e6; } + html.theme--documenter-dark .is-link.textarea:focus, html.theme--documenter-dark .is-link.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:focus, html.theme--documenter-dark .is-link.is-focused.textarea, html.theme--documenter-dark .is-link.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-link.textarea:active, html.theme--documenter-dark .is-link.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:active, html.theme--documenter-dark .is-link.is-active.textarea, html.theme--documenter-dark .is-link.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .is-info.textarea, html.theme--documenter-dark .is-info.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info { + border-color: #3489da; } + html.theme--documenter-dark .is-info.textarea:focus, html.theme--documenter-dark .is-info.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:focus, html.theme--documenter-dark .is-info.is-focused.textarea, html.theme--documenter-dark .is-info.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-info.textarea:active, html.theme--documenter-dark .is-info.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:active, html.theme--documenter-dark .is-info.is-active.textarea, html.theme--documenter-dark .is-info.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .is-success.textarea, html.theme--documenter-dark .is-success.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success { + border-color: #259a12; } + html.theme--documenter-dark .is-success.textarea:focus, html.theme--documenter-dark .is-success.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:focus, html.theme--documenter-dark .is-success.is-focused.textarea, html.theme--documenter-dark .is-success.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-success.textarea:active, html.theme--documenter-dark .is-success.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:active, html.theme--documenter-dark .is-success.is-active.textarea, html.theme--documenter-dark .is-success.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .is-warning.textarea, html.theme--documenter-dark .is-warning.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning { + border-color: #f4c72f; } + html.theme--documenter-dark .is-warning.textarea:focus, html.theme--documenter-dark .is-warning.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:focus, html.theme--documenter-dark .is-warning.is-focused.textarea, html.theme--documenter-dark .is-warning.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-warning.textarea:active, html.theme--documenter-dark .is-warning.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:active, html.theme--documenter-dark .is-warning.is-active.textarea, html.theme--documenter-dark .is-warning.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .is-danger.textarea, html.theme--documenter-dark .is-danger.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger { + border-color: #cb3c33; } + html.theme--documenter-dark .is-danger.textarea:focus, html.theme--documenter-dark .is-danger.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:focus, html.theme--documenter-dark .is-danger.is-focused.textarea, html.theme--documenter-dark .is-danger.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-danger.textarea:active, html.theme--documenter-dark .is-danger.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:active, html.theme--documenter-dark .is-danger.is-active.textarea, html.theme--documenter-dark .is-danger.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .is-small.textarea, html.theme--documenter-dark .is-small.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .is-medium.textarea, html.theme--documenter-dark .is-medium.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .is-large.textarea, html.theme--documenter-dark .is-large.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .is-fullwidth.textarea, html.theme--documenter-dark .is-fullwidth.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-fullwidth { + display: block; + width: 100%; } + html.theme--documenter-dark .is-inline.textarea, html.theme--documenter-dark .is-inline.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-inline { + display: inline; + width: auto; } + html.theme--documenter-dark .input.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + html.theme--documenter-dark .input.is-static, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-static { + background-color: transparent; + border-color: transparent; + box-shadow: none; + padding-left: 0; + padding-right: 0; } + html.theme--documenter-dark .textarea { + display: block; + max-width: 100%; + min-width: 100%; + padding: 0.625em; + resize: vertical; } + html.theme--documenter-dark .textarea:not([rows]) { + max-height: 600px; + min-height: 120px; } + html.theme--documenter-dark .textarea[rows] { + height: initial; } + html.theme--documenter-dark .textarea.has-fixed-size { + resize: none; } + html.theme--documenter-dark .radio, html.theme--documenter-dark .checkbox { + cursor: pointer; + display: inline-block; + line-height: 1.25; + position: relative; } + html.theme--documenter-dark .radio input, html.theme--documenter-dark .checkbox input { + cursor: pointer; } + html.theme--documenter-dark .radio:hover, html.theme--documenter-dark .checkbox:hover { + color: #363636; } + html.theme--documenter-dark .radio[disabled], html.theme--documenter-dark .checkbox[disabled], fieldset[disabled] html.theme--documenter-dark .radio, fieldset[disabled] html.theme--documenter-dark .checkbox { + color: #7a7a7a; + cursor: not-allowed; } + html.theme--documenter-dark .radio + .radio { + margin-left: 0.5em; } + html.theme--documenter-dark .select { + display: inline-block; + max-width: 100%; + position: relative; + vertical-align: top; } + html.theme--documenter-dark .select:not(.is-multiple) { + height: 2.25em; } + html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after { + border-color: #2ad7e6; + right: 1.125em; + z-index: 4; } + html.theme--documenter-dark .select.is-rounded select, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select select { + border-radius: 290486px; + padding-left: 1em; } + html.theme--documenter-dark .select select { + cursor: pointer; + display: block; + font-size: 1em; + max-width: 100%; + outline: none; } + html.theme--documenter-dark .select select::-ms-expand { + display: none; } + html.theme--documenter-dark .select select[disabled]:hover, fieldset[disabled] html.theme--documenter-dark .select select:hover { + border-color: whitesmoke; } + html.theme--documenter-dark .select select:not([multiple]) { + padding-right: 2.5em; } + html.theme--documenter-dark .select select[multiple] { + height: auto; + padding: 0; } + html.theme--documenter-dark .select select[multiple] option { + padding: 0.5em 1em; } + html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading):hover::after { + border-color: #363636; } + html.theme--documenter-dark .select.is-white:not(:hover)::after { + border-color: white; } + html.theme--documenter-dark .select.is-white select { + border-color: white; } + html.theme--documenter-dark .select.is-white select:hover, html.theme--documenter-dark .select.is-white select.is-hovered { + border-color: #f2f2f2; } + html.theme--documenter-dark .select.is-white select:focus, html.theme--documenter-dark .select.is-white select.is-focused, html.theme--documenter-dark .select.is-white select:active, html.theme--documenter-dark .select.is-white select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + html.theme--documenter-dark .select.is-black:not(:hover)::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .select.is-black select { + border-color: #0a0a0a; } + html.theme--documenter-dark .select.is-black select:hover, html.theme--documenter-dark .select.is-black select.is-hovered { + border-color: black; } + html.theme--documenter-dark .select.is-black select:focus, html.theme--documenter-dark .select.is-black select.is-focused, html.theme--documenter-dark .select.is-black select:active, html.theme--documenter-dark .select.is-black select.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + html.theme--documenter-dark .select.is-light:not(:hover)::after { + border-color: whitesmoke; } + html.theme--documenter-dark .select.is-light select { + border-color: whitesmoke; } + html.theme--documenter-dark .select.is-light select:hover, html.theme--documenter-dark .select.is-light select.is-hovered { + border-color: #e8e8e8; } + html.theme--documenter-dark .select.is-light select:focus, html.theme--documenter-dark .select.is-light select.is-focused, html.theme--documenter-dark .select.is-light select:active, html.theme--documenter-dark .select.is-light select.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + html.theme--documenter-dark .select.is-dark:not(:hover)::after, html.theme--documenter-dark .content kbd.select:not(:hover)::after { + border-color: #363636; } + html.theme--documenter-dark .select.is-dark select, html.theme--documenter-dark .content kbd.select select { + border-color: #363636; } + html.theme--documenter-dark .select.is-dark select:hover, html.theme--documenter-dark .content kbd.select select:hover, html.theme--documenter-dark .select.is-dark select.is-hovered, html.theme--documenter-dark .content kbd.select select.is-hovered { + border-color: #292929; } + html.theme--documenter-dark .select.is-dark select:focus, html.theme--documenter-dark .content kbd.select select:focus, html.theme--documenter-dark .select.is-dark select.is-focused, html.theme--documenter-dark .content kbd.select select.is-focused, html.theme--documenter-dark .select.is-dark select:active, html.theme--documenter-dark .content kbd.select select:active, html.theme--documenter-dark .select.is-dark select.is-active, html.theme--documenter-dark .content kbd.select select.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + html.theme--documenter-dark .select.is-primary:not(:hover)::after, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink:not(:hover)::after { + border-color: #4eb5de; } + html.theme--documenter-dark .select.is-primary select, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select { + border-color: #4eb5de; } + html.theme--documenter-dark .select.is-primary select:hover, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:hover, html.theme--documenter-dark .select.is-primary select.is-hovered, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-hovered { + border-color: #39acda; } + html.theme--documenter-dark .select.is-primary select:focus, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:focus, html.theme--documenter-dark .select.is-primary select.is-focused, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-focused, html.theme--documenter-dark .select.is-primary select:active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:active, html.theme--documenter-dark .select.is-primary select.is-active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-active { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + html.theme--documenter-dark .select.is-link:not(:hover)::after { + border-color: #2ad7e6; } + html.theme--documenter-dark .select.is-link select { + border-color: #2ad7e6; } + html.theme--documenter-dark .select.is-link select:hover, html.theme--documenter-dark .select.is-link select.is-hovered { + border-color: #1acddc; } + html.theme--documenter-dark .select.is-link select:focus, html.theme--documenter-dark .select.is-link select.is-focused, html.theme--documenter-dark .select.is-link select:active, html.theme--documenter-dark .select.is-link select.is-active { + box-shadow: 0 0 0 0.125em rgba(42, 215, 230, 0.25); } + html.theme--documenter-dark .select.is-info:not(:hover)::after { + border-color: #3489da; } + html.theme--documenter-dark .select.is-info select { + border-color: #3489da; } + html.theme--documenter-dark .select.is-info select:hover, html.theme--documenter-dark .select.is-info select.is-hovered { + border-color: #267ccf; } + html.theme--documenter-dark .select.is-info select:focus, html.theme--documenter-dark .select.is-info select.is-focused, html.theme--documenter-dark .select.is-info select:active, html.theme--documenter-dark .select.is-info select.is-active { + box-shadow: 0 0 0 0.125em rgba(52, 137, 218, 0.25); } + html.theme--documenter-dark .select.is-success:not(:hover)::after { + border-color: #259a12; } + html.theme--documenter-dark .select.is-success select { + border-color: #259a12; } + html.theme--documenter-dark .select.is-success select:hover, html.theme--documenter-dark .select.is-success select.is-hovered { + border-color: #20830f; } + html.theme--documenter-dark .select.is-success select:focus, html.theme--documenter-dark .select.is-success select.is-focused, html.theme--documenter-dark .select.is-success select:active, html.theme--documenter-dark .select.is-success select.is-active { + box-shadow: 0 0 0 0.125em rgba(37, 154, 18, 0.25); } + html.theme--documenter-dark .select.is-warning:not(:hover)::after { + border-color: #f4c72f; } + html.theme--documenter-dark .select.is-warning select { + border-color: #f4c72f; } + html.theme--documenter-dark .select.is-warning select:hover, html.theme--documenter-dark .select.is-warning select.is-hovered { + border-color: #f3c017; } + html.theme--documenter-dark .select.is-warning select:focus, html.theme--documenter-dark .select.is-warning select.is-focused, html.theme--documenter-dark .select.is-warning select:active, html.theme--documenter-dark .select.is-warning select.is-active { + box-shadow: 0 0 0 0.125em rgba(244, 199, 47, 0.25); } + html.theme--documenter-dark .select.is-danger:not(:hover)::after { + border-color: #cb3c33; } + html.theme--documenter-dark .select.is-danger select { + border-color: #cb3c33; } + html.theme--documenter-dark .select.is-danger select:hover, html.theme--documenter-dark .select.is-danger select.is-hovered { + border-color: #b7362e; } + html.theme--documenter-dark .select.is-danger select:focus, html.theme--documenter-dark .select.is-danger select.is-focused, html.theme--documenter-dark .select.is-danger select:active, html.theme--documenter-dark .select.is-danger select.is-active { + box-shadow: 0 0 0 0.125em rgba(203, 60, 51, 0.25); } + html.theme--documenter-dark .select.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select { + border-radius: 2px; + font-size: 0.75rem; } + html.theme--documenter-dark .select.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .select.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .select.is-disabled::after { + border-color: #7a7a7a; } + html.theme--documenter-dark .select.is-fullwidth { + width: 100%; } + html.theme--documenter-dark .select.is-fullwidth select { + width: 100%; } + html.theme--documenter-dark .select.is-loading::after { + margin-top: 0; + position: absolute; + right: 0.625em; + top: 0.625em; + transform: none; } + html.theme--documenter-dark .select.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + html.theme--documenter-dark .select.is-loading.is-medium:after { + font-size: 1.25rem; } + html.theme--documenter-dark .select.is-loading.is-large:after { + font-size: 1.5rem; } + html.theme--documenter-dark .file { + align-items: stretch; + display: flex; + justify-content: flex-start; + position: relative; } + html.theme--documenter-dark .file.is-white .file-cta { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:hover .file-cta, html.theme--documenter-dark .file.is-white.is-hovered .file-cta { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:focus .file-cta, html.theme--documenter-dark .file.is-white.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); + color: #0a0a0a; } + html.theme--documenter-dark .file.is-white:active .file-cta, html.theme--documenter-dark .file.is-white.is-active .file-cta { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + html.theme--documenter-dark .file.is-black .file-cta { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-black:hover .file-cta, html.theme--documenter-dark .file.is-black.is-hovered .file-cta { + background-color: #040404; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-black:focus .file-cta, html.theme--documenter-dark .file.is-black.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); + color: white; } + html.theme--documenter-dark .file.is-black:active .file-cta, html.theme--documenter-dark .file.is-black.is-active .file-cta { + background-color: black; + border-color: transparent; + color: white; } + html.theme--documenter-dark .file.is-light .file-cta { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-light:hover .file-cta, html.theme--documenter-dark .file.is-light.is-hovered .file-cta { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-light:focus .file-cta, html.theme--documenter-dark .file.is-light.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25); + color: #363636; } + html.theme--documenter-dark .file.is-light:active .file-cta, html.theme--documenter-dark .file.is-light.is-active .file-cta { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + html.theme--documenter-dark .file.is-dark .file-cta, html.theme--documenter-dark .content kbd.file .file-cta { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:hover .file-cta, html.theme--documenter-dark .content kbd.file:hover .file-cta, html.theme--documenter-dark .file.is-dark.is-hovered .file-cta, html.theme--documenter-dark .content kbd.file.is-hovered .file-cta { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:focus .file-cta, html.theme--documenter-dark .content kbd.file:focus .file-cta, html.theme--documenter-dark .file.is-dark.is-focused .file-cta, html.theme--documenter-dark .content kbd.file.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25); + color: whitesmoke; } + html.theme--documenter-dark .file.is-dark:active .file-cta, html.theme--documenter-dark .content kbd.file:active .file-cta, html.theme--documenter-dark .file.is-dark.is-active .file-cta, html.theme--documenter-dark .content kbd.file.is-active .file-cta { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + html.theme--documenter-dark .file.is-primary .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink .file-cta { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-primary:hover .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:hover .file-cta, html.theme--documenter-dark .file.is-primary.is-hovered .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-primary:focus .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:focus .file-cta, html.theme--documenter-dark .file.is-primary.is-focused .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-primary:active .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:active .file-cta, html.theme--documenter-dark .file.is-primary.is-active .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-active.docs-sourcelink .file-cta { + background-color: #39acda; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link .file-cta { + background-color: #2ad7e6; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link:hover .file-cta, html.theme--documenter-dark .file.is-link.is-hovered .file-cta { + background-color: #1ed5e5; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-link:focus .file-cta, html.theme--documenter-dark .file.is-link.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(42, 215, 230, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-link:active .file-cta, html.theme--documenter-dark .file.is-link.is-active .file-cta { + background-color: #1acddc; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info .file-cta { + background-color: #3489da; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info:hover .file-cta, html.theme--documenter-dark .file.is-info.is-hovered .file-cta { + background-color: #2983d8; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-info:focus .file-cta, html.theme--documenter-dark .file.is-info.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(52, 137, 218, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-info:active .file-cta, html.theme--documenter-dark .file.is-info.is-active .file-cta { + background-color: #267ccf; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success .file-cta { + background-color: #259a12; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success:hover .file-cta, html.theme--documenter-dark .file.is-success.is-hovered .file-cta { + background-color: #228f11; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-success:focus .file-cta, html.theme--documenter-dark .file.is-success.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(37, 154, 18, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-success:active .file-cta, html.theme--documenter-dark .file.is-success.is-active .file-cta { + background-color: #20830f; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-warning .file-cta { + background-color: #f4c72f; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:hover .file-cta, html.theme--documenter-dark .file.is-warning.is-hovered .file-cta { + background-color: #f3c423; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:focus .file-cta, html.theme--documenter-dark .file.is-warning.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(244, 199, 47, 0.25); + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-warning:active .file-cta, html.theme--documenter-dark .file.is-warning.is-active .file-cta { + background-color: #f3c017; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .file.is-danger .file-cta { + background-color: #cb3c33; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-danger:hover .file-cta, html.theme--documenter-dark .file.is-danger.is-hovered .file-cta { + background-color: #c13930; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-danger:focus .file-cta, html.theme--documenter-dark .file.is-danger.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(203, 60, 51, 0.25); + color: #fff; } + html.theme--documenter-dark .file.is-danger:active .file-cta, html.theme--documenter-dark .file.is-danger.is-active .file-cta { + background-color: #b7362e; + border-color: transparent; + color: #fff; } + html.theme--documenter-dark .file.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.file { + font-size: 0.75rem; } + html.theme--documenter-dark .file.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .file.is-medium .file-icon .fa { + font-size: 21px; } + html.theme--documenter-dark .file.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .file.is-large .file-icon .fa { + font-size: 28px; } + html.theme--documenter-dark .file.has-name .file-cta { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .file.has-name .file-name { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .file.has-name.is-empty .file-cta { + border-radius: 4px; } + html.theme--documenter-dark .file.has-name.is-empty .file-name { + display: none; } + html.theme--documenter-dark .file.is-boxed .file-label { + flex-direction: column; } + html.theme--documenter-dark .file.is-boxed .file-cta { + flex-direction: column; + height: auto; + padding: 1em 3em; } + html.theme--documenter-dark .file.is-boxed .file-name { + border-width: 0 1px 1px; } + html.theme--documenter-dark .file.is-boxed .file-icon { + height: 1.5em; + width: 1.5em; } + html.theme--documenter-dark .file.is-boxed .file-icon .fa { + font-size: 21px; } + html.theme--documenter-dark .file.is-boxed.is-small .file-icon .fa, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { + font-size: 14px; } + html.theme--documenter-dark .file.is-boxed.is-medium .file-icon .fa { + font-size: 28px; } + html.theme--documenter-dark .file.is-boxed.is-large .file-icon .fa { + font-size: 35px; } + html.theme--documenter-dark .file.is-boxed.has-name .file-cta { + border-radius: 4px 4px 0 0; } + html.theme--documenter-dark .file.is-boxed.has-name .file-name { + border-radius: 0 0 4px 4px; + border-width: 0 1px 1px; } + html.theme--documenter-dark .file.is-centered { + justify-content: center; } + html.theme--documenter-dark .file.is-fullwidth .file-label { + width: 100%; } + html.theme--documenter-dark .file.is-fullwidth .file-name { + flex-grow: 1; + max-width: none; } + html.theme--documenter-dark .file.is-right { + justify-content: flex-end; } + html.theme--documenter-dark .file.is-right .file-cta { + border-radius: 0 4px 4px 0; } + html.theme--documenter-dark .file.is-right .file-name { + border-radius: 4px 0 0 4px; + border-width: 1px 0 1px 1px; + order: -1; } + html.theme--documenter-dark .file-label { + align-items: stretch; + display: flex; + cursor: pointer; + justify-content: flex-start; + overflow: hidden; + position: relative; } + html.theme--documenter-dark .file-label:hover .file-cta { + background-color: #eeeeee; + color: #363636; } + html.theme--documenter-dark .file-label:hover .file-name { + border-color: #d5d5d5; } + html.theme--documenter-dark .file-label:active .file-cta { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .file-label:active .file-name { + border-color: #cfcfcf; } + html.theme--documenter-dark .file-input { + height: 100%; + left: 0; + opacity: 0; + outline: none; + position: absolute; + top: 0; + width: 100%; } + html.theme--documenter-dark .file-cta, + html.theme--documenter-dark .file-name { + border-color: #dbdbdb; + border-radius: 4px; + font-size: 1em; + padding-left: 1em; + padding-right: 1em; + white-space: nowrap; } + html.theme--documenter-dark .file-cta { + background-color: whitesmoke; + color: #4a4a4a; } + html.theme--documenter-dark .file-name { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px 1px 1px 0; + display: block; + max-width: 16em; + overflow: hidden; + text-align: left; + text-overflow: ellipsis; } + html.theme--documenter-dark .file-icon { + align-items: center; + display: flex; + height: 1em; + justify-content: center; + margin-right: 0.5em; + width: 1em; } + html.theme--documenter-dark .file-icon .fa { + font-size: 14px; } + html.theme--documenter-dark .label { + color: #363636; + display: block; + font-size: 1rem; + font-weight: 700; } + html.theme--documenter-dark .label:not(:last-child) { + margin-bottom: 0.5em; } + html.theme--documenter-dark .label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.label { + font-size: 0.75rem; } + html.theme--documenter-dark .label.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .label.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .help { + display: block; + font-size: 0.75rem; + margin-top: 0.25rem; } + html.theme--documenter-dark .help.is-white { + color: white; } + html.theme--documenter-dark .help.is-black { + color: #0a0a0a; } + html.theme--documenter-dark .help.is-light { + color: whitesmoke; } + html.theme--documenter-dark .help.is-dark, html.theme--documenter-dark .content kbd.help { + color: #363636; } + html.theme--documenter-dark .help.is-primary, html.theme--documenter-dark .docstring > section > a.help.docs-sourcelink { + color: #4eb5de; } + html.theme--documenter-dark .help.is-link { + color: #2ad7e6; } + html.theme--documenter-dark .help.is-info { + color: #3489da; } + html.theme--documenter-dark .help.is-success { + color: #259a12; } + html.theme--documenter-dark .help.is-warning { + color: #f4c72f; } + html.theme--documenter-dark .help.is-danger { + color: #cb3c33; } + html.theme--documenter-dark .field:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .field.has-addons { + display: flex; + justify-content: flex-start; } + html.theme--documenter-dark .field.has-addons .control:not(:last-child) { + margin-right: -1px; } + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .button, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .input, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .select select { + border-radius: 0; } + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .button, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .input, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .select select { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .button, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .input, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, + html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .select select { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-hovered:not([disabled]) { + z-index: 2; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]), html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus, + html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]), + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active, + html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]) { + z-index: 3; } + html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus:hover, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active:hover, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, + html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus:hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]):hover, + html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active:hover, + html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]):hover { + z-index: 4; } + html.theme--documenter-dark .field.has-addons .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .field.has-addons.has-addons-centered { + justify-content: center; } + html.theme--documenter-dark .field.has-addons.has-addons-right { + justify-content: flex-end; } + html.theme--documenter-dark .field.has-addons.has-addons-fullwidth .control { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .field.is-grouped { + display: flex; + justify-content: flex-start; } + html.theme--documenter-dark .field.is-grouped > .control { + flex-shrink: 0; } + html.theme--documenter-dark .field.is-grouped > .control:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + html.theme--documenter-dark .field.is-grouped > .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .field.is-grouped.is-grouped-centered { + justify-content: center; } + html.theme--documenter-dark .field.is-grouped.is-grouped-right { + justify-content: flex-end; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline { + flex-wrap: wrap; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:last-child, html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:not(:last-child) { + margin-bottom: 0; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field.is-horizontal { + display: flex; } } + html.theme--documenter-dark .field-label .label { + font-size: inherit; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .field-label { + margin-bottom: 0.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field-label { + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + margin-right: 1.5rem; + text-align: right; } + html.theme--documenter-dark .field-label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.field-label { + font-size: 0.75rem; + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-normal { + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-medium { + font-size: 1.25rem; + padding-top: 0.375em; } + html.theme--documenter-dark .field-label.is-large { + font-size: 1.5rem; + padding-top: 0.375em; } } + html.theme--documenter-dark .field-body .field .field { + margin-bottom: 0; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .field-body { + display: flex; + flex-basis: 0; + flex-grow: 5; + flex-shrink: 1; } + html.theme--documenter-dark .field-body .field { + margin-bottom: 0; } + html.theme--documenter-dark .field-body > .field { + flex-shrink: 1; } + html.theme--documenter-dark .field-body > .field:not(.is-narrow) { + flex-grow: 1; } + html.theme--documenter-dark .field-body > .field:not(:last-child) { + margin-right: 0.75rem; } } + html.theme--documenter-dark .control { + box-sizing: border-box; + clear: both; + font-size: 1rem; + position: relative; + text-align: left; } + html.theme--documenter-dark .control.has-icons-left .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select:focus ~ .icon { + color: #7a7a7a; } + html.theme--documenter-dark .control.has-icons-left .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-small ~ .icon { + font-size: 0.75rem; } + html.theme--documenter-dark .control.has-icons-left .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-medium ~ .icon { + font-size: 1.25rem; } + html.theme--documenter-dark .control.has-icons-left .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, + html.theme--documenter-dark .control.has-icons-left .select.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, + html.theme--documenter-dark .control.has-icons-right .select.is-large ~ .icon { + font-size: 1.5rem; } + html.theme--documenter-dark .control.has-icons-left .icon, html.theme--documenter-dark .control.has-icons-right .icon { + color: #dbdbdb; + height: 2.25em; + pointer-events: none; + position: absolute; + top: 0; + width: 2.25em; + z-index: 4; } + html.theme--documenter-dark .control.has-icons-left .input, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, + html.theme--documenter-dark .control.has-icons-left .select select { + padding-left: 2.25em; } + html.theme--documenter-dark .control.has-icons-left .icon.is-left { + left: 0; } + html.theme--documenter-dark .control.has-icons-right .input, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, + html.theme--documenter-dark .control.has-icons-right .select select { + padding-right: 2.25em; } + html.theme--documenter-dark .control.has-icons-right .icon.is-right { + right: 0; } + html.theme--documenter-dark .control.is-loading::after { + position: absolute !important; + right: 0.625em; + top: 0.625em; + z-index: 4; } + html.theme--documenter-dark .control.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + html.theme--documenter-dark .control.is-loading.is-medium:after { + font-size: 1.25rem; } + html.theme--documenter-dark .control.is-loading.is-large:after { + font-size: 1.5rem; } + html.theme--documenter-dark .breadcrumb { + font-size: 1rem; + white-space: nowrap; } + html.theme--documenter-dark .breadcrumb a { + align-items: center; + color: #2ad7e6; + display: flex; + justify-content: center; + padding: 0 0.75em; } + html.theme--documenter-dark .breadcrumb a:hover { + color: #97ebf3; } + html.theme--documenter-dark .breadcrumb li { + align-items: center; + display: flex; } + html.theme--documenter-dark .breadcrumb li:first-child a { + padding-left: 0; } + html.theme--documenter-dark .breadcrumb li.is-active a { + color: #cdc3e3; + cursor: default; + pointer-events: none; } + html.theme--documenter-dark .breadcrumb li + li::before { + color: #b5b5b5; + content: "\0002f"; } + html.theme--documenter-dark .breadcrumb ul, + html.theme--documenter-dark .breadcrumb ol { + align-items: flex-start; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + html.theme--documenter-dark .breadcrumb .icon:first-child { + margin-right: 0.5em; } + html.theme--documenter-dark .breadcrumb .icon:last-child { + margin-left: 0.5em; } + html.theme--documenter-dark .breadcrumb.is-centered ol, + html.theme--documenter-dark .breadcrumb.is-centered ul { + justify-content: center; } + html.theme--documenter-dark .breadcrumb.is-right ol, + html.theme--documenter-dark .breadcrumb.is-right ul { + justify-content: flex-end; } + html.theme--documenter-dark .breadcrumb.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.breadcrumb { + font-size: 0.75rem; } + html.theme--documenter-dark .breadcrumb.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .breadcrumb.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .breadcrumb.has-arrow-separator li + li::before { + content: "\02192"; } + html.theme--documenter-dark .breadcrumb.has-bullet-separator li + li::before { + content: "\02022"; } + html.theme--documenter-dark .breadcrumb.has-dot-separator li + li::before { + content: "\000b7"; } + html.theme--documenter-dark .breadcrumb.has-succeeds-separator li + li::before { + content: "\0227B"; } + html.theme--documenter-dark .card { + background-color: white; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #fbfbfb; + max-width: 100%; + position: relative; } + html.theme--documenter-dark .card-header { + background-color: transparent; + align-items: stretch; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + display: flex; } + html.theme--documenter-dark .card-header-title { + align-items: center; + color: #cdc3e3; + display: flex; + flex-grow: 1; + font-weight: 700; + padding: 0.75rem; } + html.theme--documenter-dark .card-header-title.is-centered { + justify-content: center; } + html.theme--documenter-dark .card-header-icon { + align-items: center; + cursor: pointer; + display: flex; + justify-content: center; + padding: 0.75rem; } + html.theme--documenter-dark .card-image { + display: block; + position: relative; } + html.theme--documenter-dark .card-content { + background-color: transparent; + padding: 1.5rem; } + html.theme--documenter-dark .card-footer { + background-color: transparent; + border-top: 1px solid #dbdbdb; + align-items: stretch; + display: flex; } + html.theme--documenter-dark .card-footer-item { + align-items: center; + display: flex; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + justify-content: center; + padding: 0.75rem; } + html.theme--documenter-dark .card-footer-item:not(:last-child) { + border-right: 1px solid #dbdbdb; } + html.theme--documenter-dark .card .media:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .dropdown { + display: inline-flex; + position: relative; + vertical-align: top; } + html.theme--documenter-dark .dropdown.is-active .dropdown-menu, html.theme--documenter-dark .dropdown.is-hoverable:hover .dropdown-menu { + display: block; } + html.theme--documenter-dark .dropdown.is-right .dropdown-menu { + left: auto; + right: 0; } + html.theme--documenter-dark .dropdown.is-up .dropdown-menu { + bottom: 100%; + padding-bottom: 4px; + padding-top: initial; + top: auto; } + html.theme--documenter-dark .dropdown-menu { + display: none; + left: 0; + min-width: 12rem; + padding-top: 4px; + position: absolute; + top: 100%; + z-index: 20; } + html.theme--documenter-dark .dropdown-content { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + html.theme--documenter-dark .dropdown-item { + color: #4a4a4a; + display: block; + font-size: 0.875rem; + line-height: 1.5; + padding: 0.375rem 1rem; + position: relative; } + html.theme--documenter-dark a.dropdown-item, + html.theme--documenter-dark button.dropdown-item { + padding-right: 3rem; + text-align: left; + white-space: nowrap; + width: 100%; } + html.theme--documenter-dark a.dropdown-item:hover, + html.theme--documenter-dark button.dropdown-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark a.dropdown-item.is-active, + html.theme--documenter-dark button.dropdown-item.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .dropdown-divider { + background-color: #dbdbdb; + border: none; + display: block; + height: 1px; + margin: 0.5rem 0; } + html.theme--documenter-dark .level { + align-items: center; + justify-content: space-between; } + html.theme--documenter-dark .level code { + border-radius: 4px; } + html.theme--documenter-dark .level img { + display: inline-block; + vertical-align: top; } + html.theme--documenter-dark .level.is-mobile { + display: flex; } + html.theme--documenter-dark .level.is-mobile .level-left, + html.theme--documenter-dark .level.is-mobile .level-right { + display: flex; } + html.theme--documenter-dark .level.is-mobile .level-left + .level-right { + margin-top: 0; } + html.theme--documenter-dark .level.is-mobile .level-item:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + html.theme--documenter-dark .level.is-mobile .level-item:not(.is-narrow) { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level { + display: flex; } + html.theme--documenter-dark .level > .level-item:not(.is-narrow) { + flex-grow: 1; } } + html.theme--documenter-dark .level-item { + align-items: center; + display: flex; + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; + justify-content: center; } + html.theme--documenter-dark .level-item .title, + html.theme--documenter-dark .level-item .subtitle { + margin-bottom: 0; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .level-item:not(:last-child) { + margin-bottom: 0.75rem; } } + html.theme--documenter-dark .level-left, + html.theme--documenter-dark .level-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .level-left .level-item.is-flexible, + html.theme--documenter-dark .level-right .level-item.is-flexible { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-left .level-item:not(:last-child), + html.theme--documenter-dark .level-right .level-item:not(:last-child) { + margin-right: 0.75rem; } } + html.theme--documenter-dark .level-left { + align-items: center; + justify-content: flex-start; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .level-left + .level-right { + margin-top: 1.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-left { + display: flex; } } + html.theme--documenter-dark .level-right { + align-items: center; + justify-content: flex-end; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .level-right { + display: flex; } } + html.theme--documenter-dark .list { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .list-item { + display: block; + padding: 0.5em 1em; } + html.theme--documenter-dark .list-item:not(a) { + color: #fbfbfb; } + html.theme--documenter-dark .list-item:first-child { + border-top-left-radius: 4px; + border-top-right-radius: 4px; } + html.theme--documenter-dark .list-item:last-child { + border-bottom-left-radius: 4px; + border-bottom-right-radius: 4px; } + html.theme--documenter-dark .list-item:not(:last-child) { + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .list-item.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark a.list-item { + background-color: whitesmoke; + cursor: pointer; } + html.theme--documenter-dark .media { + align-items: flex-start; + display: flex; + text-align: left; } + html.theme--documenter-dark .media .content:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .media .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + display: flex; + padding-top: 0.75rem; } + html.theme--documenter-dark .media .media .content:not(:last-child), + html.theme--documenter-dark .media .media .control:not(:last-child) { + margin-bottom: 0.5rem; } + html.theme--documenter-dark .media .media .media { + padding-top: 0.5rem; } + html.theme--documenter-dark .media .media .media + .media { + margin-top: 0.5rem; } + html.theme--documenter-dark .media + .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + margin-top: 1rem; + padding-top: 1rem; } + html.theme--documenter-dark .media.is-large + .media { + margin-top: 1.5rem; + padding-top: 1.5rem; } + html.theme--documenter-dark .media-left, + html.theme--documenter-dark .media-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .media-left { + margin-right: 1rem; } + html.theme--documenter-dark .media-right { + margin-left: 1rem; } + html.theme--documenter-dark .media-content { + flex-basis: auto; + flex-grow: 1; + flex-shrink: 1; + text-align: left; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .media-content { + overflow-x: auto; } } + html.theme--documenter-dark .menu { + font-size: 1rem; } + html.theme--documenter-dark .menu.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.menu { + font-size: 0.75rem; } + html.theme--documenter-dark .menu.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .menu.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .menu-list { + line-height: 1.25; } + html.theme--documenter-dark .menu-list a { + border-radius: 2px; + color: #fbfbfb; + display: block; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .menu-list a:hover { + background-color: whitesmoke; + color: #cdc3e3; } + html.theme--documenter-dark .menu-list a.is-active { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .menu-list li ul { + border-left: 1px solid #dbdbdb; + margin: 0.75em; + padding-left: 0.75em; } + html.theme--documenter-dark .menu-label { + color: #7a7a7a; + font-size: 0.75em; + letter-spacing: 0.1em; + text-transform: uppercase; } + html.theme--documenter-dark .menu-label:not(:first-child) { + margin-top: 1em; } + html.theme--documenter-dark .menu-label:not(:last-child) { + margin-bottom: 1em; } + html.theme--documenter-dark .message { + background-color: whitesmoke; + border-radius: 4px; + font-size: 1rem; } + html.theme--documenter-dark .message strong { + color: currentColor; } + html.theme--documenter-dark .message a:not(.button):not(.tag):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + html.theme--documenter-dark .message.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.message { + font-size: 0.75rem; } + html.theme--documenter-dark .message.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .message.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .message.is-white { + background-color: white; } + html.theme--documenter-dark .message.is-white .message-header { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .message.is-white .message-body { + border-color: white; + color: #4d4d4d; } + html.theme--documenter-dark .message.is-black { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-black .message-header { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .message.is-black .message-body { + border-color: #0a0a0a; + color: #090909; } + html.theme--documenter-dark .message.is-light { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-light .message-header { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .message.is-light .message-body { + border-color: whitesmoke; + color: #505050; } + html.theme--documenter-dark .message.is-dark, html.theme--documenter-dark .content kbd.message { + background-color: #fafafa; } + html.theme--documenter-dark .message.is-dark .message-header, html.theme--documenter-dark .content kbd.message .message-header { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .message.is-dark .message-body, html.theme--documenter-dark .content kbd.message .message-body { + border-color: #363636; + color: #2a2a2a; } + html.theme--documenter-dark .message.is-primary, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink { + background-color: #f6fbfd; } + html.theme--documenter-dark .message.is-primary .message-header, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-header { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .message.is-primary .message-body, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-body { + border-color: #4eb5de; + color: #1f556a; } + html.theme--documenter-dark .message.is-link { + background-color: #f6fdfe; } + html.theme--documenter-dark .message.is-link .message-header { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .message.is-link .message-body { + border-color: #2ad7e6; + color: #0c2f32; } + html.theme--documenter-dark .message.is-info { + background-color: #f6fafd; } + html.theme--documenter-dark .message.is-info .message-header { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .message.is-info .message-body { + border-color: #3489da; + color: #215485; } + html.theme--documenter-dark .message.is-success { + background-color: #f7fef6; } + html.theme--documenter-dark .message.is-success .message-header { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .message.is-success .message-body { + border-color: #259a12; + color: #113b0a; } + html.theme--documenter-dark .message.is-warning { + background-color: #fefcf5; } + html.theme--documenter-dark .message.is-warning .message-header { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .message.is-warning .message-body { + border-color: #f4c72f; + color: #332909; } + html.theme--documenter-dark .message.is-danger { + background-color: #fdf7f7; } + html.theme--documenter-dark .message.is-danger .message-header { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .message.is-danger .message-body { + border-color: #cb3c33; + color: #8d302a; } + html.theme--documenter-dark .message-header { + align-items: center; + background-color: #fbfbfb; + border-radius: 4px 4px 0 0; + color: rgba(0, 0, 0, 0.7); + display: flex; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.75em 1em; + position: relative; } + html.theme--documenter-dark .message-header .delete { + flex-grow: 0; + flex-shrink: 0; + margin-left: 0.75em; } + html.theme--documenter-dark .message-header + .message-body { + border-width: 0; + border-top-left-radius: 0; + border-top-right-radius: 0; } + html.theme--documenter-dark .message-body { + border-color: #dbdbdb; + border-radius: 4px; + border-style: solid; + border-width: 0 0 0 4px; + color: #fbfbfb; + padding: 1.25em 1.5em; } + html.theme--documenter-dark .message-body code, + html.theme--documenter-dark .message-body pre { + background-color: white; } + html.theme--documenter-dark .message-body pre code { + background-color: transparent; } + html.theme--documenter-dark .modal { + align-items: center; + display: none; + flex-direction: column; + justify-content: center; + overflow: hidden; + position: fixed; + z-index: 40; } + html.theme--documenter-dark .modal.is-active { + display: flex; } + html.theme--documenter-dark .modal-background { + background-color: rgba(10, 10, 10, 0.86); } + html.theme--documenter-dark .modal-content, + html.theme--documenter-dark .modal-card { + margin: 0 20px; + max-height: calc(100vh - 160px); + overflow: auto; + position: relative; + width: 100%; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .modal-content, + html.theme--documenter-dark .modal-card { + margin: 0 auto; + max-height: calc(100vh - 40px); + width: 640px; } } + html.theme--documenter-dark .modal-close { + background: none; + height: 40px; + position: fixed; + right: 20px; + top: 20px; + width: 40px; } + html.theme--documenter-dark .modal-card { + display: flex; + flex-direction: column; + max-height: calc(100vh - 40px); + overflow: hidden; + -ms-overflow-y: visible; } + html.theme--documenter-dark .modal-card-head, + html.theme--documenter-dark .modal-card-foot { + align-items: center; + background-color: whitesmoke; + display: flex; + flex-shrink: 0; + justify-content: flex-start; + padding: 20px; + position: relative; } + html.theme--documenter-dark .modal-card-head { + border-bottom: 1px solid #dbdbdb; + border-top-left-radius: 6px; + border-top-right-radius: 6px; } + html.theme--documenter-dark .modal-card-title { + color: #cdc3e3; + flex-grow: 1; + flex-shrink: 0; + font-size: 1.5rem; + line-height: 1; } + html.theme--documenter-dark .modal-card-foot { + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark .modal-card-foot .button:not(:last-child) { + margin-right: 0.5em; } + html.theme--documenter-dark .modal-card-body { + -webkit-overflow-scrolling: touch; + background-color: white; + flex-grow: 1; + flex-shrink: 1; + overflow: auto; + padding: 20px; } + html.theme--documenter-dark .navbar { + background-color: white; + min-height: 3.25rem; + position: relative; + z-index: 30; } + html.theme--documenter-dark .navbar.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link { + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-burger { + color: #0a0a0a; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-white .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link { + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link::after { + border-color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-white .navbar-dropdown a.navbar-item.is-active { + background-color: white; + color: #0a0a0a; } } + html.theme--documenter-dark .navbar.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link { + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link::after { + border-color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-burger { + color: white; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-black .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link { + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link::after { + border-color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { + background-color: black; + color: white; } + html.theme--documenter-dark .navbar.is-black .navbar-dropdown a.navbar-item.is-active { + background-color: #0a0a0a; + color: white; } } + html.theme--documenter-dark .navbar.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link { + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link::after { + border-color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-burger { + color: #363636; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-light .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link { + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link::after { + border-color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .navbar.is-light .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #363636; } } + html.theme--documenter-dark .navbar.is-dark, html.theme--documenter-dark .content kbd.navbar { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link { + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link::after { + border-color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-burger, html.theme--documenter-dark .content kbd.navbar .navbar-burger { + color: whitesmoke; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-dark .navbar-start > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-end > .navbar-item, + html.theme--documenter-dark .content kbd.navbar .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link { + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:focus, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:hover, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link.is-active, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link::after, + html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link::after { + border-color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, + html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { + background-color: #363636; + color: whitesmoke; } } + html.theme--documenter-dark .navbar.is-primary, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-burger, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-primary .navbar-start > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-end > .navbar-item, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:focus, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link::after, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, + html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { + background-color: #4eb5de; + color: #fff; } } + html.theme--documenter-dark .navbar.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-link .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .navbar.is-link .navbar-dropdown a.navbar-item.is-active { + background-color: #2ad7e6; + color: #fff; } } + html.theme--documenter-dark .navbar.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-info .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .navbar.is-info .navbar-dropdown a.navbar-item.is-active { + background-color: #3489da; + color: #fff; } } + html.theme--documenter-dark .navbar.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-success .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .navbar.is-success .navbar-dropdown a.navbar-item.is-active { + background-color: #259a12; + color: #fff; } } + html.theme--documenter-dark .navbar.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-burger { + color: rgba(0, 0, 0, 0.7); } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-warning .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } } + html.theme--documenter-dark .navbar.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar.is-danger .navbar-start > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-end > .navbar-item, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link { + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:focus, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:hover, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link::after, + html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link::after { + border-color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, + html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { + background-color: #cb3c33; + color: #fff; } } + html.theme--documenter-dark .navbar > .container { + align-items: stretch; + display: flex; + min-height: 3.25rem; + width: 100%; } + html.theme--documenter-dark .navbar.has-shadow { + box-shadow: 0 2px 0 0 whitesmoke; } + html.theme--documenter-dark .navbar.is-fixed-bottom, html.theme--documenter-dark .navbar.is-fixed-top { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom.has-shadow { + box-shadow: 0 -2px 0 0 whitesmoke; } + html.theme--documenter-dark .navbar.is-fixed-top { + top: 0; } + html.theme--documenter-dark html.has-navbar-fixed-top, + html.theme--documenter-dark body.has-navbar-fixed-top { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom, + html.theme--documenter-dark body.has-navbar-fixed-bottom { + padding-bottom: 3.25rem; } + html.theme--documenter-dark .navbar-brand, + html.theme--documenter-dark .navbar-tabs { + align-items: stretch; + display: flex; + flex-shrink: 0; + min-height: 3.25rem; } + html.theme--documenter-dark .navbar-brand a.navbar-item:focus, html.theme--documenter-dark .navbar-brand a.navbar-item:hover { + background-color: transparent; } + html.theme--documenter-dark .navbar-tabs { + -webkit-overflow-scrolling: touch; + max-width: 100vw; + overflow-x: auto; + overflow-y: hidden; } + html.theme--documenter-dark .navbar-burger { + color: #4a4a4a; + cursor: pointer; + display: block; + height: 3.25rem; + position: relative; + width: 3.25rem; + margin-left: auto; } + html.theme--documenter-dark .navbar-burger span { + background-color: currentColor; + display: block; + height: 1px; + left: calc(50% - 8px); + position: absolute; + transform-origin: center; + transition-duration: 86ms; + transition-property: background-color, opacity, transform; + transition-timing-function: ease-out; + width: 16px; } + html.theme--documenter-dark .navbar-burger span:nth-child(1) { + top: calc(50% - 6px); } + html.theme--documenter-dark .navbar-burger span:nth-child(2) { + top: calc(50% - 1px); } + html.theme--documenter-dark .navbar-burger span:nth-child(3) { + top: calc(50% + 4px); } + html.theme--documenter-dark .navbar-burger:hover { + background-color: rgba(0, 0, 0, 0.05); } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(1) { + transform: translateY(5px) rotate(45deg); } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(2) { + opacity: 0; } + html.theme--documenter-dark .navbar-burger.is-active span:nth-child(3) { + transform: translateY(-5px) rotate(-45deg); } + html.theme--documenter-dark .navbar-menu { + display: none; } + html.theme--documenter-dark .navbar-item, + html.theme--documenter-dark .navbar-link { + color: #4a4a4a; + display: block; + line-height: 1.5; + padding: 0.5rem 0.75rem; + position: relative; } + html.theme--documenter-dark .navbar-item .icon:only-child, + html.theme--documenter-dark .navbar-link .icon:only-child { + margin-left: -0.25rem; + margin-right: -0.25rem; } + html.theme--documenter-dark a.navbar-item, + html.theme--documenter-dark .navbar-link { + cursor: pointer; } + html.theme--documenter-dark a.navbar-item:focus, html.theme--documenter-dark a.navbar-item:focus-within, html.theme--documenter-dark a.navbar-item:hover, html.theme--documenter-dark a.navbar-item.is-active, + html.theme--documenter-dark .navbar-link:focus, + html.theme--documenter-dark .navbar-link:focus-within, + html.theme--documenter-dark .navbar-link:hover, + html.theme--documenter-dark .navbar-link.is-active { + background-color: #fafafa; + color: #2ad7e6; } + html.theme--documenter-dark .navbar-item { + display: block; + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .navbar-item img { + max-height: 1.75rem; } + html.theme--documenter-dark .navbar-item.has-dropdown { + padding: 0; } + html.theme--documenter-dark .navbar-item.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .navbar-item.is-tab { + border-bottom: 1px solid transparent; + min-height: 3.25rem; + padding-bottom: calc(0.5rem - 1px); } + html.theme--documenter-dark .navbar-item.is-tab:focus, html.theme--documenter-dark .navbar-item.is-tab:hover { + background-color: transparent; + border-bottom-color: #2ad7e6; } + html.theme--documenter-dark .navbar-item.is-tab.is-active { + background-color: transparent; + border-bottom-color: #2ad7e6; + border-bottom-style: solid; + border-bottom-width: 3px; + color: #2ad7e6; + padding-bottom: calc(0.5rem - 3px); } + html.theme--documenter-dark .navbar-content { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .navbar-link:not(.is-arrowless) { + padding-right: 2.5em; } + html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after { + border-color: #2ad7e6; + margin-top: -0.375em; + right: 1.125em; } + html.theme--documenter-dark .navbar-dropdown { + font-size: 0.875rem; + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + html.theme--documenter-dark .navbar-dropdown .navbar-item { + padding-left: 1.5rem; + padding-right: 1.5rem; } + html.theme--documenter-dark .navbar-divider { + background-color: whitesmoke; + border: none; + display: none; + height: 2px; + margin: 0.5rem 0; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .navbar > .container { + display: block; } + html.theme--documenter-dark .navbar-brand .navbar-item, + html.theme--documenter-dark .navbar-tabs .navbar-item { + align-items: center; + display: flex; } + html.theme--documenter-dark .navbar-link::after { + display: none; } + html.theme--documenter-dark .navbar-menu { + background-color: white; + box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); + padding: 0.5rem 0; } + html.theme--documenter-dark .navbar-menu.is-active { + display: block; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch, html.theme--documenter-dark .navbar.is-fixed-top-touch { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom-touch.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .navbar.is-fixed-top-touch { + top: 0; } + html.theme--documenter-dark .navbar.is-fixed-top .navbar-menu, html.theme--documenter-dark .navbar.is-fixed-top-touch .navbar-menu { + -webkit-overflow-scrolling: touch; + max-height: calc(100vh - 3.25rem); + overflow: auto; } + html.theme--documenter-dark html.has-navbar-fixed-top-touch, + html.theme--documenter-dark body.has-navbar-fixed-top-touch { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom-touch, + html.theme--documenter-dark body.has-navbar-fixed-bottom-touch { + padding-bottom: 3.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .navbar, + html.theme--documenter-dark .navbar-menu, + html.theme--documenter-dark .navbar-start, + html.theme--documenter-dark .navbar-end { + align-items: stretch; + display: flex; } + html.theme--documenter-dark .navbar { + min-height: 3.25rem; } + html.theme--documenter-dark .navbar.is-spaced { + padding: 1rem 2rem; } + html.theme--documenter-dark .navbar.is-spaced .navbar-start, + html.theme--documenter-dark .navbar.is-spaced .navbar-end { + align-items: center; } + html.theme--documenter-dark .navbar.is-spaced a.navbar-item, + html.theme--documenter-dark .navbar.is-spaced .navbar-link { + border-radius: 4px; } + html.theme--documenter-dark .navbar.is-transparent a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent a.navbar-item:hover, html.theme--documenter-dark .navbar.is-transparent a.navbar-item.is-active, + html.theme--documenter-dark .navbar.is-transparent .navbar-link:focus, + html.theme--documenter-dark .navbar.is-transparent .navbar-link:hover, + html.theme--documenter-dark .navbar.is-transparent .navbar-link.is-active { + background-color: transparent !important; } + html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { + background-color: transparent !important; } + html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #2ad7e6; } + html.theme--documenter-dark .navbar-burger { + display: none; } + html.theme--documenter-dark .navbar-item, + html.theme--documenter-dark .navbar-link { + align-items: center; + display: flex; } + html.theme--documenter-dark .navbar-item { + display: flex; } + html.theme--documenter-dark .navbar-item.has-dropdown { + align-items: stretch; } + html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-link::after { + transform: rotate(135deg) translate(0.25em, -0.25em); } + html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-dropdown { + border-bottom: 2px solid #dbdbdb; + border-radius: 6px 6px 0 0; + border-top: none; + bottom: 100%; + box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); + top: auto; } + html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown { + display: block; } + .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { + opacity: 1; + pointer-events: auto; + transform: translateY(0); } + html.theme--documenter-dark .navbar-menu { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .navbar-start { + justify-content: flex-start; + margin-right: auto; } + html.theme--documenter-dark .navbar-end { + justify-content: flex-end; + margin-left: auto; } + html.theme--documenter-dark .navbar-dropdown { + background-color: white; + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 2px solid #dbdbdb; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); + display: none; + font-size: 0.875rem; + left: 0; + min-width: 100%; + position: absolute; + top: 100%; + z-index: 20; } + html.theme--documenter-dark .navbar-dropdown .navbar-item { + padding: 0.375rem 1rem; + white-space: nowrap; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item { + padding-right: 3rem; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #2ad7e6; } + .navbar.is-spaced html.theme--documenter-dark .navbar-dropdown, html.theme--documenter-dark .navbar-dropdown.is-boxed { + border-radius: 6px; + border-top: none; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + display: block; + opacity: 0; + pointer-events: none; + top: calc(100% + (-4px)); + transform: translateY(-5px); + transition-duration: 86ms; + transition-property: opacity, transform; } + html.theme--documenter-dark .navbar-dropdown.is-right { + left: auto; + right: 0; } + html.theme--documenter-dark .navbar-divider { + display: block; } + html.theme--documenter-dark .navbar > .container .navbar-brand, + html.theme--documenter-dark .container > .navbar .navbar-brand { + margin-left: -.75rem; } + html.theme--documenter-dark .navbar > .container .navbar-menu, + html.theme--documenter-dark .container > .navbar .navbar-menu { + margin-right: -.75rem; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop, html.theme--documenter-dark .navbar.is-fixed-top-desktop { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop { + bottom: 0; } + html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .navbar.is-fixed-top-desktop { + top: 0; } + html.theme--documenter-dark html.has-navbar-fixed-top-desktop, + html.theme--documenter-dark body.has-navbar-fixed-top-desktop { + padding-top: 3.25rem; } + html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop, + html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop { + padding-bottom: 3.25rem; } + html.theme--documenter-dark html.has-spaced-navbar-fixed-top, + html.theme--documenter-dark body.has-spaced-navbar-fixed-top { + padding-top: 5.25rem; } + html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom, + html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom { + padding-bottom: 5.25rem; } + html.theme--documenter-dark a.navbar-item.is-active, + html.theme--documenter-dark .navbar-link.is-active { + color: #0a0a0a; } + html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover), + html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover) { + background-color: transparent; } + html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #fafafa; } } + html.theme--documenter-dark .hero.is-fullheight-with-navbar { + min-height: calc(100vh - 3.25rem); } + html.theme--documenter-dark .pagination { + font-size: 1rem; + margin: -0.25rem; } + html.theme--documenter-dark .pagination.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination { + font-size: 0.75rem; } + html.theme--documenter-dark .pagination.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .pagination.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .pagination.is-rounded .pagination-previous, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, + html.theme--documenter-dark .pagination.is-rounded .pagination-next, + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { + padding-left: 1em; + padding-right: 1em; + border-radius: 290486px; } + html.theme--documenter-dark .pagination.is-rounded .pagination-link, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { + border-radius: 290486px; } + html.theme--documenter-dark .pagination, + html.theme--documenter-dark .pagination-list { + align-items: center; + display: flex; + justify-content: center; + text-align: center; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark .pagination-link, + html.theme--documenter-dark .pagination-ellipsis { + font-size: 1em; + justify-content: center; + margin: 0.25rem; + padding-left: 0.5em; + padding-right: 0.5em; + text-align: center; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next, + html.theme--documenter-dark .pagination-link { + border-color: #dbdbdb; + color: #363636; + min-width: 2.25em; } + html.theme--documenter-dark .pagination-previous:hover, + html.theme--documenter-dark .pagination-next:hover, + html.theme--documenter-dark .pagination-link:hover { + border-color: #b5b5b5; + color: #97ebf3; } + html.theme--documenter-dark .pagination-previous:focus, + html.theme--documenter-dark .pagination-next:focus, + html.theme--documenter-dark .pagination-link:focus { + border-color: #3c5dcd; } + html.theme--documenter-dark .pagination-previous:active, + html.theme--documenter-dark .pagination-next:active, + html.theme--documenter-dark .pagination-link:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } + html.theme--documenter-dark .pagination-previous[disabled], + html.theme--documenter-dark .pagination-next[disabled], + html.theme--documenter-dark .pagination-link[disabled] { + background-color: #dbdbdb; + border-color: #dbdbdb; + box-shadow: none; + color: #7a7a7a; + opacity: 0.5; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next { + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + html.theme--documenter-dark .pagination-link.is-current { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .pagination-ellipsis { + color: #b5b5b5; + pointer-events: none; } + html.theme--documenter-dark .pagination-list { + flex-wrap: wrap; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .pagination { + flex-wrap: wrap; } + html.theme--documenter-dark .pagination-previous, + html.theme--documenter-dark .pagination-next { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .pagination-list li { + flex-grow: 1; + flex-shrink: 1; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .pagination-list { + flex-grow: 1; + flex-shrink: 1; + justify-content: flex-start; + order: 1; } + html.theme--documenter-dark .pagination-previous { + order: 2; } + html.theme--documenter-dark .pagination-next { + order: 3; } + html.theme--documenter-dark .pagination { + justify-content: space-between; } + html.theme--documenter-dark .pagination.is-centered .pagination-previous { + order: 1; } + html.theme--documenter-dark .pagination.is-centered .pagination-list { + justify-content: center; + order: 2; } + html.theme--documenter-dark .pagination.is-centered .pagination-next { + order: 3; } + html.theme--documenter-dark .pagination.is-right .pagination-previous { + order: 1; } + html.theme--documenter-dark .pagination.is-right .pagination-next { + order: 2; } + html.theme--documenter-dark .pagination.is-right .pagination-list { + justify-content: flex-end; + order: 3; } } + html.theme--documenter-dark .panel { + font-size: 1rem; } + html.theme--documenter-dark .panel:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .panel-heading, + html.theme--documenter-dark .panel-tabs, + html.theme--documenter-dark .panel-block { + border-bottom: 1px solid #dbdbdb; + border-left: 1px solid #dbdbdb; + border-right: 1px solid #dbdbdb; } + html.theme--documenter-dark .panel-heading:first-child, + html.theme--documenter-dark .panel-tabs:first-child, + html.theme--documenter-dark .panel-block:first-child { + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark .panel-heading { + background-color: whitesmoke; + border-radius: 4px 4px 0 0; + color: #cdc3e3; + font-size: 1.25em; + font-weight: 300; + line-height: 1.25; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .panel-tabs { + align-items: flex-end; + display: flex; + font-size: 0.875em; + justify-content: center; } + html.theme--documenter-dark .panel-tabs a { + border-bottom: 1px solid #dbdbdb; + margin-bottom: -1px; + padding: 0.5em; } + html.theme--documenter-dark .panel-tabs a.is-active { + border-bottom-color: #4a4a4a; + color: #363636; } + html.theme--documenter-dark .panel-list a { + color: #fbfbfb; } + html.theme--documenter-dark .panel-list a:hover { + color: #2ad7e6; } + html.theme--documenter-dark .panel-block { + align-items: center; + color: #cdc3e3; + display: flex; + justify-content: flex-start; + padding: 0.5em 0.75em; } + html.theme--documenter-dark .panel-block input[type="checkbox"] { + margin-right: 0.75em; } + html.theme--documenter-dark .panel-block > .control { + flex-grow: 1; + flex-shrink: 1; + width: 100%; } + html.theme--documenter-dark .panel-block.is-wrapped { + flex-wrap: wrap; } + html.theme--documenter-dark .panel-block.is-active { + border-left-color: #2ad7e6; + color: #363636; } + html.theme--documenter-dark .panel-block.is-active .panel-icon { + color: #2ad7e6; } + html.theme--documenter-dark a.panel-block, + html.theme--documenter-dark label.panel-block { + cursor: pointer; } + html.theme--documenter-dark a.panel-block:hover, + html.theme--documenter-dark label.panel-block:hover { + background-color: whitesmoke; } + html.theme--documenter-dark .panel-icon { + display: inline-block; + font-size: 14px; + height: 1em; + line-height: 1em; + text-align: center; + vertical-align: top; + width: 1em; + color: #7a7a7a; + margin-right: 0.75em; } + html.theme--documenter-dark .panel-icon .fa { + font-size: inherit; + line-height: inherit; } + html.theme--documenter-dark .tabs { + -webkit-overflow-scrolling: touch; + align-items: stretch; + display: flex; + font-size: 1rem; + justify-content: space-between; + overflow: hidden; + overflow-x: auto; + white-space: nowrap; } + html.theme--documenter-dark .tabs a { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + color: #fbfbfb; + display: flex; + justify-content: center; + margin-bottom: -1px; + padding: 0.5em 1em; + vertical-align: top; } + html.theme--documenter-dark .tabs a:hover { + border-bottom-color: #cdc3e3; + color: #cdc3e3; } + html.theme--documenter-dark .tabs li { + display: block; } + html.theme--documenter-dark .tabs li.is-active a { + border-bottom-color: #2ad7e6; + color: #2ad7e6; } + html.theme--documenter-dark .tabs ul { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + display: flex; + flex-grow: 1; + flex-shrink: 0; + justify-content: flex-start; } + html.theme--documenter-dark .tabs ul.is-left { + padding-right: 0.75em; } + html.theme--documenter-dark .tabs ul.is-center { + flex: none; + justify-content: center; + padding-left: 0.75em; + padding-right: 0.75em; } + html.theme--documenter-dark .tabs ul.is-right { + justify-content: flex-end; + padding-left: 0.75em; } + html.theme--documenter-dark .tabs .icon:first-child { + margin-right: 0.5em; } + html.theme--documenter-dark .tabs .icon:last-child { + margin-left: 0.5em; } + html.theme--documenter-dark .tabs.is-centered ul { + justify-content: center; } + html.theme--documenter-dark .tabs.is-right ul { + justify-content: flex-end; } + html.theme--documenter-dark .tabs.is-boxed a { + border: 1px solid transparent; + border-radius: 4px 4px 0 0; } + html.theme--documenter-dark .tabs.is-boxed a:hover { + background-color: whitesmoke; + border-bottom-color: #dbdbdb; } + html.theme--documenter-dark .tabs.is-boxed li.is-active a { + background-color: white; + border-color: #dbdbdb; + border-bottom-color: transparent !important; } + html.theme--documenter-dark .tabs.is-fullwidth li { + flex-grow: 1; + flex-shrink: 0; } + html.theme--documenter-dark .tabs.is-toggle a { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px; + margin-bottom: 0; + position: relative; } + html.theme--documenter-dark .tabs.is-toggle a:hover { + background-color: whitesmoke; + border-color: #b5b5b5; + z-index: 2; } + html.theme--documenter-dark .tabs.is-toggle li + li { + margin-left: -1px; } + html.theme--documenter-dark .tabs.is-toggle li:first-child a { + border-radius: 4px 0 0 4px; } + html.theme--documenter-dark .tabs.is-toggle li:last-child a { + border-radius: 0 4px 4px 0; } + html.theme--documenter-dark .tabs.is-toggle li.is-active a { + background-color: #2ad7e6; + border-color: #2ad7e6; + color: #fff; + z-index: 1; } + html.theme--documenter-dark .tabs.is-toggle ul { + border-bottom: none; } + html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:first-child a { + border-bottom-left-radius: 290486px; + border-top-left-radius: 290486px; + padding-left: 1.25em; } + html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:last-child a { + border-bottom-right-radius: 290486px; + border-top-right-radius: 290486px; + padding-right: 1.25em; } + html.theme--documenter-dark .tabs.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.tabs { + font-size: 0.75rem; } + html.theme--documenter-dark .tabs.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .tabs.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .column { + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + padding: 0.75rem; } + .columns.is-mobile > html.theme--documenter-dark .column.is-narrow { + flex: none; } + .columns.is-mobile > html.theme--documenter-dark .column.is-full { + flex: none; + width: 100%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-three-quarters { + flex: none; + width: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-two-thirds { + flex: none; + width: 66.6666%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-half { + flex: none; + width: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-third { + flex: none; + width: 33.3333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-quarter { + flex: none; + width: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-one-fifth { + flex: none; + width: 20%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-two-fifths { + flex: none; + width: 40%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-three-fifths { + flex: none; + width: 60%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-four-fifths { + flex: none; + width: 80%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-quarters { + margin-left: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-thirds { + margin-left: 66.6666%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-half { + margin-left: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-third { + margin-left: 33.3333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-quarter { + margin-left: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-fifth { + margin-left: 20%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-fifths { + margin-left: 40%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-fifths { + margin-left: 60%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-four-fifths { + margin-left: 80%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-0 { + flex: none; + width: 0%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-0 { + margin-left: 0%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-1 { + flex: none; + width: 8.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-1 { + margin-left: 8.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-2 { + flex: none; + width: 16.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-2 { + margin-left: 16.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-3 { + flex: none; + width: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-3 { + margin-left: 25%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-4 { + flex: none; + width: 33.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-4 { + margin-left: 33.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-5 { + flex: none; + width: 41.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-5 { + margin-left: 41.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-6 { + flex: none; + width: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-6 { + margin-left: 50%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-7 { + flex: none; + width: 58.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-7 { + margin-left: 58.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-8 { + flex: none; + width: 66.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-8 { + margin-left: 66.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-9 { + flex: none; + width: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-9 { + margin-left: 75%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-10 { + flex: none; + width: 83.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-10 { + margin-left: 83.3333333333%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-11 { + flex: none; + width: 91.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-11 { + margin-left: 91.6666666667%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-12 { + flex: none; + width: 100%; } + .columns.is-mobile > html.theme--documenter-dark .column.is-offset-12 { + margin-left: 100%; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .column.is-narrow-mobile { + flex: none; } + html.theme--documenter-dark .column.is-full-mobile { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-mobile { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-mobile { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-mobile { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-mobile { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-mobile { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-mobile { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-mobile { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-mobile { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-mobile { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-mobile { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-mobile { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-mobile { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-mobile { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-mobile { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-mobile { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-mobile { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-mobile { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-mobile { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-mobile { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-mobile { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-mobile { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-mobile { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-mobile { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-mobile { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-mobile { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-mobile { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-mobile { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-mobile { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-mobile { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-mobile { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-mobile { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-mobile { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-mobile { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-mobile { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-mobile { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-mobile { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-mobile { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-mobile { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-mobile { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-mobile { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-mobile { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-mobile { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-mobile { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-mobile { + margin-left: 100%; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .column.is-narrow, html.theme--documenter-dark .column.is-narrow-tablet { + flex: none; } + html.theme--documenter-dark .column.is-full, html.theme--documenter-dark .column.is-full-tablet { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters, html.theme--documenter-dark .column.is-three-quarters-tablet { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds, html.theme--documenter-dark .column.is-two-thirds-tablet { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half, html.theme--documenter-dark .column.is-half-tablet { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third, html.theme--documenter-dark .column.is-one-third-tablet { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter, html.theme--documenter-dark .column.is-one-quarter-tablet { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth, html.theme--documenter-dark .column.is-one-fifth-tablet { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths, html.theme--documenter-dark .column.is-two-fifths-tablet { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths, html.theme--documenter-dark .column.is-three-fifths-tablet { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths, html.theme--documenter-dark .column.is-four-fifths-tablet { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters, html.theme--documenter-dark .column.is-offset-three-quarters-tablet { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds, html.theme--documenter-dark .column.is-offset-two-thirds-tablet { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half, html.theme--documenter-dark .column.is-offset-half-tablet { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third, html.theme--documenter-dark .column.is-offset-one-third-tablet { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter, html.theme--documenter-dark .column.is-offset-one-quarter-tablet { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth, html.theme--documenter-dark .column.is-offset-one-fifth-tablet { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths, html.theme--documenter-dark .column.is-offset-two-fifths-tablet { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths, html.theme--documenter-dark .column.is-offset-three-fifths-tablet { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths, html.theme--documenter-dark .column.is-offset-four-fifths-tablet { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0, html.theme--documenter-dark .column.is-0-tablet { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0, html.theme--documenter-dark .column.is-offset-0-tablet { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1, html.theme--documenter-dark .column.is-1-tablet { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1, html.theme--documenter-dark .column.is-offset-1-tablet { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2, html.theme--documenter-dark .column.is-2-tablet { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2, html.theme--documenter-dark .column.is-offset-2-tablet { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3, html.theme--documenter-dark .column.is-3-tablet { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3, html.theme--documenter-dark .column.is-offset-3-tablet { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4, html.theme--documenter-dark .column.is-4-tablet { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4, html.theme--documenter-dark .column.is-offset-4-tablet { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5, html.theme--documenter-dark .column.is-5-tablet { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5, html.theme--documenter-dark .column.is-offset-5-tablet { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6, html.theme--documenter-dark .column.is-6-tablet { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6, html.theme--documenter-dark .column.is-offset-6-tablet { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7, html.theme--documenter-dark .column.is-7-tablet { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7, html.theme--documenter-dark .column.is-offset-7-tablet { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8, html.theme--documenter-dark .column.is-8-tablet { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8, html.theme--documenter-dark .column.is-offset-8-tablet { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9, html.theme--documenter-dark .column.is-9-tablet { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9, html.theme--documenter-dark .column.is-offset-9-tablet { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10, html.theme--documenter-dark .column.is-10-tablet { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10, html.theme--documenter-dark .column.is-offset-10-tablet { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11, html.theme--documenter-dark .column.is-11-tablet { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11, html.theme--documenter-dark .column.is-offset-11-tablet { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12, html.theme--documenter-dark .column.is-12-tablet { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12, html.theme--documenter-dark .column.is-offset-12-tablet { + margin-left: 100%; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .column.is-narrow-touch { + flex: none; } + html.theme--documenter-dark .column.is-full-touch { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-touch { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-touch { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-touch { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-touch { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-touch { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-touch { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-touch { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-touch { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-touch { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-touch { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-touch { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-touch { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-touch { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-touch { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-touch { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-touch { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-touch { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-touch { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-touch { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-touch { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-touch { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-touch { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-touch { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-touch { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-touch { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-touch { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-touch { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-touch { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-touch { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-touch { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-touch { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-touch { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-touch { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-touch { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-touch { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-touch { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-touch { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-touch { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-touch { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-touch { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-touch { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-touch { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-touch { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-touch { + margin-left: 100%; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .column.is-narrow-desktop { + flex: none; } + html.theme--documenter-dark .column.is-full-desktop { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-desktop { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-desktop { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-desktop { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-desktop { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-desktop { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-desktop { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-desktop { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-desktop { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-desktop { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-desktop { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-desktop { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-desktop { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-desktop { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-desktop { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-desktop { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-desktop { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-desktop { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-desktop { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-desktop { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-desktop { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-desktop { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-desktop { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-desktop { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-desktop { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-desktop { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-desktop { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-desktop { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-desktop { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-desktop { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-desktop { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-desktop { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-desktop { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-desktop { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-desktop { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-desktop { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-desktop { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-desktop { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-desktop { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-desktop { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-desktop { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-desktop { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-desktop { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-desktop { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-desktop { + margin-left: 100%; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .column.is-narrow-widescreen { + flex: none; } + html.theme--documenter-dark .column.is-full-widescreen { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-widescreen { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-widescreen { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-widescreen { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-widescreen { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-widescreen { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-widescreen { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-widescreen { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-widescreen { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-widescreen { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-widescreen { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-widescreen { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-widescreen { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-widescreen { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-widescreen { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-widescreen { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-widescreen { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-widescreen { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-widescreen { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-widescreen { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-widescreen { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-widescreen { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-widescreen { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-widescreen { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-widescreen { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-widescreen { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-widescreen { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-widescreen { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-widescreen { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-widescreen { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-widescreen { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-widescreen { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-widescreen { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-widescreen { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-widescreen { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-widescreen { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-widescreen { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-widescreen { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-widescreen { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-widescreen { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-widescreen { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-widescreen { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-widescreen { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-widescreen { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-widescreen { + margin-left: 100%; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .column.is-narrow-fullhd { + flex: none; } + html.theme--documenter-dark .column.is-full-fullhd { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-three-quarters-fullhd { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-two-thirds-fullhd { + flex: none; + width: 66.6666%; } + html.theme--documenter-dark .column.is-half-fullhd { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-one-third-fullhd { + flex: none; + width: 33.3333%; } + html.theme--documenter-dark .column.is-one-quarter-fullhd { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-one-fifth-fullhd { + flex: none; + width: 20%; } + html.theme--documenter-dark .column.is-two-fifths-fullhd { + flex: none; + width: 40%; } + html.theme--documenter-dark .column.is-three-fifths-fullhd { + flex: none; + width: 60%; } + html.theme--documenter-dark .column.is-four-fifths-fullhd { + flex: none; + width: 80%; } + html.theme--documenter-dark .column.is-offset-three-quarters-fullhd { + margin-left: 75%; } + html.theme--documenter-dark .column.is-offset-two-thirds-fullhd { + margin-left: 66.6666%; } + html.theme--documenter-dark .column.is-offset-half-fullhd { + margin-left: 50%; } + html.theme--documenter-dark .column.is-offset-one-third-fullhd { + margin-left: 33.3333%; } + html.theme--documenter-dark .column.is-offset-one-quarter-fullhd { + margin-left: 25%; } + html.theme--documenter-dark .column.is-offset-one-fifth-fullhd { + margin-left: 20%; } + html.theme--documenter-dark .column.is-offset-two-fifths-fullhd { + margin-left: 40%; } + html.theme--documenter-dark .column.is-offset-three-fifths-fullhd { + margin-left: 60%; } + html.theme--documenter-dark .column.is-offset-four-fifths-fullhd { + margin-left: 80%; } + html.theme--documenter-dark .column.is-0-fullhd { + flex: none; + width: 0%; } + html.theme--documenter-dark .column.is-offset-0-fullhd { + margin-left: 0%; } + html.theme--documenter-dark .column.is-1-fullhd { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .column.is-offset-1-fullhd { + margin-left: 8.3333333333%; } + html.theme--documenter-dark .column.is-2-fullhd { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .column.is-offset-2-fullhd { + margin-left: 16.6666666667%; } + html.theme--documenter-dark .column.is-3-fullhd { + flex: none; + width: 25%; } + html.theme--documenter-dark .column.is-offset-3-fullhd { + margin-left: 25%; } + html.theme--documenter-dark .column.is-4-fullhd { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .column.is-offset-4-fullhd { + margin-left: 33.3333333333%; } + html.theme--documenter-dark .column.is-5-fullhd { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .column.is-offset-5-fullhd { + margin-left: 41.6666666667%; } + html.theme--documenter-dark .column.is-6-fullhd { + flex: none; + width: 50%; } + html.theme--documenter-dark .column.is-offset-6-fullhd { + margin-left: 50%; } + html.theme--documenter-dark .column.is-7-fullhd { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .column.is-offset-7-fullhd { + margin-left: 58.3333333333%; } + html.theme--documenter-dark .column.is-8-fullhd { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .column.is-offset-8-fullhd { + margin-left: 66.6666666667%; } + html.theme--documenter-dark .column.is-9-fullhd { + flex: none; + width: 75%; } + html.theme--documenter-dark .column.is-offset-9-fullhd { + margin-left: 75%; } + html.theme--documenter-dark .column.is-10-fullhd { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .column.is-offset-10-fullhd { + margin-left: 83.3333333333%; } + html.theme--documenter-dark .column.is-11-fullhd { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .column.is-offset-11-fullhd { + margin-left: 91.6666666667%; } + html.theme--documenter-dark .column.is-12-fullhd { + flex: none; + width: 100%; } + html.theme--documenter-dark .column.is-offset-12-fullhd { + margin-left: 100%; } } + html.theme--documenter-dark .columns { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + html.theme--documenter-dark .columns:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .columns:not(:last-child) { + margin-bottom: calc(1.5rem - 0.75rem); } + html.theme--documenter-dark .columns.is-centered { + justify-content: center; } + html.theme--documenter-dark .columns.is-gapless { + margin-left: 0; + margin-right: 0; + margin-top: 0; } + html.theme--documenter-dark .columns.is-gapless > .column { + margin: 0; + padding: 0 !important; } + html.theme--documenter-dark .columns.is-gapless:not(:last-child) { + margin-bottom: 1.5rem; } + html.theme--documenter-dark .columns.is-gapless:last-child { + margin-bottom: 0; } + html.theme--documenter-dark .columns.is-mobile { + display: flex; } + html.theme--documenter-dark .columns.is-multiline { + flex-wrap: wrap; } + html.theme--documenter-dark .columns.is-vcentered { + align-items: center; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns:not(.is-desktop) { + display: flex; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-desktop { + display: flex; } } + html.theme--documenter-dark .columns.is-variable { + --columnGap: 0.75rem; + margin-left: calc(-1 * var(--columnGap)); + margin-right: calc(-1 * var(--columnGap)); } + html.theme--documenter-dark .columns.is-variable .column { + padding-left: var(--columnGap); + padding-right: var(--columnGap); } + html.theme--documenter-dark .columns.is-variable.is-0 { + --columnGap: 0rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-0-mobile { + --columnGap: 0rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-0-tablet { + --columnGap: 0rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-0-tablet-only { + --columnGap: 0rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-0-touch { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-0-desktop { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-0-desktop-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-0-widescreen { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-0-widescreen-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-0-fullhd { + --columnGap: 0rem; } } + html.theme--documenter-dark .columns.is-variable.is-1 { + --columnGap: 0.25rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-1-mobile { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-1-tablet { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-1-tablet-only { + --columnGap: 0.25rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-1-touch { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-1-desktop { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-1-desktop-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-1-widescreen { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-1-widescreen-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-1-fullhd { + --columnGap: 0.25rem; } } + html.theme--documenter-dark .columns.is-variable.is-2 { + --columnGap: 0.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-2-mobile { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-2-tablet { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-2-tablet-only { + --columnGap: 0.5rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-2-touch { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-2-desktop { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-2-desktop-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-2-widescreen { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-2-widescreen-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-2-fullhd { + --columnGap: 0.5rem; } } + html.theme--documenter-dark .columns.is-variable.is-3 { + --columnGap: 0.75rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-3-mobile { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-3-tablet { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-3-tablet-only { + --columnGap: 0.75rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-3-touch { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-3-desktop { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-3-desktop-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-3-widescreen { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-3-widescreen-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-3-fullhd { + --columnGap: 0.75rem; } } + html.theme--documenter-dark .columns.is-variable.is-4 { + --columnGap: 1rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-4-mobile { + --columnGap: 1rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-4-tablet { + --columnGap: 1rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-4-tablet-only { + --columnGap: 1rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-4-touch { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-4-desktop { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-4-desktop-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-4-widescreen { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-4-widescreen-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-4-fullhd { + --columnGap: 1rem; } } + html.theme--documenter-dark .columns.is-variable.is-5 { + --columnGap: 1.25rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-5-mobile { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-5-tablet { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-5-tablet-only { + --columnGap: 1.25rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-5-touch { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-5-desktop { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-5-desktop-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-5-widescreen { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-5-widescreen-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-5-fullhd { + --columnGap: 1.25rem; } } + html.theme--documenter-dark .columns.is-variable.is-6 { + --columnGap: 1.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-6-mobile { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-6-tablet { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-6-tablet-only { + --columnGap: 1.5rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-6-touch { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-6-desktop { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-6-desktop-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-6-widescreen { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-6-widescreen-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-6-fullhd { + --columnGap: 1.5rem; } } + html.theme--documenter-dark .columns.is-variable.is-7 { + --columnGap: 1.75rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-7-mobile { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-7-tablet { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-7-tablet-only { + --columnGap: 1.75rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-7-touch { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-7-desktop { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-7-desktop-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-7-widescreen { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-7-fullhd { + --columnGap: 1.75rem; } } + html.theme--documenter-dark .columns.is-variable.is-8 { + --columnGap: 2rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .columns.is-variable.is-8-mobile { + --columnGap: 2rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .columns.is-variable.is-8-tablet { + --columnGap: 2rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-8-tablet-only { + --columnGap: 2rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .columns.is-variable.is-8-touch { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .columns.is-variable.is-8-desktop { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + html.theme--documenter-dark .columns.is-variable.is-8-desktop-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) { + html.theme--documenter-dark .columns.is-variable.is-8-widescreen { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + html.theme--documenter-dark .columns.is-variable.is-8-widescreen-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1408px) { + html.theme--documenter-dark .columns.is-variable.is-8-fullhd { + --columnGap: 2rem; } } + html.theme--documenter-dark .tile { + align-items: stretch; + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + min-height: min-content; } + html.theme--documenter-dark .tile.is-ancestor { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + html.theme--documenter-dark .tile.is-ancestor:last-child { + margin-bottom: -0.75rem; } + html.theme--documenter-dark .tile.is-ancestor:not(:last-child) { + margin-bottom: 0.75rem; } + html.theme--documenter-dark .tile.is-child { + margin: 0 !important; } + html.theme--documenter-dark .tile.is-parent { + padding: 0.75rem; } + html.theme--documenter-dark .tile.is-vertical { + flex-direction: column; } + html.theme--documenter-dark .tile.is-vertical > .tile.is-child:not(:last-child) { + margin-bottom: 1.5rem !important; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .tile:not(.is-child) { + display: flex; } + html.theme--documenter-dark .tile.is-1 { + flex: none; + width: 8.3333333333%; } + html.theme--documenter-dark .tile.is-2 { + flex: none; + width: 16.6666666667%; } + html.theme--documenter-dark .tile.is-3 { + flex: none; + width: 25%; } + html.theme--documenter-dark .tile.is-4 { + flex: none; + width: 33.3333333333%; } + html.theme--documenter-dark .tile.is-5 { + flex: none; + width: 41.6666666667%; } + html.theme--documenter-dark .tile.is-6 { + flex: none; + width: 50%; } + html.theme--documenter-dark .tile.is-7 { + flex: none; + width: 58.3333333333%; } + html.theme--documenter-dark .tile.is-8 { + flex: none; + width: 66.6666666667%; } + html.theme--documenter-dark .tile.is-9 { + flex: none; + width: 75%; } + html.theme--documenter-dark .tile.is-10 { + flex: none; + width: 83.3333333333%; } + html.theme--documenter-dark .tile.is-11 { + flex: none; + width: 91.6666666667%; } + html.theme--documenter-dark .tile.is-12 { + flex: none; + width: 100%; } } + html.theme--documenter-dark .hero { + align-items: stretch; + display: flex; + flex-direction: column; + justify-content: space-between; } + html.theme--documenter-dark .hero .navbar { + background: none; } + html.theme--documenter-dark .hero .tabs ul { + border-bottom: none; } + html.theme--documenter-dark .hero.is-white { + background-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-white strong { + color: inherit; } + html.theme--documenter-dark .hero.is-white .title { + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .subtitle { + color: rgba(10, 10, 10, 0.9); } + html.theme--documenter-dark .hero.is-white .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-white .subtitle strong { + color: #0a0a0a; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-white .navbar-menu { + background-color: white; } } + html.theme--documenter-dark .hero.is-white .navbar-item, + html.theme--documenter-dark .hero.is-white .navbar-link { + color: rgba(10, 10, 10, 0.7); } + html.theme--documenter-dark .hero.is-white a.navbar-item:hover, html.theme--documenter-dark .hero.is-white a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-white .navbar-link:hover, + html.theme--documenter-dark .hero.is-white .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .tabs a { + color: #0a0a0a; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-white .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-white .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a { + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a:hover { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .hero.is-white.is-bold { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-white.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } + html.theme--documenter-dark .hero.is-black { + background-color: #0a0a0a; + color: white; } + html.theme--documenter-dark .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-black strong { + color: inherit; } + html.theme--documenter-dark .hero.is-black .title { + color: white; } + html.theme--documenter-dark .hero.is-black .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-black .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-black .subtitle strong { + color: white; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-black .navbar-menu { + background-color: #0a0a0a; } } + html.theme--documenter-dark .hero.is-black .navbar-item, + html.theme--documenter-dark .hero.is-black .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-black a.navbar-item:hover, html.theme--documenter-dark .hero.is-black a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-black .navbar-link:hover, + html.theme--documenter-dark .hero.is-black .navbar-link.is-active { + background-color: black; + color: white; } + html.theme--documenter-dark .hero.is-black .tabs a { + color: white; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-black .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-black .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a { + color: white; } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a:hover { + background-color: white; + border-color: white; + color: #0a0a0a; } + html.theme--documenter-dark .hero.is-black.is-bold { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-black.is-bold .navbar-menu { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } + html.theme--documenter-dark .hero.is-light { + background-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-light strong { + color: inherit; } + html.theme--documenter-dark .hero.is-light .title { + color: #363636; } + html.theme--documenter-dark .hero.is-light .subtitle { + color: rgba(54, 54, 54, 0.9); } + html.theme--documenter-dark .hero.is-light .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-light .subtitle strong { + color: #363636; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-light .navbar-menu { + background-color: whitesmoke; } } + html.theme--documenter-dark .hero.is-light .navbar-item, + html.theme--documenter-dark .hero.is-light .navbar-link { + color: rgba(54, 54, 54, 0.7); } + html.theme--documenter-dark .hero.is-light a.navbar-item:hover, html.theme--documenter-dark .hero.is-light a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-light .navbar-link:hover, + html.theme--documenter-dark .hero.is-light .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + html.theme--documenter-dark .hero.is-light .tabs a { + color: #363636; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-light .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-light .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a { + color: #363636; } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a:hover { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-light.is-bold { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-light.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } } + html.theme--documenter-dark .hero.is-dark, html.theme--documenter-dark .content kbd.hero { + background-color: #363636; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-dark strong, + html.theme--documenter-dark .content kbd.hero strong { + color: inherit; } + html.theme--documenter-dark .hero.is-dark .title, html.theme--documenter-dark .content kbd.hero .title { + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .subtitle, html.theme--documenter-dark .content kbd.hero .subtitle { + color: rgba(245, 245, 245, 0.9); } + html.theme--documenter-dark .hero.is-dark .subtitle a:not(.button), html.theme--documenter-dark .content kbd.hero .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-dark .subtitle strong, + html.theme--documenter-dark .content kbd.hero .subtitle strong { + color: whitesmoke; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-dark .navbar-menu, html.theme--documenter-dark .content kbd.hero .navbar-menu { + background-color: #363636; } } + html.theme--documenter-dark .hero.is-dark .navbar-item, html.theme--documenter-dark .content kbd.hero .navbar-item, + html.theme--documenter-dark .hero.is-dark .navbar-link, + html.theme--documenter-dark .content kbd.hero .navbar-link { + color: rgba(245, 245, 245, 0.7); } + html.theme--documenter-dark .hero.is-dark a.navbar-item:hover, html.theme--documenter-dark .content kbd.hero a.navbar-item:hover, html.theme--documenter-dark .hero.is-dark a.navbar-item.is-active, html.theme--documenter-dark .content kbd.hero a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-dark .navbar-link:hover, + html.theme--documenter-dark .content kbd.hero .navbar-link:hover, + html.theme--documenter-dark .hero.is-dark .navbar-link.is-active, + html.theme--documenter-dark .content kbd.hero .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .tabs a, html.theme--documenter-dark .content kbd.hero .tabs a { + color: whitesmoke; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-dark .tabs a:hover, html.theme--documenter-dark .content kbd.hero .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-dark .tabs li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a { + color: whitesmoke; } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a:hover { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + html.theme--documenter-dark .hero.is-dark.is-bold, html.theme--documenter-dark .content kbd.hero.is-bold { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-dark.is-bold .navbar-menu, html.theme--documenter-dark .content kbd.hero.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } } + html.theme--documenter-dark .hero.is-primary, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + html.theme--documenter-dark .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-primary strong, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink strong { + color: inherit; } + html.theme--documenter-dark .hero.is-primary .title, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .title { + color: #fff; } + html.theme--documenter-dark .hero.is-primary .subtitle, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-primary .subtitle a:not(.button), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-primary .subtitle strong, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-primary .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-menu { + background-color: #4eb5de; } } + html.theme--documenter-dark .hero.is-primary .navbar-item, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-item, + html.theme--documenter-dark .hero.is-primary .navbar-link, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-primary a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, html.theme--documenter-dark .hero.is-primary a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-primary .navbar-link:hover, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, + html.theme--documenter-dark .hero.is-primary .navbar-link.is-active, + html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + html.theme--documenter-dark .hero.is-primary .tabs a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-primary .tabs a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-primary .tabs li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #4eb5de; } + html.theme--documenter-dark .hero.is-primary.is-bold, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-primary.is-bold .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } } + html.theme--documenter-dark .hero.is-link { + background-color: #2ad7e6; + color: #fff; } + html.theme--documenter-dark .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-link strong { + color: inherit; } + html.theme--documenter-dark .hero.is-link .title { + color: #fff; } + html.theme--documenter-dark .hero.is-link .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-link .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-link .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-link .navbar-menu { + background-color: #2ad7e6; } } + html.theme--documenter-dark .hero.is-link .navbar-item, + html.theme--documenter-dark .hero.is-link .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-link a.navbar-item:hover, html.theme--documenter-dark .hero.is-link a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-link .navbar-link:hover, + html.theme--documenter-dark .hero.is-link .navbar-link.is-active { + background-color: #1acddc; + color: #fff; } + html.theme--documenter-dark .hero.is-link .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-link .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-link .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #2ad7e6; } + html.theme--documenter-dark .hero.is-link.is-bold { + background-image: linear-gradient(141deg, #0cd0bf 0%, #2ad7e6 71%, #3bc2ee 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-link.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #0cd0bf 0%, #2ad7e6 71%, #3bc2ee 100%); } } + html.theme--documenter-dark .hero.is-info { + background-color: #3489da; + color: #fff; } + html.theme--documenter-dark .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-info strong { + color: inherit; } + html.theme--documenter-dark .hero.is-info .title { + color: #fff; } + html.theme--documenter-dark .hero.is-info .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-info .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-info .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-info .navbar-menu { + background-color: #3489da; } } + html.theme--documenter-dark .hero.is-info .navbar-item, + html.theme--documenter-dark .hero.is-info .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-info a.navbar-item:hover, html.theme--documenter-dark .hero.is-info a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-info .navbar-link:hover, + html.theme--documenter-dark .hero.is-info .navbar-link.is-active { + background-color: #267ccf; + color: #fff; } + html.theme--documenter-dark .hero.is-info .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-info .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-info .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #3489da; } + html.theme--documenter-dark .hero.is-info.is-bold { + background-image: linear-gradient(141deg, #178cc4 0%, #3489da 71%, #447be3 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-info.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #178cc4 0%, #3489da 71%, #447be3 100%); } } + html.theme--documenter-dark .hero.is-success { + background-color: #259a12; + color: #fff; } + html.theme--documenter-dark .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-success strong { + color: inherit; } + html.theme--documenter-dark .hero.is-success .title { + color: #fff; } + html.theme--documenter-dark .hero.is-success .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-success .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-success .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-success .navbar-menu { + background-color: #259a12; } } + html.theme--documenter-dark .hero.is-success .navbar-item, + html.theme--documenter-dark .hero.is-success .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-success a.navbar-item:hover, html.theme--documenter-dark .hero.is-success a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-success .navbar-link:hover, + html.theme--documenter-dark .hero.is-success .navbar-link.is-active { + background-color: #20830f; + color: #fff; } + html.theme--documenter-dark .hero.is-success .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-success .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-success .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #259a12; } + html.theme--documenter-dark .hero.is-success.is-bold { + background-image: linear-gradient(141deg, #287207 0%, #259a12 71%, #10b614 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-success.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #287207 0%, #259a12 71%, #10b614 100%); } } + html.theme--documenter-dark .hero.is-warning { + background-color: #f4c72f; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-warning strong { + color: inherit; } + html.theme--documenter-dark .hero.is-warning .title { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .subtitle { + color: rgba(0, 0, 0, 0.9); } + html.theme--documenter-dark .hero.is-warning .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-warning .subtitle strong { + color: rgba(0, 0, 0, 0.7); } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-warning .navbar-menu { + background-color: #f4c72f; } } + html.theme--documenter-dark .hero.is-warning .navbar-item, + html.theme--documenter-dark .hero.is-warning .navbar-link { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning a.navbar-item:hover, html.theme--documenter-dark .hero.is-warning a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-warning .navbar-link:hover, + html.theme--documenter-dark .hero.is-warning .navbar-link.is-active { + background-color: #f3c017; + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .tabs a { + color: rgba(0, 0, 0, 0.7); + opacity: 0.9; } + html.theme--documenter-dark .hero.is-warning .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-warning .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a { + color: rgba(0, 0, 0, 0.7); } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a:hover { + background-color: rgba(0, 0, 0, 0.7); + border-color: rgba(0, 0, 0, 0.7); + color: #f4c72f; } + html.theme--documenter-dark .hero.is-warning.is-bold { + background-image: linear-gradient(141deg, #f09100 0%, #f4c72f 71%, #faef42 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-warning.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #f09100 0%, #f4c72f 71%, #faef42 100%); } } + html.theme--documenter-dark .hero.is-danger { + background-color: #cb3c33; + color: #fff; } + html.theme--documenter-dark .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + html.theme--documenter-dark .hero.is-danger strong { + color: inherit; } + html.theme--documenter-dark .hero.is-danger .title { + color: #fff; } + html.theme--documenter-dark .hero.is-danger .subtitle { + color: rgba(255, 255, 255, 0.9); } + html.theme--documenter-dark .hero.is-danger .subtitle a:not(.button), + html.theme--documenter-dark .hero.is-danger .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark .hero.is-danger .navbar-menu { + background-color: #cb3c33; } } + html.theme--documenter-dark .hero.is-danger .navbar-item, + html.theme--documenter-dark .hero.is-danger .navbar-link { + color: rgba(255, 255, 255, 0.7); } + html.theme--documenter-dark .hero.is-danger a.navbar-item:hover, html.theme--documenter-dark .hero.is-danger a.navbar-item.is-active, + html.theme--documenter-dark .hero.is-danger .navbar-link:hover, + html.theme--documenter-dark .hero.is-danger .navbar-link.is-active { + background-color: #b7362e; + color: #fff; } + html.theme--documenter-dark .hero.is-danger .tabs a { + color: #fff; + opacity: 0.9; } + html.theme--documenter-dark .hero.is-danger .tabs a:hover { + opacity: 1; } + html.theme--documenter-dark .hero.is-danger .tabs li.is-active a { + opacity: 1; } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a { + color: #fff; } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #cb3c33; } + html.theme--documenter-dark .hero.is-danger.is-bold { + background-image: linear-gradient(141deg, #ac1f2e 0%, #cb3c33 71%, #d66341 100%); } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero.is-danger.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #ac1f2e 0%, #cb3c33 71%, #d66341 100%); } } + html.theme--documenter-dark .hero.is-small .hero-body, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.hero .hero-body { + padding-bottom: 1.5rem; + padding-top: 1.5rem; } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero.is-medium .hero-body { + padding-bottom: 9rem; + padding-top: 9rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero.is-large .hero-body { + padding-bottom: 18rem; + padding-top: 18rem; } } + html.theme--documenter-dark .hero.is-halfheight .hero-body, html.theme--documenter-dark .hero.is-fullheight .hero-body, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body { + align-items: center; + display: flex; } + html.theme--documenter-dark .hero.is-halfheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body > .container { + flex-grow: 1; + flex-shrink: 1; } + html.theme--documenter-dark .hero.is-halfheight { + min-height: 50vh; } + html.theme--documenter-dark .hero.is-fullheight { + min-height: 100vh; } + html.theme--documenter-dark .hero-video { + overflow: hidden; } + html.theme--documenter-dark .hero-video video { + left: 50%; + min-height: 100%; + min-width: 100%; + position: absolute; + top: 50%; + transform: translate3d(-50%, -50%, 0); } + html.theme--documenter-dark .hero-video.is-transparent { + opacity: 0.3; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero-video { + display: none; } } + html.theme--documenter-dark .hero-buttons { + margin-top: 1.5rem; } + @media screen and (max-width: 768px) { + html.theme--documenter-dark .hero-buttons .button { + display: flex; } + html.theme--documenter-dark .hero-buttons .button:not(:last-child) { + margin-bottom: 0.75rem; } } + @media screen and (min-width: 769px), print { + html.theme--documenter-dark .hero-buttons { + display: flex; + justify-content: center; } + html.theme--documenter-dark .hero-buttons .button:not(:last-child) { + margin-right: 1.5rem; } } + html.theme--documenter-dark .hero-head, + html.theme--documenter-dark .hero-foot { + flex-grow: 0; + flex-shrink: 0; } + html.theme--documenter-dark .hero-body { + flex-grow: 1; + flex-shrink: 0; + padding: 3rem 1.5rem; } + html.theme--documenter-dark .section { + padding: 3rem 1.5rem; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark .section.is-medium { + padding: 9rem 1.5rem; } + html.theme--documenter-dark .section.is-large { + padding: 18rem 1.5rem; } } + html.theme--documenter-dark .footer { + background-color: #fafafa; + padding: 3rem 1.5rem 6rem; } + html.theme--documenter-dark h1 .docs-heading-anchor, html.theme--documenter-dark h1 .docs-heading-anchor:hover, html.theme--documenter-dark h1 .docs-heading-anchor:visited, html.theme--documenter-dark h2 .docs-heading-anchor, html.theme--documenter-dark h2 .docs-heading-anchor:hover, html.theme--documenter-dark h2 .docs-heading-anchor:visited, html.theme--documenter-dark h3 .docs-heading-anchor, html.theme--documenter-dark h3 .docs-heading-anchor:hover, html.theme--documenter-dark h3 .docs-heading-anchor:visited, html.theme--documenter-dark h4 .docs-heading-anchor, html.theme--documenter-dark h4 .docs-heading-anchor:hover, html.theme--documenter-dark h4 .docs-heading-anchor:visited, html.theme--documenter-dark h5 .docs-heading-anchor, html.theme--documenter-dark h5 .docs-heading-anchor:hover, html.theme--documenter-dark h5 .docs-heading-anchor:visited, html.theme--documenter-dark h6 .docs-heading-anchor, html.theme--documenter-dark h6 .docs-heading-anchor:hover, html.theme--documenter-dark h6 .docs-heading-anchor:visited { + color: #cdc3e3; } + html.theme--documenter-dark h1 .docs-heading-anchor-permalink, html.theme--documenter-dark h2 .docs-heading-anchor-permalink, html.theme--documenter-dark h3 .docs-heading-anchor-permalink, html.theme--documenter-dark h4 .docs-heading-anchor-permalink, html.theme--documenter-dark h5 .docs-heading-anchor-permalink, html.theme--documenter-dark h6 .docs-heading-anchor-permalink { + visibility: hidden; + vertical-align: middle; + margin-left: 0.5em; + font-size: 0.7rem; } + html.theme--documenter-dark h1 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h2 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h3 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h4 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h5 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h6 .docs-heading-anchor-permalink::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f0c1"; } + html.theme--documenter-dark h1:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h2:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h3:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h4:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h5:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h6:hover .docs-heading-anchor-permalink { + visibility: visible; } + html.theme--documenter-dark .docs-light-only { + display: none !important; } + html.theme--documenter-dark pre { + position: relative; + overflow: hidden; } + html.theme--documenter-dark pre code, html.theme--documenter-dark pre code.hljs { + padding: 0 0.75rem !important; + overflow: auto; + display: block; } + html.theme--documenter-dark pre code:first-of-type, html.theme--documenter-dark pre code.hljs:first-of-type { + padding-top: 0.5rem !important; } + html.theme--documenter-dark pre code:last-of-type, html.theme--documenter-dark pre code.hljs:last-of-type { + padding-bottom: 0.5rem !important; } + html.theme--documenter-dark pre .copy-button { + opacity: 0.2; + transition: opacity 0.2s; + position: absolute; + right: 0em; + top: 0em; + padding: 0.5em; + width: 2.5em; + height: 2.5em; + background: transparent; + border: none; + font-family: "Font Awesome 5 Free"; + color: #fbfbfb; + cursor: pointer; + text-align: center; } + html.theme--documenter-dark pre .copy-button:focus, html.theme--documenter-dark pre .copy-button:hover { + opacity: 1; + background: rgba(251, 251, 251, 0.1); + color: #2ad7e6; } + html.theme--documenter-dark pre .copy-button.success { + color: #259a12; + opacity: 1; } + html.theme--documenter-dark pre .copy-button.error { + color: #cb3c33; + opacity: 1; } + html.theme--documenter-dark pre:hover .copy-button { + opacity: 1; } + html.theme--documenter-dark .admonition { + background-color: #28282b; + border-style: solid; + border-width: 1px; + border-color: #ba3f1f; + border-radius: 4px; + font-size: 1rem; } + html.theme--documenter-dark .admonition strong { + color: currentColor; } + html.theme--documenter-dark .admonition.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.admonition { + font-size: 0.75rem; } + html.theme--documenter-dark .admonition.is-medium { + font-size: 1.25rem; } + html.theme--documenter-dark .admonition.is-large { + font-size: 1.5rem; } + html.theme--documenter-dark .admonition.is-default { + background-color: #28282b; + border-color: #ba3f1f; } + html.theme--documenter-dark .admonition.is-default > .admonition-header { + background-color: #ba3f1f; } + html.theme--documenter-dark .admonition.is-info { + background-color: #28282b; + border-color: #28c; } + html.theme--documenter-dark .admonition.is-info > .admonition-header { + background-color: #28c; } + html.theme--documenter-dark .admonition.is-success { + background-color: #28282b; + border-color: #42ac68; } + html.theme--documenter-dark .admonition.is-success > .admonition-header { + background-color: #42ac68; } + html.theme--documenter-dark .admonition.is-warning { + background-color: #28282b; + border-color: #a88b17; } + html.theme--documenter-dark .admonition.is-warning > .admonition-header { + background-color: #a88b17; } + html.theme--documenter-dark .admonition.is-danger { + background-color: #28282b; + border-color: #c7524c; } + html.theme--documenter-dark .admonition.is-danger > .admonition-header { + background-color: #c7524c; } + html.theme--documenter-dark .admonition.is-compat { + background-color: #28282b; + border-color: #00a1b7; } + html.theme--documenter-dark .admonition.is-compat > .admonition-header { + background-color: #00a1b7; } + html.theme--documenter-dark .admonition-header { + background-color: #ba3f1f; + align-items: center; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.5rem 0.75rem; + position: relative; } + html.theme--documenter-dark .admonition-header:before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + margin-right: 0.75rem; + content: "\f06a"; } + html.theme--documenter-dark .admonition-body { + color: #fbfbfb; + padding: 0.5rem 0.75rem; } + html.theme--documenter-dark .admonition-body pre { + background-color: #312550; } + html.theme--documenter-dark .admonition-body code { + background-color: #312550; } + html.theme--documenter-dark .docstring { + margin-bottom: 1em; + background-color: transparent; + border: 1px solid #dbdbdb; + box-shadow: 3px 3px 4px #444444; + max-width: 100%; } + html.theme--documenter-dark .docstring > header { + display: flex; + flex-grow: 1; + align-items: stretch; + padding: 0.5rem 0.75rem; + background-color: #28282b; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + box-shadow: none; + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .docstring > header code { + background-color: transparent; } + html.theme--documenter-dark .docstring > header .docstring-binding { + margin-right: 0.3em; } + html.theme--documenter-dark .docstring > header .docstring-category { + margin-left: 0.3em; } + html.theme--documenter-dark .docstring > section { + position: relative; + padding: 0.75rem 0.75rem; + border-bottom: 1px solid #dbdbdb; } + html.theme--documenter-dark .docstring > section:last-child { + border-bottom: none; } + html.theme--documenter-dark .docstring > section > a.docs-sourcelink { + transition: opacity 0.3s; + opacity: 0; + position: absolute; + right: 0.375rem; + bottom: 0.375rem; } + html.theme--documenter-dark .docstring > section > a.docs-sourcelink:focus { + opacity: 1 !important; } + html.theme--documenter-dark .docstring:hover > section > a.docs-sourcelink { + opacity: 0.2; } + html.theme--documenter-dark .docstring:focus-within > section > a.docs-sourcelink { + opacity: 0.2; } + html.theme--documenter-dark .docstring > section:hover a.docs-sourcelink { + opacity: 1; } + html.theme--documenter-dark .documenter-example-output { + background-color: #1e1e20; } + html.theme--documenter-dark .outdated-warning-overlay { + position: fixed; + top: 0; + left: 0; + right: 0; + box-shadow: 0 0 10px rgba(0, 0, 0, 0.3); + z-index: 999; + background-color: #28282b; + border-bottom: 3px solid #c7524c; + padding: 10px 35px; + text-align: center; + font-size: 15px; } + html.theme--documenter-dark .outdated-warning-overlay .outdated-warning-closer { + position: absolute; + top: calc(50% - 10px); + right: 18px; + cursor: pointer; + width: 12px; } + html.theme--documenter-dark .outdated-warning-overlay a { + color: #2ad7e6; } + html.theme--documenter-dark .outdated-warning-overlay a:hover { + color: #97ebf3; } + html.theme--documenter-dark .content pre { + border: 1px solid #dbdbdb; } + html.theme--documenter-dark .content code { + font-weight: inherit; } + html.theme--documenter-dark .content a code { + color: #2ad7e6; } + html.theme--documenter-dark .content h1 code, html.theme--documenter-dark .content h2 code, html.theme--documenter-dark .content h3 code, html.theme--documenter-dark .content h4 code, html.theme--documenter-dark .content h5 code, html.theme--documenter-dark .content h6 code { + color: #cdc3e3; } + html.theme--documenter-dark .content table { + display: block; + width: initial; + max-width: 100%; + overflow-x: auto; } + html.theme--documenter-dark .content blockquote > ul:first-child, html.theme--documenter-dark .content blockquote > ol:first-child, html.theme--documenter-dark .content .admonition-body > ul:first-child, html.theme--documenter-dark .content .admonition-body > ol:first-child { + margin-top: 0; } + html.theme--documenter-dark pre, html.theme--documenter-dark code { + font-variant-ligatures: no-contextual; } + html.theme--documenter-dark .breadcrumb a.is-disabled { + cursor: default; + pointer-events: none; } + html.theme--documenter-dark .breadcrumb a.is-disabled, html.theme--documenter-dark .breadcrumb a.is-disabled:hover { + color: #cdc3e3; } + html.theme--documenter-dark .hljs { + background: initial !important; } + html.theme--documenter-dark .katex .katex-mathml { + top: 0; + right: 0; } + html.theme--documenter-dark .katex-display, html.theme--documenter-dark mjx-container, html.theme--documenter-dark .MathJax_Display { + margin: 0.5em 0 !important; } + html.theme--documenter-dark html { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; } + html.theme--documenter-dark li.no-marker { + list-style: none; } + html.theme--documenter-dark #documenter .docs-main > article { + overflow-wrap: break-word; } + html.theme--documenter-dark #documenter .docs-main > article .math-container { + overflow-x: auto; + overflow-y: hidden; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-main { + max-width: 52rem; + margin-left: 20rem; + padding-right: 1rem; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main { + width: 100%; } + html.theme--documenter-dark #documenter .docs-main > article { + max-width: 52rem; + margin-left: auto; + margin-right: auto; + margin-bottom: 1rem; + padding: 0 1rem; } + html.theme--documenter-dark #documenter .docs-main > header, html.theme--documenter-dark #documenter .docs-main > nav { + max-width: 100%; + width: 100%; + margin: 0; } } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar { + background-color: #1e1e20; + border-bottom: 1px solid #dbdbdb; + z-index: 2; + min-height: 4rem; + margin-bottom: 1rem; + display: flex; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .breadcrumb { + flex-grow: 1; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right { + display: flex; + white-space: nowrap; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-icon, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + display: inline-block; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label { + padding: 0; + margin-left: 0.3em; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button { + margin: auto 0 auto 1rem; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + font-size: 1.5rem; + margin: auto 0 auto 1rem; } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar > * { + margin: auto 0; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main header.docs-navbar { + position: sticky; + top: 0; + padding: 0 1rem; + /* For Headroom.js */ + transition-property: top, box-shadow; + -webkit-transition-property: top, box-shadow; + /* Safari */ + transition-duration: 0.3s; + -webkit-transition-duration: 0.3s; + /* Safari */ } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--not-top { + box-shadow: 0.2rem 0rem 0.4rem #bbb; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } + html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { + top: -4.5rem; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } } + html.theme--documenter-dark #documenter .docs-main section.footnotes { + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-main section.footnotes li .tag:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .content kbd:first-child, html.theme--documenter-dark .content #documenter .docs-main section.footnotes li kbd:first-child { + margin-right: 1em; + margin-bottom: 0.4em; } + html.theme--documenter-dark #documenter .docs-main .docs-footer { + display: flex; + flex-wrap: wrap; + margin-left: 0; + margin-right: 0; + border-top: 1px solid #dbdbdb; + padding-top: 1rem; + padding-bottom: 1rem; } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-main .docs-footer { + padding-left: 1rem; + padding-right: 1rem; } } + html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage, html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-prevpage { + flex-grow: 1; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage { + text-align: right; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .flexbox-break { + flex-basis: 100%; + height: 0; } + html.theme--documenter-dark #documenter .docs-main .docs-footer .footer-message { + font-size: 0.8em; + margin: 0.5em auto 0 auto; + text-align: center; } + html.theme--documenter-dark #documenter .docs-sidebar { + display: flex; + flex-direction: column; + color: #fbfbfb; + background-color: #503c82; + border-right: 1px solid #dbdbdb; + padding: 0; + flex: 0 0 18rem; + z-index: 5; + font-size: 1rem; + position: fixed; + left: -18rem; + width: 18rem; + height: 100%; + transition: left 0.3s; + /* Setting up a nicer theme style for the scrollbar */ } + html.theme--documenter-dark #documenter .docs-sidebar.visible { + left: 0; + box-shadow: 0.4rem 0rem 0.8rem #bbb; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar.visible { + box-shadow: none; } } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar { + left: 0; + top: 0; } } + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo { + margin-top: 1rem; + padding: 0 1rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { + max-height: 6rem; + margin: auto; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name { + flex-shrink: 0; + font-size: 1.5rem; + font-weight: 700; + text-align: center; + white-space: nowrap; + overflow: hidden; + padding: 0.5rem 0; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name .docs-autofit { + max-width: 16.2rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a, html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a:hover { + color: #fbfbfb; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector { + border-top: 1px solid #dbdbdb; + display: none; + padding: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector.visible { + display: flex; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { + flex-grow: 1; + user-select: none; + border-top: 1px solid #dbdbdb; + padding-bottom: 1.5rem; + /* Managing collapsible submenus */ } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li > .tocitem { + font-weight: bold; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li li { + font-size: 0.95rem; + margin-left: 1em; + border-left: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input.collapse-toggle { + display: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.collapsed { + display: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed { + display: block; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem { + display: flex; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label { + flex-grow: 2; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron { + display: inline-block; + font-style: normal; + font-variant: normal; + text-rendering: auto; + line-height: 1; + font-size: 0.75rem; + margin-left: 1rem; + margin-top: auto; + margin-bottom: auto; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f054"; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before { + content: "\f078"; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem { + display: block; + padding: 0.5rem 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem:hover { + color: #fbfbfb; + background: #503c82; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem:hover { + color: #fbfbfb; + background-color: #3c2d60; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active { + border-top: 1px solid #dbdbdb; + border-bottom: 1px solid #dbdbdb; + background-color: #1e1e20; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover { + background-color: #1e1e20; + color: #fff; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover { + background-color: #3f2f66; + color: #fff; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child { + border-top: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal { + margin: 0 0.5rem 0.5rem; + border-top: 1px solid #dbdbdb; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal li { + font-size: 0.85rem; + border-left: none; + margin-left: 0; + margin-top: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem { + width: 100%; + padding: 0; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before { + content: "⚬"; + margin-right: 0.4em; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search { + margin: auto; + margin-top: 0.5rem; + margin-bottom: 0.5rem; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + width: 14.4rem; } + @media screen and (min-width: 1056px) { + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar { + width: .3rem; + background: none; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #3f2f66; } + html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover { + background: #2e224a; } } + @media screen and (max-width: 1055px) { + html.theme--documenter-dark #documenter .docs-sidebar { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar { + width: .3rem; + background: none; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #3f2f66; } + html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover { + background: #2e224a; } } + html.theme--documenter-dark #documenter .docs-main #documenter-search-info { + margin-bottom: 1rem; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results { + list-style-type: circle; + list-style-position: outside; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results li { + margin-left: 2rem; } + html.theme--documenter-dark #documenter .docs-main #documenter-search-results .docs-highlight { + background-color: yellow; } + html.theme--documenter-dark { + background-color: #1e1e20; + font-size: 16px; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + html.theme--documenter-dark #documenter .docs-sidebar { + border-right: none; + box-shadow: 0.24rem 0rem 0.4rem #444444; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { + color: #fff; + background-color: #3f2f66; + border-color: #2e224a; + margin-top: 1.0rem; + margin-bottom: 1.0rem; } + html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::placeholder { + color: #fff; } + html.theme--documenter-dark .hljs { + background: #2b2b2b; + color: #f8f8f2; } + html.theme--documenter-dark .hljs-comment, + html.theme--documenter-dark .hljs-quote { + color: #d4d0ab; } + html.theme--documenter-dark .hljs-variable, + html.theme--documenter-dark .hljs-template-variable, + html.theme--documenter-dark .hljs-tag, + html.theme--documenter-dark .hljs-name, + html.theme--documenter-dark .hljs-selector-id, + html.theme--documenter-dark .hljs-selector-class, + html.theme--documenter-dark .hljs-regexp, + html.theme--documenter-dark .hljs-deletion { + color: #ffa07a; } + html.theme--documenter-dark .hljs-number, + html.theme--documenter-dark .hljs-built_in, + html.theme--documenter-dark .hljs-literal, + html.theme--documenter-dark .hljs-type, + html.theme--documenter-dark .hljs-params, + html.theme--documenter-dark .hljs-meta, + html.theme--documenter-dark .hljs-link { + color: #f5ab35; } + html.theme--documenter-dark .hljs-attribute { + color: #ffd700; } + html.theme--documenter-dark .hljs-string, + html.theme--documenter-dark .hljs-symbol, + html.theme--documenter-dark .hljs-bullet, + html.theme--documenter-dark .hljs-addition { + color: #abe338; } + html.theme--documenter-dark .hljs-title, + html.theme--documenter-dark .hljs-section { + color: #00e0e0; } + html.theme--documenter-dark .hljs-keyword, + html.theme--documenter-dark .hljs-selector-tag { + color: #dcc6e0; } + html.theme--documenter-dark .hljs-emphasis { + font-style: italic; } + html.theme--documenter-dark .hljs-strong { + font-weight: bold; } + @media screen and (-ms-high-contrast: active) { + html.theme--documenter-dark .hljs-addition, + html.theme--documenter-dark .hljs-attribute, + html.theme--documenter-dark .hljs-built_in, + html.theme--documenter-dark .hljs-bullet, + html.theme--documenter-dark .hljs-comment, + html.theme--documenter-dark .hljs-link, + html.theme--documenter-dark .hljs-literal, + html.theme--documenter-dark .hljs-meta, + html.theme--documenter-dark .hljs-number, + html.theme--documenter-dark .hljs-params, + html.theme--documenter-dark .hljs-string, + html.theme--documenter-dark .hljs-symbol, + html.theme--documenter-dark .hljs-type, + html.theme--documenter-dark .hljs-quote { + color: highlight; } + html.theme--documenter-dark .hljs-keyword, + html.theme--documenter-dark .hljs-selector-tag { + font-weight: bold; } } + html.theme--documenter-dark .hljs-subst { + color: #f8f8f2; } diff --git a/previews/PR34/assets/themes/documenter-light.css b/previews/PR34/assets/themes/documenter-light.css new file mode 100644 index 00000000..e2c74638 --- /dev/null +++ b/previews/PR34/assets/themes/documenter-light.css @@ -0,0 +1,7750 @@ +@charset "UTF-8"; +/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */ +@keyframes spinAround { + from { + transform: rotate(0deg); } + to { + transform: rotate(359deg); } } + +.tabs, .pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis, .breadcrumb, .file, .button, .is-unselectable, .modal-close, .delete { + -webkit-touch-callout: none; + -webkit-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; } + +.navbar-link:not(.is-arrowless)::after, .select:not(.is-multiple):not(.is-loading)::after { + border: 3px solid transparent; + border-radius: 2px; + border-right: 0; + border-top: 0; + content: " "; + display: block; + height: 0.625em; + margin-top: -0.4375em; + pointer-events: none; + position: absolute; + top: 50%; + transform: rotate(-45deg); + transform-origin: center; + width: 0.625em; } + +.admonition:not(:last-child), .tabs:not(:last-child), .message:not(:last-child), .list:not(:last-child), .level:not(:last-child), .breadcrumb:not(:last-child), .highlight:not(:last-child), .block:not(:last-child), .title:not(:last-child), +.subtitle:not(:last-child), .table-container:not(:last-child), .table:not(:last-child), .progress:not(:last-child), .notification:not(:last-child), .content:not(:last-child), .box:not(:last-child) { + margin-bottom: 1.5rem; } + +.modal-close, .delete { + -moz-appearance: none; + -webkit-appearance: none; + background-color: rgba(10, 10, 10, 0.2); + border: none; + border-radius: 290486px; + cursor: pointer; + pointer-events: auto; + display: inline-block; + flex-grow: 0; + flex-shrink: 0; + font-size: 0; + height: 20px; + max-height: 20px; + max-width: 20px; + min-height: 20px; + min-width: 20px; + outline: none; + position: relative; + vertical-align: top; + width: 20px; } + .modal-close::before, .delete::before, .modal-close::after, .delete::after { + background-color: white; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + .modal-close::before, .delete::before { + height: 2px; + width: 50%; } + .modal-close::after, .delete::after { + height: 50%; + width: 2px; } + .modal-close:hover, .delete:hover, .modal-close:focus, .delete:focus { + background-color: rgba(10, 10, 10, 0.3); } + .modal-close:active, .delete:active { + background-color: rgba(10, 10, 10, 0.4); } + .is-small.modal-close, #documenter .docs-sidebar form.docs-search > input.modal-close, .is-small.delete, #documenter .docs-sidebar form.docs-search > input.delete { + height: 16px; + max-height: 16px; + max-width: 16px; + min-height: 16px; + min-width: 16px; + width: 16px; } + .is-medium.modal-close, .is-medium.delete { + height: 24px; + max-height: 24px; + max-width: 24px; + min-height: 24px; + min-width: 24px; + width: 24px; } + .is-large.modal-close, .is-large.delete { + height: 32px; + max-height: 32px; + max-width: 32px; + min-height: 32px; + min-width: 32px; + width: 32px; } + +.control.is-loading::after, .select.is-loading::after, .loader, .button.is-loading::after { + animation: spinAround 500ms infinite linear; + border: 2px solid #dbdbdb; + border-radius: 290486px; + border-right-color: transparent; + border-top-color: transparent; + content: ""; + display: block; + height: 1em; + position: relative; + width: 1em; } + +.hero-video, .modal-background, .modal, .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img, +.image.is-square .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img, +.image.is-1by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img, +.image.is-5by4 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img, +.image.is-4by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img, +.image.is-3by2 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img, +.image.is-5by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img, +.image.is-16by9 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img, +.image.is-2by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img, +.image.is-3by1 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img, +.image.is-4by5 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img, +.image.is-3by4 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img, +.image.is-2by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img, +.image.is-3by5 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img, +.image.is-9by16 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img, +.image.is-1by2 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img, +.image.is-1by3 .has-ratio, +#documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, .is-overlay { + bottom: 0; + left: 0; + position: absolute; + right: 0; + top: 0; } + +.pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis, .file-cta, +.file-name, .select select, .textarea, .input, #documenter .docs-sidebar form.docs-search > input, .button { + -moz-appearance: none; + -webkit-appearance: none; + align-items: center; + border: 1px solid transparent; + border-radius: 4px; + box-shadow: none; + display: inline-flex; + font-size: 1rem; + height: 2.25em; + justify-content: flex-start; + line-height: 1.5; + padding-bottom: calc(0.375em - 1px); + padding-left: calc(0.625em - 1px); + padding-right: calc(0.625em - 1px); + padding-top: calc(0.375em - 1px); + position: relative; + vertical-align: top; } + .pagination-previous:focus, + .pagination-next:focus, + .pagination-link:focus, + .pagination-ellipsis:focus, .file-cta:focus, + .file-name:focus, .select select:focus, .textarea:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .button:focus, .is-focused.pagination-previous, + .is-focused.pagination-next, + .is-focused.pagination-link, + .is-focused.pagination-ellipsis, .is-focused.file-cta, + .is-focused.file-name, .select select.is-focused, .is-focused.textarea, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-focused.button, .pagination-previous:active, + .pagination-next:active, + .pagination-link:active, + .pagination-ellipsis:active, .file-cta:active, + .file-name:active, .select select:active, .textarea:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .button:active, .is-active.pagination-previous, + .is-active.pagination-next, + .is-active.pagination-link, + .is-active.pagination-ellipsis, .is-active.file-cta, + .is-active.file-name, .select select.is-active, .is-active.textarea, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .is-active.button { + outline: none; } + .pagination-previous[disabled], + .pagination-next[disabled], + .pagination-link[disabled], + .pagination-ellipsis[disabled], .file-cta[disabled], + .file-name[disabled], .select select[disabled], .textarea[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], .button[disabled], fieldset[disabled] .pagination-previous, + fieldset[disabled] .pagination-next, + fieldset[disabled] .pagination-link, + fieldset[disabled] .pagination-ellipsis, fieldset[disabled] .file-cta, + fieldset[disabled] .file-name, fieldset[disabled] .select select, .select fieldset[disabled] select, fieldset[disabled] .textarea, fieldset[disabled] .input, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input, fieldset[disabled] .button { + cursor: not-allowed; } + +/*! minireset.css v0.0.4 | MIT License | github.com/jgthms/minireset.css */ +html, +body, +p, +ol, +ul, +li, +dl, +dt, +dd, +blockquote, +figure, +fieldset, +legend, +textarea, +pre, +iframe, +hr, +h1, +h2, +h3, +h4, +h5, +h6 { + margin: 0; + padding: 0; } + +h1, +h2, +h3, +h4, +h5, +h6 { + font-size: 100%; + font-weight: normal; } + +ul { + list-style: none; } + +button, +input, +select, +textarea { + margin: 0; } + +html { + box-sizing: border-box; } + +*, *::before, *::after { + box-sizing: inherit; } + +img, +embed, +iframe, +object, +video { + height: auto; + max-width: 100%; } + +audio { + max-width: 100%; } + +iframe { + border: 0; } + +table { + border-collapse: collapse; + border-spacing: 0; } + +td, +th { + padding: 0; } + td:not([align]), + th:not([align]) { + text-align: left; } + +html { + background-color: #fff; + font-size: 16px; + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + min-width: 300px; + overflow-x: auto; + overflow-y: scroll; + text-rendering: optimizeLegibility; + text-size-adjust: 100%; } + +article, +aside, +figure, +footer, +header, +hgroup, +section { + display: block; } + +body, +button, +input, +select, +textarea { + font-family: "Montserrat", sans-serif; } + +code, +pre { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; + font-family: "Source Code Pro", monospace; } + +body { + color: #202020; + font-size: 1em; + font-weight: 400; + line-height: 1.5; } + +a { + color: #149eaa; + cursor: pointer; + text-decoration: none; } + a strong { + color: currentColor; } + a:hover { + color: #107c85; } + +code { + background-color: #ebe8f4; + color: #000000; + font-size: 0.875em; + font-weight: normal; + padding: 0.1em; } + +hr { + background-color: whitesmoke; + border: none; + display: block; + height: 2px; + margin: 1.5rem 0; } + +img { + height: auto; + max-width: 100%; } + +input[type="checkbox"], +input[type="radio"] { + vertical-align: baseline; } + +small { + font-size: 0.875em; } + +span { + font-style: inherit; + font-weight: inherit; } + +strong { + color: #654ca3; + font-weight: 700; } + +fieldset { + border: none; } + +pre { + -webkit-overflow-scrolling: touch; + background-color: #ebe8f4; + color: #202020; + font-size: 0.875em; + overflow-x: auto; + padding: 1.25rem 1.5rem; + white-space: pre; + word-wrap: normal; } + pre code { + background-color: transparent; + color: currentColor; + font-size: 1em; + padding: 0; } + +table td, +table th { + vertical-align: top; } + table td:not([align]), + table th:not([align]) { + text-align: left; } + +table th { + color: #654ca3; } + +.is-clearfix::after { + clear: both; + content: " "; + display: table; } + +.is-pulled-left { + float: left !important; } + +.is-pulled-right { + float: right !important; } + +.is-clipped { + overflow: hidden !important; } + +.is-size-1 { + font-size: 3rem !important; } + +.is-size-2 { + font-size: 2.5rem !important; } + +.is-size-3 { + font-size: 2rem !important; } + +.is-size-4 { + font-size: 1.5rem !important; } + +.is-size-5 { + font-size: 1.25rem !important; } + +.is-size-6 { + font-size: 1rem !important; } + +.is-size-7, .docstring > section > a.docs-sourcelink { + font-size: 0.75rem !important; } + +@media screen and (max-width: 768px) { + .is-size-1-mobile { + font-size: 3rem !important; } + .is-size-2-mobile { + font-size: 2.5rem !important; } + .is-size-3-mobile { + font-size: 2rem !important; } + .is-size-4-mobile { + font-size: 1.5rem !important; } + .is-size-5-mobile { + font-size: 1.25rem !important; } + .is-size-6-mobile { + font-size: 1rem !important; } + .is-size-7-mobile { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 769px), print { + .is-size-1-tablet { + font-size: 3rem !important; } + .is-size-2-tablet { + font-size: 2.5rem !important; } + .is-size-3-tablet { + font-size: 2rem !important; } + .is-size-4-tablet { + font-size: 1.5rem !important; } + .is-size-5-tablet { + font-size: 1.25rem !important; } + .is-size-6-tablet { + font-size: 1rem !important; } + .is-size-7-tablet { + font-size: 0.75rem !important; } } + +@media screen and (max-width: 1055px) { + .is-size-1-touch { + font-size: 3rem !important; } + .is-size-2-touch { + font-size: 2.5rem !important; } + .is-size-3-touch { + font-size: 2rem !important; } + .is-size-4-touch { + font-size: 1.5rem !important; } + .is-size-5-touch { + font-size: 1.25rem !important; } + .is-size-6-touch { + font-size: 1rem !important; } + .is-size-7-touch { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1056px) { + .is-size-1-desktop { + font-size: 3rem !important; } + .is-size-2-desktop { + font-size: 2.5rem !important; } + .is-size-3-desktop { + font-size: 2rem !important; } + .is-size-4-desktop { + font-size: 1.5rem !important; } + .is-size-5-desktop { + font-size: 1.25rem !important; } + .is-size-6-desktop { + font-size: 1rem !important; } + .is-size-7-desktop { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1216px) { + .is-size-1-widescreen { + font-size: 3rem !important; } + .is-size-2-widescreen { + font-size: 2.5rem !important; } + .is-size-3-widescreen { + font-size: 2rem !important; } + .is-size-4-widescreen { + font-size: 1.5rem !important; } + .is-size-5-widescreen { + font-size: 1.25rem !important; } + .is-size-6-widescreen { + font-size: 1rem !important; } + .is-size-7-widescreen { + font-size: 0.75rem !important; } } + +@media screen and (min-width: 1408px) { + .is-size-1-fullhd { + font-size: 3rem !important; } + .is-size-2-fullhd { + font-size: 2.5rem !important; } + .is-size-3-fullhd { + font-size: 2rem !important; } + .is-size-4-fullhd { + font-size: 1.5rem !important; } + .is-size-5-fullhd { + font-size: 1.25rem !important; } + .is-size-6-fullhd { + font-size: 1rem !important; } + .is-size-7-fullhd { + font-size: 0.75rem !important; } } + +.has-text-centered { + text-align: center !important; } + +.has-text-justified { + text-align: justify !important; } + +.has-text-left { + text-align: left !important; } + +.has-text-right { + text-align: right !important; } + +@media screen and (max-width: 768px) { + .has-text-centered-mobile { + text-align: center !important; } } + +@media screen and (min-width: 769px), print { + .has-text-centered-tablet { + text-align: center !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-centered-tablet-only { + text-align: center !important; } } + +@media screen and (max-width: 1055px) { + .has-text-centered-touch { + text-align: center !important; } } + +@media screen and (min-width: 1056px) { + .has-text-centered-desktop { + text-align: center !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-centered-desktop-only { + text-align: center !important; } } + +@media screen and (min-width: 1216px) { + .has-text-centered-widescreen { + text-align: center !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-centered-widescreen-only { + text-align: center !important; } } + +@media screen and (min-width: 1408px) { + .has-text-centered-fullhd { + text-align: center !important; } } + +@media screen and (max-width: 768px) { + .has-text-justified-mobile { + text-align: justify !important; } } + +@media screen and (min-width: 769px), print { + .has-text-justified-tablet { + text-align: justify !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-justified-tablet-only { + text-align: justify !important; } } + +@media screen and (max-width: 1055px) { + .has-text-justified-touch { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) { + .has-text-justified-desktop { + text-align: justify !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-justified-desktop-only { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) { + .has-text-justified-widescreen { + text-align: justify !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-justified-widescreen-only { + text-align: justify !important; } } + +@media screen and (min-width: 1408px) { + .has-text-justified-fullhd { + text-align: justify !important; } } + +@media screen and (max-width: 768px) { + .has-text-left-mobile { + text-align: left !important; } } + +@media screen and (min-width: 769px), print { + .has-text-left-tablet { + text-align: left !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-left-tablet-only { + text-align: left !important; } } + +@media screen and (max-width: 1055px) { + .has-text-left-touch { + text-align: left !important; } } + +@media screen and (min-width: 1056px) { + .has-text-left-desktop { + text-align: left !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-left-desktop-only { + text-align: left !important; } } + +@media screen and (min-width: 1216px) { + .has-text-left-widescreen { + text-align: left !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-left-widescreen-only { + text-align: left !important; } } + +@media screen and (min-width: 1408px) { + .has-text-left-fullhd { + text-align: left !important; } } + +@media screen and (max-width: 768px) { + .has-text-right-mobile { + text-align: right !important; } } + +@media screen and (min-width: 769px), print { + .has-text-right-tablet { + text-align: right !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .has-text-right-tablet-only { + text-align: right !important; } } + +@media screen and (max-width: 1055px) { + .has-text-right-touch { + text-align: right !important; } } + +@media screen and (min-width: 1056px) { + .has-text-right-desktop { + text-align: right !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .has-text-right-desktop-only { + text-align: right !important; } } + +@media screen and (min-width: 1216px) { + .has-text-right-widescreen { + text-align: right !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .has-text-right-widescreen-only { + text-align: right !important; } } + +@media screen and (min-width: 1408px) { + .has-text-right-fullhd { + text-align: right !important; } } + +.is-capitalized { + text-transform: capitalize !important; } + +.is-lowercase { + text-transform: lowercase !important; } + +.is-uppercase { + text-transform: uppercase !important; } + +.is-italic { + font-style: italic !important; } + +.has-text-white { + color: white !important; } + +a.has-text-white:hover, a.has-text-white:focus { + color: #e6e6e6 !important; } + +.has-background-white { + background-color: white !important; } + +.has-text-black { + color: #0a0a0a !important; } + +a.has-text-black:hover, a.has-text-black:focus { + color: black !important; } + +.has-background-black { + background-color: #0a0a0a !important; } + +.has-text-light { + color: whitesmoke !important; } + +a.has-text-light:hover, a.has-text-light:focus { + color: #dbdbdb !important; } + +.has-background-light { + background-color: whitesmoke !important; } + +.has-text-dark { + color: #363636 !important; } + +a.has-text-dark:hover, a.has-text-dark:focus { + color: #1c1c1c !important; } + +.has-background-dark { + background-color: #363636 !important; } + +.has-text-primary { + color: #4eb5de !important; } + +a.has-text-primary:hover, a.has-text-primary:focus { + color: #27a1d2 !important; } + +.has-background-primary { + background-color: #4eb5de !important; } + +.has-text-link { + color: #149eaa !important; } + +a.has-text-link:hover, a.has-text-link:focus { + color: #0f747c !important; } + +.has-background-link { + background-color: #149eaa !important; } + +.has-text-info { + color: #209cee !important; } + +a.has-text-info:hover, a.has-text-info:focus { + color: #1081cb !important; } + +.has-background-info { + background-color: #209cee !important; } + +.has-text-success { + color: #22c35b !important; } + +a.has-text-success:hover, a.has-text-success:focus { + color: #1a9847 !important; } + +.has-background-success { + background-color: #22c35b !important; } + +.has-text-warning { + color: #ffdd57 !important; } + +a.has-text-warning:hover, a.has-text-warning:focus { + color: #ffd324 !important; } + +.has-background-warning { + background-color: #ffdd57 !important; } + +.has-text-danger { + color: #da0b00 !important; } + +a.has-text-danger:hover, a.has-text-danger:focus { + color: #a70800 !important; } + +.has-background-danger { + background-color: #da0b00 !important; } + +.has-text-black-bis { + color: #121212 !important; } + +.has-background-black-bis { + background-color: #121212 !important; } + +.has-text-black-ter { + color: #242424 !important; } + +.has-background-black-ter { + background-color: #242424 !important; } + +.has-text-grey-darker { + color: #363636 !important; } + +.has-background-grey-darker { + background-color: #363636 !important; } + +.has-text-grey-dark { + color: #4a4a4a !important; } + +.has-background-grey-dark { + background-color: #4a4a4a !important; } + +.has-text-grey { + color: #6b6b6b !important; } + +.has-background-grey { + background-color: #6b6b6b !important; } + +.has-text-grey-light { + color: #b5b5b5 !important; } + +.has-background-grey-light { + background-color: #b5b5b5 !important; } + +.has-text-grey-lighter { + color: #dbdbdb !important; } + +.has-background-grey-lighter { + background-color: #dbdbdb !important; } + +.has-text-white-ter { + color: whitesmoke !important; } + +.has-background-white-ter { + background-color: whitesmoke !important; } + +.has-text-white-bis { + color: #fafafa !important; } + +.has-background-white-bis { + background-color: #fafafa !important; } + +.has-text-weight-light { + font-weight: 300 !important; } + +.has-text-weight-normal { + font-weight: 400 !important; } + +.has-text-weight-medium { + font-weight: 500 !important; } + +.has-text-weight-semibold { + font-weight: 600 !important; } + +.has-text-weight-bold { + font-weight: 700 !important; } + +.is-family-primary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-secondary { + font-family: "Montserrat", sans-serif !important; } + +.is-family-sans-serif { + font-family: "Montserrat", sans-serif !important; } + +.is-family-monospace { + font-family: "Source Code Pro", monospace !important; } + +.is-family-code { + font-family: "Source Code Pro", monospace !important; } + +.is-block { + display: block !important; } + +@media screen and (max-width: 768px) { + .is-block-mobile { + display: block !important; } } + +@media screen and (min-width: 769px), print { + .is-block-tablet { + display: block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-block-tablet-only { + display: block !important; } } + +@media screen and (max-width: 1055px) { + .is-block-touch { + display: block !important; } } + +@media screen and (min-width: 1056px) { + .is-block-desktop { + display: block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-block-desktop-only { + display: block !important; } } + +@media screen and (min-width: 1216px) { + .is-block-widescreen { + display: block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-block-widescreen-only { + display: block !important; } } + +@media screen and (min-width: 1408px) { + .is-block-fullhd { + display: block !important; } } + +.is-flex { + display: flex !important; } + +@media screen and (max-width: 768px) { + .is-flex-mobile { + display: flex !important; } } + +@media screen and (min-width: 769px), print { + .is-flex-tablet { + display: flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-flex-tablet-only { + display: flex !important; } } + +@media screen and (max-width: 1055px) { + .is-flex-touch { + display: flex !important; } } + +@media screen and (min-width: 1056px) { + .is-flex-desktop { + display: flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-flex-desktop-only { + display: flex !important; } } + +@media screen and (min-width: 1216px) { + .is-flex-widescreen { + display: flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-flex-widescreen-only { + display: flex !important; } } + +@media screen and (min-width: 1408px) { + .is-flex-fullhd { + display: flex !important; } } + +.is-inline { + display: inline !important; } + +@media screen and (max-width: 768px) { + .is-inline-mobile { + display: inline !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-tablet { + display: inline !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-tablet-only { + display: inline !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-touch { + display: inline !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-desktop { + display: inline !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-desktop-only { + display: inline !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-widescreen { + display: inline !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-widescreen-only { + display: inline !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-fullhd { + display: inline !important; } } + +.is-inline-block { + display: inline-block !important; } + +@media screen and (max-width: 768px) { + .is-inline-block-mobile { + display: inline-block !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-block-tablet { + display: inline-block !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-block-tablet-only { + display: inline-block !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-block-touch { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-block-desktop { + display: inline-block !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-block-desktop-only { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-block-widescreen { + display: inline-block !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-block-widescreen-only { + display: inline-block !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-block-fullhd { + display: inline-block !important; } } + +.is-inline-flex { + display: inline-flex !important; } + +@media screen and (max-width: 768px) { + .is-inline-flex-mobile { + display: inline-flex !important; } } + +@media screen and (min-width: 769px), print { + .is-inline-flex-tablet { + display: inline-flex !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-inline-flex-tablet-only { + display: inline-flex !important; } } + +@media screen and (max-width: 1055px) { + .is-inline-flex-touch { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) { + .is-inline-flex-desktop { + display: inline-flex !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-inline-flex-desktop-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) { + .is-inline-flex-widescreen { + display: inline-flex !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-inline-flex-widescreen-only { + display: inline-flex !important; } } + +@media screen and (min-width: 1408px) { + .is-inline-flex-fullhd { + display: inline-flex !important; } } + +.is-hidden { + display: none !important; } + +.is-sr-only { + border: none !important; + clip: rect(0, 0, 0, 0) !important; + height: 0.01em !important; + overflow: hidden !important; + padding: 0 !important; + position: absolute !important; + white-space: nowrap !important; + width: 0.01em !important; } + +@media screen and (max-width: 768px) { + .is-hidden-mobile { + display: none !important; } } + +@media screen and (min-width: 769px), print { + .is-hidden-tablet { + display: none !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-hidden-tablet-only { + display: none !important; } } + +@media screen and (max-width: 1055px) { + .is-hidden-touch { + display: none !important; } } + +@media screen and (min-width: 1056px) { + .is-hidden-desktop { + display: none !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-hidden-desktop-only { + display: none !important; } } + +@media screen and (min-width: 1216px) { + .is-hidden-widescreen { + display: none !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-hidden-widescreen-only { + display: none !important; } } + +@media screen and (min-width: 1408px) { + .is-hidden-fullhd { + display: none !important; } } + +.is-invisible { + visibility: hidden !important; } + +@media screen and (max-width: 768px) { + .is-invisible-mobile { + visibility: hidden !important; } } + +@media screen and (min-width: 769px), print { + .is-invisible-tablet { + visibility: hidden !important; } } + +@media screen and (min-width: 769px) and (max-width: 1055px) { + .is-invisible-tablet-only { + visibility: hidden !important; } } + +@media screen and (max-width: 1055px) { + .is-invisible-touch { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) { + .is-invisible-desktop { + visibility: hidden !important; } } + +@media screen and (min-width: 1056px) and (max-width: 1215px) { + .is-invisible-desktop-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) { + .is-invisible-widescreen { + visibility: hidden !important; } } + +@media screen and (min-width: 1216px) and (max-width: 1407px) { + .is-invisible-widescreen-only { + visibility: hidden !important; } } + +@media screen and (min-width: 1408px) { + .is-invisible-fullhd { + visibility: hidden !important; } } + +.is-marginless { + margin: 0 !important; } + +.is-paddingless { + padding: 0 !important; } + +.is-radiusless { + border-radius: 0 !important; } + +.is-shadowless { + box-shadow: none !important; } + +.is-relative { + position: relative !important; } + +.box { + background-color: white; + border-radius: 6px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #202020; + display: block; + padding: 1.25rem; } + +a.box:hover, a.box:focus { + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #149eaa; } + +a.box:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #149eaa; } + +.button { + background-color: white; + border-color: #dbdbdb; + border-width: 1px; + color: #363636; + cursor: pointer; + justify-content: center; + padding-bottom: calc(0.375em - 1px); + padding-left: 0.75em; + padding-right: 0.75em; + padding-top: calc(0.375em - 1px); + text-align: center; + white-space: nowrap; } + .button strong { + color: inherit; } + .button .icon, .button .icon.is-small, .button #documenter .docs-sidebar form.docs-search > input.icon, #documenter .docs-sidebar .button form.docs-search > input.icon, .button .icon.is-medium, .button .icon.is-large { + height: 1.5em; + width: 1.5em; } + .button .icon:first-child:not(:last-child) { + margin-left: calc(-0.375em - 1px); + margin-right: 0.1875em; } + .button .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: calc(-0.375em - 1px); } + .button .icon:first-child:last-child { + margin-left: calc(-0.375em - 1px); + margin-right: calc(-0.375em - 1px); } + .button:hover, .button.is-hovered { + border-color: #b5b5b5; + color: #107c85; } + .button:focus, .button.is-focused { + border-color: #3c5dcd; + color: #363636; } + .button:focus:not(:active), .button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .button:active, .button.is-active { + border-color: #4a4a4a; + color: #363636; } + .button.is-text { + background-color: transparent; + border-color: transparent; + color: #202020; + text-decoration: underline; } + .button.is-text:hover, .button.is-text.is-hovered, .button.is-text:focus, .button.is-text.is-focused { + background-color: whitesmoke; + color: #654ca3; } + .button.is-text:active, .button.is-text.is-active { + background-color: #e8e8e8; + color: #654ca3; } + .button.is-text[disabled], fieldset[disabled] .button.is-text { + background-color: transparent; + border-color: transparent; + box-shadow: none; } + .button.is-white { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + .button.is-white:hover, .button.is-white.is-hovered { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + .button.is-white:focus, .button.is-white.is-focused { + border-color: transparent; + color: #0a0a0a; } + .button.is-white:focus:not(:active), .button.is-white.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .button.is-white:active, .button.is-white.is-active { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + .button.is-white[disabled], fieldset[disabled] .button.is-white { + background-color: white; + border-color: transparent; + box-shadow: none; } + .button.is-white.is-inverted { + background-color: #0a0a0a; + color: white; } + .button.is-white.is-inverted:hover, .button.is-white.is-inverted.is-hovered { + background-color: black; } + .button.is-white.is-inverted[disabled], fieldset[disabled] .button.is-white.is-inverted { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; + color: white; } + .button.is-white.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + .button.is-white.is-outlined:hover, .button.is-white.is-outlined.is-hovered, .button.is-white.is-outlined:focus, .button.is-white.is-outlined.is-focused { + background-color: white; + border-color: white; + color: #0a0a0a; } + .button.is-white.is-outlined.is-loading::after { + border-color: transparent transparent white white !important; } + .button.is-white.is-outlined.is-loading:hover::after, .button.is-white.is-outlined.is-loading.is-hovered::after, .button.is-white.is-outlined.is-loading:focus::after, .button.is-white.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-white.is-outlined[disabled], fieldset[disabled] .button.is-white.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + .button.is-white.is-inverted.is-outlined:hover, .button.is-white.is-inverted.is-outlined.is-hovered, .button.is-white.is-inverted.is-outlined:focus, .button.is-white.is-inverted.is-outlined.is-focused { + background-color: #0a0a0a; + color: white; } + .button.is-white.is-inverted.is-outlined.is-loading:hover::after, .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-white.is-inverted.is-outlined.is-loading:focus::after, .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + .button.is-white.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-white.is-inverted.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + .button.is-black:hover, .button.is-black.is-hovered { + background-color: #040404; + border-color: transparent; + color: white; } + .button.is-black:focus, .button.is-black.is-focused { + border-color: transparent; + color: white; } + .button.is-black:focus:not(:active), .button.is-black.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .button.is-black:active, .button.is-black.is-active { + background-color: black; + border-color: transparent; + color: white; } + .button.is-black[disabled], fieldset[disabled] .button.is-black { + background-color: #0a0a0a; + border-color: transparent; + box-shadow: none; } + .button.is-black.is-inverted { + background-color: white; + color: #0a0a0a; } + .button.is-black.is-inverted:hover, .button.is-black.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-black.is-inverted[disabled], fieldset[disabled] .button.is-black.is-inverted { + background-color: white; + border-color: transparent; + box-shadow: none; + color: #0a0a0a; } + .button.is-black.is-loading::after { + border-color: transparent transparent white white !important; } + .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + color: #0a0a0a; } + .button.is-black.is-outlined:hover, .button.is-black.is-outlined.is-hovered, .button.is-black.is-outlined:focus, .button.is-black.is-outlined.is-focused { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .button.is-black.is-outlined.is-loading::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-black.is-outlined.is-loading:hover::after, .button.is-black.is-outlined.is-loading.is-hovered::after, .button.is-black.is-outlined.is-loading:focus::after, .button.is-black.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent white white !important; } + .button.is-black.is-outlined[disabled], fieldset[disabled] .button.is-black.is-outlined { + background-color: transparent; + border-color: #0a0a0a; + box-shadow: none; + color: #0a0a0a; } + .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + color: white; } + .button.is-black.is-inverted.is-outlined:hover, .button.is-black.is-inverted.is-outlined.is-hovered, .button.is-black.is-inverted.is-outlined:focus, .button.is-black.is-inverted.is-outlined.is-focused { + background-color: white; + color: #0a0a0a; } + .button.is-black.is-inverted.is-outlined.is-loading:hover::after, .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-black.is-inverted.is-outlined.is-loading:focus::after, .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #0a0a0a #0a0a0a !important; } + .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-black.is-inverted.is-outlined { + background-color: transparent; + border-color: white; + box-shadow: none; + color: white; } + .button.is-light { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + .button.is-light:hover, .button.is-light.is-hovered { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + .button.is-light:focus, .button.is-light.is-focused { + border-color: transparent; + color: #363636; } + .button.is-light:focus:not(:active), .button.is-light.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .button.is-light:active, .button.is-light.is-active { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + .button.is-light[disabled], fieldset[disabled] .button.is-light { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; } + .button.is-light.is-inverted { + background-color: #363636; + color: whitesmoke; } + .button.is-light.is-inverted:hover, .button.is-light.is-inverted.is-hovered { + background-color: #292929; } + .button.is-light.is-inverted[disabled], fieldset[disabled] .button.is-light.is-inverted { + background-color: #363636; + border-color: transparent; + box-shadow: none; + color: whitesmoke; } + .button.is-light.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + .button.is-light.is-outlined:hover, .button.is-light.is-outlined.is-hovered, .button.is-light.is-outlined:focus, .button.is-light.is-outlined.is-focused { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .button.is-light.is-outlined.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-light.is-outlined.is-loading:hover::after, .button.is-light.is-outlined.is-loading.is-hovered::after, .button.is-light.is-outlined.is-loading:focus::after, .button.is-light.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-light.is-outlined[disabled], fieldset[disabled] .button.is-light.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + .button.is-light.is-inverted.is-outlined:hover, .button.is-light.is-inverted.is-outlined.is-hovered, .button.is-light.is-inverted.is-outlined:focus, .button.is-light.is-inverted.is-outlined.is-focused { + background-color: #363636; + color: whitesmoke; } + .button.is-light.is-inverted.is-outlined.is-loading:hover::after, .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-light.is-inverted.is-outlined.is-loading:focus::after, .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-light.is-inverted.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + .button.is-dark, .content kbd.button { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + .button.is-dark:hover, .content kbd.button:hover, .button.is-dark.is-hovered, .content kbd.button.is-hovered { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + .button.is-dark:focus, .content kbd.button:focus, .button.is-dark.is-focused, .content kbd.button.is-focused { + border-color: transparent; + color: whitesmoke; } + .button.is-dark:focus:not(:active), .content kbd.button:focus:not(:active), .button.is-dark.is-focused:not(:active), .content kbd.button.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .button.is-dark:active, .content kbd.button:active, .button.is-dark.is-active, .content kbd.button.is-active { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + .button.is-dark[disabled], .content kbd.button[disabled], fieldset[disabled] .button.is-dark, fieldset[disabled] .content kbd.button, .content fieldset[disabled] kbd.button { + background-color: #363636; + border-color: transparent; + box-shadow: none; } + .button.is-dark.is-inverted, .content kbd.button.is-inverted { + background-color: whitesmoke; + color: #363636; } + .button.is-dark.is-inverted:hover, .content kbd.button.is-inverted:hover, .button.is-dark.is-inverted.is-hovered, .content kbd.button.is-inverted.is-hovered { + background-color: #e8e8e8; } + .button.is-dark.is-inverted[disabled], .content kbd.button.is-inverted[disabled], fieldset[disabled] .button.is-dark.is-inverted, fieldset[disabled] .content kbd.button.is-inverted, .content fieldset[disabled] kbd.button.is-inverted { + background-color: whitesmoke; + border-color: transparent; + box-shadow: none; + color: #363636; } + .button.is-dark.is-loading::after, .content kbd.button.is-loading::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-dark.is-outlined, .content kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + color: #363636; } + .button.is-dark.is-outlined:hover, .content kbd.button.is-outlined:hover, .button.is-dark.is-outlined.is-hovered, .content kbd.button.is-outlined.is-hovered, .button.is-dark.is-outlined:focus, .content kbd.button.is-outlined:focus, .button.is-dark.is-outlined.is-focused, .content kbd.button.is-outlined.is-focused { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .button.is-dark.is-outlined.is-loading::after, .content kbd.button.is-outlined.is-loading::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-dark.is-outlined.is-loading:hover::after, .content kbd.button.is-outlined.is-loading:hover::after, .button.is-dark.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-outlined.is-loading:focus::after, .content kbd.button.is-outlined.is-loading:focus::after, .button.is-dark.is-outlined.is-loading.is-focused::after, .content kbd.button.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent whitesmoke whitesmoke !important; } + .button.is-dark.is-outlined[disabled], .content kbd.button.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-outlined, fieldset[disabled] .content kbd.button.is-outlined, .content fieldset[disabled] kbd.button.is-outlined { + background-color: transparent; + border-color: #363636; + box-shadow: none; + color: #363636; } + .button.is-dark.is-inverted.is-outlined, .content kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + color: whitesmoke; } + .button.is-dark.is-inverted.is-outlined:hover, .content kbd.button.is-inverted.is-outlined:hover, .button.is-dark.is-inverted.is-outlined.is-hovered, .content kbd.button.is-inverted.is-outlined.is-hovered, .button.is-dark.is-inverted.is-outlined:focus, .content kbd.button.is-inverted.is-outlined:focus, .button.is-dark.is-inverted.is-outlined.is-focused, .content kbd.button.is-inverted.is-outlined.is-focused { + background-color: whitesmoke; + color: #363636; } + .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #363636 #363636 !important; } + .button.is-dark.is-inverted.is-outlined[disabled], .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-inverted.is-outlined, fieldset[disabled] .content kbd.button.is-inverted.is-outlined, .content fieldset[disabled] kbd.button.is-inverted.is-outlined { + background-color: transparent; + border-color: whitesmoke; + box-shadow: none; + color: whitesmoke; } + .button.is-primary, .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + .button.is-primary:hover, .docstring > section > a.button.docs-sourcelink:hover, .button.is-primary.is-hovered, .docstring > section > a.button.is-hovered.docs-sourcelink { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + .button.is-primary:focus, .docstring > section > a.button.docs-sourcelink:focus, .button.is-primary.is-focused, .docstring > section > a.button.is-focused.docs-sourcelink { + border-color: transparent; + color: #fff; } + .button.is-primary:focus:not(:active), .docstring > section > a.button.docs-sourcelink:focus:not(:active), .button.is-primary.is-focused:not(:active), .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .button.is-primary:active, .docstring > section > a.button.docs-sourcelink:active, .button.is-primary.is-active, .docstring > section > a.button.is-active.docs-sourcelink { + background-color: #39acda; + border-color: transparent; + color: #fff; } + .button.is-primary[disabled], .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary, fieldset[disabled] .docstring > section > a.button.docs-sourcelink { + background-color: #4eb5de; + border-color: transparent; + box-shadow: none; } + .button.is-primary.is-inverted, .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + .button.is-primary.is-inverted:hover, .docstring > section > a.button.is-inverted.docs-sourcelink:hover, .button.is-primary.is-inverted.is-hovered, .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { + background-color: #f2f2f2; } + .button.is-primary.is-inverted[disabled], .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted, fieldset[disabled] .docstring > section > a.button.is-inverted.docs-sourcelink { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #4eb5de; } + .button.is-primary.is-loading::after, .docstring > section > a.button.is-loading.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-primary.is-outlined, .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + color: #4eb5de; } + .button.is-primary.is-outlined:hover, .docstring > section > a.button.is-outlined.docs-sourcelink:hover, .button.is-primary.is-outlined.is-hovered, .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-outlined:focus, .docstring > section > a.button.is-outlined.docs-sourcelink:focus, .button.is-primary.is-outlined.is-focused, .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + .button.is-primary.is-outlined.is-loading::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + .button.is-primary.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-primary.is-outlined[disabled], .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-outlined, fieldset[disabled] .docstring > section > a.button.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #4eb5de; + box-shadow: none; + color: #4eb5de; } + .button.is-primary.is-inverted.is-outlined, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-primary.is-inverted.is-outlined:hover, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, .button.is-primary.is-inverted.is-outlined.is-hovered, .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-inverted.is-outlined:focus, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, .button.is-primary.is-inverted.is-outlined.is-focused, .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { + background-color: #fff; + color: #4eb5de; } + .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { + border-color: transparent transparent #4eb5de #4eb5de !important; } + .button.is-primary.is-inverted.is-outlined[disabled], .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted.is-outlined, fieldset[disabled] .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-link { + background-color: #149eaa; + border-color: transparent; + color: #fff; } + .button.is-link:hover, .button.is-link.is-hovered { + background-color: #13939f; + border-color: transparent; + color: #fff; } + .button.is-link:focus, .button.is-link.is-focused { + border-color: transparent; + color: #fff; } + .button.is-link:focus:not(:active), .button.is-link.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .button.is-link:active, .button.is-link.is-active { + background-color: #118993; + border-color: transparent; + color: #fff; } + .button.is-link[disabled], fieldset[disabled] .button.is-link { + background-color: #149eaa; + border-color: transparent; + box-shadow: none; } + .button.is-link.is-inverted { + background-color: #fff; + color: #149eaa; } + .button.is-link.is-inverted:hover, .button.is-link.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-link.is-inverted[disabled], fieldset[disabled] .button.is-link.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #149eaa; } + .button.is-link.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-link.is-outlined { + background-color: transparent; + border-color: #149eaa; + color: #149eaa; } + .button.is-link.is-outlined:hover, .button.is-link.is-outlined.is-hovered, .button.is-link.is-outlined:focus, .button.is-link.is-outlined.is-focused { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + .button.is-link.is-outlined.is-loading::after { + border-color: transparent transparent #149eaa #149eaa !important; } + .button.is-link.is-outlined.is-loading:hover::after, .button.is-link.is-outlined.is-loading.is-hovered::after, .button.is-link.is-outlined.is-loading:focus::after, .button.is-link.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-link.is-outlined[disabled], fieldset[disabled] .button.is-link.is-outlined { + background-color: transparent; + border-color: #149eaa; + box-shadow: none; + color: #149eaa; } + .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-link.is-inverted.is-outlined:hover, .button.is-link.is-inverted.is-outlined.is-hovered, .button.is-link.is-inverted.is-outlined:focus, .button.is-link.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #149eaa; } + .button.is-link.is-inverted.is-outlined.is-loading:hover::after, .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-link.is-inverted.is-outlined.is-loading:focus::after, .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #149eaa #149eaa !important; } + .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-link.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-info { + background-color: #209cee; + border-color: transparent; + color: #fff; } + .button.is-info:hover, .button.is-info.is-hovered { + background-color: #1497ed; + border-color: transparent; + color: #fff; } + .button.is-info:focus, .button.is-info.is-focused { + border-color: transparent; + color: #fff; } + .button.is-info:focus:not(:active), .button.is-info.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .button.is-info:active, .button.is-info.is-active { + background-color: #1190e3; + border-color: transparent; + color: #fff; } + .button.is-info[disabled], fieldset[disabled] .button.is-info { + background-color: #209cee; + border-color: transparent; + box-shadow: none; } + .button.is-info.is-inverted { + background-color: #fff; + color: #209cee; } + .button.is-info.is-inverted:hover, .button.is-info.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-info.is-inverted[disabled], fieldset[disabled] .button.is-info.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #209cee; } + .button.is-info.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-info.is-outlined { + background-color: transparent; + border-color: #209cee; + color: #209cee; } + .button.is-info.is-outlined:hover, .button.is-info.is-outlined.is-hovered, .button.is-info.is-outlined:focus, .button.is-info.is-outlined.is-focused { + background-color: #209cee; + border-color: #209cee; + color: #fff; } + .button.is-info.is-outlined.is-loading::after { + border-color: transparent transparent #209cee #209cee !important; } + .button.is-info.is-outlined.is-loading:hover::after, .button.is-info.is-outlined.is-loading.is-hovered::after, .button.is-info.is-outlined.is-loading:focus::after, .button.is-info.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-info.is-outlined[disabled], fieldset[disabled] .button.is-info.is-outlined { + background-color: transparent; + border-color: #209cee; + box-shadow: none; + color: #209cee; } + .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-info.is-inverted.is-outlined:hover, .button.is-info.is-inverted.is-outlined.is-hovered, .button.is-info.is-inverted.is-outlined:focus, .button.is-info.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #209cee; } + .button.is-info.is-inverted.is-outlined.is-loading:hover::after, .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-info.is-inverted.is-outlined.is-loading:focus::after, .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #209cee #209cee !important; } + .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-info.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-success { + background-color: #22c35b; + border-color: transparent; + color: #fff; } + .button.is-success:hover, .button.is-success.is-hovered { + background-color: #20b856; + border-color: transparent; + color: #fff; } + .button.is-success:focus, .button.is-success.is-focused { + border-color: transparent; + color: #fff; } + .button.is-success:focus:not(:active), .button.is-success.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .button.is-success:active, .button.is-success.is-active { + background-color: #1ead51; + border-color: transparent; + color: #fff; } + .button.is-success[disabled], fieldset[disabled] .button.is-success { + background-color: #22c35b; + border-color: transparent; + box-shadow: none; } + .button.is-success.is-inverted { + background-color: #fff; + color: #22c35b; } + .button.is-success.is-inverted:hover, .button.is-success.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-success.is-inverted[disabled], fieldset[disabled] .button.is-success.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #22c35b; } + .button.is-success.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-success.is-outlined { + background-color: transparent; + border-color: #22c35b; + color: #22c35b; } + .button.is-success.is-outlined:hover, .button.is-success.is-outlined.is-hovered, .button.is-success.is-outlined:focus, .button.is-success.is-outlined.is-focused { + background-color: #22c35b; + border-color: #22c35b; + color: #fff; } + .button.is-success.is-outlined.is-loading::after { + border-color: transparent transparent #22c35b #22c35b !important; } + .button.is-success.is-outlined.is-loading:hover::after, .button.is-success.is-outlined.is-loading.is-hovered::after, .button.is-success.is-outlined.is-loading:focus::after, .button.is-success.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-success.is-outlined[disabled], fieldset[disabled] .button.is-success.is-outlined { + background-color: transparent; + border-color: #22c35b; + box-shadow: none; + color: #22c35b; } + .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-success.is-inverted.is-outlined:hover, .button.is-success.is-inverted.is-outlined.is-hovered, .button.is-success.is-inverted.is-outlined:focus, .button.is-success.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #22c35b; } + .button.is-success.is-inverted.is-outlined.is-loading:hover::after, .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-success.is-inverted.is-outlined.is-loading:focus::after, .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #22c35b #22c35b !important; } + .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-success.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-warning { + background-color: #ffdd57; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:hover, .button.is-warning.is-hovered { + background-color: #ffda4a; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:focus, .button.is-warning.is-focused { + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning:focus:not(:active), .button.is-warning.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .button.is-warning:active, .button.is-warning.is-active { + background-color: #ffd83e; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning[disabled], fieldset[disabled] .button.is-warning { + background-color: #ffdd57; + border-color: transparent; + box-shadow: none; } + .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .button.is-warning.is-inverted:hover, .button.is-warning.is-inverted.is-hovered { + background-color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-inverted[disabled], fieldset[disabled] .button.is-warning.is-inverted { + background-color: rgba(0, 0, 0, 0.7); + border-color: transparent; + box-shadow: none; + color: #ffdd57; } + .button.is-warning.is-loading::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + .button.is-warning.is-outlined { + background-color: transparent; + border-color: #ffdd57; + color: #ffdd57; } + .button.is-warning.is-outlined:hover, .button.is-warning.is-outlined.is-hovered, .button.is-warning.is-outlined:focus, .button.is-warning.is-outlined.is-focused { + background-color: #ffdd57; + border-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-outlined.is-loading::after { + border-color: transparent transparent #ffdd57 #ffdd57 !important; } + .button.is-warning.is-outlined.is-loading:hover::after, .button.is-warning.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-outlined.is-loading:focus::after, .button.is-warning.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } + .button.is-warning.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-outlined { + background-color: transparent; + border-color: #ffdd57; + box-shadow: none; + color: #ffdd57; } + .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + color: rgba(0, 0, 0, 0.7); } + .button.is-warning.is-inverted.is-outlined:hover, .button.is-warning.is-inverted.is-outlined.is-hovered, .button.is-warning.is-inverted.is-outlined:focus, .button.is-warning.is-inverted.is-outlined.is-focused { + background-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #ffdd57 #ffdd57 !important; } + .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-inverted.is-outlined { + background-color: transparent; + border-color: rgba(0, 0, 0, 0.7); + box-shadow: none; + color: rgba(0, 0, 0, 0.7); } + .button.is-danger { + background-color: #da0b00; + border-color: transparent; + color: #fff; } + .button.is-danger:hover, .button.is-danger.is-hovered { + background-color: #cd0a00; + border-color: transparent; + color: #fff; } + .button.is-danger:focus, .button.is-danger.is-focused { + border-color: transparent; + color: #fff; } + .button.is-danger:focus:not(:active), .button.is-danger.is-focused:not(:active) { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .button.is-danger:active, .button.is-danger.is-active { + background-color: #c10a00; + border-color: transparent; + color: #fff; } + .button.is-danger[disabled], fieldset[disabled] .button.is-danger { + background-color: #da0b00; + border-color: transparent; + box-shadow: none; } + .button.is-danger.is-inverted { + background-color: #fff; + color: #da0b00; } + .button.is-danger.is-inverted:hover, .button.is-danger.is-inverted.is-hovered { + background-color: #f2f2f2; } + .button.is-danger.is-inverted[disabled], fieldset[disabled] .button.is-danger.is-inverted { + background-color: #fff; + border-color: transparent; + box-shadow: none; + color: #da0b00; } + .button.is-danger.is-loading::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-danger.is-outlined { + background-color: transparent; + border-color: #da0b00; + color: #da0b00; } + .button.is-danger.is-outlined:hover, .button.is-danger.is-outlined.is-hovered, .button.is-danger.is-outlined:focus, .button.is-danger.is-outlined.is-focused { + background-color: #da0b00; + border-color: #da0b00; + color: #fff; } + .button.is-danger.is-outlined.is-loading::after { + border-color: transparent transparent #da0b00 #da0b00 !important; } + .button.is-danger.is-outlined.is-loading:hover::after, .button.is-danger.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-outlined.is-loading:focus::after, .button.is-danger.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #fff #fff !important; } + .button.is-danger.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-outlined { + background-color: transparent; + border-color: #da0b00; + box-shadow: none; + color: #da0b00; } + .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + color: #fff; } + .button.is-danger.is-inverted.is-outlined:hover, .button.is-danger.is-inverted.is-outlined.is-hovered, .button.is-danger.is-inverted.is-outlined:focus, .button.is-danger.is-inverted.is-outlined.is-focused { + background-color: #fff; + color: #da0b00; } + .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { + border-color: transparent transparent #da0b00 #da0b00 !important; } + .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-inverted.is-outlined { + background-color: transparent; + border-color: #fff; + box-shadow: none; + color: #fff; } + .button.is-small, #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 2px; + font-size: 0.75rem; } + .button.is-normal { + font-size: 1rem; } + .button.is-medium { + font-size: 1.25rem; } + .button.is-large { + font-size: 1.5rem; } + .button[disabled], fieldset[disabled] .button { + background-color: white; + border-color: #dbdbdb; + box-shadow: none; + opacity: 0.5; } + .button.is-fullwidth { + display: flex; + width: 100%; } + .button.is-loading { + color: transparent !important; + pointer-events: none; } + .button.is-loading::after { + position: absolute; + left: calc(50% - (1em / 2)); + top: calc(50% - (1em / 2)); + position: absolute !important; } + .button.is-static { + background-color: whitesmoke; + border-color: #dbdbdb; + color: #6b6b6b; + box-shadow: none; + pointer-events: none; } + .button.is-rounded, #documenter .docs-sidebar form.docs-search > input.button { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + +.buttons { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .buttons .button { + margin-bottom: 0.5rem; } + .buttons .button:not(:last-child):not(.is-fullwidth) { + margin-right: 0.5rem; } + .buttons:last-child { + margin-bottom: -0.5rem; } + .buttons:not(:last-child) { + margin-bottom: 1rem; } + .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { + border-radius: 2px; + font-size: 0.75rem; } + .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { + font-size: 1.25rem; } + .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { + font-size: 1.5rem; } + .buttons.has-addons .button:not(:first-child) { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .buttons.has-addons .button:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; + margin-right: -1px; } + .buttons.has-addons .button:last-child { + margin-right: 0; } + .buttons.has-addons .button:hover, .buttons.has-addons .button.is-hovered { + z-index: 2; } + .buttons.has-addons .button:focus, .buttons.has-addons .button.is-focused, .buttons.has-addons .button:active, .buttons.has-addons .button.is-active, .buttons.has-addons .button.is-selected { + z-index: 3; } + .buttons.has-addons .button:focus:hover, .buttons.has-addons .button.is-focused:hover, .buttons.has-addons .button:active:hover, .buttons.has-addons .button.is-active:hover, .buttons.has-addons .button.is-selected:hover { + z-index: 4; } + .buttons.has-addons .button.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .buttons.is-centered { + justify-content: center; } + .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + .buttons.is-right { + justify-content: flex-end; } + .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { + margin-left: 0.25rem; + margin-right: 0.25rem; } + +.container { + flex-grow: 1; + margin: 0 auto; + position: relative; + width: auto; } + @media screen and (min-width: 1056px) { + .container { + max-width: 992px; } + .container.is-fluid { + margin-left: 32px; + margin-right: 32px; + max-width: none; } } + @media screen and (max-width: 1215px) { + .container.is-widescreen { + max-width: 1152px; } } + @media screen and (max-width: 1407px) { + .container.is-fullhd { + max-width: 1344px; } } + @media screen and (min-width: 1216px) { + .container { + max-width: 1152px; } } + @media screen and (min-width: 1408px) { + .container { + max-width: 1344px; } } +.content li + li { + margin-top: 0.25em; } + +.content p:not(:last-child), +.content dl:not(:last-child), +.content ol:not(:last-child), +.content ul:not(:last-child), +.content blockquote:not(:last-child), +.content pre:not(:last-child), +.content table:not(:last-child) { + margin-bottom: 1em; } + +.content h1, +.content h2, +.content h3, +.content h4, +.content h5, +.content h6 { + color: #654ca3; + font-weight: 600; + line-height: 1.125; } + +.content h1 { + font-size: 2em; + margin-bottom: 0.5em; } + .content h1:not(:first-child) { + margin-top: 1em; } + +.content h2 { + font-size: 1.75em; + margin-bottom: 0.5714em; } + .content h2:not(:first-child) { + margin-top: 1.1428em; } + +.content h3 { + font-size: 1.5em; + margin-bottom: 0.6666em; } + .content h3:not(:first-child) { + margin-top: 1.3333em; } + +.content h4 { + font-size: 1.25em; + margin-bottom: 0.8em; } + +.content h5 { + font-size: 1.125em; + margin-bottom: 0.8888em; } + +.content h6 { + font-size: 1em; + margin-bottom: 1em; } + +.content blockquote { + background-color: whitesmoke; + border-left: 5px solid #dbdbdb; + padding: 1.25em 1.5em; } + +.content ol { + list-style-position: outside; + margin-left: 2em; + margin-top: 1em; } + .content ol:not([type]) { + list-style-type: decimal; } + .content ol.is-lower-alpha:not([type]) { + list-style-type: lower-alpha; } + .content ol.is-lower-roman:not([type]) { + list-style-type: lower-roman; } + .content ol.is-upper-alpha:not([type]) { + list-style-type: upper-alpha; } + .content ol.is-upper-roman:not([type]) { + list-style-type: upper-roman; } + +.content ul { + list-style: disc outside; + margin-left: 2em; + margin-top: 1em; } + .content ul ul { + list-style-type: circle; + margin-top: 0.5em; } + .content ul ul ul { + list-style-type: square; } + +.content dd { + margin-left: 2em; } + +.content figure { + margin-left: 2em; + margin-right: 2em; + text-align: center; } + .content figure:not(:first-child) { + margin-top: 2em; } + .content figure:not(:last-child) { + margin-bottom: 2em; } + .content figure img { + display: inline-block; } + .content figure figcaption { + font-style: italic; } + +.content pre { + -webkit-overflow-scrolling: touch; + overflow-x: auto; + padding: 0; + white-space: pre; + word-wrap: normal; } + +.content sup, +.content sub { + font-size: 75%; } + +.content table { + width: 100%; } + .content table td, + .content table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + .content table th { + color: #654ca3; } + .content table th:not([align]) { + text-align: left; } + .content table thead td, + .content table thead th { + border-width: 0 0 2px; + color: #654ca3; } + .content table tfoot td, + .content table tfoot th { + border-width: 2px 0 0; + color: #654ca3; } + .content table tbody tr:last-child td, + .content table tbody tr:last-child th { + border-bottom-width: 0; } + +.content .tabs li + li { + margin-top: 0; } + +.content.is-small, #documenter .docs-sidebar form.docs-search > input.content { + font-size: 0.75rem; } + +.content.is-medium { + font-size: 1.25rem; } + +.content.is-large { + font-size: 1.5rem; } + +.icon { + align-items: center; + display: inline-flex; + justify-content: center; + height: 1.5rem; + width: 1.5rem; } + .icon.is-small, #documenter .docs-sidebar form.docs-search > input.icon { + height: 1rem; + width: 1rem; } + .icon.is-medium { + height: 2rem; + width: 2rem; } + .icon.is-large { + height: 3rem; + width: 3rem; } + +.image, #documenter .docs-sidebar .docs-logo > img { + display: block; + position: relative; } + .image img, #documenter .docs-sidebar .docs-logo > img img { + display: block; + height: auto; + width: 100%; } + .image img.is-rounded, #documenter .docs-sidebar .docs-logo > img img.is-rounded { + border-radius: 290486px; } + .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img, + .image.is-square .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img, + .image.is-1by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img, + .image.is-5by4 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img, + .image.is-4by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img, + .image.is-3by2 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img, + .image.is-5by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img, + .image.is-16by9 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img, + .image.is-2by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img, + .image.is-3by1 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img, + .image.is-4by5 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img, + .image.is-3by4 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img, + .image.is-2by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img, + .image.is-3by5 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img, + .image.is-9by16 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img, + .image.is-1by2 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img, + .image.is-1by3 .has-ratio, + #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { + height: 100%; + width: 100%; } + .image.is-square, #documenter .docs-sidebar .docs-logo > img.is-square, .image.is-1by1, #documenter .docs-sidebar .docs-logo > img.is-1by1 { + padding-top: 100%; } + .image.is-5by4, #documenter .docs-sidebar .docs-logo > img.is-5by4 { + padding-top: 80%; } + .image.is-4by3, #documenter .docs-sidebar .docs-logo > img.is-4by3 { + padding-top: 75%; } + .image.is-3by2, #documenter .docs-sidebar .docs-logo > img.is-3by2 { + padding-top: 66.6666%; } + .image.is-5by3, #documenter .docs-sidebar .docs-logo > img.is-5by3 { + padding-top: 60%; } + .image.is-16by9, #documenter .docs-sidebar .docs-logo > img.is-16by9 { + padding-top: 56.25%; } + .image.is-2by1, #documenter .docs-sidebar .docs-logo > img.is-2by1 { + padding-top: 50%; } + .image.is-3by1, #documenter .docs-sidebar .docs-logo > img.is-3by1 { + padding-top: 33.3333%; } + .image.is-4by5, #documenter .docs-sidebar .docs-logo > img.is-4by5 { + padding-top: 125%; } + .image.is-3by4, #documenter .docs-sidebar .docs-logo > img.is-3by4 { + padding-top: 133.3333%; } + .image.is-2by3, #documenter .docs-sidebar .docs-logo > img.is-2by3 { + padding-top: 150%; } + .image.is-3by5, #documenter .docs-sidebar .docs-logo > img.is-3by5 { + padding-top: 166.6666%; } + .image.is-9by16, #documenter .docs-sidebar .docs-logo > img.is-9by16 { + padding-top: 177.7777%; } + .image.is-1by2, #documenter .docs-sidebar .docs-logo > img.is-1by2 { + padding-top: 200%; } + .image.is-1by3, #documenter .docs-sidebar .docs-logo > img.is-1by3 { + padding-top: 300%; } + .image.is-16x16, #documenter .docs-sidebar .docs-logo > img.is-16x16 { + height: 16px; + width: 16px; } + .image.is-24x24, #documenter .docs-sidebar .docs-logo > img.is-24x24 { + height: 24px; + width: 24px; } + .image.is-32x32, #documenter .docs-sidebar .docs-logo > img.is-32x32 { + height: 32px; + width: 32px; } + .image.is-48x48, #documenter .docs-sidebar .docs-logo > img.is-48x48 { + height: 48px; + width: 48px; } + .image.is-64x64, #documenter .docs-sidebar .docs-logo > img.is-64x64 { + height: 64px; + width: 64px; } + .image.is-96x96, #documenter .docs-sidebar .docs-logo > img.is-96x96 { + height: 96px; + width: 96px; } + .image.is-128x128, #documenter .docs-sidebar .docs-logo > img.is-128x128 { + height: 128px; + width: 128px; } + +.notification { + background-color: whitesmoke; + border-radius: 4px; + padding: 1.25rem 2.5rem 1.25rem 1.5rem; + position: relative; } + .notification a:not(.button):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + .notification strong { + color: currentColor; } + .notification code, + .notification pre { + background: white; } + .notification pre code { + background: transparent; } + .notification > .delete { + position: absolute; + right: 0.5rem; + top: 0.5rem; } + .notification .title, + .notification .subtitle, + .notification .content { + color: currentColor; } + .notification.is-white { + background-color: white; + color: #0a0a0a; } + .notification.is-black { + background-color: #0a0a0a; + color: white; } + .notification.is-light { + background-color: whitesmoke; + color: #363636; } + .notification.is-dark, .content kbd.notification { + background-color: #363636; + color: whitesmoke; } + .notification.is-primary, .docstring > section > a.notification.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .notification.is-link { + background-color: #149eaa; + color: #fff; } + .notification.is-info { + background-color: #209cee; + color: #fff; } + .notification.is-success { + background-color: #22c35b; + color: #fff; } + .notification.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .notification.is-danger { + background-color: #da0b00; + color: #fff; } + +.progress { + -moz-appearance: none; + -webkit-appearance: none; + border: none; + border-radius: 290486px; + display: block; + height: 1rem; + overflow: hidden; + padding: 0; + width: 100%; } + .progress::-webkit-progress-bar { + background-color: #dbdbdb; } + .progress::-webkit-progress-value { + background-color: #202020; } + .progress::-moz-progress-bar { + background-color: #202020; } + .progress::-ms-fill { + background-color: #202020; + border: none; } + .progress.is-white::-webkit-progress-value { + background-color: white; } + .progress.is-white::-moz-progress-bar { + background-color: white; } + .progress.is-white::-ms-fill { + background-color: white; } + .progress.is-white:indeterminate { + background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); } + .progress.is-black::-webkit-progress-value { + background-color: #0a0a0a; } + .progress.is-black::-moz-progress-bar { + background-color: #0a0a0a; } + .progress.is-black::-ms-fill { + background-color: #0a0a0a; } + .progress.is-black:indeterminate { + background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); } + .progress.is-light::-webkit-progress-value { + background-color: whitesmoke; } + .progress.is-light::-moz-progress-bar { + background-color: whitesmoke; } + .progress.is-light::-ms-fill { + background-color: whitesmoke; } + .progress.is-light:indeterminate { + background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); } + .progress.is-dark::-webkit-progress-value, .content kbd.progress::-webkit-progress-value { + background-color: #363636; } + .progress.is-dark::-moz-progress-bar, .content kbd.progress::-moz-progress-bar { + background-color: #363636; } + .progress.is-dark::-ms-fill, .content kbd.progress::-ms-fill { + background-color: #363636; } + .progress.is-dark:indeterminate, .content kbd.progress:indeterminate { + background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); } + .progress.is-primary::-webkit-progress-value, .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { + background-color: #4eb5de; } + .progress.is-primary::-moz-progress-bar, .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { + background-color: #4eb5de; } + .progress.is-primary::-ms-fill, .docstring > section > a.progress.docs-sourcelink::-ms-fill { + background-color: #4eb5de; } + .progress.is-primary:indeterminate, .docstring > section > a.progress.docs-sourcelink:indeterminate { + background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); } + .progress.is-link::-webkit-progress-value { + background-color: #149eaa; } + .progress.is-link::-moz-progress-bar { + background-color: #149eaa; } + .progress.is-link::-ms-fill { + background-color: #149eaa; } + .progress.is-link:indeterminate { + background-image: linear-gradient(to right, #149eaa 30%, #dbdbdb 30%); } + .progress.is-info::-webkit-progress-value { + background-color: #209cee; } + .progress.is-info::-moz-progress-bar { + background-color: #209cee; } + .progress.is-info::-ms-fill { + background-color: #209cee; } + .progress.is-info:indeterminate { + background-image: linear-gradient(to right, #209cee 30%, #dbdbdb 30%); } + .progress.is-success::-webkit-progress-value { + background-color: #22c35b; } + .progress.is-success::-moz-progress-bar { + background-color: #22c35b; } + .progress.is-success::-ms-fill { + background-color: #22c35b; } + .progress.is-success:indeterminate { + background-image: linear-gradient(to right, #22c35b 30%, #dbdbdb 30%); } + .progress.is-warning::-webkit-progress-value { + background-color: #ffdd57; } + .progress.is-warning::-moz-progress-bar { + background-color: #ffdd57; } + .progress.is-warning::-ms-fill { + background-color: #ffdd57; } + .progress.is-warning:indeterminate { + background-image: linear-gradient(to right, #ffdd57 30%, #dbdbdb 30%); } + .progress.is-danger::-webkit-progress-value { + background-color: #da0b00; } + .progress.is-danger::-moz-progress-bar { + background-color: #da0b00; } + .progress.is-danger::-ms-fill { + background-color: #da0b00; } + .progress.is-danger:indeterminate { + background-image: linear-gradient(to right, #da0b00 30%, #dbdbdb 30%); } + .progress:indeterminate { + animation-duration: 1.5s; + animation-iteration-count: infinite; + animation-name: moveIndeterminate; + animation-timing-function: linear; + background-color: #dbdbdb; + background-image: linear-gradient(to right, #202020 30%, #dbdbdb 30%); + background-position: top left; + background-repeat: no-repeat; + background-size: 150% 150%; } + .progress:indeterminate::-webkit-progress-bar { + background-color: transparent; } + .progress:indeterminate::-moz-progress-bar { + background-color: transparent; } + .progress.is-small, #documenter .docs-sidebar form.docs-search > input.progress { + height: 0.75rem; } + .progress.is-medium { + height: 1.25rem; } + .progress.is-large { + height: 1.5rem; } + +@keyframes moveIndeterminate { + from { + background-position: 200% 0; } + to { + background-position: -200% 0; } } + +.table { + background-color: white; + color: #363636; } + .table td, + .table th { + border: 1px solid #dbdbdb; + border-width: 0 0 1px; + padding: 0.5em 0.75em; + vertical-align: top; } + .table td.is-white, + .table th.is-white { + background-color: white; + border-color: white; + color: #0a0a0a; } + .table td.is-black, + .table th.is-black { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .table td.is-light, + .table th.is-light { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .table td.is-dark, + .table th.is-dark { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .table td.is-primary, + .table th.is-primary { + background-color: #4eb5de; + border-color: #4eb5de; + color: #fff; } + .table td.is-link, + .table th.is-link { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + .table td.is-info, + .table th.is-info { + background-color: #209cee; + border-color: #209cee; + color: #fff; } + .table td.is-success, + .table th.is-success { + background-color: #22c35b; + border-color: #22c35b; + color: #fff; } + .table td.is-warning, + .table th.is-warning { + background-color: #ffdd57; + border-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .table td.is-danger, + .table th.is-danger { + background-color: #da0b00; + border-color: #da0b00; + color: #fff; } + .table td.is-narrow, + .table th.is-narrow { + white-space: nowrap; + width: 1%; } + .table td.is-selected, + .table th.is-selected { + background-color: #4eb5de; + color: #fff; } + .table td.is-selected a, + .table td.is-selected strong, + .table th.is-selected a, + .table th.is-selected strong { + color: currentColor; } + .table th { + color: #654ca3; } + .table th:not([align]) { + text-align: left; } + .table tr.is-selected { + background-color: #4eb5de; + color: #fff; } + .table tr.is-selected a, + .table tr.is-selected strong { + color: currentColor; } + .table tr.is-selected td, + .table tr.is-selected th { + border-color: #fff; + color: currentColor; } + .table thead { + background-color: transparent; } + .table thead td, + .table thead th { + border-width: 0 0 2px; + color: #654ca3; } + .table tfoot { + background-color: transparent; } + .table tfoot td, + .table tfoot th { + border-width: 2px 0 0; + color: #654ca3; } + .table tbody { + background-color: transparent; } + .table tbody tr:last-child td, + .table tbody tr:last-child th { + border-bottom-width: 0; } + .table.is-bordered td, + .table.is-bordered th { + border-width: 1px; } + .table.is-bordered tr:last-child td, + .table.is-bordered tr:last-child th { + border-bottom-width: 1px; } + .table.is-fullwidth { + width: 100%; } + .table.is-hoverable tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { + background-color: #fafafa; } + .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { + background-color: whitesmoke; } + .table.is-narrow td, + .table.is-narrow th { + padding: 0.25em 0.5em; } + .table.is-striped tbody tr:not(.is-selected):nth-child(even) { + background-color: #fafafa; } + +.table-container { + -webkit-overflow-scrolling: touch; + overflow: auto; + overflow-y: hidden; + max-width: 100%; } + +.tags { + align-items: center; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .tags .tag, .tags .content kbd, .content .tags kbd, .tags .docstring > section > a.docs-sourcelink { + margin-bottom: 0.5rem; } + .tags .tag:not(:last-child), .tags .content kbd:not(:last-child), .content .tags kbd:not(:last-child), .tags .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0.5rem; } + .tags:last-child { + margin-bottom: -0.5rem; } + .tags:not(:last-child) { + margin-bottom: 1rem; } + .tags.are-medium .tag:not(.is-normal):not(.is-large), .tags.are-medium .content kbd:not(.is-normal):not(.is-large), .content .tags.are-medium kbd:not(.is-normal):not(.is-large), .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { + font-size: 1rem; } + .tags.are-large .tag:not(.is-normal):not(.is-medium), .tags.are-large .content kbd:not(.is-normal):not(.is-medium), .content .tags.are-large kbd:not(.is-normal):not(.is-medium), .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { + font-size: 1.25rem; } + .tags.is-centered { + justify-content: center; } + .tags.is-centered .tag, .tags.is-centered .content kbd, .content .tags.is-centered kbd, .tags.is-centered .docstring > section > a.docs-sourcelink { + margin-right: 0.25rem; + margin-left: 0.25rem; } + .tags.is-right { + justify-content: flex-end; } + .tags.is-right .tag:not(:first-child), .tags.is-right .content kbd:not(:first-child), .content .tags.is-right kbd:not(:first-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0.5rem; } + .tags.is-right .tag:not(:last-child), .tags.is-right .content kbd:not(:last-child), .content .tags.is-right kbd:not(:last-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { + margin-right: 0; } + .tags.has-addons .tag, .tags.has-addons .content kbd, .content .tags.has-addons kbd, .tags.has-addons .docstring > section > a.docs-sourcelink { + margin-right: 0; } + .tags.has-addons .tag:not(:first-child), .tags.has-addons .content kbd:not(:first-child), .content .tags.has-addons kbd:not(:first-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { + margin-left: 0; + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .tags.has-addons .tag:not(:last-child), .tags.has-addons .content kbd:not(:last-child), .content .tags.has-addons kbd:not(:last-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + +.tag:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink:not(body) { + align-items: center; + background-color: whitesmoke; + border-radius: 4px; + color: #202020; + display: inline-flex; + font-size: 0.75rem; + height: 2em; + justify-content: center; + line-height: 1.5; + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + .tag:not(body) .delete, .content kbd:not(body) .delete, .docstring > section > a.docs-sourcelink:not(body) .delete { + margin-left: 0.25rem; + margin-right: -0.375rem; } + .tag.is-white:not(body), .content kbd.is-white:not(body), .docstring > section > a.docs-sourcelink.is-white:not(body) { + background-color: white; + color: #0a0a0a; } + .tag.is-black:not(body), .content kbd.is-black:not(body), .docstring > section > a.docs-sourcelink.is-black:not(body) { + background-color: #0a0a0a; + color: white; } + .tag.is-light:not(body), .content kbd.is-light:not(body), .docstring > section > a.docs-sourcelink.is-light:not(body) { + background-color: whitesmoke; + color: #363636; } + .tag.is-dark:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink.is-dark:not(body), .content .docstring > section > kbd:not(body) { + background-color: #363636; + color: whitesmoke; } + .tag.is-primary:not(body), .content kbd.is-primary:not(body), .docstring > section > a.docs-sourcelink:not(body) { + background-color: #4eb5de; + color: #fff; } + .tag.is-link:not(body), .content kbd.is-link:not(body), .docstring > section > a.docs-sourcelink.is-link:not(body) { + background-color: #149eaa; + color: #fff; } + .tag.is-info:not(body), .content kbd.is-info:not(body), .docstring > section > a.docs-sourcelink.is-info:not(body) { + background-color: #209cee; + color: #fff; } + .tag.is-success:not(body), .content kbd.is-success:not(body), .docstring > section > a.docs-sourcelink.is-success:not(body) { + background-color: #22c35b; + color: #fff; } + .tag.is-warning:not(body), .content kbd.is-warning:not(body), .docstring > section > a.docs-sourcelink.is-warning:not(body) { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .tag.is-danger:not(body), .content kbd.is-danger:not(body), .docstring > section > a.docs-sourcelink.is-danger:not(body) { + background-color: #da0b00; + color: #fff; } + .tag.is-normal:not(body), .content kbd.is-normal:not(body), .docstring > section > a.docs-sourcelink.is-normal:not(body) { + font-size: 0.75rem; } + .tag.is-medium:not(body), .content kbd.is-medium:not(body), .docstring > section > a.docs-sourcelink.is-medium:not(body) { + font-size: 1rem; } + .tag.is-large:not(body), .content kbd.is-large:not(body), .docstring > section > a.docs-sourcelink.is-large:not(body) { + font-size: 1.25rem; } + .tag:not(body) .icon:first-child:not(:last-child), .content kbd:not(body) .icon:first-child:not(:last-child), .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { + margin-left: -0.375em; + margin-right: 0.1875em; } + .tag:not(body) .icon:last-child:not(:first-child), .content kbd:not(body) .icon:last-child:not(:first-child), .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { + margin-left: 0.1875em; + margin-right: -0.375em; } + .tag:not(body) .icon:first-child:last-child, .content kbd:not(body) .icon:first-child:last-child, .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { + margin-left: -0.375em; + margin-right: -0.375em; } + .tag.is-delete:not(body), .content kbd.is-delete:not(body), .docstring > section > a.docs-sourcelink.is-delete:not(body) { + margin-left: 1px; + padding: 0; + position: relative; + width: 2em; } + .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + background-color: currentColor; + content: ""; + display: block; + left: 50%; + position: absolute; + top: 50%; + transform: translateX(-50%) translateY(-50%) rotate(45deg); + transform-origin: center center; } + .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { + height: 1px; + width: 50%; } + .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { + height: 50%; + width: 1px; } + .tag.is-delete:not(body):hover, .content kbd.is-delete:not(body):hover, .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, .tag.is-delete:not(body):focus, .content kbd.is-delete:not(body):focus, .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { + background-color: #e8e8e8; } + .tag.is-delete:not(body):active, .content kbd.is-delete:not(body):active, .docstring > section > a.docs-sourcelink.is-delete:not(body):active { + background-color: #dbdbdb; } + .tag.is-rounded:not(body), #documenter .docs-sidebar form.docs-search > input:not(body), .content kbd.is-rounded:not(body), #documenter .docs-sidebar .content form.docs-search > input:not(body), .docstring > section > a.docs-sourcelink.is-rounded:not(body) { + border-radius: 290486px; } + +a.tag:hover, .docstring > section > a.docs-sourcelink:hover { + text-decoration: underline; } + +.title, +.subtitle { + word-break: break-word; } + .title em, + .title span, + .subtitle em, + .subtitle span { + font-weight: inherit; } + .title sub, + .subtitle sub { + font-size: 0.75em; } + .title sup, + .subtitle sup { + font-size: 0.75em; } + .title .tag, .title .content kbd, .content .title kbd, .title .docstring > section > a.docs-sourcelink, + .subtitle .tag, + .subtitle .content kbd, + .content .subtitle kbd, + .subtitle .docstring > section > a.docs-sourcelink { + vertical-align: middle; } + +.title { + color: #363636; + font-size: 2rem; + font-weight: 600; + line-height: 1.125; } + .title strong { + color: inherit; + font-weight: inherit; } + .title + .highlight { + margin-top: -0.75rem; } + .title:not(.is-spaced) + .subtitle { + margin-top: -1.25rem; } + .title.is-1 { + font-size: 3rem; } + .title.is-2 { + font-size: 2.5rem; } + .title.is-3 { + font-size: 2rem; } + .title.is-4 { + font-size: 1.5rem; } + .title.is-5 { + font-size: 1.25rem; } + .title.is-6 { + font-size: 1rem; } + .title.is-7 { + font-size: 0.75rem; } + +.subtitle { + color: #4a4a4a; + font-size: 1.25rem; + font-weight: 400; + line-height: 1.25; } + .subtitle strong { + color: #363636; + font-weight: 600; } + .subtitle:not(.is-spaced) + .title { + margin-top: -1.25rem; } + .subtitle.is-1 { + font-size: 3rem; } + .subtitle.is-2 { + font-size: 2.5rem; } + .subtitle.is-3 { + font-size: 2rem; } + .subtitle.is-4 { + font-size: 1.5rem; } + .subtitle.is-5 { + font-size: 1.25rem; } + .subtitle.is-6 { + font-size: 1rem; } + .subtitle.is-7 { + font-size: 0.75rem; } + +.heading { + display: block; + font-size: 11px; + letter-spacing: 1px; + margin-bottom: 5px; + text-transform: uppercase; } + +.highlight { + font-weight: 400; + max-width: 100%; + overflow: hidden; + padding: 0; } + .highlight pre { + overflow: auto; + max-width: 100%; } + +.number { + align-items: center; + background-color: whitesmoke; + border-radius: 290486px; + display: inline-flex; + font-size: 1.25rem; + height: 2em; + justify-content: center; + margin-right: 1.5rem; + min-width: 2.5em; + padding: 0.25rem 0.5rem; + text-align: center; + vertical-align: top; } + +.select select, .textarea, .input, #documenter .docs-sidebar form.docs-search > input { + background-color: white; + border-color: #dbdbdb; + border-radius: 4px; + color: #363636; } + .select select::-moz-placeholder, .textarea::-moz-placeholder, .input::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select::-webkit-input-placeholder, .textarea::-webkit-input-placeholder, .input::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:-moz-placeholder, .textarea:-moz-placeholder, .input:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:-ms-input-placeholder, .textarea:-ms-input-placeholder, .input:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { + color: rgba(54, 54, 54, 0.3); } + .select select:hover, .textarea:hover, .input:hover, #documenter .docs-sidebar form.docs-search > input:hover, .select select.is-hovered, .is-hovered.textarea, .is-hovered.input, #documenter .docs-sidebar form.docs-search > input.is-hovered { + border-color: #149eaa; } + .select select:focus, .textarea:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .select select.is-focused, .is-focused.textarea, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .select select:active, .textarea:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .select select.is-active, .is-active.textarea, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + border-color: #fff; + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .select select[disabled], .textarea[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] .select select, .select fieldset[disabled] select, fieldset[disabled] .textarea, fieldset[disabled] .input, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input { + background-color: whitesmoke; + border-color: whitesmoke; + box-shadow: none; + color: #6b6b6b; } + .select select[disabled]::-moz-placeholder, .textarea[disabled]::-moz-placeholder, .input[disabled]::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] .select select::-moz-placeholder, .select fieldset[disabled] select::-moz-placeholder, fieldset[disabled] .textarea::-moz-placeholder, fieldset[disabled] .input::-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-moz-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]::-webkit-input-placeholder, .textarea[disabled]::-webkit-input-placeholder, .input[disabled]::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] .select select::-webkit-input-placeholder, .select fieldset[disabled] select::-webkit-input-placeholder, fieldset[disabled] .textarea::-webkit-input-placeholder, fieldset[disabled] .input::-webkit-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-webkit-input-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]:-moz-placeholder, .textarea[disabled]:-moz-placeholder, .input[disabled]:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] .select select:-moz-placeholder, .select fieldset[disabled] select:-moz-placeholder, fieldset[disabled] .textarea:-moz-placeholder, fieldset[disabled] .input:-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-moz-placeholder { + color: rgba(107, 107, 107, 0.3); } + .select select[disabled]:-ms-input-placeholder, .textarea[disabled]:-ms-input-placeholder, .input[disabled]:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] .select select:-ms-input-placeholder, .select fieldset[disabled] select:-ms-input-placeholder, fieldset[disabled] .textarea:-ms-input-placeholder, fieldset[disabled] .input:-ms-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-ms-input-placeholder { + color: rgba(107, 107, 107, 0.3); } + +.textarea, .input, #documenter .docs-sidebar form.docs-search > input { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); + max-width: 100%; + width: 100%; } + .textarea[readonly], .input[readonly], #documenter .docs-sidebar form.docs-search > input[readonly] { + box-shadow: none; } + .is-white.textarea, .is-white.input, #documenter .docs-sidebar form.docs-search > input.is-white { + border-color: white; } + .is-white.textarea:focus, .is-white.input:focus, #documenter .docs-sidebar form.docs-search > input.is-white:focus, .is-white.is-focused.textarea, .is-white.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-white.textarea:active, .is-white.input:active, #documenter .docs-sidebar form.docs-search > input.is-white:active, .is-white.is-active.textarea, .is-white.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .is-black.textarea, .is-black.input, #documenter .docs-sidebar form.docs-search > input.is-black { + border-color: #0a0a0a; } + .is-black.textarea:focus, .is-black.input:focus, #documenter .docs-sidebar form.docs-search > input.is-black:focus, .is-black.is-focused.textarea, .is-black.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-black.textarea:active, .is-black.input:active, #documenter .docs-sidebar form.docs-search > input.is-black:active, .is-black.is-active.textarea, .is-black.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .is-light.textarea, .is-light.input, #documenter .docs-sidebar form.docs-search > input.is-light { + border-color: whitesmoke; } + .is-light.textarea:focus, .is-light.input:focus, #documenter .docs-sidebar form.docs-search > input.is-light:focus, .is-light.is-focused.textarea, .is-light.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-light.textarea:active, .is-light.input:active, #documenter .docs-sidebar form.docs-search > input.is-light:active, .is-light.is-active.textarea, .is-light.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .is-dark.textarea, .content kbd.textarea, .is-dark.input, #documenter .docs-sidebar form.docs-search > input.is-dark, .content kbd.input { + border-color: #363636; } + .is-dark.textarea:focus, .content kbd.textarea:focus, .is-dark.input:focus, #documenter .docs-sidebar form.docs-search > input.is-dark:focus, .content kbd.input:focus, .is-dark.is-focused.textarea, .content kbd.is-focused.textarea, .is-dark.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .content kbd.is-focused.input, #documenter .docs-sidebar .content form.docs-search > input.is-focused, .is-dark.textarea:active, .content kbd.textarea:active, .is-dark.input:active, #documenter .docs-sidebar form.docs-search > input.is-dark:active, .content kbd.input:active, .is-dark.is-active.textarea, .content kbd.is-active.textarea, .is-dark.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .content kbd.is-active.input, #documenter .docs-sidebar .content form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .is-primary.textarea, .docstring > section > a.textarea.docs-sourcelink, .is-primary.input, #documenter .docs-sidebar form.docs-search > input.is-primary, .docstring > section > a.input.docs-sourcelink { + border-color: #4eb5de; } + .is-primary.textarea:focus, .docstring > section > a.textarea.docs-sourcelink:focus, .is-primary.input:focus, #documenter .docs-sidebar form.docs-search > input.is-primary:focus, .docstring > section > a.input.docs-sourcelink:focus, .is-primary.is-focused.textarea, .docstring > section > a.is-focused.textarea.docs-sourcelink, .is-primary.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .docstring > section > a.is-focused.input.docs-sourcelink, .is-primary.textarea:active, .docstring > section > a.textarea.docs-sourcelink:active, .is-primary.input:active, #documenter .docs-sidebar form.docs-search > input.is-primary:active, .docstring > section > a.input.docs-sourcelink:active, .is-primary.is-active.textarea, .docstring > section > a.is-active.textarea.docs-sourcelink, .is-primary.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .docstring > section > a.is-active.input.docs-sourcelink { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .is-link.textarea, .is-link.input, #documenter .docs-sidebar form.docs-search > input.is-link { + border-color: #149eaa; } + .is-link.textarea:focus, .is-link.input:focus, #documenter .docs-sidebar form.docs-search > input.is-link:focus, .is-link.is-focused.textarea, .is-link.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-link.textarea:active, .is-link.input:active, #documenter .docs-sidebar form.docs-search > input.is-link:active, .is-link.is-active.textarea, .is-link.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .is-info.textarea, .is-info.input, #documenter .docs-sidebar form.docs-search > input.is-info { + border-color: #209cee; } + .is-info.textarea:focus, .is-info.input:focus, #documenter .docs-sidebar form.docs-search > input.is-info:focus, .is-info.is-focused.textarea, .is-info.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-info.textarea:active, .is-info.input:active, #documenter .docs-sidebar form.docs-search > input.is-info:active, .is-info.is-active.textarea, .is-info.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .is-success.textarea, .is-success.input, #documenter .docs-sidebar form.docs-search > input.is-success { + border-color: #22c35b; } + .is-success.textarea:focus, .is-success.input:focus, #documenter .docs-sidebar form.docs-search > input.is-success:focus, .is-success.is-focused.textarea, .is-success.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-success.textarea:active, .is-success.input:active, #documenter .docs-sidebar form.docs-search > input.is-success:active, .is-success.is-active.textarea, .is-success.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .is-warning.textarea, .is-warning.input, #documenter .docs-sidebar form.docs-search > input.is-warning { + border-color: #ffdd57; } + .is-warning.textarea:focus, .is-warning.input:focus, #documenter .docs-sidebar form.docs-search > input.is-warning:focus, .is-warning.is-focused.textarea, .is-warning.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-warning.textarea:active, .is-warning.input:active, #documenter .docs-sidebar form.docs-search > input.is-warning:active, .is-warning.is-active.textarea, .is-warning.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .is-danger.textarea, .is-danger.input, #documenter .docs-sidebar form.docs-search > input.is-danger { + border-color: #da0b00; } + .is-danger.textarea:focus, .is-danger.input:focus, #documenter .docs-sidebar form.docs-search > input.is-danger:focus, .is-danger.is-focused.textarea, .is-danger.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-danger.textarea:active, .is-danger.input:active, #documenter .docs-sidebar form.docs-search > input.is-danger:active, .is-danger.is-active.textarea, .is-danger.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .is-small.textarea, .is-small.input, #documenter .docs-sidebar form.docs-search > input { + border-radius: 2px; + font-size: 0.75rem; } + .is-medium.textarea, .is-medium.input, #documenter .docs-sidebar form.docs-search > input.is-medium { + font-size: 1.25rem; } + .is-large.textarea, .is-large.input, #documenter .docs-sidebar form.docs-search > input.is-large { + font-size: 1.5rem; } + .is-fullwidth.textarea, .is-fullwidth.input, #documenter .docs-sidebar form.docs-search > input.is-fullwidth { + display: block; + width: 100%; } + .is-inline.textarea, .is-inline.input, #documenter .docs-sidebar form.docs-search > input.is-inline { + display: inline; + width: auto; } + +.input.is-rounded, #documenter .docs-sidebar form.docs-search > input { + border-radius: 290486px; + padding-left: 1em; + padding-right: 1em; } + +.input.is-static, #documenter .docs-sidebar form.docs-search > input.is-static { + background-color: transparent; + border-color: transparent; + box-shadow: none; + padding-left: 0; + padding-right: 0; } + +.textarea { + display: block; + max-width: 100%; + min-width: 100%; + padding: 0.625em; + resize: vertical; } + .textarea:not([rows]) { + max-height: 600px; + min-height: 120px; } + .textarea[rows] { + height: initial; } + .textarea.has-fixed-size { + resize: none; } + +.radio, .checkbox { + cursor: pointer; + display: inline-block; + line-height: 1.25; + position: relative; } + .radio input, .checkbox input { + cursor: pointer; } + .radio:hover, .checkbox:hover { + color: #363636; } + .radio[disabled], .checkbox[disabled], fieldset[disabled] .radio, fieldset[disabled] .checkbox { + color: #6b6b6b; + cursor: not-allowed; } + +.radio + .radio { + margin-left: 0.5em; } + +.select { + display: inline-block; + max-width: 100%; + position: relative; + vertical-align: top; } + .select:not(.is-multiple) { + height: 2.25em; } + .select:not(.is-multiple):not(.is-loading)::after { + border-color: #149eaa; + right: 1.125em; + z-index: 4; } + .select.is-rounded select, #documenter .docs-sidebar form.docs-search > input.select select { + border-radius: 290486px; + padding-left: 1em; } + .select select { + cursor: pointer; + display: block; + font-size: 1em; + max-width: 100%; + outline: none; } + .select select::-ms-expand { + display: none; } + .select select[disabled]:hover, fieldset[disabled] .select select:hover { + border-color: whitesmoke; } + .select select:not([multiple]) { + padding-right: 2.5em; } + .select select[multiple] { + height: auto; + padding: 0; } + .select select[multiple] option { + padding: 0.5em 1em; } + .select:not(.is-multiple):not(.is-loading):hover::after { + border-color: #363636; } + .select.is-white:not(:hover)::after { + border-color: white; } + .select.is-white select { + border-color: white; } + .select.is-white select:hover, .select.is-white select.is-hovered { + border-color: #f2f2f2; } + .select.is-white select:focus, .select.is-white select.is-focused, .select.is-white select:active, .select.is-white select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } + .select.is-black:not(:hover)::after { + border-color: #0a0a0a; } + .select.is-black select { + border-color: #0a0a0a; } + .select.is-black select:hover, .select.is-black select.is-hovered { + border-color: black; } + .select.is-black select:focus, .select.is-black select.is-focused, .select.is-black select:active, .select.is-black select.is-active { + box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } + .select.is-light:not(:hover)::after { + border-color: whitesmoke; } + .select.is-light select { + border-color: whitesmoke; } + .select.is-light select:hover, .select.is-light select.is-hovered { + border-color: #e8e8e8; } + .select.is-light select:focus, .select.is-light select.is-focused, .select.is-light select:active, .select.is-light select.is-active { + box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } + .select.is-dark:not(:hover)::after, .content kbd.select:not(:hover)::after { + border-color: #363636; } + .select.is-dark select, .content kbd.select select { + border-color: #363636; } + .select.is-dark select:hover, .content kbd.select select:hover, .select.is-dark select.is-hovered, .content kbd.select select.is-hovered { + border-color: #292929; } + .select.is-dark select:focus, .content kbd.select select:focus, .select.is-dark select.is-focused, .content kbd.select select.is-focused, .select.is-dark select:active, .content kbd.select select:active, .select.is-dark select.is-active, .content kbd.select select.is-active { + box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } + .select.is-primary:not(:hover)::after, .docstring > section > a.select.docs-sourcelink:not(:hover)::after { + border-color: #4eb5de; } + .select.is-primary select, .docstring > section > a.select.docs-sourcelink select { + border-color: #4eb5de; } + .select.is-primary select:hover, .docstring > section > a.select.docs-sourcelink select:hover, .select.is-primary select.is-hovered, .docstring > section > a.select.docs-sourcelink select.is-hovered { + border-color: #39acda; } + .select.is-primary select:focus, .docstring > section > a.select.docs-sourcelink select:focus, .select.is-primary select.is-focused, .docstring > section > a.select.docs-sourcelink select.is-focused, .select.is-primary select:active, .docstring > section > a.select.docs-sourcelink select:active, .select.is-primary select.is-active, .docstring > section > a.select.docs-sourcelink select.is-active { + box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } + .select.is-link:not(:hover)::after { + border-color: #149eaa; } + .select.is-link select { + border-color: #149eaa; } + .select.is-link select:hover, .select.is-link select.is-hovered { + border-color: #118993; } + .select.is-link select:focus, .select.is-link select.is-focused, .select.is-link select:active, .select.is-link select.is-active { + box-shadow: 0 0 0 0.125em rgba(20, 158, 170, 0.25); } + .select.is-info:not(:hover)::after { + border-color: #209cee; } + .select.is-info select { + border-color: #209cee; } + .select.is-info select:hover, .select.is-info select.is-hovered { + border-color: #1190e3; } + .select.is-info select:focus, .select.is-info select.is-focused, .select.is-info select:active, .select.is-info select.is-active { + box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } + .select.is-success:not(:hover)::after { + border-color: #22c35b; } + .select.is-success select { + border-color: #22c35b; } + .select.is-success select:hover, .select.is-success select.is-hovered { + border-color: #1ead51; } + .select.is-success select:focus, .select.is-success select.is-focused, .select.is-success select:active, .select.is-success select.is-active { + box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } + .select.is-warning:not(:hover)::after { + border-color: #ffdd57; } + .select.is-warning select { + border-color: #ffdd57; } + .select.is-warning select:hover, .select.is-warning select.is-hovered { + border-color: #ffd83e; } + .select.is-warning select:focus, .select.is-warning select.is-focused, .select.is-warning select:active, .select.is-warning select.is-active { + box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } + .select.is-danger:not(:hover)::after { + border-color: #da0b00; } + .select.is-danger select { + border-color: #da0b00; } + .select.is-danger select:hover, .select.is-danger select.is-hovered { + border-color: #c10a00; } + .select.is-danger select:focus, .select.is-danger select.is-focused, .select.is-danger select:active, .select.is-danger select.is-active { + box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } + .select.is-small, #documenter .docs-sidebar form.docs-search > input.select { + border-radius: 2px; + font-size: 0.75rem; } + .select.is-medium { + font-size: 1.25rem; } + .select.is-large { + font-size: 1.5rem; } + .select.is-disabled::after { + border-color: #6b6b6b; } + .select.is-fullwidth { + width: 100%; } + .select.is-fullwidth select { + width: 100%; } + .select.is-loading::after { + margin-top: 0; + position: absolute; + right: 0.625em; + top: 0.625em; + transform: none; } + .select.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + .select.is-loading.is-medium:after { + font-size: 1.25rem; } + .select.is-loading.is-large:after { + font-size: 1.5rem; } + +.file { + align-items: stretch; + display: flex; + justify-content: flex-start; + position: relative; } + .file.is-white .file-cta { + background-color: white; + border-color: transparent; + color: #0a0a0a; } + .file.is-white:hover .file-cta, .file.is-white.is-hovered .file-cta { + background-color: #f9f9f9; + border-color: transparent; + color: #0a0a0a; } + .file.is-white:focus .file-cta, .file.is-white.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); + color: #0a0a0a; } + .file.is-white:active .file-cta, .file.is-white.is-active .file-cta { + background-color: #f2f2f2; + border-color: transparent; + color: #0a0a0a; } + .file.is-black .file-cta { + background-color: #0a0a0a; + border-color: transparent; + color: white; } + .file.is-black:hover .file-cta, .file.is-black.is-hovered .file-cta { + background-color: #040404; + border-color: transparent; + color: white; } + .file.is-black:focus .file-cta, .file.is-black.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); + color: white; } + .file.is-black:active .file-cta, .file.is-black.is-active .file-cta { + background-color: black; + border-color: transparent; + color: white; } + .file.is-light .file-cta { + background-color: whitesmoke; + border-color: transparent; + color: #363636; } + .file.is-light:hover .file-cta, .file.is-light.is-hovered .file-cta { + background-color: #eeeeee; + border-color: transparent; + color: #363636; } + .file.is-light:focus .file-cta, .file.is-light.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25); + color: #363636; } + .file.is-light:active .file-cta, .file.is-light.is-active .file-cta { + background-color: #e8e8e8; + border-color: transparent; + color: #363636; } + .file.is-dark .file-cta, .content kbd.file .file-cta { + background-color: #363636; + border-color: transparent; + color: whitesmoke; } + .file.is-dark:hover .file-cta, .content kbd.file:hover .file-cta, .file.is-dark.is-hovered .file-cta, .content kbd.file.is-hovered .file-cta { + background-color: #2f2f2f; + border-color: transparent; + color: whitesmoke; } + .file.is-dark:focus .file-cta, .content kbd.file:focus .file-cta, .file.is-dark.is-focused .file-cta, .content kbd.file.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25); + color: whitesmoke; } + .file.is-dark:active .file-cta, .content kbd.file:active .file-cta, .file.is-dark.is-active .file-cta, .content kbd.file.is-active .file-cta { + background-color: #292929; + border-color: transparent; + color: whitesmoke; } + .file.is-primary .file-cta, .docstring > section > a.file.docs-sourcelink .file-cta { + background-color: #4eb5de; + border-color: transparent; + color: #fff; } + .file.is-primary:hover .file-cta, .docstring > section > a.file.docs-sourcelink:hover .file-cta, .file.is-primary.is-hovered .file-cta, .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { + background-color: #43b1dc; + border-color: transparent; + color: #fff; } + .file.is-primary:focus .file-cta, .docstring > section > a.file.docs-sourcelink:focus .file-cta, .file.is-primary.is-focused .file-cta, .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25); + color: #fff; } + .file.is-primary:active .file-cta, .docstring > section > a.file.docs-sourcelink:active .file-cta, .file.is-primary.is-active .file-cta, .docstring > section > a.file.is-active.docs-sourcelink .file-cta { + background-color: #39acda; + border-color: transparent; + color: #fff; } + .file.is-link .file-cta { + background-color: #149eaa; + border-color: transparent; + color: #fff; } + .file.is-link:hover .file-cta, .file.is-link.is-hovered .file-cta { + background-color: #13939f; + border-color: transparent; + color: #fff; } + .file.is-link:focus .file-cta, .file.is-link.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(20, 158, 170, 0.25); + color: #fff; } + .file.is-link:active .file-cta, .file.is-link.is-active .file-cta { + background-color: #118993; + border-color: transparent; + color: #fff; } + .file.is-info .file-cta { + background-color: #209cee; + border-color: transparent; + color: #fff; } + .file.is-info:hover .file-cta, .file.is-info.is-hovered .file-cta { + background-color: #1497ed; + border-color: transparent; + color: #fff; } + .file.is-info:focus .file-cta, .file.is-info.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(32, 156, 238, 0.25); + color: #fff; } + .file.is-info:active .file-cta, .file.is-info.is-active .file-cta { + background-color: #1190e3; + border-color: transparent; + color: #fff; } + .file.is-success .file-cta { + background-color: #22c35b; + border-color: transparent; + color: #fff; } + .file.is-success:hover .file-cta, .file.is-success.is-hovered .file-cta { + background-color: #20b856; + border-color: transparent; + color: #fff; } + .file.is-success:focus .file-cta, .file.is-success.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(34, 195, 91, 0.25); + color: #fff; } + .file.is-success:active .file-cta, .file.is-success.is-active .file-cta { + background-color: #1ead51; + border-color: transparent; + color: #fff; } + .file.is-warning .file-cta { + background-color: #ffdd57; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:hover .file-cta, .file.is-warning.is-hovered .file-cta { + background-color: #ffda4a; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:focus .file-cta, .file.is-warning.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(255, 221, 87, 0.25); + color: rgba(0, 0, 0, 0.7); } + .file.is-warning:active .file-cta, .file.is-warning.is-active .file-cta { + background-color: #ffd83e; + border-color: transparent; + color: rgba(0, 0, 0, 0.7); } + .file.is-danger .file-cta { + background-color: #da0b00; + border-color: transparent; + color: #fff; } + .file.is-danger:hover .file-cta, .file.is-danger.is-hovered .file-cta { + background-color: #cd0a00; + border-color: transparent; + color: #fff; } + .file.is-danger:focus .file-cta, .file.is-danger.is-focused .file-cta { + border-color: transparent; + box-shadow: 0 0 0.5em rgba(218, 11, 0, 0.25); + color: #fff; } + .file.is-danger:active .file-cta, .file.is-danger.is-active .file-cta { + background-color: #c10a00; + border-color: transparent; + color: #fff; } + .file.is-small, #documenter .docs-sidebar form.docs-search > input.file { + font-size: 0.75rem; } + .file.is-medium { + font-size: 1.25rem; } + .file.is-medium .file-icon .fa { + font-size: 21px; } + .file.is-large { + font-size: 1.5rem; } + .file.is-large .file-icon .fa { + font-size: 28px; } + .file.has-name .file-cta { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + .file.has-name .file-name { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .file.has-name.is-empty .file-cta { + border-radius: 4px; } + .file.has-name.is-empty .file-name { + display: none; } + .file.is-boxed .file-label { + flex-direction: column; } + .file.is-boxed .file-cta { + flex-direction: column; + height: auto; + padding: 1em 3em; } + .file.is-boxed .file-name { + border-width: 0 1px 1px; } + .file.is-boxed .file-icon { + height: 1.5em; + width: 1.5em; } + .file.is-boxed .file-icon .fa { + font-size: 21px; } + .file.is-boxed.is-small .file-icon .fa, #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { + font-size: 14px; } + .file.is-boxed.is-medium .file-icon .fa { + font-size: 28px; } + .file.is-boxed.is-large .file-icon .fa { + font-size: 35px; } + .file.is-boxed.has-name .file-cta { + border-radius: 4px 4px 0 0; } + .file.is-boxed.has-name .file-name { + border-radius: 0 0 4px 4px; + border-width: 0 1px 1px; } + .file.is-centered { + justify-content: center; } + .file.is-fullwidth .file-label { + width: 100%; } + .file.is-fullwidth .file-name { + flex-grow: 1; + max-width: none; } + .file.is-right { + justify-content: flex-end; } + .file.is-right .file-cta { + border-radius: 0 4px 4px 0; } + .file.is-right .file-name { + border-radius: 4px 0 0 4px; + border-width: 1px 0 1px 1px; + order: -1; } + +.file-label { + align-items: stretch; + display: flex; + cursor: pointer; + justify-content: flex-start; + overflow: hidden; + position: relative; } + .file-label:hover .file-cta { + background-color: #eeeeee; + color: #363636; } + .file-label:hover .file-name { + border-color: #d5d5d5; } + .file-label:active .file-cta { + background-color: #e8e8e8; + color: #363636; } + .file-label:active .file-name { + border-color: #cfcfcf; } + +.file-input { + height: 100%; + left: 0; + opacity: 0; + outline: none; + position: absolute; + top: 0; + width: 100%; } + +.file-cta, +.file-name { + border-color: #dbdbdb; + border-radius: 4px; + font-size: 1em; + padding-left: 1em; + padding-right: 1em; + white-space: nowrap; } + +.file-cta { + background-color: whitesmoke; + color: #4a4a4a; } + +.file-name { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px 1px 1px 0; + display: block; + max-width: 16em; + overflow: hidden; + text-align: left; + text-overflow: ellipsis; } + +.file-icon { + align-items: center; + display: flex; + height: 1em; + justify-content: center; + margin-right: 0.5em; + width: 1em; } + .file-icon .fa { + font-size: 14px; } + +.label { + color: #363636; + display: block; + font-size: 1rem; + font-weight: 700; } + .label:not(:last-child) { + margin-bottom: 0.5em; } + .label.is-small, #documenter .docs-sidebar form.docs-search > input.label { + font-size: 0.75rem; } + .label.is-medium { + font-size: 1.25rem; } + .label.is-large { + font-size: 1.5rem; } + +.help { + display: block; + font-size: 0.75rem; + margin-top: 0.25rem; } + .help.is-white { + color: white; } + .help.is-black { + color: #0a0a0a; } + .help.is-light { + color: whitesmoke; } + .help.is-dark, .content kbd.help { + color: #363636; } + .help.is-primary, .docstring > section > a.help.docs-sourcelink { + color: #4eb5de; } + .help.is-link { + color: #149eaa; } + .help.is-info { + color: #209cee; } + .help.is-success { + color: #22c35b; } + .help.is-warning { + color: #ffdd57; } + .help.is-danger { + color: #da0b00; } + +.field:not(:last-child) { + margin-bottom: 0.75rem; } + +.field.has-addons { + display: flex; + justify-content: flex-start; } + .field.has-addons .control:not(:last-child) { + margin-right: -1px; } + .field.has-addons .control:not(:first-child):not(:last-child) .button, + .field.has-addons .control:not(:first-child):not(:last-child) .input, + .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, + .field.has-addons .control:not(:first-child):not(:last-child) .select select { + border-radius: 0; } + .field.has-addons .control:first-child:not(:only-child) .button, + .field.has-addons .control:first-child:not(:only-child) .input, + .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, + .field.has-addons .control:first-child:not(:only-child) .select select { + border-bottom-right-radius: 0; + border-top-right-radius: 0; } + .field.has-addons .control:last-child:not(:only-child) .button, + .field.has-addons .control:last-child:not(:only-child) .input, + .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, + #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, + .field.has-addons .control:last-child:not(:only-child) .select select { + border-bottom-left-radius: 0; + border-top-left-radius: 0; } + .field.has-addons .control .button:not([disabled]):hover, .field.has-addons .control .button.is-hovered:not([disabled]), + .field.has-addons .control .input:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, + .field.has-addons .control .input.is-hovered:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), + .field.has-addons .control .select select:not([disabled]):hover, + .field.has-addons .control .select select.is-hovered:not([disabled]) { + z-index: 2; } + .field.has-addons .control .button:not([disabled]):focus, .field.has-addons .control .button.is-focused:not([disabled]), .field.has-addons .control .button:not([disabled]):active, .field.has-addons .control .button.is-active:not([disabled]), + .field.has-addons .control .input:not([disabled]):focus, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, + .field.has-addons .control .input.is-focused:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), + .field.has-addons .control .input:not([disabled]):active, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, + .field.has-addons .control .input.is-active:not([disabled]), + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), + .field.has-addons .control .select select:not([disabled]):focus, + .field.has-addons .control .select select.is-focused:not([disabled]), + .field.has-addons .control .select select:not([disabled]):active, + .field.has-addons .control .select select.is-active:not([disabled]) { + z-index: 3; } + .field.has-addons .control .button:not([disabled]):focus:hover, .field.has-addons .control .button.is-focused:not([disabled]):hover, .field.has-addons .control .button:not([disabled]):active:hover, .field.has-addons .control .button.is-active:not([disabled]):hover, + .field.has-addons .control .input:not([disabled]):focus:hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, + .field.has-addons .control .input.is-focused:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, + .field.has-addons .control .input:not([disabled]):active:hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, + .field.has-addons .control .input.is-active:not([disabled]):hover, + .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, + #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, + .field.has-addons .control .select select:not([disabled]):focus:hover, + .field.has-addons .control .select select.is-focused:not([disabled]):hover, + .field.has-addons .control .select select:not([disabled]):active:hover, + .field.has-addons .control .select select.is-active:not([disabled]):hover { + z-index: 4; } + .field.has-addons .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .field.has-addons.has-addons-centered { + justify-content: center; } + .field.has-addons.has-addons-right { + justify-content: flex-end; } + .field.has-addons.has-addons-fullwidth .control { + flex-grow: 1; + flex-shrink: 0; } + +.field.is-grouped { + display: flex; + justify-content: flex-start; } + .field.is-grouped > .control { + flex-shrink: 0; } + .field.is-grouped > .control:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + .field.is-grouped > .control.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .field.is-grouped.is-grouped-centered { + justify-content: center; } + .field.is-grouped.is-grouped-right { + justify-content: flex-end; } + .field.is-grouped.is-grouped-multiline { + flex-wrap: wrap; } + .field.is-grouped.is-grouped-multiline > .control:last-child, .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { + margin-bottom: 0.75rem; } + .field.is-grouped.is-grouped-multiline:last-child { + margin-bottom: -0.75rem; } + .field.is-grouped.is-grouped-multiline:not(:last-child) { + margin-bottom: 0; } + +@media screen and (min-width: 769px), print { + .field.is-horizontal { + display: flex; } } + +.field-label .label { + font-size: inherit; } + +@media screen and (max-width: 768px) { + .field-label { + margin-bottom: 0.5rem; } } + +@media screen and (min-width: 769px), print { + .field-label { + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + margin-right: 1.5rem; + text-align: right; } + .field-label.is-small, #documenter .docs-sidebar form.docs-search > input.field-label { + font-size: 0.75rem; + padding-top: 0.375em; } + .field-label.is-normal { + padding-top: 0.375em; } + .field-label.is-medium { + font-size: 1.25rem; + padding-top: 0.375em; } + .field-label.is-large { + font-size: 1.5rem; + padding-top: 0.375em; } } + +.field-body .field .field { + margin-bottom: 0; } + +@media screen and (min-width: 769px), print { + .field-body { + display: flex; + flex-basis: 0; + flex-grow: 5; + flex-shrink: 1; } + .field-body .field { + margin-bottom: 0; } + .field-body > .field { + flex-shrink: 1; } + .field-body > .field:not(.is-narrow) { + flex-grow: 1; } + .field-body > .field:not(:last-child) { + margin-right: 0.75rem; } } + +.control { + box-sizing: border-box; + clear: both; + font-size: 1rem; + position: relative; + text-align: left; } + .control.has-icons-left .input:focus ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, + .control.has-icons-left .select:focus ~ .icon, .control.has-icons-right .input:focus ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, + .control.has-icons-right .select:focus ~ .icon { + color: #6b6b6b; } + .control.has-icons-left .input.is-small ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, + .control.has-icons-left .select.is-small ~ .icon, .control.has-icons-right .input.is-small ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, + .control.has-icons-right .select.is-small ~ .icon { + font-size: 0.75rem; } + .control.has-icons-left .input.is-medium ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, + .control.has-icons-left .select.is-medium ~ .icon, .control.has-icons-right .input.is-medium ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, + .control.has-icons-right .select.is-medium ~ .icon { + font-size: 1.25rem; } + .control.has-icons-left .input.is-large ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, + .control.has-icons-left .select.is-large ~ .icon, .control.has-icons-right .input.is-large ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, + .control.has-icons-right .select.is-large ~ .icon { + font-size: 1.5rem; } + .control.has-icons-left .icon, .control.has-icons-right .icon { + color: #dbdbdb; + height: 2.25em; + pointer-events: none; + position: absolute; + top: 0; + width: 2.25em; + z-index: 4; } + .control.has-icons-left .input, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, + .control.has-icons-left .select select { + padding-left: 2.25em; } + .control.has-icons-left .icon.is-left { + left: 0; } + .control.has-icons-right .input, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, + .control.has-icons-right .select select { + padding-right: 2.25em; } + .control.has-icons-right .icon.is-right { + right: 0; } + .control.is-loading::after { + position: absolute !important; + right: 0.625em; + top: 0.625em; + z-index: 4; } + .control.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { + font-size: 0.75rem; } + .control.is-loading.is-medium:after { + font-size: 1.25rem; } + .control.is-loading.is-large:after { + font-size: 1.5rem; } + +.breadcrumb { + font-size: 1rem; + white-space: nowrap; } + .breadcrumb a { + align-items: center; + color: #149eaa; + display: flex; + justify-content: center; + padding: 0 0.75em; } + .breadcrumb a:hover { + color: #107c85; } + .breadcrumb li { + align-items: center; + display: flex; } + .breadcrumb li:first-child a { + padding-left: 0; } + .breadcrumb li.is-active a { + color: #654ca3; + cursor: default; + pointer-events: none; } + .breadcrumb li + li::before { + color: #b5b5b5; + content: "\0002f"; } + .breadcrumb ul, + .breadcrumb ol { + align-items: flex-start; + display: flex; + flex-wrap: wrap; + justify-content: flex-start; } + .breadcrumb .icon:first-child { + margin-right: 0.5em; } + .breadcrumb .icon:last-child { + margin-left: 0.5em; } + .breadcrumb.is-centered ol, + .breadcrumb.is-centered ul { + justify-content: center; } + .breadcrumb.is-right ol, + .breadcrumb.is-right ul { + justify-content: flex-end; } + .breadcrumb.is-small, #documenter .docs-sidebar form.docs-search > input.breadcrumb { + font-size: 0.75rem; } + .breadcrumb.is-medium { + font-size: 1.25rem; } + .breadcrumb.is-large { + font-size: 1.5rem; } + .breadcrumb.has-arrow-separator li + li::before { + content: "\02192"; } + .breadcrumb.has-bullet-separator li + li::before { + content: "\02022"; } + .breadcrumb.has-dot-separator li + li::before { + content: "\000b7"; } + .breadcrumb.has-succeeds-separator li + li::before { + content: "\0227B"; } + +.card { + background-color: white; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + color: #202020; + max-width: 100%; + position: relative; } + +.card-header { + background-color: transparent; + align-items: stretch; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + display: flex; } + +.card-header-title { + align-items: center; + color: #654ca3; + display: flex; + flex-grow: 1; + font-weight: 700; + padding: 0.75rem; } + .card-header-title.is-centered { + justify-content: center; } + +.card-header-icon { + align-items: center; + cursor: pointer; + display: flex; + justify-content: center; + padding: 0.75rem; } + +.card-image { + display: block; + position: relative; } + +.card-content { + background-color: transparent; + padding: 1.5rem; } + +.card-footer { + background-color: transparent; + border-top: 1px solid #dbdbdb; + align-items: stretch; + display: flex; } + +.card-footer-item { + align-items: center; + display: flex; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 0; + justify-content: center; + padding: 0.75rem; } + .card-footer-item:not(:last-child) { + border-right: 1px solid #dbdbdb; } + +.card .media:not(:last-child) { + margin-bottom: 1.5rem; } + +.dropdown { + display: inline-flex; + position: relative; + vertical-align: top; } + .dropdown.is-active .dropdown-menu, .dropdown.is-hoverable:hover .dropdown-menu { + display: block; } + .dropdown.is-right .dropdown-menu { + left: auto; + right: 0; } + .dropdown.is-up .dropdown-menu { + bottom: 100%; + padding-bottom: 4px; + padding-top: initial; + top: auto; } + +.dropdown-menu { + display: none; + left: 0; + min-width: 12rem; + padding-top: 4px; + position: absolute; + top: 100%; + z-index: 20; } + +.dropdown-content { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + +.dropdown-item { + color: #4a4a4a; + display: block; + font-size: 0.875rem; + line-height: 1.5; + padding: 0.375rem 1rem; + position: relative; } + +a.dropdown-item, +button.dropdown-item { + padding-right: 3rem; + text-align: left; + white-space: nowrap; + width: 100%; } + a.dropdown-item:hover, + button.dropdown-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + a.dropdown-item.is-active, + button.dropdown-item.is-active { + background-color: #149eaa; + color: #fff; } + +.dropdown-divider { + background-color: #dbdbdb; + border: none; + display: block; + height: 1px; + margin: 0.5rem 0; } + +.level { + align-items: center; + justify-content: space-between; } + .level code { + border-radius: 4px; } + .level img { + display: inline-block; + vertical-align: top; } + .level.is-mobile { + display: flex; } + .level.is-mobile .level-left, + .level.is-mobile .level-right { + display: flex; } + .level.is-mobile .level-left + .level-right { + margin-top: 0; } + .level.is-mobile .level-item:not(:last-child) { + margin-bottom: 0; + margin-right: 0.75rem; } + .level.is-mobile .level-item:not(.is-narrow) { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + .level { + display: flex; } + .level > .level-item:not(.is-narrow) { + flex-grow: 1; } } +.level-item { + align-items: center; + display: flex; + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; + justify-content: center; } + .level-item .title, + .level-item .subtitle { + margin-bottom: 0; } + @media screen and (max-width: 768px) { + .level-item:not(:last-child) { + margin-bottom: 0.75rem; } } +.level-left, +.level-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + .level-left .level-item.is-flexible, + .level-right .level-item.is-flexible { + flex-grow: 1; } + @media screen and (min-width: 769px), print { + .level-left .level-item:not(:last-child), + .level-right .level-item:not(:last-child) { + margin-right: 0.75rem; } } +.level-left { + align-items: center; + justify-content: flex-start; } + @media screen and (max-width: 768px) { + .level-left + .level-right { + margin-top: 1.5rem; } } + @media screen and (min-width: 769px), print { + .level-left { + display: flex; } } +.level-right { + align-items: center; + justify-content: flex-end; } + @media screen and (min-width: 769px), print { + .level-right { + display: flex; } } +.list { + background-color: white; + border-radius: 4px; + box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } + +.list-item { + display: block; + padding: 0.5em 1em; } + .list-item:not(a) { + color: #202020; } + .list-item:first-child { + border-top-left-radius: 4px; + border-top-right-radius: 4px; } + .list-item:last-child { + border-bottom-left-radius: 4px; + border-bottom-right-radius: 4px; } + .list-item:not(:last-child) { + border-bottom: 1px solid #dbdbdb; } + .list-item.is-active { + background-color: #149eaa; + color: #fff; } + +a.list-item { + background-color: whitesmoke; + cursor: pointer; } + +.media { + align-items: flex-start; + display: flex; + text-align: left; } + .media .content:not(:last-child) { + margin-bottom: 0.75rem; } + .media .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + display: flex; + padding-top: 0.75rem; } + .media .media .content:not(:last-child), + .media .media .control:not(:last-child) { + margin-bottom: 0.5rem; } + .media .media .media { + padding-top: 0.5rem; } + .media .media .media + .media { + margin-top: 0.5rem; } + .media + .media { + border-top: 1px solid rgba(219, 219, 219, 0.5); + margin-top: 1rem; + padding-top: 1rem; } + .media.is-large + .media { + margin-top: 1.5rem; + padding-top: 1.5rem; } + +.media-left, +.media-right { + flex-basis: auto; + flex-grow: 0; + flex-shrink: 0; } + +.media-left { + margin-right: 1rem; } + +.media-right { + margin-left: 1rem; } + +.media-content { + flex-basis: auto; + flex-grow: 1; + flex-shrink: 1; + text-align: left; } + +@media screen and (max-width: 768px) { + .media-content { + overflow-x: auto; } } + +.menu { + font-size: 1rem; } + .menu.is-small, #documenter .docs-sidebar form.docs-search > input.menu { + font-size: 0.75rem; } + .menu.is-medium { + font-size: 1.25rem; } + .menu.is-large { + font-size: 1.5rem; } + +.menu-list { + line-height: 1.25; } + .menu-list a { + border-radius: 2px; + color: #202020; + display: block; + padding: 0.5em 0.75em; } + .menu-list a:hover { + background-color: whitesmoke; + color: #654ca3; } + .menu-list a.is-active { + background-color: #149eaa; + color: #fff; } + .menu-list li ul { + border-left: 1px solid #dbdbdb; + margin: 0.75em; + padding-left: 0.75em; } + +.menu-label { + color: #6b6b6b; + font-size: 0.75em; + letter-spacing: 0.1em; + text-transform: uppercase; } + .menu-label:not(:first-child) { + margin-top: 1em; } + .menu-label:not(:last-child) { + margin-bottom: 1em; } + +.message { + background-color: whitesmoke; + border-radius: 4px; + font-size: 1rem; } + .message strong { + color: currentColor; } + .message a:not(.button):not(.tag):not(.dropdown-item) { + color: currentColor; + text-decoration: underline; } + .message.is-small, #documenter .docs-sidebar form.docs-search > input.message { + font-size: 0.75rem; } + .message.is-medium { + font-size: 1.25rem; } + .message.is-large { + font-size: 1.5rem; } + .message.is-white { + background-color: white; } + .message.is-white .message-header { + background-color: white; + color: #0a0a0a; } + .message.is-white .message-body { + border-color: white; + color: #4d4d4d; } + .message.is-black { + background-color: #fafafa; } + .message.is-black .message-header { + background-color: #0a0a0a; + color: white; } + .message.is-black .message-body { + border-color: #0a0a0a; + color: #090909; } + .message.is-light { + background-color: #fafafa; } + .message.is-light .message-header { + background-color: whitesmoke; + color: #363636; } + .message.is-light .message-body { + border-color: whitesmoke; + color: #505050; } + .message.is-dark, .content kbd.message { + background-color: #fafafa; } + .message.is-dark .message-header, .content kbd.message .message-header { + background-color: #363636; + color: whitesmoke; } + .message.is-dark .message-body, .content kbd.message .message-body { + border-color: #363636; + color: #2a2a2a; } + .message.is-primary, .docstring > section > a.message.docs-sourcelink { + background-color: #f6fbfd; } + .message.is-primary .message-header, .docstring > section > a.message.docs-sourcelink .message-header { + background-color: #4eb5de; + color: #fff; } + .message.is-primary .message-body, .docstring > section > a.message.docs-sourcelink .message-body { + border-color: #4eb5de; + color: #1f556a; } + .message.is-link { + background-color: #f6fdfe; } + .message.is-link .message-header { + background-color: #149eaa; + color: #fff; } + .message.is-link .message-body { + border-color: #149eaa; + color: #0b393d; } + .message.is-info { + background-color: #f6fbfe; } + .message.is-info .message-header { + background-color: #209cee; + color: #fff; } + .message.is-info .message-body { + border-color: #209cee; + color: #12537d; } + .message.is-success { + background-color: #f6fdf9; } + .message.is-success .message-header { + background-color: #22c35b; + color: #fff; } + .message.is-success .message-body { + border-color: #22c35b; + color: #0f361d; } + .message.is-warning { + background-color: #fffdf5; } + .message.is-warning .message-header { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .message.is-warning .message-body { + border-color: #ffdd57; + color: #3c3108; } + .message.is-danger { + background-color: #fff5f5; } + .message.is-danger .message-header { + background-color: #da0b00; + color: #fff; } + .message.is-danger .message-body { + border-color: #da0b00; + color: #9b0c04; } + +.message-header { + align-items: center; + background-color: #202020; + border-radius: 4px 4px 0 0; + color: #fff; + display: flex; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.75em 1em; + position: relative; } + .message-header .delete { + flex-grow: 0; + flex-shrink: 0; + margin-left: 0.75em; } + .message-header + .message-body { + border-width: 0; + border-top-left-radius: 0; + border-top-right-radius: 0; } + +.message-body { + border-color: #dbdbdb; + border-radius: 4px; + border-style: solid; + border-width: 0 0 0 4px; + color: #202020; + padding: 1.25em 1.5em; } + .message-body code, + .message-body pre { + background-color: white; } + .message-body pre code { + background-color: transparent; } + +.modal { + align-items: center; + display: none; + flex-direction: column; + justify-content: center; + overflow: hidden; + position: fixed; + z-index: 40; } + .modal.is-active { + display: flex; } + +.modal-background { + background-color: rgba(10, 10, 10, 0.86); } + +.modal-content, +.modal-card { + margin: 0 20px; + max-height: calc(100vh - 160px); + overflow: auto; + position: relative; + width: 100%; } + @media screen and (min-width: 769px), print { + .modal-content, + .modal-card { + margin: 0 auto; + max-height: calc(100vh - 40px); + width: 640px; } } +.modal-close { + background: none; + height: 40px; + position: fixed; + right: 20px; + top: 20px; + width: 40px; } + +.modal-card { + display: flex; + flex-direction: column; + max-height: calc(100vh - 40px); + overflow: hidden; + -ms-overflow-y: visible; } + +.modal-card-head, +.modal-card-foot { + align-items: center; + background-color: whitesmoke; + display: flex; + flex-shrink: 0; + justify-content: flex-start; + padding: 20px; + position: relative; } + +.modal-card-head { + border-bottom: 1px solid #dbdbdb; + border-top-left-radius: 6px; + border-top-right-radius: 6px; } + +.modal-card-title { + color: #654ca3; + flex-grow: 1; + flex-shrink: 0; + font-size: 1.5rem; + line-height: 1; } + +.modal-card-foot { + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 1px solid #dbdbdb; } + .modal-card-foot .button:not(:last-child) { + margin-right: 0.5em; } + +.modal-card-body { + -webkit-overflow-scrolling: touch; + background-color: white; + flex-grow: 1; + flex-shrink: 1; + overflow: auto; + padding: 20px; } + +.navbar { + background-color: white; + min-height: 3.25rem; + position: relative; + z-index: 30; } + .navbar.is-white { + background-color: white; + color: #0a0a0a; } + .navbar.is-white .navbar-brand > .navbar-item, + .navbar.is-white .navbar-brand .navbar-link { + color: #0a0a0a; } + .navbar.is-white .navbar-brand > a.navbar-item:focus, .navbar.is-white .navbar-brand > a.navbar-item:hover, .navbar.is-white .navbar-brand > a.navbar-item.is-active, + .navbar.is-white .navbar-brand .navbar-link:focus, + .navbar.is-white .navbar-brand .navbar-link:hover, + .navbar.is-white .navbar-brand .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-brand .navbar-link::after { + border-color: #0a0a0a; } + .navbar.is-white .navbar-burger { + color: #0a0a0a; } + @media screen and (min-width: 1056px) { + .navbar.is-white .navbar-start > .navbar-item, + .navbar.is-white .navbar-start .navbar-link, + .navbar.is-white .navbar-end > .navbar-item, + .navbar.is-white .navbar-end .navbar-link { + color: #0a0a0a; } + .navbar.is-white .navbar-start > a.navbar-item:focus, .navbar.is-white .navbar-start > a.navbar-item:hover, .navbar.is-white .navbar-start > a.navbar-item.is-active, + .navbar.is-white .navbar-start .navbar-link:focus, + .navbar.is-white .navbar-start .navbar-link:hover, + .navbar.is-white .navbar-start .navbar-link.is-active, + .navbar.is-white .navbar-end > a.navbar-item:focus, + .navbar.is-white .navbar-end > a.navbar-item:hover, + .navbar.is-white .navbar-end > a.navbar-item.is-active, + .navbar.is-white .navbar-end .navbar-link:focus, + .navbar.is-white .navbar-end .navbar-link:hover, + .navbar.is-white .navbar-end .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-start .navbar-link::after, + .navbar.is-white .navbar-end .navbar-link::after { + border-color: #0a0a0a; } + .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #f2f2f2; + color: #0a0a0a; } + .navbar.is-white .navbar-dropdown a.navbar-item.is-active { + background-color: white; + color: #0a0a0a; } } + .navbar.is-black { + background-color: #0a0a0a; + color: white; } + .navbar.is-black .navbar-brand > .navbar-item, + .navbar.is-black .navbar-brand .navbar-link { + color: white; } + .navbar.is-black .navbar-brand > a.navbar-item:focus, .navbar.is-black .navbar-brand > a.navbar-item:hover, .navbar.is-black .navbar-brand > a.navbar-item.is-active, + .navbar.is-black .navbar-brand .navbar-link:focus, + .navbar.is-black .navbar-brand .navbar-link:hover, + .navbar.is-black .navbar-brand .navbar-link.is-active { + background-color: black; + color: white; } + .navbar.is-black .navbar-brand .navbar-link::after { + border-color: white; } + .navbar.is-black .navbar-burger { + color: white; } + @media screen and (min-width: 1056px) { + .navbar.is-black .navbar-start > .navbar-item, + .navbar.is-black .navbar-start .navbar-link, + .navbar.is-black .navbar-end > .navbar-item, + .navbar.is-black .navbar-end .navbar-link { + color: white; } + .navbar.is-black .navbar-start > a.navbar-item:focus, .navbar.is-black .navbar-start > a.navbar-item:hover, .navbar.is-black .navbar-start > a.navbar-item.is-active, + .navbar.is-black .navbar-start .navbar-link:focus, + .navbar.is-black .navbar-start .navbar-link:hover, + .navbar.is-black .navbar-start .navbar-link.is-active, + .navbar.is-black .navbar-end > a.navbar-item:focus, + .navbar.is-black .navbar-end > a.navbar-item:hover, + .navbar.is-black .navbar-end > a.navbar-item.is-active, + .navbar.is-black .navbar-end .navbar-link:focus, + .navbar.is-black .navbar-end .navbar-link:hover, + .navbar.is-black .navbar-end .navbar-link.is-active { + background-color: black; + color: white; } + .navbar.is-black .navbar-start .navbar-link::after, + .navbar.is-black .navbar-end .navbar-link::after { + border-color: white; } + .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { + background-color: black; + color: white; } + .navbar.is-black .navbar-dropdown a.navbar-item.is-active { + background-color: #0a0a0a; + color: white; } } + .navbar.is-light { + background-color: whitesmoke; + color: #363636; } + .navbar.is-light .navbar-brand > .navbar-item, + .navbar.is-light .navbar-brand .navbar-link { + color: #363636; } + .navbar.is-light .navbar-brand > a.navbar-item:focus, .navbar.is-light .navbar-brand > a.navbar-item:hover, .navbar.is-light .navbar-brand > a.navbar-item.is-active, + .navbar.is-light .navbar-brand .navbar-link:focus, + .navbar.is-light .navbar-brand .navbar-link:hover, + .navbar.is-light .navbar-brand .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-brand .navbar-link::after { + border-color: #363636; } + .navbar.is-light .navbar-burger { + color: #363636; } + @media screen and (min-width: 1056px) { + .navbar.is-light .navbar-start > .navbar-item, + .navbar.is-light .navbar-start .navbar-link, + .navbar.is-light .navbar-end > .navbar-item, + .navbar.is-light .navbar-end .navbar-link { + color: #363636; } + .navbar.is-light .navbar-start > a.navbar-item:focus, .navbar.is-light .navbar-start > a.navbar-item:hover, .navbar.is-light .navbar-start > a.navbar-item.is-active, + .navbar.is-light .navbar-start .navbar-link:focus, + .navbar.is-light .navbar-start .navbar-link:hover, + .navbar.is-light .navbar-start .navbar-link.is-active, + .navbar.is-light .navbar-end > a.navbar-item:focus, + .navbar.is-light .navbar-end > a.navbar-item:hover, + .navbar.is-light .navbar-end > a.navbar-item.is-active, + .navbar.is-light .navbar-end .navbar-link:focus, + .navbar.is-light .navbar-end .navbar-link:hover, + .navbar.is-light .navbar-end .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-start .navbar-link::after, + .navbar.is-light .navbar-end .navbar-link::after { + border-color: #363636; } + .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #e8e8e8; + color: #363636; } + .navbar.is-light .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #363636; } } + .navbar.is-dark, .content kbd.navbar { + background-color: #363636; + color: whitesmoke; } + .navbar.is-dark .navbar-brand > .navbar-item, .content kbd.navbar .navbar-brand > .navbar-item, + .navbar.is-dark .navbar-brand .navbar-link, + .content kbd.navbar .navbar-brand .navbar-link { + color: whitesmoke; } + .navbar.is-dark .navbar-brand > a.navbar-item:focus, .content kbd.navbar .navbar-brand > a.navbar-item:focus, .navbar.is-dark .navbar-brand > a.navbar-item:hover, .content kbd.navbar .navbar-brand > a.navbar-item:hover, .navbar.is-dark .navbar-brand > a.navbar-item.is-active, .content kbd.navbar .navbar-brand > a.navbar-item.is-active, + .navbar.is-dark .navbar-brand .navbar-link:focus, + .content kbd.navbar .navbar-brand .navbar-link:focus, + .navbar.is-dark .navbar-brand .navbar-link:hover, + .content kbd.navbar .navbar-brand .navbar-link:hover, + .navbar.is-dark .navbar-brand .navbar-link.is-active, + .content kbd.navbar .navbar-brand .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-brand .navbar-link::after, .content kbd.navbar .navbar-brand .navbar-link::after { + border-color: whitesmoke; } + .navbar.is-dark .navbar-burger, .content kbd.navbar .navbar-burger { + color: whitesmoke; } + @media screen and (min-width: 1056px) { + .navbar.is-dark .navbar-start > .navbar-item, .content kbd.navbar .navbar-start > .navbar-item, + .navbar.is-dark .navbar-start .navbar-link, + .content kbd.navbar .navbar-start .navbar-link, + .navbar.is-dark .navbar-end > .navbar-item, + .content kbd.navbar .navbar-end > .navbar-item, + .navbar.is-dark .navbar-end .navbar-link, + .content kbd.navbar .navbar-end .navbar-link { + color: whitesmoke; } + .navbar.is-dark .navbar-start > a.navbar-item:focus, .content kbd.navbar .navbar-start > a.navbar-item:focus, .navbar.is-dark .navbar-start > a.navbar-item:hover, .content kbd.navbar .navbar-start > a.navbar-item:hover, .navbar.is-dark .navbar-start > a.navbar-item.is-active, .content kbd.navbar .navbar-start > a.navbar-item.is-active, + .navbar.is-dark .navbar-start .navbar-link:focus, + .content kbd.navbar .navbar-start .navbar-link:focus, + .navbar.is-dark .navbar-start .navbar-link:hover, + .content kbd.navbar .navbar-start .navbar-link:hover, + .navbar.is-dark .navbar-start .navbar-link.is-active, + .content kbd.navbar .navbar-start .navbar-link.is-active, + .navbar.is-dark .navbar-end > a.navbar-item:focus, + .content kbd.navbar .navbar-end > a.navbar-item:focus, + .navbar.is-dark .navbar-end > a.navbar-item:hover, + .content kbd.navbar .navbar-end > a.navbar-item:hover, + .navbar.is-dark .navbar-end > a.navbar-item.is-active, + .content kbd.navbar .navbar-end > a.navbar-item.is-active, + .navbar.is-dark .navbar-end .navbar-link:focus, + .content kbd.navbar .navbar-end .navbar-link:focus, + .navbar.is-dark .navbar-end .navbar-link:hover, + .content kbd.navbar .navbar-end .navbar-link:hover, + .navbar.is-dark .navbar-end .navbar-link.is-active, + .content kbd.navbar .navbar-end .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-start .navbar-link::after, .content kbd.navbar .navbar-start .navbar-link::after, + .navbar.is-dark .navbar-end .navbar-link::after, + .content kbd.navbar .navbar-end .navbar-link::after { + border-color: whitesmoke; } + .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, + .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, + .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #292929; + color: whitesmoke; } + .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { + background-color: #363636; + color: whitesmoke; } } + .navbar.is-primary, .docstring > section > a.navbar.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .navbar.is-primary .navbar-brand > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, + .navbar.is-primary .navbar-brand .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-primary .navbar-brand > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, .navbar.is-primary .navbar-brand > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, .navbar.is-primary .navbar-brand > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, + .navbar.is-primary .navbar-brand .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, + .navbar.is-primary .navbar-brand .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, + .navbar.is-primary .navbar-brand .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-brand .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-primary .navbar-burger, .docstring > section > a.navbar.docs-sourcelink .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-primary .navbar-start > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, + .navbar.is-primary .navbar-start .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, + .navbar.is-primary .navbar-end > .navbar-item, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, + .navbar.is-primary .navbar-end .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { + color: #fff; } + .navbar.is-primary .navbar-start > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, .navbar.is-primary .navbar-start > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, .navbar.is-primary .navbar-start > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, + .navbar.is-primary .navbar-start .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, + .navbar.is-primary .navbar-start .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, + .navbar.is-primary .navbar-start .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, + .navbar.is-primary .navbar-end > a.navbar-item:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, + .navbar.is-primary .navbar-end > a.navbar-item:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, + .navbar.is-primary .navbar-end > a.navbar-item.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, + .navbar.is-primary .navbar-end .navbar-link:focus, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, + .navbar.is-primary .navbar-end .navbar-link:hover, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, + .navbar.is-primary .navbar-end .navbar-link.is-active, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-start .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, + .navbar.is-primary .navbar-end .navbar-link::after, + .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, + .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #39acda; + color: #fff; } + .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { + background-color: #4eb5de; + color: #fff; } } + .navbar.is-link { + background-color: #149eaa; + color: #fff; } + .navbar.is-link .navbar-brand > .navbar-item, + .navbar.is-link .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-link .navbar-brand > a.navbar-item:focus, .navbar.is-link .navbar-brand > a.navbar-item:hover, .navbar.is-link .navbar-brand > a.navbar-item.is-active, + .navbar.is-link .navbar-brand .navbar-link:focus, + .navbar.is-link .navbar-brand .navbar-link:hover, + .navbar.is-link .navbar-brand .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-link .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-link .navbar-start > .navbar-item, + .navbar.is-link .navbar-start .navbar-link, + .navbar.is-link .navbar-end > .navbar-item, + .navbar.is-link .navbar-end .navbar-link { + color: #fff; } + .navbar.is-link .navbar-start > a.navbar-item:focus, .navbar.is-link .navbar-start > a.navbar-item:hover, .navbar.is-link .navbar-start > a.navbar-item.is-active, + .navbar.is-link .navbar-start .navbar-link:focus, + .navbar.is-link .navbar-start .navbar-link:hover, + .navbar.is-link .navbar-start .navbar-link.is-active, + .navbar.is-link .navbar-end > a.navbar-item:focus, + .navbar.is-link .navbar-end > a.navbar-item:hover, + .navbar.is-link .navbar-end > a.navbar-item.is-active, + .navbar.is-link .navbar-end .navbar-link:focus, + .navbar.is-link .navbar-end .navbar-link:hover, + .navbar.is-link .navbar-end .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-start .navbar-link::after, + .navbar.is-link .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #118993; + color: #fff; } + .navbar.is-link .navbar-dropdown a.navbar-item.is-active { + background-color: #149eaa; + color: #fff; } } + .navbar.is-info { + background-color: #209cee; + color: #fff; } + .navbar.is-info .navbar-brand > .navbar-item, + .navbar.is-info .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-info .navbar-brand > a.navbar-item:focus, .navbar.is-info .navbar-brand > a.navbar-item:hover, .navbar.is-info .navbar-brand > a.navbar-item.is-active, + .navbar.is-info .navbar-brand .navbar-link:focus, + .navbar.is-info .navbar-brand .navbar-link:hover, + .navbar.is-info .navbar-brand .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-info .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-info .navbar-start > .navbar-item, + .navbar.is-info .navbar-start .navbar-link, + .navbar.is-info .navbar-end > .navbar-item, + .navbar.is-info .navbar-end .navbar-link { + color: #fff; } + .navbar.is-info .navbar-start > a.navbar-item:focus, .navbar.is-info .navbar-start > a.navbar-item:hover, .navbar.is-info .navbar-start > a.navbar-item.is-active, + .navbar.is-info .navbar-start .navbar-link:focus, + .navbar.is-info .navbar-start .navbar-link:hover, + .navbar.is-info .navbar-start .navbar-link.is-active, + .navbar.is-info .navbar-end > a.navbar-item:focus, + .navbar.is-info .navbar-end > a.navbar-item:hover, + .navbar.is-info .navbar-end > a.navbar-item.is-active, + .navbar.is-info .navbar-end .navbar-link:focus, + .navbar.is-info .navbar-end .navbar-link:hover, + .navbar.is-info .navbar-end .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-start .navbar-link::after, + .navbar.is-info .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1190e3; + color: #fff; } + .navbar.is-info .navbar-dropdown a.navbar-item.is-active { + background-color: #209cee; + color: #fff; } } + .navbar.is-success { + background-color: #22c35b; + color: #fff; } + .navbar.is-success .navbar-brand > .navbar-item, + .navbar.is-success .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-success .navbar-brand > a.navbar-item:focus, .navbar.is-success .navbar-brand > a.navbar-item:hover, .navbar.is-success .navbar-brand > a.navbar-item.is-active, + .navbar.is-success .navbar-brand .navbar-link:focus, + .navbar.is-success .navbar-brand .navbar-link:hover, + .navbar.is-success .navbar-brand .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-success .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-success .navbar-start > .navbar-item, + .navbar.is-success .navbar-start .navbar-link, + .navbar.is-success .navbar-end > .navbar-item, + .navbar.is-success .navbar-end .navbar-link { + color: #fff; } + .navbar.is-success .navbar-start > a.navbar-item:focus, .navbar.is-success .navbar-start > a.navbar-item:hover, .navbar.is-success .navbar-start > a.navbar-item.is-active, + .navbar.is-success .navbar-start .navbar-link:focus, + .navbar.is-success .navbar-start .navbar-link:hover, + .navbar.is-success .navbar-start .navbar-link.is-active, + .navbar.is-success .navbar-end > a.navbar-item:focus, + .navbar.is-success .navbar-end > a.navbar-item:hover, + .navbar.is-success .navbar-end > a.navbar-item.is-active, + .navbar.is-success .navbar-end .navbar-link:focus, + .navbar.is-success .navbar-end .navbar-link:hover, + .navbar.is-success .navbar-end .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-start .navbar-link::after, + .navbar.is-success .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #1ead51; + color: #fff; } + .navbar.is-success .navbar-dropdown a.navbar-item.is-active { + background-color: #22c35b; + color: #fff; } } + .navbar.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand > .navbar-item, + .navbar.is-warning .navbar-brand .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand > a.navbar-item:focus, .navbar.is-warning .navbar-brand > a.navbar-item:hover, .navbar.is-warning .navbar-brand > a.navbar-item.is-active, + .navbar.is-warning .navbar-brand .navbar-link:focus, + .navbar.is-warning .navbar-brand .navbar-link:hover, + .navbar.is-warning .navbar-brand .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-brand .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-burger { + color: rgba(0, 0, 0, 0.7); } + @media screen and (min-width: 1056px) { + .navbar.is-warning .navbar-start > .navbar-item, + .navbar.is-warning .navbar-start .navbar-link, + .navbar.is-warning .navbar-end > .navbar-item, + .navbar.is-warning .navbar-end .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-start > a.navbar-item:focus, .navbar.is-warning .navbar-start > a.navbar-item:hover, .navbar.is-warning .navbar-start > a.navbar-item.is-active, + .navbar.is-warning .navbar-start .navbar-link:focus, + .navbar.is-warning .navbar-start .navbar-link:hover, + .navbar.is-warning .navbar-start .navbar-link.is-active, + .navbar.is-warning .navbar-end > a.navbar-item:focus, + .navbar.is-warning .navbar-end > a.navbar-item:hover, + .navbar.is-warning .navbar-end > a.navbar-item.is-active, + .navbar.is-warning .navbar-end .navbar-link:focus, + .navbar.is-warning .navbar-end .navbar-link:hover, + .navbar.is-warning .navbar-end .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-start .navbar-link::after, + .navbar.is-warning .navbar-end .navbar-link::after { + border-color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } } + .navbar.is-danger { + background-color: #da0b00; + color: #fff; } + .navbar.is-danger .navbar-brand > .navbar-item, + .navbar.is-danger .navbar-brand .navbar-link { + color: #fff; } + .navbar.is-danger .navbar-brand > a.navbar-item:focus, .navbar.is-danger .navbar-brand > a.navbar-item:hover, .navbar.is-danger .navbar-brand > a.navbar-item.is-active, + .navbar.is-danger .navbar-brand .navbar-link:focus, + .navbar.is-danger .navbar-brand .navbar-link:hover, + .navbar.is-danger .navbar-brand .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-brand .navbar-link::after { + border-color: #fff; } + .navbar.is-danger .navbar-burger { + color: #fff; } + @media screen and (min-width: 1056px) { + .navbar.is-danger .navbar-start > .navbar-item, + .navbar.is-danger .navbar-start .navbar-link, + .navbar.is-danger .navbar-end > .navbar-item, + .navbar.is-danger .navbar-end .navbar-link { + color: #fff; } + .navbar.is-danger .navbar-start > a.navbar-item:focus, .navbar.is-danger .navbar-start > a.navbar-item:hover, .navbar.is-danger .navbar-start > a.navbar-item.is-active, + .navbar.is-danger .navbar-start .navbar-link:focus, + .navbar.is-danger .navbar-start .navbar-link:hover, + .navbar.is-danger .navbar-start .navbar-link.is-active, + .navbar.is-danger .navbar-end > a.navbar-item:focus, + .navbar.is-danger .navbar-end > a.navbar-item:hover, + .navbar.is-danger .navbar-end > a.navbar-item.is-active, + .navbar.is-danger .navbar-end .navbar-link:focus, + .navbar.is-danger .navbar-end .navbar-link:hover, + .navbar.is-danger .navbar-end .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-start .navbar-link::after, + .navbar.is-danger .navbar-end .navbar-link::after { + border-color: #fff; } + .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, + .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, + .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #c10a00; + color: #fff; } + .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { + background-color: #da0b00; + color: #fff; } } + .navbar > .container { + align-items: stretch; + display: flex; + min-height: 3.25rem; + width: 100%; } + .navbar.has-shadow { + box-shadow: 0 2px 0 0 whitesmoke; } + .navbar.is-fixed-bottom, .navbar.is-fixed-top { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom { + bottom: 0; } + .navbar.is-fixed-bottom.has-shadow { + box-shadow: 0 -2px 0 0 whitesmoke; } + .navbar.is-fixed-top { + top: 0; } + +html.has-navbar-fixed-top, +body.has-navbar-fixed-top { + padding-top: 3.25rem; } + +html.has-navbar-fixed-bottom, +body.has-navbar-fixed-bottom { + padding-bottom: 3.25rem; } + +.navbar-brand, +.navbar-tabs { + align-items: stretch; + display: flex; + flex-shrink: 0; + min-height: 3.25rem; } + +.navbar-brand a.navbar-item:focus, .navbar-brand a.navbar-item:hover { + background-color: transparent; } + +.navbar-tabs { + -webkit-overflow-scrolling: touch; + max-width: 100vw; + overflow-x: auto; + overflow-y: hidden; } + +.navbar-burger { + color: #4a4a4a; + cursor: pointer; + display: block; + height: 3.25rem; + position: relative; + width: 3.25rem; + margin-left: auto; } + .navbar-burger span { + background-color: currentColor; + display: block; + height: 1px; + left: calc(50% - 8px); + position: absolute; + transform-origin: center; + transition-duration: 86ms; + transition-property: background-color, opacity, transform; + transition-timing-function: ease-out; + width: 16px; } + .navbar-burger span:nth-child(1) { + top: calc(50% - 6px); } + .navbar-burger span:nth-child(2) { + top: calc(50% - 1px); } + .navbar-burger span:nth-child(3) { + top: calc(50% + 4px); } + .navbar-burger:hover { + background-color: rgba(0, 0, 0, 0.05); } + .navbar-burger.is-active span:nth-child(1) { + transform: translateY(5px) rotate(45deg); } + .navbar-burger.is-active span:nth-child(2) { + opacity: 0; } + .navbar-burger.is-active span:nth-child(3) { + transform: translateY(-5px) rotate(-45deg); } + +.navbar-menu { + display: none; } + +.navbar-item, +.navbar-link { + color: #4a4a4a; + display: block; + line-height: 1.5; + padding: 0.5rem 0.75rem; + position: relative; } + .navbar-item .icon:only-child, + .navbar-link .icon:only-child { + margin-left: -0.25rem; + margin-right: -0.25rem; } + +a.navbar-item, +.navbar-link { + cursor: pointer; } + a.navbar-item:focus, a.navbar-item:focus-within, a.navbar-item:hover, a.navbar-item.is-active, + .navbar-link:focus, + .navbar-link:focus-within, + .navbar-link:hover, + .navbar-link.is-active { + background-color: #fafafa; + color: #149eaa; } + +.navbar-item { + display: block; + flex-grow: 0; + flex-shrink: 0; } + .navbar-item img { + max-height: 1.75rem; } + .navbar-item.has-dropdown { + padding: 0; } + .navbar-item.is-expanded { + flex-grow: 1; + flex-shrink: 1; } + .navbar-item.is-tab { + border-bottom: 1px solid transparent; + min-height: 3.25rem; + padding-bottom: calc(0.5rem - 1px); } + .navbar-item.is-tab:focus, .navbar-item.is-tab:hover { + background-color: transparent; + border-bottom-color: #149eaa; } + .navbar-item.is-tab.is-active { + background-color: transparent; + border-bottom-color: #149eaa; + border-bottom-style: solid; + border-bottom-width: 3px; + color: #149eaa; + padding-bottom: calc(0.5rem - 3px); } + +.navbar-content { + flex-grow: 1; + flex-shrink: 1; } + +.navbar-link:not(.is-arrowless) { + padding-right: 2.5em; } + .navbar-link:not(.is-arrowless)::after { + border-color: #149eaa; + margin-top: -0.375em; + right: 1.125em; } + +.navbar-dropdown { + font-size: 0.875rem; + padding-bottom: 0.5rem; + padding-top: 0.5rem; } + .navbar-dropdown .navbar-item { + padding-left: 1.5rem; + padding-right: 1.5rem; } + +.navbar-divider { + background-color: whitesmoke; + border: none; + display: none; + height: 2px; + margin: 0.5rem 0; } + +@media screen and (max-width: 1055px) { + .navbar > .container { + display: block; } + .navbar-brand .navbar-item, + .navbar-tabs .navbar-item { + align-items: center; + display: flex; } + .navbar-link::after { + display: none; } + .navbar-menu { + background-color: white; + box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); + padding: 0.5rem 0; } + .navbar-menu.is-active { + display: block; } + .navbar.is-fixed-bottom-touch, .navbar.is-fixed-top-touch { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom-touch { + bottom: 0; } + .navbar.is-fixed-bottom-touch.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + .navbar.is-fixed-top-touch { + top: 0; } + .navbar.is-fixed-top .navbar-menu, .navbar.is-fixed-top-touch .navbar-menu { + -webkit-overflow-scrolling: touch; + max-height: calc(100vh - 3.25rem); + overflow: auto; } + html.has-navbar-fixed-top-touch, + body.has-navbar-fixed-top-touch { + padding-top: 3.25rem; } + html.has-navbar-fixed-bottom-touch, + body.has-navbar-fixed-bottom-touch { + padding-bottom: 3.25rem; } } + +@media screen and (min-width: 1056px) { + .navbar, + .navbar-menu, + .navbar-start, + .navbar-end { + align-items: stretch; + display: flex; } + .navbar { + min-height: 3.25rem; } + .navbar.is-spaced { + padding: 1rem 2rem; } + .navbar.is-spaced .navbar-start, + .navbar.is-spaced .navbar-end { + align-items: center; } + .navbar.is-spaced a.navbar-item, + .navbar.is-spaced .navbar-link { + border-radius: 4px; } + .navbar.is-transparent a.navbar-item:focus, .navbar.is-transparent a.navbar-item:hover, .navbar.is-transparent a.navbar-item.is-active, + .navbar.is-transparent .navbar-link:focus, + .navbar.is-transparent .navbar-link:hover, + .navbar.is-transparent .navbar-link.is-active { + background-color: transparent !important; } + .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { + background-color: transparent !important; } + .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #149eaa; } + .navbar-burger { + display: none; } + .navbar-item, + .navbar-link { + align-items: center; + display: flex; } + .navbar-item { + display: flex; } + .navbar-item.has-dropdown { + align-items: stretch; } + .navbar-item.has-dropdown-up .navbar-link::after { + transform: rotate(135deg) translate(0.25em, -0.25em); } + .navbar-item.has-dropdown-up .navbar-dropdown { + border-bottom: 2px solid #dbdbdb; + border-radius: 6px 6px 0 0; + border-top: none; + bottom: 100%; + box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); + top: auto; } + .navbar-item.is-active .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown { + display: block; } + .navbar.is-spaced .navbar-item.is-active .navbar-dropdown, .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:hover .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { + opacity: 1; + pointer-events: auto; + transform: translateY(0); } + .navbar-menu { + flex-grow: 1; + flex-shrink: 0; } + .navbar-start { + justify-content: flex-start; + margin-right: auto; } + .navbar-end { + justify-content: flex-end; + margin-left: auto; } + .navbar-dropdown { + background-color: white; + border-bottom-left-radius: 6px; + border-bottom-right-radius: 6px; + border-top: 2px solid #dbdbdb; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); + display: none; + font-size: 0.875rem; + left: 0; + min-width: 100%; + position: absolute; + top: 100%; + z-index: 20; } + .navbar-dropdown .navbar-item { + padding: 0.375rem 1rem; + white-space: nowrap; } + .navbar-dropdown a.navbar-item { + padding-right: 3rem; } + .navbar-dropdown a.navbar-item:focus, .navbar-dropdown a.navbar-item:hover { + background-color: whitesmoke; + color: #0a0a0a; } + .navbar-dropdown a.navbar-item.is-active { + background-color: whitesmoke; + color: #149eaa; } + .navbar.is-spaced .navbar-dropdown, .navbar-dropdown.is-boxed { + border-radius: 6px; + border-top: none; + box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); + display: block; + opacity: 0; + pointer-events: none; + top: calc(100% + (-4px)); + transform: translateY(-5px); + transition-duration: 86ms; + transition-property: opacity, transform; } + .navbar-dropdown.is-right { + left: auto; + right: 0; } + .navbar-divider { + display: block; } + .navbar > .container .navbar-brand, + .container > .navbar .navbar-brand { + margin-left: -.75rem; } + .navbar > .container .navbar-menu, + .container > .navbar .navbar-menu { + margin-right: -.75rem; } + .navbar.is-fixed-bottom-desktop, .navbar.is-fixed-top-desktop { + left: 0; + position: fixed; + right: 0; + z-index: 30; } + .navbar.is-fixed-bottom-desktop { + bottom: 0; } + .navbar.is-fixed-bottom-desktop.has-shadow { + box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } + .navbar.is-fixed-top-desktop { + top: 0; } + html.has-navbar-fixed-top-desktop, + body.has-navbar-fixed-top-desktop { + padding-top: 3.25rem; } + html.has-navbar-fixed-bottom-desktop, + body.has-navbar-fixed-bottom-desktop { + padding-bottom: 3.25rem; } + html.has-spaced-navbar-fixed-top, + body.has-spaced-navbar-fixed-top { + padding-top: 5.25rem; } + html.has-spaced-navbar-fixed-bottom, + body.has-spaced-navbar-fixed-bottom { + padding-bottom: 5.25rem; } + a.navbar-item.is-active, + .navbar-link.is-active { + color: #0a0a0a; } + a.navbar-item.is-active:not(:focus):not(:hover), + .navbar-link.is-active:not(:focus):not(:hover) { + background-color: transparent; } + .navbar-item.has-dropdown:focus .navbar-link, .navbar-item.has-dropdown:hover .navbar-link, .navbar-item.has-dropdown.is-active .navbar-link { + background-color: #fafafa; } } + +.hero.is-fullheight-with-navbar { + min-height: calc(100vh - 3.25rem); } + +.pagination { + font-size: 1rem; + margin: -0.25rem; } + .pagination.is-small, #documenter .docs-sidebar form.docs-search > input.pagination { + font-size: 0.75rem; } + .pagination.is-medium { + font-size: 1.25rem; } + .pagination.is-large { + font-size: 1.5rem; } + .pagination.is-rounded .pagination-previous, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, + .pagination.is-rounded .pagination-next, + #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { + padding-left: 1em; + padding-right: 1em; + border-radius: 290486px; } + .pagination.is-rounded .pagination-link, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { + border-radius: 290486px; } + +.pagination, +.pagination-list { + align-items: center; + display: flex; + justify-content: center; + text-align: center; } + +.pagination-previous, +.pagination-next, +.pagination-link, +.pagination-ellipsis { + font-size: 1em; + justify-content: center; + margin: 0.25rem; + padding-left: 0.5em; + padding-right: 0.5em; + text-align: center; } + +.pagination-previous, +.pagination-next, +.pagination-link { + border-color: #dbdbdb; + color: #363636; + min-width: 2.25em; } + .pagination-previous:hover, + .pagination-next:hover, + .pagination-link:hover { + border-color: #b5b5b5; + color: #107c85; } + .pagination-previous:focus, + .pagination-next:focus, + .pagination-link:focus { + border-color: #3c5dcd; } + .pagination-previous:active, + .pagination-next:active, + .pagination-link:active { + box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } + .pagination-previous[disabled], + .pagination-next[disabled], + .pagination-link[disabled] { + background-color: #dbdbdb; + border-color: #dbdbdb; + box-shadow: none; + color: #6b6b6b; + opacity: 0.5; } + +.pagination-previous, +.pagination-next { + padding-left: 0.75em; + padding-right: 0.75em; + white-space: nowrap; } + +.pagination-link.is-current { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; } + +.pagination-ellipsis { + color: #b5b5b5; + pointer-events: none; } + +.pagination-list { + flex-wrap: wrap; } + +@media screen and (max-width: 768px) { + .pagination { + flex-wrap: wrap; } + .pagination-previous, + .pagination-next { + flex-grow: 1; + flex-shrink: 1; } + .pagination-list li { + flex-grow: 1; + flex-shrink: 1; } } + +@media screen and (min-width: 769px), print { + .pagination-list { + flex-grow: 1; + flex-shrink: 1; + justify-content: flex-start; + order: 1; } + .pagination-previous { + order: 2; } + .pagination-next { + order: 3; } + .pagination { + justify-content: space-between; } + .pagination.is-centered .pagination-previous { + order: 1; } + .pagination.is-centered .pagination-list { + justify-content: center; + order: 2; } + .pagination.is-centered .pagination-next { + order: 3; } + .pagination.is-right .pagination-previous { + order: 1; } + .pagination.is-right .pagination-next { + order: 2; } + .pagination.is-right .pagination-list { + justify-content: flex-end; + order: 3; } } + +.panel { + font-size: 1rem; } + .panel:not(:last-child) { + margin-bottom: 1.5rem; } + +.panel-heading, +.panel-tabs, +.panel-block { + border-bottom: 1px solid #dbdbdb; + border-left: 1px solid #dbdbdb; + border-right: 1px solid #dbdbdb; } + .panel-heading:first-child, + .panel-tabs:first-child, + .panel-block:first-child { + border-top: 1px solid #dbdbdb; } + +.panel-heading { + background-color: whitesmoke; + border-radius: 4px 4px 0 0; + color: #654ca3; + font-size: 1.25em; + font-weight: 300; + line-height: 1.25; + padding: 0.5em 0.75em; } + +.panel-tabs { + align-items: flex-end; + display: flex; + font-size: 0.875em; + justify-content: center; } + .panel-tabs a { + border-bottom: 1px solid #dbdbdb; + margin-bottom: -1px; + padding: 0.5em; } + .panel-tabs a.is-active { + border-bottom-color: #4a4a4a; + color: #363636; } + +.panel-list a { + color: #202020; } + .panel-list a:hover { + color: #149eaa; } + +.panel-block { + align-items: center; + color: #654ca3; + display: flex; + justify-content: flex-start; + padding: 0.5em 0.75em; } + .panel-block input[type="checkbox"] { + margin-right: 0.75em; } + .panel-block > .control { + flex-grow: 1; + flex-shrink: 1; + width: 100%; } + .panel-block.is-wrapped { + flex-wrap: wrap; } + .panel-block.is-active { + border-left-color: #149eaa; + color: #363636; } + .panel-block.is-active .panel-icon { + color: #149eaa; } + +a.panel-block, +label.panel-block { + cursor: pointer; } + a.panel-block:hover, + label.panel-block:hover { + background-color: whitesmoke; } + +.panel-icon { + display: inline-block; + font-size: 14px; + height: 1em; + line-height: 1em; + text-align: center; + vertical-align: top; + width: 1em; + color: #6b6b6b; + margin-right: 0.75em; } + .panel-icon .fa { + font-size: inherit; + line-height: inherit; } + +.tabs { + -webkit-overflow-scrolling: touch; + align-items: stretch; + display: flex; + font-size: 1rem; + justify-content: space-between; + overflow: hidden; + overflow-x: auto; + white-space: nowrap; } + .tabs a { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + color: #202020; + display: flex; + justify-content: center; + margin-bottom: -1px; + padding: 0.5em 1em; + vertical-align: top; } + .tabs a:hover { + border-bottom-color: #654ca3; + color: #654ca3; } + .tabs li { + display: block; } + .tabs li.is-active a { + border-bottom-color: #149eaa; + color: #149eaa; } + .tabs ul { + align-items: center; + border-bottom-color: #dbdbdb; + border-bottom-style: solid; + border-bottom-width: 1px; + display: flex; + flex-grow: 1; + flex-shrink: 0; + justify-content: flex-start; } + .tabs ul.is-left { + padding-right: 0.75em; } + .tabs ul.is-center { + flex: none; + justify-content: center; + padding-left: 0.75em; + padding-right: 0.75em; } + .tabs ul.is-right { + justify-content: flex-end; + padding-left: 0.75em; } + .tabs .icon:first-child { + margin-right: 0.5em; } + .tabs .icon:last-child { + margin-left: 0.5em; } + .tabs.is-centered ul { + justify-content: center; } + .tabs.is-right ul { + justify-content: flex-end; } + .tabs.is-boxed a { + border: 1px solid transparent; + border-radius: 4px 4px 0 0; } + .tabs.is-boxed a:hover { + background-color: whitesmoke; + border-bottom-color: #dbdbdb; } + .tabs.is-boxed li.is-active a { + background-color: white; + border-color: #dbdbdb; + border-bottom-color: transparent !important; } + .tabs.is-fullwidth li { + flex-grow: 1; + flex-shrink: 0; } + .tabs.is-toggle a { + border-color: #dbdbdb; + border-style: solid; + border-width: 1px; + margin-bottom: 0; + position: relative; } + .tabs.is-toggle a:hover { + background-color: whitesmoke; + border-color: #b5b5b5; + z-index: 2; } + .tabs.is-toggle li + li { + margin-left: -1px; } + .tabs.is-toggle li:first-child a { + border-radius: 4px 0 0 4px; } + .tabs.is-toggle li:last-child a { + border-radius: 0 4px 4px 0; } + .tabs.is-toggle li.is-active a { + background-color: #149eaa; + border-color: #149eaa; + color: #fff; + z-index: 1; } + .tabs.is-toggle ul { + border-bottom: none; } + .tabs.is-toggle.is-toggle-rounded li:first-child a { + border-bottom-left-radius: 290486px; + border-top-left-radius: 290486px; + padding-left: 1.25em; } + .tabs.is-toggle.is-toggle-rounded li:last-child a { + border-bottom-right-radius: 290486px; + border-top-right-radius: 290486px; + padding-right: 1.25em; } + .tabs.is-small, #documenter .docs-sidebar form.docs-search > input.tabs { + font-size: 0.75rem; } + .tabs.is-medium { + font-size: 1.25rem; } + .tabs.is-large { + font-size: 1.5rem; } + +.column { + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + padding: 0.75rem; } + .columns.is-mobile > .column.is-narrow { + flex: none; } + .columns.is-mobile > .column.is-full { + flex: none; + width: 100%; } + .columns.is-mobile > .column.is-three-quarters { + flex: none; + width: 75%; } + .columns.is-mobile > .column.is-two-thirds { + flex: none; + width: 66.6666%; } + .columns.is-mobile > .column.is-half { + flex: none; + width: 50%; } + .columns.is-mobile > .column.is-one-third { + flex: none; + width: 33.3333%; } + .columns.is-mobile > .column.is-one-quarter { + flex: none; + width: 25%; } + .columns.is-mobile > .column.is-one-fifth { + flex: none; + width: 20%; } + .columns.is-mobile > .column.is-two-fifths { + flex: none; + width: 40%; } + .columns.is-mobile > .column.is-three-fifths { + flex: none; + width: 60%; } + .columns.is-mobile > .column.is-four-fifths { + flex: none; + width: 80%; } + .columns.is-mobile > .column.is-offset-three-quarters { + margin-left: 75%; } + .columns.is-mobile > .column.is-offset-two-thirds { + margin-left: 66.6666%; } + .columns.is-mobile > .column.is-offset-half { + margin-left: 50%; } + .columns.is-mobile > .column.is-offset-one-third { + margin-left: 33.3333%; } + .columns.is-mobile > .column.is-offset-one-quarter { + margin-left: 25%; } + .columns.is-mobile > .column.is-offset-one-fifth { + margin-left: 20%; } + .columns.is-mobile > .column.is-offset-two-fifths { + margin-left: 40%; } + .columns.is-mobile > .column.is-offset-three-fifths { + margin-left: 60%; } + .columns.is-mobile > .column.is-offset-four-fifths { + margin-left: 80%; } + .columns.is-mobile > .column.is-0 { + flex: none; + width: 0%; } + .columns.is-mobile > .column.is-offset-0 { + margin-left: 0%; } + .columns.is-mobile > .column.is-1 { + flex: none; + width: 8.3333333333%; } + .columns.is-mobile > .column.is-offset-1 { + margin-left: 8.3333333333%; } + .columns.is-mobile > .column.is-2 { + flex: none; + width: 16.6666666667%; } + .columns.is-mobile > .column.is-offset-2 { + margin-left: 16.6666666667%; } + .columns.is-mobile > .column.is-3 { + flex: none; + width: 25%; } + .columns.is-mobile > .column.is-offset-3 { + margin-left: 25%; } + .columns.is-mobile > .column.is-4 { + flex: none; + width: 33.3333333333%; } + .columns.is-mobile > .column.is-offset-4 { + margin-left: 33.3333333333%; } + .columns.is-mobile > .column.is-5 { + flex: none; + width: 41.6666666667%; } + .columns.is-mobile > .column.is-offset-5 { + margin-left: 41.6666666667%; } + .columns.is-mobile > .column.is-6 { + flex: none; + width: 50%; } + .columns.is-mobile > .column.is-offset-6 { + margin-left: 50%; } + .columns.is-mobile > .column.is-7 { + flex: none; + width: 58.3333333333%; } + .columns.is-mobile > .column.is-offset-7 { + margin-left: 58.3333333333%; } + .columns.is-mobile > .column.is-8 { + flex: none; + width: 66.6666666667%; } + .columns.is-mobile > .column.is-offset-8 { + margin-left: 66.6666666667%; } + .columns.is-mobile > .column.is-9 { + flex: none; + width: 75%; } + .columns.is-mobile > .column.is-offset-9 { + margin-left: 75%; } + .columns.is-mobile > .column.is-10 { + flex: none; + width: 83.3333333333%; } + .columns.is-mobile > .column.is-offset-10 { + margin-left: 83.3333333333%; } + .columns.is-mobile > .column.is-11 { + flex: none; + width: 91.6666666667%; } + .columns.is-mobile > .column.is-offset-11 { + margin-left: 91.6666666667%; } + .columns.is-mobile > .column.is-12 { + flex: none; + width: 100%; } + .columns.is-mobile > .column.is-offset-12 { + margin-left: 100%; } + @media screen and (max-width: 768px) { + .column.is-narrow-mobile { + flex: none; } + .column.is-full-mobile { + flex: none; + width: 100%; } + .column.is-three-quarters-mobile { + flex: none; + width: 75%; } + .column.is-two-thirds-mobile { + flex: none; + width: 66.6666%; } + .column.is-half-mobile { + flex: none; + width: 50%; } + .column.is-one-third-mobile { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-mobile { + flex: none; + width: 25%; } + .column.is-one-fifth-mobile { + flex: none; + width: 20%; } + .column.is-two-fifths-mobile { + flex: none; + width: 40%; } + .column.is-three-fifths-mobile { + flex: none; + width: 60%; } + .column.is-four-fifths-mobile { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-mobile { + margin-left: 75%; } + .column.is-offset-two-thirds-mobile { + margin-left: 66.6666%; } + .column.is-offset-half-mobile { + margin-left: 50%; } + .column.is-offset-one-third-mobile { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-mobile { + margin-left: 25%; } + .column.is-offset-one-fifth-mobile { + margin-left: 20%; } + .column.is-offset-two-fifths-mobile { + margin-left: 40%; } + .column.is-offset-three-fifths-mobile { + margin-left: 60%; } + .column.is-offset-four-fifths-mobile { + margin-left: 80%; } + .column.is-0-mobile { + flex: none; + width: 0%; } + .column.is-offset-0-mobile { + margin-left: 0%; } + .column.is-1-mobile { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-mobile { + margin-left: 8.3333333333%; } + .column.is-2-mobile { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-mobile { + margin-left: 16.6666666667%; } + .column.is-3-mobile { + flex: none; + width: 25%; } + .column.is-offset-3-mobile { + margin-left: 25%; } + .column.is-4-mobile { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-mobile { + margin-left: 33.3333333333%; } + .column.is-5-mobile { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-mobile { + margin-left: 41.6666666667%; } + .column.is-6-mobile { + flex: none; + width: 50%; } + .column.is-offset-6-mobile { + margin-left: 50%; } + .column.is-7-mobile { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-mobile { + margin-left: 58.3333333333%; } + .column.is-8-mobile { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-mobile { + margin-left: 66.6666666667%; } + .column.is-9-mobile { + flex: none; + width: 75%; } + .column.is-offset-9-mobile { + margin-left: 75%; } + .column.is-10-mobile { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-mobile { + margin-left: 83.3333333333%; } + .column.is-11-mobile { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-mobile { + margin-left: 91.6666666667%; } + .column.is-12-mobile { + flex: none; + width: 100%; } + .column.is-offset-12-mobile { + margin-left: 100%; } } + @media screen and (min-width: 769px), print { + .column.is-narrow, .column.is-narrow-tablet { + flex: none; } + .column.is-full, .column.is-full-tablet { + flex: none; + width: 100%; } + .column.is-three-quarters, .column.is-three-quarters-tablet { + flex: none; + width: 75%; } + .column.is-two-thirds, .column.is-two-thirds-tablet { + flex: none; + width: 66.6666%; } + .column.is-half, .column.is-half-tablet { + flex: none; + width: 50%; } + .column.is-one-third, .column.is-one-third-tablet { + flex: none; + width: 33.3333%; } + .column.is-one-quarter, .column.is-one-quarter-tablet { + flex: none; + width: 25%; } + .column.is-one-fifth, .column.is-one-fifth-tablet { + flex: none; + width: 20%; } + .column.is-two-fifths, .column.is-two-fifths-tablet { + flex: none; + width: 40%; } + .column.is-three-fifths, .column.is-three-fifths-tablet { + flex: none; + width: 60%; } + .column.is-four-fifths, .column.is-four-fifths-tablet { + flex: none; + width: 80%; } + .column.is-offset-three-quarters, .column.is-offset-three-quarters-tablet { + margin-left: 75%; } + .column.is-offset-two-thirds, .column.is-offset-two-thirds-tablet { + margin-left: 66.6666%; } + .column.is-offset-half, .column.is-offset-half-tablet { + margin-left: 50%; } + .column.is-offset-one-third, .column.is-offset-one-third-tablet { + margin-left: 33.3333%; } + .column.is-offset-one-quarter, .column.is-offset-one-quarter-tablet { + margin-left: 25%; } + .column.is-offset-one-fifth, .column.is-offset-one-fifth-tablet { + margin-left: 20%; } + .column.is-offset-two-fifths, .column.is-offset-two-fifths-tablet { + margin-left: 40%; } + .column.is-offset-three-fifths, .column.is-offset-three-fifths-tablet { + margin-left: 60%; } + .column.is-offset-four-fifths, .column.is-offset-four-fifths-tablet { + margin-left: 80%; } + .column.is-0, .column.is-0-tablet { + flex: none; + width: 0%; } + .column.is-offset-0, .column.is-offset-0-tablet { + margin-left: 0%; } + .column.is-1, .column.is-1-tablet { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1, .column.is-offset-1-tablet { + margin-left: 8.3333333333%; } + .column.is-2, .column.is-2-tablet { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2, .column.is-offset-2-tablet { + margin-left: 16.6666666667%; } + .column.is-3, .column.is-3-tablet { + flex: none; + width: 25%; } + .column.is-offset-3, .column.is-offset-3-tablet { + margin-left: 25%; } + .column.is-4, .column.is-4-tablet { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4, .column.is-offset-4-tablet { + margin-left: 33.3333333333%; } + .column.is-5, .column.is-5-tablet { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5, .column.is-offset-5-tablet { + margin-left: 41.6666666667%; } + .column.is-6, .column.is-6-tablet { + flex: none; + width: 50%; } + .column.is-offset-6, .column.is-offset-6-tablet { + margin-left: 50%; } + .column.is-7, .column.is-7-tablet { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7, .column.is-offset-7-tablet { + margin-left: 58.3333333333%; } + .column.is-8, .column.is-8-tablet { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8, .column.is-offset-8-tablet { + margin-left: 66.6666666667%; } + .column.is-9, .column.is-9-tablet { + flex: none; + width: 75%; } + .column.is-offset-9, .column.is-offset-9-tablet { + margin-left: 75%; } + .column.is-10, .column.is-10-tablet { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10, .column.is-offset-10-tablet { + margin-left: 83.3333333333%; } + .column.is-11, .column.is-11-tablet { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11, .column.is-offset-11-tablet { + margin-left: 91.6666666667%; } + .column.is-12, .column.is-12-tablet { + flex: none; + width: 100%; } + .column.is-offset-12, .column.is-offset-12-tablet { + margin-left: 100%; } } + @media screen and (max-width: 1055px) { + .column.is-narrow-touch { + flex: none; } + .column.is-full-touch { + flex: none; + width: 100%; } + .column.is-three-quarters-touch { + flex: none; + width: 75%; } + .column.is-two-thirds-touch { + flex: none; + width: 66.6666%; } + .column.is-half-touch { + flex: none; + width: 50%; } + .column.is-one-third-touch { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-touch { + flex: none; + width: 25%; } + .column.is-one-fifth-touch { + flex: none; + width: 20%; } + .column.is-two-fifths-touch { + flex: none; + width: 40%; } + .column.is-three-fifths-touch { + flex: none; + width: 60%; } + .column.is-four-fifths-touch { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-touch { + margin-left: 75%; } + .column.is-offset-two-thirds-touch { + margin-left: 66.6666%; } + .column.is-offset-half-touch { + margin-left: 50%; } + .column.is-offset-one-third-touch { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-touch { + margin-left: 25%; } + .column.is-offset-one-fifth-touch { + margin-left: 20%; } + .column.is-offset-two-fifths-touch { + margin-left: 40%; } + .column.is-offset-three-fifths-touch { + margin-left: 60%; } + .column.is-offset-four-fifths-touch { + margin-left: 80%; } + .column.is-0-touch { + flex: none; + width: 0%; } + .column.is-offset-0-touch { + margin-left: 0%; } + .column.is-1-touch { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-touch { + margin-left: 8.3333333333%; } + .column.is-2-touch { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-touch { + margin-left: 16.6666666667%; } + .column.is-3-touch { + flex: none; + width: 25%; } + .column.is-offset-3-touch { + margin-left: 25%; } + .column.is-4-touch { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-touch { + margin-left: 33.3333333333%; } + .column.is-5-touch { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-touch { + margin-left: 41.6666666667%; } + .column.is-6-touch { + flex: none; + width: 50%; } + .column.is-offset-6-touch { + margin-left: 50%; } + .column.is-7-touch { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-touch { + margin-left: 58.3333333333%; } + .column.is-8-touch { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-touch { + margin-left: 66.6666666667%; } + .column.is-9-touch { + flex: none; + width: 75%; } + .column.is-offset-9-touch { + margin-left: 75%; } + .column.is-10-touch { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-touch { + margin-left: 83.3333333333%; } + .column.is-11-touch { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-touch { + margin-left: 91.6666666667%; } + .column.is-12-touch { + flex: none; + width: 100%; } + .column.is-offset-12-touch { + margin-left: 100%; } } + @media screen and (min-width: 1056px) { + .column.is-narrow-desktop { + flex: none; } + .column.is-full-desktop { + flex: none; + width: 100%; } + .column.is-three-quarters-desktop { + flex: none; + width: 75%; } + .column.is-two-thirds-desktop { + flex: none; + width: 66.6666%; } + .column.is-half-desktop { + flex: none; + width: 50%; } + .column.is-one-third-desktop { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-desktop { + flex: none; + width: 25%; } + .column.is-one-fifth-desktop { + flex: none; + width: 20%; } + .column.is-two-fifths-desktop { + flex: none; + width: 40%; } + .column.is-three-fifths-desktop { + flex: none; + width: 60%; } + .column.is-four-fifths-desktop { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-desktop { + margin-left: 75%; } + .column.is-offset-two-thirds-desktop { + margin-left: 66.6666%; } + .column.is-offset-half-desktop { + margin-left: 50%; } + .column.is-offset-one-third-desktop { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-desktop { + margin-left: 25%; } + .column.is-offset-one-fifth-desktop { + margin-left: 20%; } + .column.is-offset-two-fifths-desktop { + margin-left: 40%; } + .column.is-offset-three-fifths-desktop { + margin-left: 60%; } + .column.is-offset-four-fifths-desktop { + margin-left: 80%; } + .column.is-0-desktop { + flex: none; + width: 0%; } + .column.is-offset-0-desktop { + margin-left: 0%; } + .column.is-1-desktop { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-desktop { + margin-left: 8.3333333333%; } + .column.is-2-desktop { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-desktop { + margin-left: 16.6666666667%; } + .column.is-3-desktop { + flex: none; + width: 25%; } + .column.is-offset-3-desktop { + margin-left: 25%; } + .column.is-4-desktop { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-desktop { + margin-left: 33.3333333333%; } + .column.is-5-desktop { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-desktop { + margin-left: 41.6666666667%; } + .column.is-6-desktop { + flex: none; + width: 50%; } + .column.is-offset-6-desktop { + margin-left: 50%; } + .column.is-7-desktop { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-desktop { + margin-left: 58.3333333333%; } + .column.is-8-desktop { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-desktop { + margin-left: 66.6666666667%; } + .column.is-9-desktop { + flex: none; + width: 75%; } + .column.is-offset-9-desktop { + margin-left: 75%; } + .column.is-10-desktop { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-desktop { + margin-left: 83.3333333333%; } + .column.is-11-desktop { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-desktop { + margin-left: 91.6666666667%; } + .column.is-12-desktop { + flex: none; + width: 100%; } + .column.is-offset-12-desktop { + margin-left: 100%; } } + @media screen and (min-width: 1216px) { + .column.is-narrow-widescreen { + flex: none; } + .column.is-full-widescreen { + flex: none; + width: 100%; } + .column.is-three-quarters-widescreen { + flex: none; + width: 75%; } + .column.is-two-thirds-widescreen { + flex: none; + width: 66.6666%; } + .column.is-half-widescreen { + flex: none; + width: 50%; } + .column.is-one-third-widescreen { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-widescreen { + flex: none; + width: 25%; } + .column.is-one-fifth-widescreen { + flex: none; + width: 20%; } + .column.is-two-fifths-widescreen { + flex: none; + width: 40%; } + .column.is-three-fifths-widescreen { + flex: none; + width: 60%; } + .column.is-four-fifths-widescreen { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-widescreen { + margin-left: 75%; } + .column.is-offset-two-thirds-widescreen { + margin-left: 66.6666%; } + .column.is-offset-half-widescreen { + margin-left: 50%; } + .column.is-offset-one-third-widescreen { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-widescreen { + margin-left: 25%; } + .column.is-offset-one-fifth-widescreen { + margin-left: 20%; } + .column.is-offset-two-fifths-widescreen { + margin-left: 40%; } + .column.is-offset-three-fifths-widescreen { + margin-left: 60%; } + .column.is-offset-four-fifths-widescreen { + margin-left: 80%; } + .column.is-0-widescreen { + flex: none; + width: 0%; } + .column.is-offset-0-widescreen { + margin-left: 0%; } + .column.is-1-widescreen { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-widescreen { + margin-left: 8.3333333333%; } + .column.is-2-widescreen { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-widescreen { + margin-left: 16.6666666667%; } + .column.is-3-widescreen { + flex: none; + width: 25%; } + .column.is-offset-3-widescreen { + margin-left: 25%; } + .column.is-4-widescreen { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-widescreen { + margin-left: 33.3333333333%; } + .column.is-5-widescreen { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-widescreen { + margin-left: 41.6666666667%; } + .column.is-6-widescreen { + flex: none; + width: 50%; } + .column.is-offset-6-widescreen { + margin-left: 50%; } + .column.is-7-widescreen { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-widescreen { + margin-left: 58.3333333333%; } + .column.is-8-widescreen { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-widescreen { + margin-left: 66.6666666667%; } + .column.is-9-widescreen { + flex: none; + width: 75%; } + .column.is-offset-9-widescreen { + margin-left: 75%; } + .column.is-10-widescreen { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-widescreen { + margin-left: 83.3333333333%; } + .column.is-11-widescreen { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-widescreen { + margin-left: 91.6666666667%; } + .column.is-12-widescreen { + flex: none; + width: 100%; } + .column.is-offset-12-widescreen { + margin-left: 100%; } } + @media screen and (min-width: 1408px) { + .column.is-narrow-fullhd { + flex: none; } + .column.is-full-fullhd { + flex: none; + width: 100%; } + .column.is-three-quarters-fullhd { + flex: none; + width: 75%; } + .column.is-two-thirds-fullhd { + flex: none; + width: 66.6666%; } + .column.is-half-fullhd { + flex: none; + width: 50%; } + .column.is-one-third-fullhd { + flex: none; + width: 33.3333%; } + .column.is-one-quarter-fullhd { + flex: none; + width: 25%; } + .column.is-one-fifth-fullhd { + flex: none; + width: 20%; } + .column.is-two-fifths-fullhd { + flex: none; + width: 40%; } + .column.is-three-fifths-fullhd { + flex: none; + width: 60%; } + .column.is-four-fifths-fullhd { + flex: none; + width: 80%; } + .column.is-offset-three-quarters-fullhd { + margin-left: 75%; } + .column.is-offset-two-thirds-fullhd { + margin-left: 66.6666%; } + .column.is-offset-half-fullhd { + margin-left: 50%; } + .column.is-offset-one-third-fullhd { + margin-left: 33.3333%; } + .column.is-offset-one-quarter-fullhd { + margin-left: 25%; } + .column.is-offset-one-fifth-fullhd { + margin-left: 20%; } + .column.is-offset-two-fifths-fullhd { + margin-left: 40%; } + .column.is-offset-three-fifths-fullhd { + margin-left: 60%; } + .column.is-offset-four-fifths-fullhd { + margin-left: 80%; } + .column.is-0-fullhd { + flex: none; + width: 0%; } + .column.is-offset-0-fullhd { + margin-left: 0%; } + .column.is-1-fullhd { + flex: none; + width: 8.3333333333%; } + .column.is-offset-1-fullhd { + margin-left: 8.3333333333%; } + .column.is-2-fullhd { + flex: none; + width: 16.6666666667%; } + .column.is-offset-2-fullhd { + margin-left: 16.6666666667%; } + .column.is-3-fullhd { + flex: none; + width: 25%; } + .column.is-offset-3-fullhd { + margin-left: 25%; } + .column.is-4-fullhd { + flex: none; + width: 33.3333333333%; } + .column.is-offset-4-fullhd { + margin-left: 33.3333333333%; } + .column.is-5-fullhd { + flex: none; + width: 41.6666666667%; } + .column.is-offset-5-fullhd { + margin-left: 41.6666666667%; } + .column.is-6-fullhd { + flex: none; + width: 50%; } + .column.is-offset-6-fullhd { + margin-left: 50%; } + .column.is-7-fullhd { + flex: none; + width: 58.3333333333%; } + .column.is-offset-7-fullhd { + margin-left: 58.3333333333%; } + .column.is-8-fullhd { + flex: none; + width: 66.6666666667%; } + .column.is-offset-8-fullhd { + margin-left: 66.6666666667%; } + .column.is-9-fullhd { + flex: none; + width: 75%; } + .column.is-offset-9-fullhd { + margin-left: 75%; } + .column.is-10-fullhd { + flex: none; + width: 83.3333333333%; } + .column.is-offset-10-fullhd { + margin-left: 83.3333333333%; } + .column.is-11-fullhd { + flex: none; + width: 91.6666666667%; } + .column.is-offset-11-fullhd { + margin-left: 91.6666666667%; } + .column.is-12-fullhd { + flex: none; + width: 100%; } + .column.is-offset-12-fullhd { + margin-left: 100%; } } +.columns { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + .columns:last-child { + margin-bottom: -0.75rem; } + .columns:not(:last-child) { + margin-bottom: calc(1.5rem - 0.75rem); } + .columns.is-centered { + justify-content: center; } + .columns.is-gapless { + margin-left: 0; + margin-right: 0; + margin-top: 0; } + .columns.is-gapless > .column { + margin: 0; + padding: 0 !important; } + .columns.is-gapless:not(:last-child) { + margin-bottom: 1.5rem; } + .columns.is-gapless:last-child { + margin-bottom: 0; } + .columns.is-mobile { + display: flex; } + .columns.is-multiline { + flex-wrap: wrap; } + .columns.is-vcentered { + align-items: center; } + @media screen and (min-width: 769px), print { + .columns:not(.is-desktop) { + display: flex; } } + @media screen and (min-width: 1056px) { + .columns.is-desktop { + display: flex; } } +.columns.is-variable { + --columnGap: 0.75rem; + margin-left: calc(-1 * var(--columnGap)); + margin-right: calc(-1 * var(--columnGap)); } + .columns.is-variable .column { + padding-left: var(--columnGap); + padding-right: var(--columnGap); } + .columns.is-variable.is-0 { + --columnGap: 0rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-0-mobile { + --columnGap: 0rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-0-tablet { + --columnGap: 0rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-0-tablet-only { + --columnGap: 0rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-0-touch { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-0-desktop { + --columnGap: 0rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-0-desktop-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-0-widescreen { + --columnGap: 0rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-0-widescreen-only { + --columnGap: 0rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-0-fullhd { + --columnGap: 0rem; } } + .columns.is-variable.is-1 { + --columnGap: 0.25rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-1-mobile { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-1-tablet { + --columnGap: 0.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-1-tablet-only { + --columnGap: 0.25rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-1-touch { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-1-desktop { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-1-desktop-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-1-widescreen { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-1-widescreen-only { + --columnGap: 0.25rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-1-fullhd { + --columnGap: 0.25rem; } } + .columns.is-variable.is-2 { + --columnGap: 0.5rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-2-mobile { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-2-tablet { + --columnGap: 0.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-2-tablet-only { + --columnGap: 0.5rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-2-touch { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-2-desktop { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-2-desktop-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-2-widescreen { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-2-widescreen-only { + --columnGap: 0.5rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-2-fullhd { + --columnGap: 0.5rem; } } + .columns.is-variable.is-3 { + --columnGap: 0.75rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-3-mobile { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-3-tablet { + --columnGap: 0.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-3-tablet-only { + --columnGap: 0.75rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-3-touch { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-3-desktop { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-3-desktop-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-3-widescreen { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-3-widescreen-only { + --columnGap: 0.75rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-3-fullhd { + --columnGap: 0.75rem; } } + .columns.is-variable.is-4 { + --columnGap: 1rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-4-mobile { + --columnGap: 1rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-4-tablet { + --columnGap: 1rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-4-tablet-only { + --columnGap: 1rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-4-touch { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-4-desktop { + --columnGap: 1rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-4-desktop-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-4-widescreen { + --columnGap: 1rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-4-widescreen-only { + --columnGap: 1rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-4-fullhd { + --columnGap: 1rem; } } + .columns.is-variable.is-5 { + --columnGap: 1.25rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-5-mobile { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-5-tablet { + --columnGap: 1.25rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-5-tablet-only { + --columnGap: 1.25rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-5-touch { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-5-desktop { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-5-desktop-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-5-widescreen { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-5-widescreen-only { + --columnGap: 1.25rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-5-fullhd { + --columnGap: 1.25rem; } } + .columns.is-variable.is-6 { + --columnGap: 1.5rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-6-mobile { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-6-tablet { + --columnGap: 1.5rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-6-tablet-only { + --columnGap: 1.5rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-6-touch { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-6-desktop { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-6-desktop-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-6-widescreen { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-6-widescreen-only { + --columnGap: 1.5rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-6-fullhd { + --columnGap: 1.5rem; } } + .columns.is-variable.is-7 { + --columnGap: 1.75rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-7-mobile { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-7-tablet { + --columnGap: 1.75rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-7-tablet-only { + --columnGap: 1.75rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-7-touch { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-7-desktop { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-7-desktop-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-7-widescreen { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-7-widescreen-only { + --columnGap: 1.75rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-7-fullhd { + --columnGap: 1.75rem; } } + .columns.is-variable.is-8 { + --columnGap: 2rem; } + @media screen and (max-width: 768px) { + .columns.is-variable.is-8-mobile { + --columnGap: 2rem; } } + @media screen and (min-width: 769px), print { + .columns.is-variable.is-8-tablet { + --columnGap: 2rem; } } + @media screen and (min-width: 769px) and (max-width: 1055px) { + .columns.is-variable.is-8-tablet-only { + --columnGap: 2rem; } } + @media screen and (max-width: 1055px) { + .columns.is-variable.is-8-touch { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) { + .columns.is-variable.is-8-desktop { + --columnGap: 2rem; } } + @media screen and (min-width: 1056px) and (max-width: 1215px) { + .columns.is-variable.is-8-desktop-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) { + .columns.is-variable.is-8-widescreen { + --columnGap: 2rem; } } + @media screen and (min-width: 1216px) and (max-width: 1407px) { + .columns.is-variable.is-8-widescreen-only { + --columnGap: 2rem; } } + @media screen and (min-width: 1408px) { + .columns.is-variable.is-8-fullhd { + --columnGap: 2rem; } } +.tile { + align-items: stretch; + display: block; + flex-basis: 0; + flex-grow: 1; + flex-shrink: 1; + min-height: min-content; } + .tile.is-ancestor { + margin-left: -0.75rem; + margin-right: -0.75rem; + margin-top: -0.75rem; } + .tile.is-ancestor:last-child { + margin-bottom: -0.75rem; } + .tile.is-ancestor:not(:last-child) { + margin-bottom: 0.75rem; } + .tile.is-child { + margin: 0 !important; } + .tile.is-parent { + padding: 0.75rem; } + .tile.is-vertical { + flex-direction: column; } + .tile.is-vertical > .tile.is-child:not(:last-child) { + margin-bottom: 1.5rem !important; } + @media screen and (min-width: 769px), print { + .tile:not(.is-child) { + display: flex; } + .tile.is-1 { + flex: none; + width: 8.3333333333%; } + .tile.is-2 { + flex: none; + width: 16.6666666667%; } + .tile.is-3 { + flex: none; + width: 25%; } + .tile.is-4 { + flex: none; + width: 33.3333333333%; } + .tile.is-5 { + flex: none; + width: 41.6666666667%; } + .tile.is-6 { + flex: none; + width: 50%; } + .tile.is-7 { + flex: none; + width: 58.3333333333%; } + .tile.is-8 { + flex: none; + width: 66.6666666667%; } + .tile.is-9 { + flex: none; + width: 75%; } + .tile.is-10 { + flex: none; + width: 83.3333333333%; } + .tile.is-11 { + flex: none; + width: 91.6666666667%; } + .tile.is-12 { + flex: none; + width: 100%; } } +.hero { + align-items: stretch; + display: flex; + flex-direction: column; + justify-content: space-between; } + .hero .navbar { + background: none; } + .hero .tabs ul { + border-bottom: none; } + .hero.is-white { + background-color: white; + color: #0a0a0a; } + .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-white strong { + color: inherit; } + .hero.is-white .title { + color: #0a0a0a; } + .hero.is-white .subtitle { + color: rgba(10, 10, 10, 0.9); } + .hero.is-white .subtitle a:not(.button), + .hero.is-white .subtitle strong { + color: #0a0a0a; } + @media screen and (max-width: 1055px) { + .hero.is-white .navbar-menu { + background-color: white; } } + .hero.is-white .navbar-item, + .hero.is-white .navbar-link { + color: rgba(10, 10, 10, 0.7); } + .hero.is-white a.navbar-item:hover, .hero.is-white a.navbar-item.is-active, + .hero.is-white .navbar-link:hover, + .hero.is-white .navbar-link.is-active { + background-color: #f2f2f2; + color: #0a0a0a; } + .hero.is-white .tabs a { + color: #0a0a0a; + opacity: 0.9; } + .hero.is-white .tabs a:hover { + opacity: 1; } + .hero.is-white .tabs li.is-active a { + opacity: 1; } + .hero.is-white .tabs.is-boxed a, .hero.is-white .tabs.is-toggle a { + color: #0a0a0a; } + .hero.is-white .tabs.is-boxed a:hover, .hero.is-white .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-white .tabs.is-boxed li.is-active a, .hero.is-white .tabs.is-boxed li.is-active a:hover, .hero.is-white .tabs.is-toggle li.is-active a, .hero.is-white .tabs.is-toggle li.is-active a:hover { + background-color: #0a0a0a; + border-color: #0a0a0a; + color: white; } + .hero.is-white.is-bold { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } + @media screen and (max-width: 768px) { + .hero.is-white.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } + .hero.is-black { + background-color: #0a0a0a; + color: white; } + .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-black strong { + color: inherit; } + .hero.is-black .title { + color: white; } + .hero.is-black .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-black .subtitle a:not(.button), + .hero.is-black .subtitle strong { + color: white; } + @media screen and (max-width: 1055px) { + .hero.is-black .navbar-menu { + background-color: #0a0a0a; } } + .hero.is-black .navbar-item, + .hero.is-black .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-black a.navbar-item:hover, .hero.is-black a.navbar-item.is-active, + .hero.is-black .navbar-link:hover, + .hero.is-black .navbar-link.is-active { + background-color: black; + color: white; } + .hero.is-black .tabs a { + color: white; + opacity: 0.9; } + .hero.is-black .tabs a:hover { + opacity: 1; } + .hero.is-black .tabs li.is-active a { + opacity: 1; } + .hero.is-black .tabs.is-boxed a, .hero.is-black .tabs.is-toggle a { + color: white; } + .hero.is-black .tabs.is-boxed a:hover, .hero.is-black .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-black .tabs.is-boxed li.is-active a, .hero.is-black .tabs.is-boxed li.is-active a:hover, .hero.is-black .tabs.is-toggle li.is-active a, .hero.is-black .tabs.is-toggle li.is-active a:hover { + background-color: white; + border-color: white; + color: #0a0a0a; } + .hero.is-black.is-bold { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } + @media screen and (max-width: 768px) { + .hero.is-black.is-bold .navbar-menu { + background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } + .hero.is-light { + background-color: whitesmoke; + color: #363636; } + .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-light strong { + color: inherit; } + .hero.is-light .title { + color: #363636; } + .hero.is-light .subtitle { + color: rgba(54, 54, 54, 0.9); } + .hero.is-light .subtitle a:not(.button), + .hero.is-light .subtitle strong { + color: #363636; } + @media screen and (max-width: 1055px) { + .hero.is-light .navbar-menu { + background-color: whitesmoke; } } + .hero.is-light .navbar-item, + .hero.is-light .navbar-link { + color: rgba(54, 54, 54, 0.7); } + .hero.is-light a.navbar-item:hover, .hero.is-light a.navbar-item.is-active, + .hero.is-light .navbar-link:hover, + .hero.is-light .navbar-link.is-active { + background-color: #e8e8e8; + color: #363636; } + .hero.is-light .tabs a { + color: #363636; + opacity: 0.9; } + .hero.is-light .tabs a:hover { + opacity: 1; } + .hero.is-light .tabs li.is-active a { + opacity: 1; } + .hero.is-light .tabs.is-boxed a, .hero.is-light .tabs.is-toggle a { + color: #363636; } + .hero.is-light .tabs.is-boxed a:hover, .hero.is-light .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-light .tabs.is-boxed li.is-active a, .hero.is-light .tabs.is-boxed li.is-active a:hover, .hero.is-light .tabs.is-toggle li.is-active a, .hero.is-light .tabs.is-toggle li.is-active a:hover { + background-color: #363636; + border-color: #363636; + color: whitesmoke; } + .hero.is-light.is-bold { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } + @media screen and (max-width: 768px) { + .hero.is-light.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } } + .hero.is-dark, .content kbd.hero { + background-color: #363636; + color: whitesmoke; } + .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-dark strong, + .content kbd.hero strong { + color: inherit; } + .hero.is-dark .title, .content kbd.hero .title { + color: whitesmoke; } + .hero.is-dark .subtitle, .content kbd.hero .subtitle { + color: rgba(245, 245, 245, 0.9); } + .hero.is-dark .subtitle a:not(.button), .content kbd.hero .subtitle a:not(.button), + .hero.is-dark .subtitle strong, + .content kbd.hero .subtitle strong { + color: whitesmoke; } + @media screen and (max-width: 1055px) { + .hero.is-dark .navbar-menu, .content kbd.hero .navbar-menu { + background-color: #363636; } } + .hero.is-dark .navbar-item, .content kbd.hero .navbar-item, + .hero.is-dark .navbar-link, + .content kbd.hero .navbar-link { + color: rgba(245, 245, 245, 0.7); } + .hero.is-dark a.navbar-item:hover, .content kbd.hero a.navbar-item:hover, .hero.is-dark a.navbar-item.is-active, .content kbd.hero a.navbar-item.is-active, + .hero.is-dark .navbar-link:hover, + .content kbd.hero .navbar-link:hover, + .hero.is-dark .navbar-link.is-active, + .content kbd.hero .navbar-link.is-active { + background-color: #292929; + color: whitesmoke; } + .hero.is-dark .tabs a, .content kbd.hero .tabs a { + color: whitesmoke; + opacity: 0.9; } + .hero.is-dark .tabs a:hover, .content kbd.hero .tabs a:hover { + opacity: 1; } + .hero.is-dark .tabs li.is-active a, .content kbd.hero .tabs li.is-active a { + opacity: 1; } + .hero.is-dark .tabs.is-boxed a, .content kbd.hero .tabs.is-boxed a, .hero.is-dark .tabs.is-toggle a, .content kbd.hero .tabs.is-toggle a { + color: whitesmoke; } + .hero.is-dark .tabs.is-boxed a:hover, .content kbd.hero .tabs.is-boxed a:hover, .hero.is-dark .tabs.is-toggle a:hover, .content kbd.hero .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-dark .tabs.is-boxed li.is-active a, .content kbd.hero .tabs.is-boxed li.is-active a, .hero.is-dark .tabs.is-boxed li.is-active a:hover, .hero.is-dark .tabs.is-toggle li.is-active a, .content kbd.hero .tabs.is-toggle li.is-active a, .hero.is-dark .tabs.is-toggle li.is-active a:hover { + background-color: whitesmoke; + border-color: whitesmoke; + color: #363636; } + .hero.is-dark.is-bold, .content kbd.hero.is-bold { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } + @media screen and (max-width: 768px) { + .hero.is-dark.is-bold .navbar-menu, .content kbd.hero.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } } + .hero.is-primary, .docstring > section > a.hero.docs-sourcelink { + background-color: #4eb5de; + color: #fff; } + .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-primary strong, + .docstring > section > a.hero.docs-sourcelink strong { + color: inherit; } + .hero.is-primary .title, .docstring > section > a.hero.docs-sourcelink .title { + color: #fff; } + .hero.is-primary .subtitle, .docstring > section > a.hero.docs-sourcelink .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-primary .subtitle a:not(.button), .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), + .hero.is-primary .subtitle strong, + .docstring > section > a.hero.docs-sourcelink .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-primary .navbar-menu, .docstring > section > a.hero.docs-sourcelink .navbar-menu { + background-color: #4eb5de; } } + .hero.is-primary .navbar-item, .docstring > section > a.hero.docs-sourcelink .navbar-item, + .hero.is-primary .navbar-link, + .docstring > section > a.hero.docs-sourcelink .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-primary a.navbar-item:hover, .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, .hero.is-primary a.navbar-item.is-active, .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, + .hero.is-primary .navbar-link:hover, + .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, + .hero.is-primary .navbar-link.is-active, + .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { + background-color: #39acda; + color: #fff; } + .hero.is-primary .tabs a, .docstring > section > a.hero.docs-sourcelink .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-primary .tabs a:hover, .docstring > section > a.hero.docs-sourcelink .tabs a:hover { + opacity: 1; } + .hero.is-primary .tabs li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { + opacity: 1; } + .hero.is-primary .tabs.is-boxed a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, .hero.is-primary .tabs.is-toggle a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { + color: #fff; } + .hero.is-primary .tabs.is-boxed a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, .hero.is-primary .tabs.is-toggle a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-primary .tabs.is-boxed li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, .hero.is-primary .tabs.is-boxed li.is-active a:hover, .hero.is-primary .tabs.is-toggle li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, .hero.is-primary .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #4eb5de; } + .hero.is-primary.is-bold, .docstring > section > a.hero.is-bold.docs-sourcelink { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } + @media screen and (max-width: 768px) { + .hero.is-primary.is-bold .navbar-menu, .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { + background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } } + .hero.is-link { + background-color: #149eaa; + color: #fff; } + .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-link strong { + color: inherit; } + .hero.is-link .title { + color: #fff; } + .hero.is-link .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-link .subtitle a:not(.button), + .hero.is-link .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-link .navbar-menu { + background-color: #149eaa; } } + .hero.is-link .navbar-item, + .hero.is-link .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-link a.navbar-item:hover, .hero.is-link a.navbar-item.is-active, + .hero.is-link .navbar-link:hover, + .hero.is-link .navbar-link.is-active { + background-color: #118993; + color: #fff; } + .hero.is-link .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-link .tabs a:hover { + opacity: 1; } + .hero.is-link .tabs li.is-active a { + opacity: 1; } + .hero.is-link .tabs.is-boxed a, .hero.is-link .tabs.is-toggle a { + color: #fff; } + .hero.is-link .tabs.is-boxed a:hover, .hero.is-link .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-link .tabs.is-boxed li.is-active a, .hero.is-link .tabs.is-boxed li.is-active a:hover, .hero.is-link .tabs.is-toggle li.is-active a, .hero.is-link .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #149eaa; } + .hero.is-link.is-bold { + background-image: linear-gradient(141deg, #088379 0%, #149eaa 71%, #119ac6 100%); } + @media screen and (max-width: 768px) { + .hero.is-link.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #088379 0%, #149eaa 71%, #119ac6 100%); } } + .hero.is-info { + background-color: #209cee; + color: #fff; } + .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-info strong { + color: inherit; } + .hero.is-info .title { + color: #fff; } + .hero.is-info .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-info .subtitle a:not(.button), + .hero.is-info .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-info .navbar-menu { + background-color: #209cee; } } + .hero.is-info .navbar-item, + .hero.is-info .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-info a.navbar-item:hover, .hero.is-info a.navbar-item.is-active, + .hero.is-info .navbar-link:hover, + .hero.is-info .navbar-link.is-active { + background-color: #1190e3; + color: #fff; } + .hero.is-info .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-info .tabs a:hover { + opacity: 1; } + .hero.is-info .tabs li.is-active a { + opacity: 1; } + .hero.is-info .tabs.is-boxed a, .hero.is-info .tabs.is-toggle a { + color: #fff; } + .hero.is-info .tabs.is-boxed a:hover, .hero.is-info .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-info .tabs.is-boxed li.is-active a, .hero.is-info .tabs.is-boxed li.is-active a:hover, .hero.is-info .tabs.is-toggle li.is-active a, .hero.is-info .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #209cee; } + .hero.is-info.is-bold { + background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } + @media screen and (max-width: 768px) { + .hero.is-info.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } } + .hero.is-success { + background-color: #22c35b; + color: #fff; } + .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-success strong { + color: inherit; } + .hero.is-success .title { + color: #fff; } + .hero.is-success .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-success .subtitle a:not(.button), + .hero.is-success .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-success .navbar-menu { + background-color: #22c35b; } } + .hero.is-success .navbar-item, + .hero.is-success .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-success a.navbar-item:hover, .hero.is-success a.navbar-item.is-active, + .hero.is-success .navbar-link:hover, + .hero.is-success .navbar-link.is-active { + background-color: #1ead51; + color: #fff; } + .hero.is-success .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-success .tabs a:hover { + opacity: 1; } + .hero.is-success .tabs li.is-active a { + opacity: 1; } + .hero.is-success .tabs.is-boxed a, .hero.is-success .tabs.is-toggle a { + color: #fff; } + .hero.is-success .tabs.is-boxed a:hover, .hero.is-success .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-success .tabs.is-boxed li.is-active a, .hero.is-success .tabs.is-boxed li.is-active a:hover, .hero.is-success .tabs.is-toggle li.is-active a, .hero.is-success .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #22c35b; } + .hero.is-success.is-bold { + background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } + @media screen and (max-width: 768px) { + .hero.is-success.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } } + .hero.is-warning { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-warning strong { + color: inherit; } + .hero.is-warning .title { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .subtitle { + color: rgba(0, 0, 0, 0.9); } + .hero.is-warning .subtitle a:not(.button), + .hero.is-warning .subtitle strong { + color: rgba(0, 0, 0, 0.7); } + @media screen and (max-width: 1055px) { + .hero.is-warning .navbar-menu { + background-color: #ffdd57; } } + .hero.is-warning .navbar-item, + .hero.is-warning .navbar-link { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning a.navbar-item:hover, .hero.is-warning a.navbar-item.is-active, + .hero.is-warning .navbar-link:hover, + .hero.is-warning .navbar-link.is-active { + background-color: #ffd83e; + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .tabs a { + color: rgba(0, 0, 0, 0.7); + opacity: 0.9; } + .hero.is-warning .tabs a:hover { + opacity: 1; } + .hero.is-warning .tabs li.is-active a { + opacity: 1; } + .hero.is-warning .tabs.is-boxed a, .hero.is-warning .tabs.is-toggle a { + color: rgba(0, 0, 0, 0.7); } + .hero.is-warning .tabs.is-boxed a:hover, .hero.is-warning .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-warning .tabs.is-boxed li.is-active a, .hero.is-warning .tabs.is-boxed li.is-active a:hover, .hero.is-warning .tabs.is-toggle li.is-active a, .hero.is-warning .tabs.is-toggle li.is-active a:hover { + background-color: rgba(0, 0, 0, 0.7); + border-color: rgba(0, 0, 0, 0.7); + color: #ffdd57; } + .hero.is-warning.is-bold { + background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } + @media screen and (max-width: 768px) { + .hero.is-warning.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } } + .hero.is-danger { + background-color: #da0b00; + color: #fff; } + .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), + .hero.is-danger strong { + color: inherit; } + .hero.is-danger .title { + color: #fff; } + .hero.is-danger .subtitle { + color: rgba(255, 255, 255, 0.9); } + .hero.is-danger .subtitle a:not(.button), + .hero.is-danger .subtitle strong { + color: #fff; } + @media screen and (max-width: 1055px) { + .hero.is-danger .navbar-menu { + background-color: #da0b00; } } + .hero.is-danger .navbar-item, + .hero.is-danger .navbar-link { + color: rgba(255, 255, 255, 0.7); } + .hero.is-danger a.navbar-item:hover, .hero.is-danger a.navbar-item.is-active, + .hero.is-danger .navbar-link:hover, + .hero.is-danger .navbar-link.is-active { + background-color: #c10a00; + color: #fff; } + .hero.is-danger .tabs a { + color: #fff; + opacity: 0.9; } + .hero.is-danger .tabs a:hover { + opacity: 1; } + .hero.is-danger .tabs li.is-active a { + opacity: 1; } + .hero.is-danger .tabs.is-boxed a, .hero.is-danger .tabs.is-toggle a { + color: #fff; } + .hero.is-danger .tabs.is-boxed a:hover, .hero.is-danger .tabs.is-toggle a:hover { + background-color: rgba(10, 10, 10, 0.1); } + .hero.is-danger .tabs.is-boxed li.is-active a, .hero.is-danger .tabs.is-boxed li.is-active a:hover, .hero.is-danger .tabs.is-toggle li.is-active a, .hero.is-danger .tabs.is-toggle li.is-active a:hover { + background-color: #fff; + border-color: #fff; + color: #da0b00; } + .hero.is-danger.is-bold { + background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } + @media screen and (max-width: 768px) { + .hero.is-danger.is-bold .navbar-menu { + background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } } + .hero.is-small .hero-body, #documenter .docs-sidebar form.docs-search > input.hero .hero-body { + padding-bottom: 1.5rem; + padding-top: 1.5rem; } + @media screen and (min-width: 769px), print { + .hero.is-medium .hero-body { + padding-bottom: 9rem; + padding-top: 9rem; } } + @media screen and (min-width: 769px), print { + .hero.is-large .hero-body { + padding-bottom: 18rem; + padding-top: 18rem; } } + .hero.is-halfheight .hero-body, .hero.is-fullheight .hero-body, .hero.is-fullheight-with-navbar .hero-body { + align-items: center; + display: flex; } + .hero.is-halfheight .hero-body > .container, .hero.is-fullheight .hero-body > .container, .hero.is-fullheight-with-navbar .hero-body > .container { + flex-grow: 1; + flex-shrink: 1; } + .hero.is-halfheight { + min-height: 50vh; } + .hero.is-fullheight { + min-height: 100vh; } + +.hero-video { + overflow: hidden; } + .hero-video video { + left: 50%; + min-height: 100%; + min-width: 100%; + position: absolute; + top: 50%; + transform: translate3d(-50%, -50%, 0); } + .hero-video.is-transparent { + opacity: 0.3; } + @media screen and (max-width: 768px) { + .hero-video { + display: none; } } +.hero-buttons { + margin-top: 1.5rem; } + @media screen and (max-width: 768px) { + .hero-buttons .button { + display: flex; } + .hero-buttons .button:not(:last-child) { + margin-bottom: 0.75rem; } } + @media screen and (min-width: 769px), print { + .hero-buttons { + display: flex; + justify-content: center; } + .hero-buttons .button:not(:last-child) { + margin-right: 1.5rem; } } +.hero-head, +.hero-foot { + flex-grow: 0; + flex-shrink: 0; } + +.hero-body { + flex-grow: 1; + flex-shrink: 0; + padding: 3rem 1.5rem; } + +.section { + padding: 3rem 1.5rem; } + @media screen and (min-width: 1056px) { + .section.is-medium { + padding: 9rem 1.5rem; } + .section.is-large { + padding: 18rem 1.5rem; } } +.footer { + background-color: #fafafa; + padding: 3rem 1.5rem 6rem; } + +h1 .docs-heading-anchor, h1 .docs-heading-anchor:hover, h1 .docs-heading-anchor:visited, h2 .docs-heading-anchor, h2 .docs-heading-anchor:hover, h2 .docs-heading-anchor:visited, h3 .docs-heading-anchor, h3 .docs-heading-anchor:hover, h3 .docs-heading-anchor:visited, h4 .docs-heading-anchor, h4 .docs-heading-anchor:hover, h4 .docs-heading-anchor:visited, h5 .docs-heading-anchor, h5 .docs-heading-anchor:hover, h5 .docs-heading-anchor:visited, h6 .docs-heading-anchor, h6 .docs-heading-anchor:hover, h6 .docs-heading-anchor:visited { + color: #654ca3; } + +h1 .docs-heading-anchor-permalink, h2 .docs-heading-anchor-permalink, h3 .docs-heading-anchor-permalink, h4 .docs-heading-anchor-permalink, h5 .docs-heading-anchor-permalink, h6 .docs-heading-anchor-permalink { + visibility: hidden; + vertical-align: middle; + margin-left: 0.5em; + font-size: 0.7rem; } + h1 .docs-heading-anchor-permalink::before, h2 .docs-heading-anchor-permalink::before, h3 .docs-heading-anchor-permalink::before, h4 .docs-heading-anchor-permalink::before, h5 .docs-heading-anchor-permalink::before, h6 .docs-heading-anchor-permalink::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f0c1"; } + +h1:hover .docs-heading-anchor-permalink, h2:hover .docs-heading-anchor-permalink, h3:hover .docs-heading-anchor-permalink, h4:hover .docs-heading-anchor-permalink, h5:hover .docs-heading-anchor-permalink, h6:hover .docs-heading-anchor-permalink { + visibility: visible; } + +.docs-dark-only { + display: none !important; } + +pre { + position: relative; + overflow: hidden; } + pre code, pre code.hljs { + padding: 0 0.75rem !important; + overflow: auto; + display: block; } + pre code:first-of-type, pre code.hljs:first-of-type { + padding-top: 0.5rem !important; } + pre code:last-of-type, pre code.hljs:last-of-type { + padding-bottom: 0.5rem !important; } + pre .copy-button { + opacity: 0.2; + transition: opacity 0.2s; + position: absolute; + right: 0em; + top: 0em; + padding: 0.5em; + width: 2.5em; + height: 2.5em; + background: transparent; + border: none; + font-family: "Font Awesome 5 Free"; + color: #202020; + cursor: pointer; + text-align: center; } + pre .copy-button:focus, pre .copy-button:hover { + opacity: 1; + background: rgba(32, 32, 32, 0.1); + color: #149eaa; } + pre .copy-button.success { + color: #259a12; + opacity: 1; } + pre .copy-button.error { + color: #cb3c33; + opacity: 1; } + pre:hover .copy-button { + opacity: 1; } + +.admonition { + background-color: #b5b5b5; + border-style: solid; + border-width: 1px; + border-color: #363636; + border-radius: 4px; + font-size: 1rem; } + .admonition strong { + color: currentColor; } + .admonition.is-small, #documenter .docs-sidebar form.docs-search > input.admonition { + font-size: 0.75rem; } + .admonition.is-medium { + font-size: 1.25rem; } + .admonition.is-large { + font-size: 1.5rem; } + .admonition.is-default { + background-color: #b5b5b5; + border-color: #363636; } + .admonition.is-default > .admonition-header { + background-color: #363636; + color: #fff; } + .admonition.is-default > .admonition-body { + color: #fff; } + .admonition.is-info { + background-color: #def0fc; + border-color: #209cee; } + .admonition.is-info > .admonition-header { + background-color: #209cee; + color: #fff; } + .admonition.is-info > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-success { + background-color: #bdf4d1; + border-color: #22c35b; } + .admonition.is-success > .admonition-header { + background-color: #22c35b; + color: #fff; } + .admonition.is-success > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-warning { + background-color: #fff3c5; + border-color: #ffdd57; } + .admonition.is-warning > .admonition-header { + background-color: #ffdd57; + color: rgba(0, 0, 0, 0.7); } + .admonition.is-warning > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-danger { + background-color: #ffaba7; + border-color: #da0b00; } + .admonition.is-danger > .admonition-header { + background-color: #da0b00; + color: #fff; } + .admonition.is-danger > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + .admonition.is-compat { + background-color: #bdeff5; + border-color: #1db5c9; } + .admonition.is-compat > .admonition-header { + background-color: #1db5c9; + color: #fff; } + .admonition.is-compat > .admonition-body { + color: rgba(0, 0, 0, 0.7); } + +.admonition-header { + color: #fff; + background-color: #363636; + align-items: center; + font-weight: 700; + justify-content: space-between; + line-height: 1.25; + padding: 0.5rem 0.75rem; + position: relative; } + .admonition-header:before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + margin-right: 0.75rem; + content: "\f06a"; } + +.admonition-body { + color: #202020; + padding: 0.5rem 0.75rem; } + .admonition-body pre { + background-color: #ebe8f4; } + .admonition-body code { + background-color: #ebe8f4; } + +.docstring { + margin-bottom: 1em; + background-color: transparent; + border: 1px solid #dbdbdb; + box-shadow: 2px 2px 3px rgba(10, 10, 10, 0.1); + max-width: 100%; } + .docstring > header { + display: flex; + flex-grow: 1; + align-items: stretch; + padding: 0.5rem 0.75rem; + background-color: #f7f7f7; + box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); + box-shadow: none; + border-bottom: 1px solid #dbdbdb; } + .docstring > header code { + background-color: transparent; } + .docstring > header .docstring-binding { + margin-right: 0.3em; } + .docstring > header .docstring-category { + margin-left: 0.3em; } + .docstring > section { + position: relative; + padding: 0.75rem 0.75rem; + border-bottom: 1px solid #dbdbdb; } + .docstring > section:last-child { + border-bottom: none; } + .docstring > section > a.docs-sourcelink { + transition: opacity 0.3s; + opacity: 0; + position: absolute; + right: 0.375rem; + bottom: 0.375rem; } + .docstring > section > a.docs-sourcelink:focus { + opacity: 1 !important; } + .docstring:hover > section > a.docs-sourcelink { + opacity: 0.2; } + .docstring:focus-within > section > a.docs-sourcelink { + opacity: 0.2; } + .docstring > section:hover a.docs-sourcelink { + opacity: 1; } + +.documenter-example-output { + background-color: #fff; } + +.outdated-warning-overlay { + position: fixed; + top: 0; + left: 0; + right: 0; + box-shadow: 0 0 10px rgba(0, 0, 0, 0.3); + z-index: 999; + background-color: #ffaba7; + color: rgba(0, 0, 0, 0.7); + border-bottom: 3px solid #da0b00; + padding: 10px 35px; + text-align: center; + font-size: 15px; } + .outdated-warning-overlay .outdated-warning-closer { + position: absolute; + top: calc(50% - 10px); + right: 18px; + cursor: pointer; + width: 12px; } + .outdated-warning-overlay a { + color: #149eaa; } + .outdated-warning-overlay a:hover { + color: #107c85; } + +.content pre { + border: 1px solid #dbdbdb; } + +.content code { + font-weight: inherit; } + +.content a code { + color: #149eaa; } + +.content h1 code, .content h2 code, .content h3 code, .content h4 code, .content h5 code, .content h6 code { + color: #654ca3; } + +.content table { + display: block; + width: initial; + max-width: 100%; + overflow-x: auto; } + +.content blockquote > ul:first-child, .content blockquote > ol:first-child, .content .admonition-body > ul:first-child, .content .admonition-body > ol:first-child { + margin-top: 0; } + +pre, code { + font-variant-ligatures: no-contextual; } + +.breadcrumb a.is-disabled { + cursor: default; + pointer-events: none; } + .breadcrumb a.is-disabled, .breadcrumb a.is-disabled:hover { + color: #654ca3; } + +.hljs { + background: initial !important; } + +.katex .katex-mathml { + top: 0; + right: 0; } + +.katex-display, mjx-container, .MathJax_Display { + margin: 0.5em 0 !important; } + +html { + -moz-osx-font-smoothing: auto; + -webkit-font-smoothing: auto; } + +li.no-marker { + list-style: none; } + +/* This file contain the overall layout. + * + * The main container is
            that is identified by id #documenter. + */ +#documenter .docs-main > article { + overflow-wrap: break-word; } + #documenter .docs-main > article .math-container { + overflow-x: auto; + overflow-y: hidden; } + +@media screen and (min-width: 1056px) { + #documenter .docs-main { + max-width: 52rem; + margin-left: 20rem; + padding-right: 1rem; } } + +@media screen and (max-width: 1055px) { + #documenter .docs-main { + width: 100%; } + #documenter .docs-main > article { + max-width: 52rem; + margin-left: auto; + margin-right: auto; + margin-bottom: 1rem; + padding: 0 1rem; } + #documenter .docs-main > header, #documenter .docs-main > nav { + max-width: 100%; + width: 100%; + margin: 0; } } + +#documenter .docs-main header.docs-navbar { + background-color: #fff; + border-bottom: 1px solid #dbdbdb; + z-index: 2; + min-height: 4rem; + margin-bottom: 1rem; + display: flex; } + #documenter .docs-main header.docs-navbar .breadcrumb { + flex-grow: 1; } + #documenter .docs-main header.docs-navbar .docs-right { + display: flex; + white-space: nowrap; } + #documenter .docs-main header.docs-navbar .docs-right .docs-icon, #documenter .docs-main header.docs-navbar .docs-right .docs-label, #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + display: inline-block; } + #documenter .docs-main header.docs-navbar .docs-right .docs-label { + padding: 0; + margin-left: 0.3em; } + #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button { + margin: auto 0 auto 1rem; } + #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { + font-size: 1.5rem; + margin: auto 0 auto 1rem; } + #documenter .docs-main header.docs-navbar > * { + margin: auto 0; } + @media screen and (max-width: 1055px) { + #documenter .docs-main header.docs-navbar { + position: sticky; + top: 0; + padding: 0 1rem; + /* For Headroom.js */ + transition-property: top, box-shadow; + -webkit-transition-property: top, box-shadow; + /* Safari */ + transition-duration: 0.3s; + -webkit-transition-duration: 0.3s; + /* Safari */ } + #documenter .docs-main header.docs-navbar.headroom--not-top { + box-shadow: 0.2rem 0rem 0.4rem #bbb; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } + #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { + top: -4.5rem; + transition-duration: 0.7s; + -webkit-transition-duration: 0.7s; + /* Safari */ } } +#documenter .docs-main section.footnotes { + border-top: 1px solid #dbdbdb; } + #documenter .docs-main section.footnotes li .tag:first-child, #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, #documenter .docs-main section.footnotes li .content kbd:first-child, .content #documenter .docs-main section.footnotes li kbd:first-child { + margin-right: 1em; + margin-bottom: 0.4em; } + +#documenter .docs-main .docs-footer { + display: flex; + flex-wrap: wrap; + margin-left: 0; + margin-right: 0; + border-top: 1px solid #dbdbdb; + padding-top: 1rem; + padding-bottom: 1rem; } + @media screen and (max-width: 1055px) { + #documenter .docs-main .docs-footer { + padding-left: 1rem; + padding-right: 1rem; } } + #documenter .docs-main .docs-footer .docs-footer-nextpage, #documenter .docs-main .docs-footer .docs-footer-prevpage { + flex-grow: 1; } + #documenter .docs-main .docs-footer .docs-footer-nextpage { + text-align: right; } + #documenter .docs-main .docs-footer .flexbox-break { + flex-basis: 100%; + height: 0; } + #documenter .docs-main .docs-footer .footer-message { + font-size: 0.8em; + margin: 0.5em auto 0 auto; + text-align: center; } + +#documenter .docs-sidebar { + display: flex; + flex-direction: column; + color: #fff; + background-color: #654ca3; + border-right: 1px solid #dbdbdb; + padding: 0; + flex: 0 0 18rem; + z-index: 5; + font-size: 1em; + position: fixed; + left: -18rem; + width: 18rem; + height: 100%; + transition: left 0.3s; + /* Setting up a nicer theme style for the scrollbar */ } + #documenter .docs-sidebar.visible { + left: 0; + box-shadow: 0.4rem 0rem 0.8rem #bbb; } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar.visible { + box-shadow: none; } } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar { + left: 0; + top: 0; } } + #documenter .docs-sidebar .docs-logo { + margin-top: 1rem; + padding: 0 1rem; } + #documenter .docs-sidebar .docs-logo > img { + max-height: 6rem; + margin: auto; } + #documenter .docs-sidebar .docs-package-name { + flex-shrink: 0; + font-size: 1.5rem; + font-weight: 700; + text-align: center; + white-space: nowrap; + overflow: hidden; + padding: 0.5rem 0; } + #documenter .docs-sidebar .docs-package-name .docs-autofit { + max-width: 16.2rem; } + #documenter .docs-sidebar .docs-package-name a, #documenter .docs-sidebar .docs-package-name a:hover { + color: #fff; } + #documenter .docs-sidebar .docs-version-selector { + border-top: 1px solid #dbdbdb; + display: none; + padding: 0.5rem; } + #documenter .docs-sidebar .docs-version-selector.visible { + display: flex; } + #documenter .docs-sidebar ul.docs-menu { + flex-grow: 1; + user-select: none; + border-top: 1px solid #dbdbdb; + padding-bottom: 1.5rem; + /* Managing collapsible submenus */ } + #documenter .docs-sidebar ul.docs-menu > li > .tocitem { + font-weight: bold; } + #documenter .docs-sidebar ul.docs-menu > li li { + font-size: 0.95em; + margin-left: 1em; + border-left: 1px solid #dbdbdb; } + #documenter .docs-sidebar ul.docs-menu input.collapse-toggle { + display: none; } + #documenter .docs-sidebar ul.docs-menu ul.collapsed { + display: none; } + #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed { + display: block; } + #documenter .docs-sidebar ul.docs-menu label.tocitem { + display: flex; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label { + flex-grow: 2; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron { + display: inline-block; + font-style: normal; + font-variant: normal; + text-rendering: auto; + line-height: 1; + font-size: 0.75em; + margin-left: 1rem; + margin-top: auto; + margin-bottom: auto; } + #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before { + font-family: "Font Awesome 5 Free"; + font-weight: 900; + content: "\f054"; } + #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before { + content: "\f078"; } + #documenter .docs-sidebar ul.docs-menu .tocitem { + display: block; + padding: 0.5rem 0.5rem; } + #documenter .docs-sidebar ul.docs-menu .tocitem, #documenter .docs-sidebar ul.docs-menu .tocitem:hover { + color: #fff; + background: #654ca3; } + #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, #documenter .docs-sidebar ul.docs-menu label.tocitem:hover { + color: #fff; + background-color: #4b3979; } + #documenter .docs-sidebar ul.docs-menu li.is-active { + border-top: 1px solid #dbdbdb; + border-bottom: 1px solid #dbdbdb; + background-color: #fff; } + #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover { + background-color: #fff; + color: #202020; } + #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover { + background-color: #ddd7ec; + color: #202020; } + #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child { + border-top: none; } + #documenter .docs-sidebar ul.docs-menu ul.internal { + margin: 0 0.5rem 0.5rem; + border-top: 1px solid #dbdbdb; } + #documenter .docs-sidebar ul.docs-menu ul.internal li { + font-size: 0.85em; + border-left: none; + margin-left: 0; + margin-top: 0.5rem; } + #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem { + width: 100%; + padding: 0; } + #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before { + content: "⚬"; + margin-right: 0.4em; } + #documenter .docs-sidebar form.docs-search { + margin: auto; + margin-top: 0.5rem; + margin-bottom: 0.5rem; } + #documenter .docs-sidebar form.docs-search > input { + width: 14.4rem; } + @media screen and (min-width: 1056px) { + #documenter .docs-sidebar ul.docs-menu { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar { + width: .3rem; + background: none; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #543f87; } + #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover { + background: #43326b; } } + @media screen and (max-width: 1055px) { + #documenter .docs-sidebar { + overflow-y: auto; + -webkit-overflow-scroll: touch; } + #documenter .docs-sidebar::-webkit-scrollbar { + width: .3rem; + background: none; } + #documenter .docs-sidebar::-webkit-scrollbar-thumb { + border-radius: 5px 0px 0px 5px; + background: #543f87; } + #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover { + background: #43326b; } } +#documenter .docs-main #documenter-search-info { + margin-bottom: 1rem; } + +#documenter .docs-main #documenter-search-results { + list-style-type: circle; + list-style-position: outside; } + #documenter .docs-main #documenter-search-results li { + margin-left: 2rem; 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Gets put into the tag.. +function set_theme_from_local_storage() { + // Intialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if(window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the browser supports user color preference + var darkPreference = false; + // Check if the users preference is for dark color scheme + if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { + darkPreference = true; + } + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; var disabled = []; var darkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. 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            Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/previews/PR34/index.html b/previews/PR34/index.html new file mode 100644 index 00000000..2133852e --- /dev/null +++ b/previews/PR34/index.html @@ -0,0 +1,2 @@ + +TransitionIndicators.jl · TransitionIndicators.jl
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            TransitionIndicators.jl

            TransitionIndicators.jl

            TransitionIndicators — Module

            TransitionIndicators.jl

            CI codecov Package Downloads

            A Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

            This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

            add https://github.com/JuliaDynamics/TransitionIndicators.jl

            All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

            source
            Star us on GitHub!

            If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

            Content

            Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionIndicators.jl sticks to the latter terminology and provides an interface that:

            • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
            • Makes the surrogate analysis to test for significance under the hub.
            • Can be easily extended by any user without touching the source code.
            • Reduces the programming overhead for any researcher willing to benchmark new methods.
            • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
            • Increases trustworthiness thanks to a large test suite.
            Similar projects

            An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

            Approaches

            Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionIndicators.jl is designed to allow these cutting-edge methods and foster the development of new ones.

            diff --git a/previews/PR34/search/index.html b/previews/PR34/search/index.html new file mode 100644 index 00000000..79473719 --- /dev/null +++ b/previews/PR34/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionIndicators.jl

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              diff --git a/previews/PR34/search_index.js b/previews/PR34/search_index.js new file mode 100644 index 00000000..efc576f6 --- /dev/null +++ b/previews/PR34/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionIndicators.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionIndicators.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"api/#Indicators-analysis","page":"API","title":"Indicators analysis","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute_metrics\nIndicatorsConfig\nSignificanceConfig\nindicators_analysis\nIndicatorsResults","category":"page"},{"location":"api/#TransitionIndicators.PrecomputableFunction","page":"API","title":"TransitionIndicators.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.precompute_metrics","page":"API","title":"TransitionIndicators.precompute_metrics","text":"precompute_metrics(metrics::Vector, t::AbstractVector)\n\nPrecompute functions contained in metrics that can be precomputed based on the time vector t. Relies on abstract type PrecomputableFunction.\n\nThe output f::Vector{Function} contains the ready-to-use metrics.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.IndicatorsConfig","page":"API","title":"TransitionIndicators.IndicatorsConfig","text":"IndicatorsConfig(t::AbstractVector, f::Function, indicators...; kwargs...)\n\nA configuration for computing indicators from timeseries with time t. Indicators are standard Julia functions that input an ::AbstractVector and output a ::Real. Any number of indicators can be given. Indicators typically used in the literature are listed in the documentation section Indicators.\n\nKeywords are propagated into WindowViewer to create a sliding window for estimating the indicators. The time vector resulting from the sliding window is obtained under the hood by:\n\nt_indicator = windowmap(f, t, kwargs...)\n\nCommon choices for f are:\n\nlast: use x[k-width:k] to estimate the indicator at time step k.\nmidpoint: use x[k-width÷2:k+width÷2] to estimate the indicator at time step k.\nfirst: use x[k:k+width] to estimate the indicator at time step k.\n\nAlong with SignificanceConfig it is given to indicators_analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.SignificanceConfig","page":"API","title":"TransitionIndicators.SignificanceConfig","text":"SignificanceConfig(indconfig, f, change_metrics...; kwargs...)\n\nA configuration for estimating a significant change of indicators based on a sliding window and and indconfig::IndicatorsConfig. The time vector resulting from the sliding window is obtained under the hood by:\n\nt_change = windowmap(f, indconfig.t_indicator, kwargs...)\n\nCommon choices for f are:\n\nlast: use x[k-width:k] to estimate the indicator change at time step k.\nmidpoint: use x[k-width÷2:k+width÷2] to estimate the indicator change\n\nat time step k.\n\nfirst: use x[k:k+width] to estimate the indicator change at time step k.\n\nAlong with IndicatorsConfig, SignificanceConfig is given to indicators_analysis.\n\nchange_metrics can be a single Julia function, in which case the same metric is applied over all indicators in IndicatorsConfig. change_metrics can also be many functions, each one for each indicator.\n\nKeyword arguments\n\nn_surrogates::Int = 10_000: how many surrogates to create.\nsurrogate_method::S = RandomFourier(): what method to use to create the surrogates. Any Surrogate subtype from TimeseriesSurrogates.jl is valid.\nrng::AbstractRNG = Random.default_rng()`: a random number generator for the surrogates. See the Julia manual for more.\nwidth::Int: width given to the WindowViewer of the indicator timeseries to estimate transient changes of the indicator.\nstride::Int: stride given to the WindowViewer of the indicator timeseries to estimate transient changes of the indicator.\ntail::Symbol: kind of tail test to do (one of :left, :right, :both).\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.indicators_analysis","page":"API","title":"TransitionIndicators.indicators_analysis","text":"indicators_analysis(t, x, indicators::IndicatorsConfig, sigconfig::SignificanceConfig)\n\nPerform an analysis of transition indicators for input timeseries x with time vector t by specifying which indicators to use and with what sliding window (IndicatorsConfig), as well as how to measure significant changes in the indicators (SignificanceConfig). If t is not provided, it is assumed that t=eachindex(x).\n\nReturn the output as IndicatorsResults.\n\nThis function performs the analysis described in the documentation Example sections. It computes various indicators over sliding windows of x, and then computes change metrics of over sliding windows of the indicators. It does exactly the same computations for surrogates of x and use this result to check for significance of the change metrics by computing the p-value. The returned output contains all these computed timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.IndicatorsResults","page":"API","title":"TransitionIndicators.IndicatorsResults","text":"IndicatorsResults\n\nA struct containing the output of indicators_analysis, which is the main computational part of TransitionIndicators.jl. It can be used for analysis and visualization purposes.\n\nIt has the following fields:\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nindicators::Vector{Function}: indicators used in the processing.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nchange_metrics::Vector{Function}: change metrics used in the processing.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\npval, the p-value of the change metrics w.r.t. the surrogates. It is a 2-dimensional array, where first dimension = time, second dimension = change metric. I.e. pval[:, k] will give the time series of p-value of the k-th change metric.\n\n\n\n\n\n","category":"type"},{"location":"api/#Indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatistics.var(::AbstractArray)\nStatsBase.skewness\nStatsBase.kurtosis\nar1_whitenoise\nLowfreqPowerSpectrum\nPrecomputedLowfreqPowerSpectrum\nPermutationEntropy()\nPermutationEntropy(::AbstractVector)","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.ar1_whitenoise","page":"API","title":"TransitionIndicators.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient θ of a time series x. Computation based on the analytic solution of the least-square parameter estimation:\n\n hattheta = dfracsum_i=2^n x_i x_i-1sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.LowfreqPowerSpectrum","page":"API","title":"TransitionIndicators.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.PrecomputedLowfreqPowerSpectrum","page":"API","title":"TransitionIndicators.PrecomputedLowfreqPowerSpectrum","text":"PrecomputedLowfreqPowerSpectrum(x::AbstractVector)\n\nA struct containing all the precomputed fields to efficiently perform repetitive computation of the low-frequency power spectrum (LFPS), a number between 0 and 1 that characterizes the amount of power contained in the low frequencies of the power density spectrum of x. Once lfps::PrecomputedLowfreqPowerSpectrum is initialized, it can be used as a function to obtain the LFPS of x::AbstractVector by:\n\nlfps(x)\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.PermutationEntropy-Tuple{AbstractVector}","page":"API","title":"TransitionIndicators.PermutationEntropy","text":"PermutationEntropy(x::AbstractVector)\n\nReturn the permutation entropy of x. This computation breaks down in computing the entropy_normalized of a SymbolicPermutation.\n\n\n\n\n\n","category":"method"},{"location":"api/#Change-metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope\nPrecomputedRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionIndicators.kendalltau","page":"API","title":"TransitionIndicators.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.spearman","page":"API","title":"TransitionIndicators.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.RidgeRegressionSlope","page":"API","title":"TransitionIndicators.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. The latter can be initialized by precompute:\n\nrr = precompute( RidgeRegressionSlope() )\n\nKeyword arguments:\n\nlambda: a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.PrecomputedRidgeRegressionSlope","page":"API","title":"TransitionIndicators.PrecomputedRidgeRegressionSlope","text":"PrecomputedRidgeRegressionSlope(x::AbstractVector)\n\nReturn the slope of the ridge regression of x.\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionIndicators.WindowViewer","page":"API","title":"TransitionIndicators.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionIndicators.windowmap","page":"API","title":"TransitionIndicators.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionIndicators.windowmap!","page":"API","title":"TransitionIndicators.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"#TransitionIndicators.jl","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"(Image: TransitionIndicators.jl)","category":"page"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"TransitionIndicators","category":"page"},{"location":"#TransitionIndicators","page":"TransitionIndicators.jl","title":"TransitionIndicators","text":"TransitionIndicators.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionIndicators.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionIndicators.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionIndicators.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionIndicators.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionIndicators.jl","title":"TransitionIndicators.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionIndicators.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any pre-processing of raw data first such as detrending (not part of TransitionIndicators.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionIndicators.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionIndicators, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_nlinear)\nlines!(ax, t, x_linear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionIndicators.jl\nAny timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionIndicators.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window.\n# This therefore only uses information from `k-width` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionIndicators, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\nfig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))\nlines!(ax, tfluct, s .- 0.05; color = Cycled(3))\nax.title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = \"nonlin\")\nlines!(ax, t_change, change_s; color = Cycled(3), label = \"surrogate\")\naxislegend()\nax.title = \"change metric\"\n\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig = Figure()\naxl = Axis(fig[1,1]; title = \"linear\")\naxnl = Axis(fig[1,2]; title = \"nonlinear\")\naxsigl = Axis(fig[2,1])\naxsignl = Axis(fig[2,2])\n\nfor (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change; color = Cycled(j))\n lines!(axsig, t_change, pval; color = Cycled(j+2))\nend\n\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionIndicators.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionIndicators.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow as follows:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Create an instance of IndicatorsConfig, that dictates which indicators will be used, and over what sliding window.\nCreate an instance of SignificanceConfig, that dictates what change metrics, surrogate types, and sliding window will be used to quantify a significant change of the indicators.\nAlong with the input timeseries x these three are plugged into indicators_analysis.\nThe output, which is an IndicatorsResults, can be used to visualize the results.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks apply this process, and visualize it, for the examples we used in the educational part of the tutorial. First we load, and do the necessary pre-processing, to get input data:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionIndicators, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_nl_fluct)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Then we decide what indicators and change metrics to use and run the analysis.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = [var, ar1_whitenoise]\nindconfig = IndicatorsConfig(tfluct, last, indicators; width = 400)\n\n\n# use the ridge regression slope for both indicators\nchange_metrics = [RidgeRegressionSlope()]\nsigconfig = SignificanceConfig(indconfig, last, change_metrics;\n width = 30, n_surrogates = 1000)\n\n# perform the full analysis\nresults = indicators_analysis(tfluct, x_nl_fluct, indconfig, sigconfig)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"That's it, just a couple of lines! To get insight on the results, we plot the obtained p-values vs. the original time series:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2), label = \"input\")\naxpval, = lines(fig[2,1], sigconfig.t_change, results.pval[:, 1]; color = Cycled(3), label = \"p-value of var\")\nlines!(axpval, sigconfig.t_change, results.pval[:, 2]; color = Cycled(4), label = \"p-value of ar1\")\nxlims!(ax, (0, 50))\nxlims!(axpval, (0, 50))\naxislegend(axpval)\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Thresholding the p-value results in a loss of information and it is therefore preferable to be avoided. For automation purposes it might however be unavoidable. Here we show an example where we consider that both the variance and the AR1-regression coefficient need to show a p-value below 0.05 for a transition to be indicated in a binary sense:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"threshold = 0.05\nsignif_idxs = vec(count(results.pval .< threshold, dims = 2) .>= 2)\ntflags = results.t_change[signif_idxs]\nvlines!(ax, tflags; label = \"flags\", color = Cycled(3), linestyle = :dash)\naxislegend(ax)\nfig","category":"page"}] +} diff --git a/previews/PR34/siteinfo.js b/previews/PR34/siteinfo.js new file mode 100644 index 00000000..15966a93 --- /dev/null +++ b/previews/PR34/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR34"; diff --git a/previews/PR34/tutorial/index.html b/previews/PR34/tutorial/index.html new file mode 100644 index 00000000..a15619dd --- /dev/null +++ b/previews/PR34/tutorial/index.html @@ -0,0 +1,120 @@ + +Tutorial · TransitionIndicators.jl
              Edit on GitHub

              Tutorial

              Workflow

              Computing transition indicators consists of the following steps:

              1. Doing any pre-processing of raw data first such as detrending (not part of TransitionIndicators.jl). This yields the input timeseries.
              2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
              3. Computing the changes of the indicator by sliding a window over its timeseries.
              4. Generating many surrogates that preserve important statistical properties of the original timeseries.
              5. Performing step 2 and 3 for the surrogate timeseries.
              6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

              These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionIndicators.jl exports.

              Tutorial – Educational

              Raw input data

              Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

              \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

              with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

              using TransitionIndicators, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_nlinear)
+lines!(ax, t, x_linear)
+ax.title = "raw data"
+fig

              Preprocessing

              Not part of TransitionIndicators.jl

              Any timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionIndicators.jl and is the responsibility of the researcher.

              The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

              x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

              At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

              Detrending in Julia

              Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

              Indicator timeseries

              We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

              indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window.
+# This therefore only uses information from `k-width` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

              The lines plotted above are the indicator timeseries.

              Change metric timeseries

              From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

              change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

              Timeseries surrogates

              As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

              In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionIndicators, so that you don't have to using both of them.

              To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

              # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))
+lines!(ax, tfluct, s .- 0.05; color = Cycled(3))
+ax.title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin")
+lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate")
+axislegend()
+ax.title = "change metric"
+
+fig

              Quantifying significance

              To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

              n_surrogates = 1_000
+fig = Figure()
+axl = Axis(fig[1,1]; title = "linear")
+axnl = Axis(fig[1,2]; title = "nonlinear")
+axsigl = Axis(fig[2,1])
+axsignl = Axis(fig[2,2])
+
+for (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change; color = Cycled(j))
+    lines!(axsig, t_change, pval; color = Cycled(j+2))
+end
+
+fig

              As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

              Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

              Tutorial – TransitionIndicators.jl

              TransitionIndicators.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

              The interface is simple, and directly parallelizes the Workflow as follows:

              1. Create an instance of IndicatorsConfig, that dictates which indicators will be used, and over what sliding window.
              2. Create an instance of SignificanceConfig, that dictates what change metrics, surrogate types, and sliding window will be used to quantify a significant change of the indicators.
              3. Along with the input timeseries x these three are plugged into indicators_analysis.
              4. The output, which is an IndicatorsResults, can be used to visualize the results.

              The following blocks apply this process, and visualize it, for the examples we used in the educational part of the tutorial. First we load, and do the necessary pre-processing, to get input data:

              using TransitionIndicators, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_nl_fluct)
+ax.title = "input timeseries"
+fig

              Then we decide what indicators and change metrics to use and run the analysis.

              # These indicators are suitable for Critical Slowing Down
+indicators = [var, ar1_whitenoise]
+indconfig = IndicatorsConfig(tfluct, last, indicators; width = 400)
+
+
+# use the ridge regression slope for both indicators
+change_metrics = [RidgeRegressionSlope()]
+sigconfig = SignificanceConfig(indconfig, last, change_metrics;
+    width = 30, n_surrogates = 1000)
+
+# perform the full analysis
+results = indicators_analysis(tfluct, x_nl_fluct, indconfig, sigconfig)
              IndicatorsResults
+ input timeseries: 2500-element Vector{Float64}
+ indicators:       Function[Statistics.var, TransitionIndicators.ar1_whitenoise]
+ indicator length: 2101
+ change metrics:   Function[PrecomputedRidgeRegressionSlope{Float64}(true, [-0.32258064516103246 -0.3003337041154417 … 0.300333704115447 0.322580645161036; 2.707526881718266 2.52309974045032 … -2.4564330737836997 -2.6408602150516174])]
+ surrogate:        RandomFourier(true)
+ p-value:          2072×2 Matrix{Float64}
+

              That's it, just a couple of lines! To get insight on the results, we plot the obtained p-values vs. the original time series:

              fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2), label = "input")
+axpval, = lines(fig[2,1], sigconfig.t_change, results.pval[:, 1]; color = Cycled(3), label = "p-value of var")
+lines!(axpval, sigconfig.t_change, results.pval[:, 2]; color = Cycled(4), label = "p-value of ar1")
+xlims!(ax, (0, 50))
+xlims!(axpval, (0, 50))
+axislegend(axpval)
+fig

              Thresholding the p-value results in a loss of information and it is therefore preferable to be avoided. For automation purposes it might however be unavoidable. Here we show an example where we consider that both the variance and the AR1-regression coefficient need to show a p-value below 0.05 for a transition to be indicated in a binary sense:

              threshold = 0.05
+signif_idxs = vec(count(results.pval .< threshold, dims = 2) .>= 2)
+tflags = results.t_change[signif_idxs]
+vlines!(ax, tflags; label = "flags", color = Cycled(3), linestyle = :dash)
+axislegend(ax)
+fig
              diff --git a/previews/PR34/tutorial_literate.jl b/previews/PR34/tutorial_literate.jl new file mode 100644 index 00000000..8f97f7db --- /dev/null +++ b/previews/PR34/tutorial_literate.jl @@ -0,0 +1,140 @@ +using TransitionIndicators, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_nlinear) +lines!(ax, t, x_linear) +ax.title = "raw data" +fig + +# +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +# +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window. +# This therefore only uses information from `k-width` to `k` at time step `k`. +# Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +# +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + + +# + +# Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2)) +lines!(ax, tfluct, s .- 0.05; color = Cycled(3)) +ax.title = "real signal vs. surrogate(s)" + +# compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin") +lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate") +axislegend() +ax.title = "change metric" + +fig +# + + +n_surrogates = 1_000 +fig = Figure() +axl = Axis(fig[1,1]; title = "linear") +axnl = Axis(fig[1,2]; title = "nonlinear") +axsigl = Axis(fig[2,1]) +axsignl = Axis(fig[2,2]) + +for (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + # Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change; color = Cycled(j)) + lines!(axsig, t_change, pval; color = Cycled(j+2)) +end + +fig + +# %% +# Tutorial short + +using TransitionIndicators, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_nl_fluct) +ax.title = "input timeseries" +fig + +# These indicators are suitable for Critical Slowing Down +indicators = [var, ar1_whitenoise] +indconfig = IndicatorsConfig(tfluct, last, indicators; width = 400) + + +# use the ridge regression slope for both indicators +change_metrics = [RidgeRegressionSlope()] +sigconfig = SignificanceConfig(indconfig, last, change_metrics; + width = 30, n_surrogates = 1000) + +# perform the full analysis +results = indicators_analysis(tfluct, x_nl_fluct, indconfig, sigconfig) + +# Plot the original timeseries vs. p-value time series +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2), label = "input") +axpval, = lines(fig[2,1], sigconfig.t_change, results.pval[:, 1]; color = Cycled(3), label = "p-value of var") +lines!(axpval, sigconfig.t_change, results.pval[:, 2]; color = Cycled(4), label = "p-value of ar1") +xlims!(ax, (0, 50)) +xlims!(axpval, (0, 50)) +axislegend(axpval) +fig + + +flags_indicators, flags_andicators = transition_flags(results, 0.05) +vlines!(ax, flags_andicators; label = "flags", color = Cycled(3), linestyle = :dash) +axislegend(ax) +fig \ No newline at end of file diff --git a/previews/PR39/api/index.html b/previews/PR39/api/index.html new file mode 100644 index 00000000..1cc96302 --- /dev/null +++ b/previews/PR39/api/index.html @@ -0,0 +1,15 @@ + +API · TransitionsInTimeseries.jl
              Edit on GitHub

              API

              Main analysis functions

              TransitionsInTimeseries.TransitionsSurrogatesConfig — Type
              TransitionsSurrogatesConfig(indicators, change_metrics [, surrogate]; kwargs...)

              A configuration struct for TransitionsInTimeseries.jl that can be given to estimate_transitions. It contains all information necessary to perform the basic Workflow of the package to detect significant transitions in the input timeseries, using the method of surrogate testing to quantify significance:

              1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
              2. Estimate changes for an indicator by sliding a window over its timeseries.
              3. Generate many surrogates that preserve important statistical properties of the original input timeseries.
              4. Perform steps 1 and 2 for the surrogate timeseries (and for all provided indicators).
              5. Estimate when an indicators timeseries shows significant change (trend, jump or anything else) when compared to the surrogate timeseries when compared to the surrogate data. Significance is estimated from the p-values of the real data vs surrogate data.

              Arguments

              • indicators::AbstractVector{<:Function} a vector of indicators. Some indicators typically used in the literature are listed in the documentation section on indicators. The analysis is performed efficiently for all indicators given.
              • change_metrics change metrics corresponding to the given indicators. If given a function, the same function is used for all indicators. Otherwise, it should be a vetor of functions of the same size as indicators, using change metric for its corresponding indicator. Some change metrics typically used in the literature are listed in the documentation section on change metrics.
              • surrogate::Surrogate the method to use to generate surrogates of the input timeseries. This is an optional argument that defaults to RandomFourier(), see Surrogates for alternative options.

              Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.

              Keyword arguments

              • width_ind::Int=100, stride_ind::Int=1: width and stride given to the WindowViewer to compute the indicator from the input timeseries.

              • width_cha::Int=50, stride_cha::Int=1: width and stride given to the WindowViewer to compute the change metric timeseries from the indicator timeseries.

              • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseriesm is obtained from t using the keyword whichtime. Options include:

                • last: use the last timepoint of each window
                • midpoint: use the mid timepoint of each time window
                • first: use first timepoint of each window

                In fact, the indicators time vector is computed simply via

                t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)

                so any other function of the time window may be given to extract the time point itself, such as mean or median.

              • n_surrogates::Int = 10_000: how many surrogates to create.

              • rng::AbstractRNG = Random.default_rng()`: a random number generator for the surrogates.

              • tail::Symbol = :both: kind of tail test to do (one of :left, :right, :both) when estimating the p-value from the distribution of surrogate data.

              • T = Float64: Element type of input timeseries to initialize some computations.

              source
              Missing docstring.

              Missing docstring for TransitionsResults. Check Documenter's build log for details.

              TransitionsInTimeseries.transition_flags — Function
              transition_flags(results::TransitionsResults, p_threshold::Real) → flags

              Return flags::Matrix{Bool}, which is an n × (c+1) sized matrix. Each column flags[:, c] is the Boolean flags that correspond to a p-value below the threshold p for each change metric timeseries. There are c change metric timeseries in total, but the c+1-th column of flags is simply the Boolean addition of all previous columns (i.e., time points where all indicators pass the significance).

              To obtain the time windows where the c-th change metric is significant, simply do:

              timepoints = results.t_change[flags[:, c]]
              source

              Indicators

              Value distribution

              Statistics.mean — Method
              mean(itr)

              Compute the mean of all elements in a collection.

              Note

              If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

              Examples

              julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
              StatsBase.skewness — Function
              skewness(v, [wv::AbstractWeights], m=mean(v))

              Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

              StatsBase.kurtosis — Function
              kurtosis(v, [wv::AbstractWeights], m=mean(v))

              Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

              Critical Slowing Down

              Statistics.var — Method
              var(itr; corrected::Bool=true, mean=nothing[, dims])

              Compute the sample variance of collection itr.

              The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

              If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

              A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

              Note

              If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

              TransitionsInTimeseries.ar1_whitenoise — Function
              ar1_whitenoise(x::AbstractVector)

              Return the AR1 regression coefficient θ of a time series x. Computation based on the analytic solution of the least-square parameter estimation:

              \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

              source

              Spectrum

              TransitionsInTimeseries.LowfreqPowerSpectrum — Type
              LowfreqPowerSpectrum(; q_lofreq = 0.1)

              Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

              lfps = precompute( LowfreqPowerSpectrum() )

              Keyword arguments:

              • q_lofreq: a number between 0 and 1 that characterises which portion of the

              frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

              source
              TransitionsInTimeseries.PrecomputedLowfreqPowerSpectrum — Type
              PrecomputedLowfreqPowerSpectrum(x::AbstractVector)

              A struct containing all the precomputed fields to efficiently perform repetitive computation of the low-frequency power spectrum (LFPS), a number between 0 and 1 that characterizes the amount of power contained in the low frequencies of the power density spectrum of x. Once lfps::PrecomputedLowfreqPowerSpectrum is initialized, it can be used as a function to obtain the LFPS of x::AbstractVector by:

              lfps(x)
              source

              Nonlinear dynamics

              Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:

              function PermutationEntropy(; m = 3, τ = 1)
+    est = SymbolicPermutation(; m, τ)
+    return x -> entropy_normalized(est, x)
+end
              Missing docstring.

              Missing docstring for entropy. Check Documenter's build log for details.

              Change metrics

              Slope

              Difference in value distribution

              Make your own indicator/metric!

              The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

              There are situations where you may optimize such a function based on knowledge of input x type and length.

              TODO: Here explain how to use precomputable functions

              Missing docstring.

              Missing docstring for precompute. Check Documenter's build log for details.

              Surrogates

              For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

              Sliding windows

              TransitionsInTimeseries.WindowViewer — Type
              WindowViewer(x; width, stride)

              Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

              If not given, the keywords width, stride are taken as default_window_width(x) and 1.

              source
              TransitionsInTimeseries.windowmap — Function
              windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

              A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

              source

              Load data

              diff --git a/previews/PR39/assets/documenter.js b/previews/PR39/assets/documenter.js new file mode 100644 index 00000000..6adfbbbf --- /dev/null +++ b/previews/PR39/assets/documenter.js @@ -0,0 +1,331 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); 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+ + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); + }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR39/assets/search.js b/previews/PR39/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR39/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
            • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR39/assets/themes/documenter-dark.css b/previews/PR39/assets/themes/documenter-dark.css new file mode 100644 index 00000000..89fbb493 --- /dev/null +++ b/previews/PR39/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ +@keyframes spinAround{from{transform:rotate(0deg)}to{transform:rotate(359deg)}}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark .button,.is-unselectable,html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after,html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after{border:3px solid rgba(0,0,0,0);border-radius:2px;border-right:0;border-top:0;content:" 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.button.is-warning:focus:not(:active),html.theme--documenter-dark .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(244,199,47,0.25)}html.theme--documenter-dark .button.is-warning:active,html.theme--documenter-dark .button.is-warning.is-active{background-color:#f3c017;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#f4c72f;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark 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.button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:2px;font-size:.75rem}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#fff;border-color:#dbdbdb;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em / 2));top:calc(50% - (1em / 2));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#f5f5f5;border-color:#dbdbdb;color:#7a7a7a;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:290486px;padding-left:1em;padding-right:1em}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:0.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){border-radius:2px;font-size:.75rem}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}html.theme--documenter-dark .container.is-fluid{margin-left:32px;margin-right:32px;max-width:none}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen{max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd{max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container{max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container{max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#cdc3e3;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#f5f5f5;border-left:5px solid #dbdbdb;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #dbdbdb;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#cdc3e3}html.theme--documenter-dark .content table th:not([align]){text-align:left}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#cdc3e3}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#cdc3e3}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:290486px}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 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1055px){html.theme--documenter-dark .columns.is-variable.is-7-tablet-only{--columnGap: 1.75rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-7-touch{--columnGap: 1.75rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-7-desktop{--columnGap: 1.75rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-7-desktop-only{--columnGap: 1.75rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-7-widescreen{--columnGap: 1.75rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only{--columnGap: 1.75rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-7-fullhd{--columnGap: 1.75rem}}html.theme--documenter-dark .columns.is-variable.is-8{--columnGap: 2rem}@media screen and (max-width: 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              Edit on GitHub

              TransitionsInTimeseries.jl

              TransitionsInTimeseries.jl

              TransitionsInTimeseries — Module

              TransitionsInTimeseries.jl

              CI codecov Package Downloads

              A Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

              This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

              add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

              All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

              source
              Star us on GitHub!

              If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

              Content

              Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

              • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
              • Makes the surrogate analysis to test for significance under the hub.
              • Can be easily extended by any user without touching the source code.
              • Reduces the programming overhead for any researcher willing to benchmark new methods.
              • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
              • Increases trustworthiness thanks to a large test suite.
              Similar projects

              An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

              Approaches

              Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

              diff --git a/previews/PR39/search/index.html b/previews/PR39/search/index.html new file mode 100644 index 00000000..b6a47f05 --- /dev/null +++ b/previews/PR39/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

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                diff --git a/previews/PR39/search_index.js b/previews/PR39/search_index.js new file mode 100644 index 00000000..35916c38 --- /dev/null +++ b/previews/PR39/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"TransitionsSurrogatesConfig\nestimate_transitions\nTransitionsResults\ntransition_flags","category":"page"},{"location":"api/#TransitionsInTimeseries.TransitionsSurrogatesConfig","page":"API","title":"TransitionsInTimeseries.TransitionsSurrogatesConfig","text":"TransitionsSurrogatesConfig(indicators, change_metrics [, surrogate]; kwargs...)\n\nA configuration struct for TransitionsInTimeseries.jl that can be given to estimate_transitions. It contains all information necessary to perform the basic Workflow of the package to detect significant transitions in the input timeseries, using the method of surrogate testing to quantify significance:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes for an indicator by sliding a window over its timeseries.\nGenerate many surrogates that preserve important statistical properties of the original input timeseries.\nPerform steps 1 and 2 for the surrogate timeseries (and for all provided indicators).\nEstimate when an indicators timeseries shows significant change (trend, jump or anything else) when compared to the surrogate timeseries when compared to the surrogate data. Significance is estimated from the p-values of the real data vs surrogate data.\n\nArguments\n\nindicators::AbstractVector{<:Function} a vector of indicators. Some indicators typically used in the literature are listed in the documentation section on indicators. The analysis is performed efficiently for all indicators given.\nchange_metrics change metrics corresponding to the given indicators. If given a function, the same function is used for all indicators. Otherwise, it should be a vetor of functions of the same size as indicators, using change metric for its corresponding indicator. Some change metrics typically used in the literature are listed in the documentation section on change metrics.\nsurrogate::Surrogate the method to use to generate surrogates of the input timeseries. This is an optional argument that defaults to RandomFourier(), see Surrogates for alternative options.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to the WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to the WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseriesm is obtained from t using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nn_surrogates::Int = 10_000: how many surrogates to create.\nrng::AbstractRNG = Random.default_rng()`: a random number generator for the surrogates.\ntail::Symbol = :both: kind of tail test to do (one of :left, :right, :both) when estimating the p-value from the distribution of surrogate data.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.estimate_transitions","page":"API","title":"TransitionsInTimeseries.estimate_transitions","text":"estimate_transitions([t, ] x, config::TransitionsSurrogatesConfig)\n\nEstimate possible transitions for input timeseries x according to the configuration. If t (the time vector of x), is not provided, it is assumed t = eachindex(x).\n\nReturn the output as TransitionsResults. You can use this output also in transition_flags.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.transition_flags","page":"API","title":"TransitionsInTimeseries.transition_flags","text":"transition_flags(results::TransitionsResults, p_threshold::Real) → flags\n\nReturn flags::Matrix{Bool}, which is an n × (c+1) sized matrix. Each column flags[:, c] is the Boolean flags that correspond to a p-value below the threshold p for each change metric timeseries. There are c change metric timeseries in total, but the c+1-th column of flags is simply the Boolean addition of all previous columns (i.e., time points where all indicators pass the significance).\n\nTo obtain the time windows where the c-th change metric is significant, simply do:\n\ntimepoints = results.t_change[flags[:, c]]\n\n\n\n\n\n","category":"function"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient θ of a time series x. Computation based on the analytic solution of the least-square parameter estimation:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum\nPrecomputedLowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.PrecomputedLowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.PrecomputedLowfreqPowerSpectrum","text":"PrecomputedLowfreqPowerSpectrum(x::AbstractVector)\n\nA struct containing all the precomputed fields to efficiently perform repetitive computation of the low-frequency power spectrum (LFPS), a number between 0 and 1 that characterizes the amount of power contained in the low frequencies of the power density spectrum of x. Once lfps::PrecomputedLowfreqPowerSpectrum is initialized, it can be used as a function to obtain the LFPS of x::AbstractVector by:\n\nlfps(x)\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:","category":"page"},{"location":"api/","page":"API","title":"API","text":"function PermutationEntropy(; m = 3, τ = 1)\n est = SymbolicPermutation(; m, τ)\n return x -> entropy_normalized(est, x)\nend","category":"page"},{"location":"api/","page":"API","title":"API","text":"PermutationEntropy\nentropy","category":"page"},{"location":"api/#TransitionsInTimeseries.PermutationEntropy","page":"API","title":"TransitionsInTimeseries.PermutationEntropy","text":"PermutationEntropy(; m = 3, τ = 1) → f\n\nReturn a function that given timeseries x it computes the normalized permutation entropy of order m with time delay τ.\n\n\n\n\n\n","category":"function"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope\nPrecomputedRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. The latter can be initialized by precompute:\n\nrr = precompute(RidgeRegressionSlope(), x)\n\nKeyword arguments:\n\nlambda: a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.PrecomputedRidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.PrecomputedRidgeRegressionSlope","text":"PrecomputedRidgeRegressionSlope(x::AbstractVector)\n\nReturn the slope of the ridge regression of x.\n\n\n\n\n\n","category":"type"},{"location":"api/#Difference-in-value-distribution","page":"API","title":"Difference in value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"","category":"page"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length.","category":"page"},{"location":"api/","page":"API","title":"API","text":"TODO: Here explain how to use precomputable functions","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any pre-processing of raw data first such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_nlinear)\nlines!(ax, t, x_linear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window.\n# This therefore only uses information from `k-width` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\nfig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))\nlines!(ax, tfluct, s .- 0.05; color = Cycled(3))\nax.title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = \"nonlin\")\nlines!(ax, t_change, change_s; color = Cycled(3), label = \"surrogate\")\naxislegend()\nax.title = \"change metric\"\n\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig = Figure()\naxl = Axis(fig[1,1]; title = \"linear\")\naxnl = Axis(fig[1,2]; title = \"nonlinear\")\naxsigl = Axis(fig[2,1])\naxsignl = Axis(fig[2,2])\n\nfor (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change; color = Cycled(j))\n lines!(axsig, t_change, pval; color = Cycled(j+2))\nend\n\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\ninput = x_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_nl_fluct)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We decide what indicators and change metrics to use and run the analysis, and leave the surrogate generation method to its default (random Fourier surrogates).","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = [var, ar1_whitenoise]\n\n# use the ridge regression slope for both indicators\nchange_metrics = [RidgeRegressionSlope()]\nconfig = TransitionsSurrogatesConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, n_surrogates = 1000, whichtime = last\n)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we simply plug in our timeseries and this special config type into estimate_transitions.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"results = estimate_transitions(tfluct, x_nl_fluct, config)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"That's it, just a couple of lines!","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To get insight on the results, we can plot the obtained p-values and the original timeseries:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2), label = \"input\")\naxpval, = scatter(fig[2,1], results.t_change, results.pvalues[:, 1]; color = Cycled(3), label = \"p-value of var\")\nscatter!(axpval, results.t_change, results.pvalues[:, 2]; color = Cycled(4), label = \"p-value of ar1\")\nxlims!(ax, (0, 50))\nxlims!(axpval, (0, 50))\naxislegend(axpval; position = :lt)\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Thresholding the p-value results in a loss of information and therefore should only happen as a last step. It is typically done to obtain Boolean \"flags\" for which time windows a significant transition has been detected. This can be done using the transition_flags function, which gives Boolean timeseries of true/false given a confidence level for the p value:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"threshold = 0.05\nflags = transition_flags(results, 0.05)\n\nvlines!(axpval, results.t_change[flags[:, end]]; label = \"both flags\")\naxislegend(axpval; position = :lt)\nfig","category":"page"}] +} diff --git a/previews/PR39/siteinfo.js b/previews/PR39/siteinfo.js new file mode 100644 index 00000000..c08dc8b2 --- /dev/null +++ b/previews/PR39/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR39"; diff --git a/previews/PR39/tutorial/index.html b/previews/PR39/tutorial/index.html new file mode 100644 index 00000000..9dc33ca9 --- /dev/null +++ b/previews/PR39/tutorial/index.html @@ -0,0 +1,114 @@ + +Tutorial · TransitionsInTimeseries.jl
                Edit on GitHub

                Tutorial

                Workflow

                Computing transition indicators consists of the following steps:

                1. Doing any pre-processing of raw data first such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                3. Computing the changes of the indicator by sliding a window over its timeseries.
                4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                5. Performing step 2 and 3 for the surrogate timeseries.
                6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                Tutorial – Educational

                Raw input data

                Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_nlinear)
+lines!(ax, t, x_linear)
+ax.title = "raw data"
+fig

                Preprocessing

                Not part of TransitionsInTimeseries.jl

                Any timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                Detrending in Julia

                Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                Indicator timeseries

                We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window.
+# This therefore only uses information from `k-width` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                The lines plotted above are the indicator timeseries.

                Change metric timeseries

                From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                Timeseries surrogates

                As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))
+lines!(ax, tfluct, s .- 0.05; color = Cycled(3))
+ax.title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin")
+lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate")
+axislegend()
+ax.title = "change metric"
+
+fig

                Quantifying significance

                To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                n_surrogates = 1_000
+fig = Figure()
+axl = Axis(fig[1,1]; title = "linear")
+axnl = Axis(fig[1,2]; title = "nonlinear")
+axsigl = Axis(fig[2,1])
+axsignl = Axis(fig[2,2])
+
+for (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change; color = Cycled(j))
+    lines!(axsig, t_change, pval; color = Cycled(j+2))
+end
+
+fig

                As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                Tutorial – TransitionsInTimeseries.jl

                TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

                The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

                using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+input = x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_nl_fluct)
+ax.title = "input timeseries"
+fig

                We decide what indicators and change metrics to use and run the analysis, and leave the surrogate generation method to its default (random Fourier surrogates).

                # These indicators are suitable for Critical Slowing Down
+indicators = [var, ar1_whitenoise]
+
+# use the ridge regression slope for both indicators
+change_metrics = [RidgeRegressionSlope()]
+config = TransitionsSurrogatesConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, n_surrogates = 1000, whichtime = last
+)
                TransitionsSurrogatesConfig{Function, Function, RandomFourier, typeof(last), Random.TaskLocalRNG}(Function[Statistics.var, TransitionsInTimeseries.ar1_whitenoise], Function[PrecomputedRidgeRegressionSlope{Float64}(true, [-0.006451612903225804 -0.006006674082313679 … 0.006006674082313681 0.006451612903225805; 0.1333333333333333 0.12643678160919536 … -0.05977011494252871 -0.06666666666666662])], RandomFourier(true), 400, 1, 30, 1, last, 1000, Random.TaskLocalRNG(), :both)

                To perform all of the above analysis we simply plug in our timeseries and this special config type into estimate_transitions.

                results = estimate_transitions(tfluct, x_nl_fluct, config)
                TransitionsResults
+ input timeseries: 2500-element Vector{Float64}
+ indicators:       [:var, :ar1_whitenoise]
+ change metrics:   [:PrecomputedRidgeRegressionSlope]
+ surrogate:        RandomFourier(true)
+

                That's it, just a couple of lines!

                To get insight on the results, we can plot the obtained p-values and the original timeseries:

                fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2), label = "input")
+axpval, = scatter(fig[2,1], results.t_change, results.pvalues[:, 1]; color = Cycled(3), label = "p-value of var")
+scatter!(axpval, results.t_change, results.pvalues[:, 2]; color = Cycled(4), label = "p-value of ar1")
+xlims!(ax, (0, 50))
+xlims!(axpval, (0, 50))
+axislegend(axpval; position = :lt)
+fig

                Thresholding the p-value results in a loss of information and therefore should only happen as a last step. It is typically done to obtain Boolean "flags" for which time windows a significant transition has been detected. This can be done using the transition_flags function, which gives Boolean timeseries of true/false given a confidence level for the p value:

                threshold = 0.05
+flags = transition_flags(results, 0.05)
+
+vlines!(axpval, results.t_change[flags[:, end]]; label = "both flags")
+axislegend(axpval; position = :lt)
+fig
                diff --git a/previews/PR39/tutorial_literate.jl b/previews/PR39/tutorial_literate.jl new file mode 100644 index 00000000..2f491843 --- /dev/null +++ b/previews/PR39/tutorial_literate.jl @@ -0,0 +1,140 @@ +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_nlinear) +lines!(ax, t, x_linear) +ax.title = "raw data" +fig + +# +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +# +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window. +# This therefore only uses information from `k-width` to `k` at time step `k`. +# Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +# +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + + +# + +# Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2)) +lines!(ax, tfluct, s .- 0.05; color = Cycled(3)) +ax.title = "real signal vs. surrogate(s)" + +# compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin") +lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate") +axislegend() +ax.title = "change metric" + +fig +# + + +n_surrogates = 1_000 +fig = Figure() +axl = Axis(fig[1,1]; title = "linear") +axnl = Axis(fig[1,2]; title = "nonlinear") +axsigl = Axis(fig[2,1]) +axsignl = Axis(fig[2,2]) + +for (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + # Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change; color = Cycled(j)) + lines!(axsig, t_change, pval; color = Cycled(j+2)) +end + +fig + +# %% +# Tutorial short + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_nl_fluct) +ax.title = "input timeseries" +fig + +# These indicators are suitable for Critical Slowing Down +indicators = [var, ar1_whitenoise] +indconfig = IndicatorsConfig(tfluct, last, indicators; width = 400) + + +# use the ridge regression slope for both indicators +change_metrics = [RidgeRegressionSlope()] +sigconfig = SignificanceConfig(indconfig, last, change_metrics; + width = 30, n_surrogates = 1000) + +# perform the full analysis +results = indicators_analysis(tfluct, x_nl_fluct, indconfig, sigconfig) + +# Plot the original timeseries vs. p-value time series +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2), label = "input") +axpval, = lines(fig[2,1], sigconfig.t_change, results.pval[:, 1]; color = Cycled(3), label = "p-value of var") +lines!(axpval, sigconfig.t_change, results.pval[:, 2]; color = Cycled(4), label = "p-value of ar1") +xlims!(ax, (0, 50)) +xlims!(axpval, (0, 50)) +axislegend(axpval) +fig + + +flags_indicators, flags_andicators = transition_flags(results, 0.05) +vlines!(ax, flags_andicators; label = "flags", color = Cycled(3), linestyle = :dash) +axislegend(ax) +fig \ No newline at end of file diff --git a/previews/PR41/api/index.html b/previews/PR41/api/index.html new file mode 100644 index 00000000..dc36b3f2 --- /dev/null +++ b/previews/PR41/api/index.html @@ -0,0 +1,20 @@ + +API · TransitionsInTimeseries.jl
                Edit on GitHub

                API

                Main analysis functions

                TransitionsInTimeseries.WindowedIndicatorConfig — Type
                WindowedIndicatorConfig(indicators, change_metrics; kwargs...) → config

                A configuration struct for TransitionsInTimeseries.jl that collects what indicators and corresponding metrics to use in the transitions_analysis.

                indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.

                Keyword arguments

                • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.

                • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.

                • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in transitions_analysis using the keyword whichtime. Options include:

                  • last: use the last timepoint of each window
                  • midpoint: use the mid timepoint of each time window
                  • first: use first timepoint of each window

                  In fact, the indicators time vector is computed simply via

                  t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)

                  so any other function of the time window may be given to extract the time point itself, such as mean or median.

                • T = Float64: Element type of input timeseries to initialize some computations.

                source
                TransitionsInTimeseries.estimate_transitions — Function
                estimate_transitions(config::WindowedIndicatorConfig, x [,t]) → output

                Estimate possible transitions for input timeseries x using a sliding window approach as described by config:

                1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                If t (the time vector of x), is not provided, it is assumed t = eachindex(x).

                Return the output as WindowedIndicatorResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                source
                TransitionsInTimeseries.WindowedIndicatorResults — Type
                WindowedIndicatorResults

                A struct containing the output of estimate_transitions used with WindowedIndicatorConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                It has the following fields that the user may access

                • x: the input timeseries.

                • t: the time vector of the input timeseries.

                • indicators::Vector{Function}: indicators used in the processing.

                • x_indicator, the indicator timeseries (matrix with each column one indicator).

                • t_indicator, the time vector of the indicator timeseries.

                • change_metrics::Vector{Function}: change metrics used in the processing.

                • x_change, the change metric timeseries (matrix with each column one change metric).

                • t_change, the time vector of the change metric timeseries.

                source

                Significance testing

                TransitionsInTimeseries.SurrogatesSignificance — Type
                SurrogatesSignificance <: TransitionsSignificance
+SurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)

                A configuration struct containing instructions on how to test for significance in the function significant_transitions when combined with the output of estimate_transitions.

                Description

                When used with WindowedIndicatorResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surrogate, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail.

                the p-value is simply the proportion of surrogate values that exceed (for tail = :right) or subseed (tail = :left) the discriminatory statistic computed from the input data. Use tail = :right if the surrogate data are expected to have higher discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both.

                An iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowedIndicatorResults.

                Keyword rng = Random.default_rng() may specify a random number generator for the surrogates.

                source
                TransitionsInTimeseries.significant_transitions — Function
                significant_transitions(res::WindowedIndicatorResults, signif::SurrogatesSignificance)

                Estimate significant transtions in res using the method described by SurrogatesSignificance. Return pvalues, a matrix with identical size as res.x_change. It contains the associated p-value timeseries for each change metric (each column).

                source

                Indicators

                Value distribution

                Statistics.mean — Method
                mean(itr)

                Compute the mean of all elements in a collection.

                Note

                If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

                Examples

                julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
                StatsBase.skewness — Function
                skewness(v, [wv::AbstractWeights], m=mean(v))

                Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                StatsBase.kurtosis — Function
                kurtosis(v, [wv::AbstractWeights], m=mean(v))

                Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                Critical Slowing Down

                Statistics.var — Method
                var(itr; corrected::Bool=true, mean=nothing[, dims])

                Compute the sample variance of collection itr.

                The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

                If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

                A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

                Note

                If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

                TransitionsInTimeseries.ar1_whitenoise — Function
                ar1_whitenoise(x::AbstractVector)

                Return the AR1 regression coefficient θ of a time series x. Computation based on the analytic solution of the least-square parameter estimation:

                \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                source

                Spectrum

                TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                LowfreqPowerSpectrum(; q_lofreq = 0.1)

                Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                lfps = precompute( LowfreqPowerSpectrum() )

                Keyword arguments:

                • q_lofreq: a number between 0 and 1 that characterises which portion of the

                frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                source

                Nonlinear dynamics

                Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:

                function permutation_entropy(; m = 3, τ = 1)
+    est = SymbolicPermutation(; m, τ)
+    return x -> entropy_normalized(est, x)
+end
                StatsBase.entropy — Function
                entropy(p, [b])

                Compute the entropy of a collection of probabilities p, optionally specifying a real number b such that the entropy is scaled by 1/log(b). Elements with probability 0 or 1 add 0 to the entropy.

                Change metrics

                Slope

                TransitionsInTimeseries.kendalltau — Function
                kendalltau(x::AbstractVector)

                Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                source
                TransitionsInTimeseries.spearman — Function
                spearman(x::AbstractVector)

                Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                source

                Value distribution differences

                TransitionsInTimeseries.difference_of_means — Function
                difference_of_means(x::AbstractArray)

                Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                source

                Make your own indicator/metric!

                The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                There are situations where you may optimize such a function based on knowledge of input x type and length.

                TODO: Here explain how to use precomputable functions

                Missing docstring.

                Missing docstring for precompute. Check Documenter's build log for details.

                Surrogates

                For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                Sliding windows

                TransitionsInTimeseries.WindowViewer — Type
                WindowViewer(x; width, stride)

                Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                If not given, the keywords width, stride are taken as default_window_width(x) and 1.

                source
                TransitionsInTimeseries.windowmap — Function
                windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                source

                Load data

                diff --git a/previews/PR41/assets/documenter.js b/previews/PR41/assets/documenter.js new file mode 100644 index 00000000..6adfbbbf --- /dev/null +++ b/previews/PR41/assets/documenter.js @@ -0,0 +1,331 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fas", "fa-copy"); + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-times"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-times"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); + }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR41/assets/search.js b/previews/PR41/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR41/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
              • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR41/assets/themes/documenter-dark.css b/previews/PR41/assets/themes/documenter-dark.css new file mode 100644 index 00000000..89fbb493 --- /dev/null +++ b/previews/PR41/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ +@keyframes spinAround{from{transform:rotate(0deg)}to{transform:rotate(359deg)}}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark .button,.is-unselectable,html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after,html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after{border:3px solid rgba(0,0,0,0);border-radius:2px;border-right:0;border-top:0;content:" 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.button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#2f2f2f;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,54,54,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#292929;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#e8e8e8}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark 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.docstring>section>a.button.is-inverted.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;border-color:transparent;box-shadow:none;color:#4eb5de}html.theme--documenter-dark .button.is-primary.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-loading.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#4eb5de;color:#4eb5de}html.theme--documenter-dark .button.is-primary.is-outlined:hover,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#4eb5de;border-color:#4eb5de;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #4eb5de #4eb5de !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark 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.button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined{background-color:transparent;border-color:#3489da;box-shadow:none;color:#3489da}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#3489da}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #3489da #3489da !important}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-success{background-color:#259a12;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:hover,html.theme--documenter-dark .button.is-success.is-hovered{background-color:#228f11;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus,html.theme--documenter-dark .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus:not(:active),html.theme--documenter-dark .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(37,154,18,0.25)}html.theme--documenter-dark .button.is-success:active,html.theme--documenter-dark .button.is-success.is-active{background-color:#20830f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success{background-color:#259a12;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;color:#259a12}html.theme--documenter-dark .button.is-success.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-outlined.is-focused{background-color:#259a12;border-color:#259a12;color:#fff}html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning{background-color:#f4c72f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning:hover,html.theme--documenter-dark .button.is-warning.is-hovered{background-color:#f3c423;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning:focus,html.theme--documenter-dark .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark 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.button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:2px;font-size:.75rem}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#fff;border-color:#dbdbdb;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em / 2));top:calc(50% - (1em / 2));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#f5f5f5;border-color:#dbdbdb;color:#7a7a7a;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:290486px;padding-left:1em;padding-right:1em}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:0.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){border-radius:2px;font-size:.75rem}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark 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body.has-navbar-fixed-bottom{padding-bottom:3.25rem}html.theme--documenter-dark .navbar-brand,html.theme--documenter-dark .navbar-tabs{align-items:stretch;display:flex;flex-shrink:0;min-height:3.25rem}html.theme--documenter-dark .navbar-brand a.navbar-item:focus,html.theme--documenter-dark .navbar-brand a.navbar-item:hover{background-color:transparent}html.theme--documenter-dark .navbar-tabs{-webkit-overflow-scrolling:touch;max-width:100vw;overflow-x:auto;overflow-y:hidden}html.theme--documenter-dark .navbar-burger{color:#4a4a4a;cursor:pointer;display:block;height:3.25rem;position:relative;width:3.25rem;margin-left:auto}html.theme--documenter-dark .navbar-burger span{background-color:currentColor;display:block;height:1px;left:calc(50% - 8px);position:absolute;transform-origin:center;transition-duration:86ms;transition-property:background-color, opacity, transform;transition-timing-function:ease-out;width:16px}html.theme--documenter-dark .navbar-burger span:nth-child(1){top:calc(50% - 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a.navbar-item,html.theme--documenter-dark .navbar-link{cursor:pointer}html.theme--documenter-dark a.navbar-item:focus,html.theme--documenter-dark a.navbar-item:focus-within,html.theme--documenter-dark a.navbar-item:hover,html.theme--documenter-dark a.navbar-item.is-active,html.theme--documenter-dark .navbar-link:focus,html.theme--documenter-dark .navbar-link:focus-within,html.theme--documenter-dark .navbar-link:hover,html.theme--documenter-dark .navbar-link.is-active{background-color:#fafafa;color:#2ad7e6}html.theme--documenter-dark .navbar-item{display:block;flex-grow:0;flex-shrink:0}html.theme--documenter-dark .navbar-item img{max-height:1.75rem}html.theme--documenter-dark .navbar-item.has-dropdown{padding:0}html.theme--documenter-dark .navbar-item.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .navbar-item.is-tab{border-bottom:1px solid transparent;min-height:3.25rem;padding-bottom:calc(0.5rem - 1px)}html.theme--documenter-dark .navbar-item.is-tab:focus,html.theme--documenter-dark .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#2ad7e6}html.theme--documenter-dark .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#2ad7e6;border-bottom-style:solid;border-bottom-width:3px;color:#2ad7e6;padding-bottom:calc(0.5rem - 3px)}html.theme--documenter-dark .navbar-content{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after{border-color:#2ad7e6;margin-top:-0.375em;right:1.125em}html.theme--documenter-dark .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--documenter-dark .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--documenter-dark .navbar-divider{background-color:#f5f5f5;border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--documenter-dark .navbar>.container{display:block}html.theme--documenter-dark .navbar-brand .navbar-item,html.theme--documenter-dark .navbar-tabs .navbar-item{align-items:center;display:flex}html.theme--documenter-dark .navbar-link::after{display:none}html.theme--documenter-dark .navbar-menu{background-color:#fff;box-shadow:0 8px 16px rgba(10,10,10,0.1);padding:0.5rem 0}html.theme--documenter-dark .navbar-menu.is-active{display:block}html.theme--documenter-dark .navbar.is-fixed-bottom-touch,html.theme--documenter-dark .navbar.is-fixed-top-touch{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark .navbar.is-fixed-bottom-touch{bottom:0}html.theme--documenter-dark .navbar.is-fixed-bottom-touch.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--documenter-dark .navbar.is-fixed-top-touch{top:0}html.theme--documenter-dark .navbar.is-fixed-top .navbar-menu,html.theme--documenter-dark .navbar.is-fixed-top-touch 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a.navbar-item:hover{background-color:#f5f5f5;color:#0a0a0a}html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active{background-color:#f5f5f5;color:#2ad7e6}.navbar.is-spaced html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:6px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop{bottom:0}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--documenter-dark .navbar.is-fixed-top-desktop{top:0}html.theme--documenter-dark html.has-navbar-fixed-top-desktop,html.theme--documenter-dark body.has-navbar-fixed-top-desktop{padding-top:3.25rem}html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop,html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop{padding-bottom:3.25rem}html.theme--documenter-dark html.has-spaced-navbar-fixed-top,html.theme--documenter-dark body.has-spaced-navbar-fixed-top{padding-top:5.25rem}html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom,html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom{padding-bottom:5.25rem}html.theme--documenter-dark a.navbar-item.is-active,html.theme--documenter-dark .navbar-link.is-active{color:#0a0a0a}html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:#fafafa}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 3.25rem)}html.theme--documenter-dark .pagination{font-size:1rem;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--documenter-dark .pagination.is-rounded .pagination-next,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:290486px}html.theme--documenter-dark .pagination.is-rounded .pagination-link,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:290486px}html.theme--documenter-dark .pagination,html.theme--documenter-dark .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link{border-color:#dbdbdb;color:#363636;min-width:2.25em}html.theme--documenter-dark .pagination-previous:hover,html.theme--documenter-dark .pagination-next:hover,html.theme--documenter-dark .pagination-link:hover{border-color:#b5b5b5;color:#97ebf3}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus{border-color:#3c5dcd}html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2)}html.theme--documenter-dark .pagination-previous[disabled],html.theme--documenter-dark 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.pagination-list{flex-grow:1;flex-shrink:1;justify-content:flex-start;order:1}html.theme--documenter-dark .pagination-previous{order:2}html.theme--documenter-dark .pagination-next{order:3}html.theme--documenter-dark .pagination{justify-content:space-between}html.theme--documenter-dark .pagination.is-centered .pagination-previous{order:1}html.theme--documenter-dark .pagination.is-centered .pagination-list{justify-content:center;order:2}html.theme--documenter-dark .pagination.is-centered .pagination-next{order:3}html.theme--documenter-dark .pagination.is-right .pagination-previous{order:1}html.theme--documenter-dark .pagination.is-right .pagination-next{order:2}html.theme--documenter-dark .pagination.is-right .pagination-list{justify-content:flex-end;order:3}}html.theme--documenter-dark .panel{font-size:1rem}html.theme--documenter-dark .panel:not(:last-child){margin-bottom:1.5rem}html.theme--documenter-dark .panel-heading,html.theme--documenter-dark .panel-tabs,html.theme--documenter-dark .panel-block{border-bottom:1px solid #dbdbdb;border-left:1px solid #dbdbdb;border-right:1px solid #dbdbdb}html.theme--documenter-dark .panel-heading:first-child,html.theme--documenter-dark .panel-tabs:first-child,html.theme--documenter-dark .panel-block:first-child{border-top:1px solid #dbdbdb}html.theme--documenter-dark .panel-heading{background-color:#f5f5f5;border-radius:4px 4px 0 0;color:#cdc3e3;font-size:1.25em;font-weight:300;line-height:1.25;padding:0.5em 0.75em}html.theme--documenter-dark .panel-tabs{align-items:flex-end;display:flex;font-size:.875em;justify-content:center}html.theme--documenter-dark .panel-tabs a{border-bottom:1px solid #dbdbdb;margin-bottom:-1px;padding:0.5em}html.theme--documenter-dark .panel-tabs a.is-active{border-bottom-color:#4a4a4a;color:#363636}html.theme--documenter-dark .panel-list a{color:#fbfbfb}html.theme--documenter-dark .panel-list a:hover{color:#2ad7e6}html.theme--documenter-dark .panel-block{align-items:center;color:#cdc3e3;display:flex;justify-content:flex-start;padding:0.5em 0.75em}html.theme--documenter-dark .panel-block input[type="checkbox"]{margin-right:0.75em}html.theme--documenter-dark .panel-block>.control{flex-grow:1;flex-shrink:1;width:100%}html.theme--documenter-dark .panel-block.is-wrapped{flex-wrap:wrap}html.theme--documenter-dark .panel-block.is-active{border-left-color:#2ad7e6;color:#363636}html.theme--documenter-dark .panel-block.is-active .panel-icon{color:#2ad7e6}html.theme--documenter-dark a.panel-block,html.theme--documenter-dark label.panel-block{cursor:pointer}html.theme--documenter-dark a.panel-block:hover,html.theme--documenter-dark label.panel-block:hover{background-color:#f5f5f5}html.theme--documenter-dark .panel-icon{display:inline-block;font-size:14px;height:1em;line-height:1em;text-align:center;vertical-align:top;width:1em;color:#7a7a7a;margin-right:0.75em}html.theme--documenter-dark .panel-icon .fa{font-size:inherit;line-height:inherit}html.theme--documenter-dark .tabs{-webkit-overflow-scrolling:touch;align-items:stretch;display:flex;font-size:1rem;justify-content:space-between;overflow:hidden;overflow-x:auto;white-space:nowrap}html.theme--documenter-dark .tabs a{align-items:center;border-bottom-color:#dbdbdb;border-bottom-style:solid;border-bottom-width:1px;color:#fbfbfb;display:flex;justify-content:center;margin-bottom:-1px;padding:0.5em 1em;vertical-align:top}html.theme--documenter-dark .tabs a:hover{border-bottom-color:#cdc3e3;color:#cdc3e3}html.theme--documenter-dark .tabs li{display:block}html.theme--documenter-dark .tabs li.is-active a{border-bottom-color:#2ad7e6;color:#2ad7e6}html.theme--documenter-dark .tabs ul{align-items:center;border-bottom-color:#dbdbdb;border-bottom-style:solid;border-bottom-width:1px;display:flex;flex-grow:1;flex-shrink:0;justify-content:flex-start}html.theme--documenter-dark .tabs ul.is-left{padding-right:0.75em}html.theme--documenter-dark 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file mode 100644 index 00000000..c58e993e --- /dev/null +++ b/previews/PR41/assets/themeswap.js @@ -0,0 +1,66 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Intialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if(window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the browser supports user color preference + var darkPreference = false; + // Check if the users preference is for dark color scheme + if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { + darkPreference = true; + } + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; var disabled = []; var darkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if(themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); + // Check if the theme is primary dark theme + var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null); + // If ss is for dark theme then set the value of darkTheme to the name of the theme + if(isDarkTheme) darkTheme = themename; + // If we find a matching theme (and it's not the default), we'll set active to non-null + if(themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if(themename !== theme) disabled.push(ss); + } + if(active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + theme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + else if(darkTheme !== null && darkPreference === true) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + darkTheme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + if (ss.ownerNode.getAttribute("data-theme-name") !== darkTheme) { + ss.disabled = true; + } + }); + } +} +set_theme_from_local_storage(); diff --git a/previews/PR41/assets/warner.js b/previews/PR41/assets/warner.js new file mode 100644 index 00000000..5531c885 --- /dev/null +++ b/previews/PR41/assets/warner.js @@ -0,0 +1,49 @@ +function maybeAddWarning () { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return + }; + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return + }; + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return + }; + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement('meta'); + meta.name = 'robots'; + meta.content = 'noindex'; + + document.getElementsByTagName('head')[0].appendChild(meta); + }; + + const div = document.createElement('div'); + div.classList.add('outdated-warning-overlay'); + const closer = document.createElement('button'); + closer.classList.add('outdated-warning-closer', 'delete'); + closer.addEventListener('click', function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + '/../' + window.DOCUMENTER_STABLE; + div.innerHTML = 'This documentation is not for the latest stable release, but for either the development version or an older release.
                Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/previews/PR41/examples.jl b/previews/PR41/examples.jl new file mode 100644 index 00000000..b120d83f --- /dev/null +++ b/previews/PR41/examples.jl @@ -0,0 +1,76 @@ +# # Examples for TransitionsInTimeseries.jl + +# ## Permutation entropy + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. A simple example of this is transitions from periodic to periodic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using TransitionsInTimeseries +using DynamicalSystemsBase +using CairoMakie + +logistic_rule(u, p, t) = @inbounds SVector(p[1]*u[1]*(1 - u[1])) +ds = DeterministicIteratedMap(logistic_rule, [0.5], [1.0]) + +r1 = 3.83 +# r1 = 3.8 +r2 = 3.86 +# r2 = 3.9 +N = 2000 +rs = range(r1, r2; length = N) +x = zeros(N) +for (i, r) in enumerate(rs) + set_parameter!(ds, 1, r) + step!(ds) + x[i] = current_state(ds)[1] +end + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.857. However, there is also a subtle transition +# to weak chaos at r ≈ 3.849. This transition is barely visible in the +# timeseries. + +# Now, let's compute and plot various indicators +indicators = [mean, var, ar1_whitenoise, PermutationEntropy(m = 4)] +indistrings = ["mean", "var", "ar1", "pe"] +# In this example there is no critical slowing down; +# instead, there is a sharp transition between period-3 and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +metric = difference_of_means + +# And we perform the standard package analysis as in the [Tutorial](@ref), +# but with a crucial difference: the type of surrogates to generate _must_ be +# different. Fourier TODO: +surrogate = RandomFourier() + +config = TransitionsSurrogatesConfig(indicators, metric, surrogate; + width_ind = N÷100, stride_ind = 5, width_cha = 2, n_surrogates = 100 +) + +results = estimate_transitions(rs, x, config) + +flags = transition_flags(results, 0.05) + +# And we visualize the timeseries and some +# %% #src +fig, ax = lines(rs, x; axis = (ylabel = "input",)) +hidexdecorations!(ax; grid = false) +## plot all change metrics +for (i, c) in enumerate(eachcol(results.x_change)) + # plot change metric + ax, = scatterlines(fig[i+1, 1], results.t_change, c, axis = (ylabel = indistrings[i],)) + # + i < 4 && hidexdecorations!(ax; grid = false) +end +fig \ No newline at end of file diff --git a/previews/PR41/index.html b/previews/PR41/index.html new file mode 100644 index 00000000..186d375b --- /dev/null +++ b/previews/PR41/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
                Edit on GitHub

                TransitionsInTimeseries.jl

                TransitionsInTimeseries.jl

                TransitionsInTimeseries — Module

                TransitionsInTimeseries.jl

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                A Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

                add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

                All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                source
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                If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                Content

                Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                • Makes the surrogate analysis to test for significance under the hub.
                • Can be easily extended by any user without touching the source code.
                • Reduces the programming overhead for any researcher willing to benchmark new methods.
                • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                • Increases trustworthiness thanks to a large test suite.
                Similar projects

                An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                Approaches

                Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                diff --git a/previews/PR41/search/index.html b/previews/PR41/search/index.html new file mode 100644 index 00000000..bb23e97b --- /dev/null +++ b/previews/PR41/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

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                  diff --git a/previews/PR41/search_index.js b/previews/PR41/search_index.js new file mode 100644 index 00000000..bf634f5c --- /dev/null +++ b/previews/PR41/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowedIndicatorConfig\nestimate_transitions\nWindowedIndicatorResults","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowedIndicatorConfig","page":"API","title":"TransitionsInTimeseries.WindowedIndicatorConfig","text":"WindowedIndicatorConfig(indicators, change_metrics; kwargs...) → config\n\nA configuration struct for TransitionsInTimeseries.jl that collects what indicators and corresponding metrics to use in the transitions_analysis.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in transitions_analysis using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.estimate_transitions","page":"API","title":"TransitionsInTimeseries.estimate_transitions","text":"estimate_transitions(config::WindowedIndicatorConfig, x [,t]) → output\n\nEstimate possible transitions for input timeseries x using a sliding window approach as described by config:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nIf t (the time vector of x), is not provided, it is assumed t = eachindex(x).\n\nReturn the output as WindowedIndicatorResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.WindowedIndicatorResults","page":"API","title":"TransitionsInTimeseries.WindowedIndicatorResults","text":"WindowedIndicatorResults\n\nA struct containing the output of estimate_transitions used with WindowedIndicatorConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nindicators::Vector{Function}: indicators used in the processing.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nchange_metrics::Vector{Function}: change metrics used in the processing.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"SurrogatesSignificance\nsignificant_transitions","category":"page"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: TransitionsSignificance\nSurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)\n\nA configuration struct containing instructions on how to test for significance in the function significant_transitions when combined with the output of estimate_transitions.\n\nDescription\n\nWhen used with WindowedIndicatorResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surrogate, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail.\n\nthe p-value is simply the proportion of surrogate values that exceed (for tail = :right) or subseed (tail = :left) the discriminatory statistic computed from the input data. Use tail = :right if the surrogate data are expected to have higher discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both.\n\nAn iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowedIndicatorResults.\n\nKeyword rng = Random.default_rng() may specify a random number generator for the surrogates.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::WindowedIndicatorResults, signif::SurrogatesSignificance)\n\nEstimate significant transtions in res using the method described by SurrogatesSignificance. Return pvalues, a matrix with identical size as res.x_change. It contains the associated p-value timeseries for each change metric (each column).\n\n\n\n\n\n","category":"function"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient θ of a time series x. Computation based on the analytic solution of the least-square parameter estimation:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:","category":"page"},{"location":"api/","page":"API","title":"API","text":"function permutation_entropy(; m = 3, τ = 1)\n est = SymbolicPermutation(; m, τ)\n return x -> entropy_normalized(est, x)\nend","category":"page"},{"location":"api/","page":"API","title":"API","text":"permutation_entropy\nentropy","category":"page"},{"location":"api/#TransitionsInTimeseries.permutation_entropy","page":"API","title":"TransitionsInTimeseries.permutation_entropy","text":"permutation_entropy(; m = 3, τ = 1) → f\n\nReturn a function that given timeseries x it computes the normalized permutation entropy of order m with time delay τ.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.entropy","page":"API","title":"StatsBase.entropy","text":"entropy(p, [b])\n\nCompute the entropy of a collection of probabilities p, optionally specifying a real number b such that the entropy is scaled by 1/log(b). Elements with probability 0 or 1 add 0 to the entropy.\n\n\n\n\n\n","category":"function"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length.","category":"page"},{"location":"api/","page":"API","title":"API","text":"TODO: Here explain how to use precomputable functions","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any pre-processing of raw data first such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_nlinear)\nlines!(ax, t, x_linear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window.\n# This therefore only uses information from `k-width` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\nfig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))\nlines!(ax, tfluct, s .- 0.05; color = Cycled(3))\nax.title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = \"nonlin\")\nlines!(ax, t_change, change_s; color = Cycled(3), label = \"surrogate\")\naxislegend()\nax.title = \"change metric\"\n\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig = Figure()\naxl = Axis(fig[1,1]; title = \"linear\")\naxnl = Axis(fig[1,2]; title = \"nonlinear\")\naxsigl = Axis(fig[2,1])\naxsignl = Axis(fig[2,2])\n\nfor (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change; color = Cycled(j))\n lines!(axsig, t_change, pval; color = Cycled(j+2))\nend\n\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in WindowedIndicatorConfig and apply those via a sliding window to the input timeseries using estimate_transitions.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = RidgeRegressionSlope()\n\n# choices go into a configuration struct\nconfig = WindowedIndicatorConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last\n)\n\n# choices are processed\nresults = estimate_transitions(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From result we can plot the change metric timeseries","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, ax = lines(t, input; color = Cycled(2), label = \"input\")\naxpval, = scatter(fig[2,1], results.t_change, results.x_change[:, 1]; color = Cycled(3), label = \"var slopes\")\naxpval, = scatter(fig[3,1], results.t_change, results.x_change[:, 2]; color = Cycled(4), label = \"ar1 slopes\")","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesSignificance and the function significant_transitions.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = :both)\npvalues = significant_transitions(results, signif)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"So now we can plot the p-values corresponding to each timeseries change metric","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, ax = lines(t, input; color = Cycled(2), label = \"input\")\naxpval, = scatter(fig[2,1], results.t_change, pvalues[:, 1]; color = Cycled(3), label = \"var p-values\")\nscatter!(axpval, results.t_change, pvalues[:, 2]; color = Cycled(4), label = \"ar1 p-values\")\naxislegend(axpval)\nxlims!(ax, 0, 50)\nxlims!(axpval, 0, 50)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can convert the p-values into flags by thresholding. Here we want the time points where both p-values are simultaneously below 0.05.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"pthres = pvalues .< 0.05\nflags = vec(reduce(&, pthres; dims = 2))\n\nvlines!(ax, results.t_change[flags]; label = \"flags\", color = (\"black\", 0.1))\naxislegend(ax)\nfig","category":"page"}] +} diff --git a/previews/PR41/siteinfo.js b/previews/PR41/siteinfo.js new file mode 100644 index 00000000..87f54ecf --- /dev/null +++ b/previews/PR41/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR41"; diff --git a/previews/PR41/tutorial/index.html b/previews/PR41/tutorial/index.html new file mode 100644 index 00000000..b55abed1 --- /dev/null +++ b/previews/PR41/tutorial/index.html @@ -0,0 +1,143 @@ + +Tutorial · TransitionsInTimeseries.jl
                  Edit on GitHub

                  Tutorial

                  Workflow

                  Computing transition indicators consists of the following steps:

                  1. Doing any pre-processing of raw data first such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                  2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                  3. Computing the changes of the indicator by sliding a window over its timeseries.
                  4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                  5. Performing step 2 and 3 for the surrogate timeseries.
                  6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                  These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                  Tutorial – Educational

                  Raw input data

                  Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                  \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                  with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                  using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_nlinear)
+lines!(ax, t, x_linear)
+ax.title = "raw data"
+fig

                  Preprocessing

                  Not part of TransitionsInTimeseries.jl

                  Any timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                  The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                  x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                  At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                  Detrending in Julia

                  Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                  Indicator timeseries

                  We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                  indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window.
+# This therefore only uses information from `k-width` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                  The lines plotted above are the indicator timeseries.

                  Change metric timeseries

                  From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                  change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                  Timeseries surrogates

                  As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                  In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                  To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                  # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))
+lines!(ax, tfluct, s .- 0.05; color = Cycled(3))
+ax.title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin")
+lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate")
+axislegend()
+ax.title = "change metric"
+
+fig

                  Quantifying significance

                  To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                  n_surrogates = 1_000
+fig = Figure()
+axl = Axis(fig[1,1]; title = "linear")
+axnl = Axis(fig[1,2]; title = "nonlinear")
+axsigl = Axis(fig[2,1])
+axsignl = Axis(fig[2,2])
+
+for (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change; color = Cycled(j))
+    lines!(axsig, t_change, pval; color = Cycled(j+2))
+end
+
+fig

                  As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                  Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                  Tutorial – TransitionsInTimeseries.jl

                  TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                  The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

                  The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

                  using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig

                  To perform all of the above analysis we follow a 2-step process.

                  Step 1, we decide what indicators and change metrics to use in WindowedIndicatorConfig and apply those via a sliding window to the input timeseries using estimate_transitions.

                  # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = RidgeRegressionSlope()
+
+# choices go into a configuration struct
+config = WindowedIndicatorConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last
+)
+
+# choices are processed
+results = estimate_transitions(config, input, t)
                  WindowedIndicatorResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                  From result we can plot the change metric timeseries

                  fig, ax = lines(t, input; color = Cycled(2), label = "input")
+axpval, = scatter(fig[2,1], results.t_change, results.x_change[:, 1]; color = Cycled(3), label = "var slopes")
+axpval, = scatter(fig[3,1], results.t_change, results.x_change[:, 2]; color = Cycled(4), label = "ar1 slopes")
                  Makie.AxisPlot(Axis (1 plots), Scatter{Tuple{Vector{Point{2, Float32}}}})

                  Step 2 is to estimate significance using SurrogatesSignificance and the function significant_transitions.

                  signif = SurrogatesSignificance(n = 1000, tail = :both)
+pvalues = significant_transitions(results, signif)
                  2072×2 Matrix{Float64}:
+ 0.922  0.736
+ 0.85   0.682
+ 0.8    0.568
+ 0.736  0.52
+ 0.61   0.452
+ 0.522  0.41
+ 0.43   0.38
+ 0.38   0.35
+ 0.35   0.33
+ 0.274  0.322
+ ⋮      
+ 0.314  0.69
+ 0.282  0.718
+ 0.274  0.746
+ 0.272  0.792
+ 0.276  0.818
+ 0.288  0.844
+ 0.326  0.902
+ 0.404  0.986
+ 0.498  0.97

                  So now we can plot the p-values corresponding to each timeseries change metric

                  fig, ax = lines(t, input; color = Cycled(2), label = "input")
+axpval, = scatter(fig[2,1], results.t_change, pvalues[:, 1]; color = Cycled(3), label = "var p-values")
+scatter!(axpval, results.t_change, pvalues[:, 2]; color = Cycled(4), label = "ar1 p-values")
+axislegend(axpval)
+xlims!(ax, 0, 50)
+xlims!(axpval, 0, 50)

                  We can convert the p-values into flags by thresholding. Here we want the time points where both p-values are simultaneously below 0.05.

                  pthres = pvalues .< 0.05
+flags = vec(reduce(&, pthres; dims = 2))
+
+vlines!(ax, results.t_change[flags]; label = "flags", color = ("black", 0.1))
+axislegend(ax)
+fig
                  diff --git a/previews/PR41/tutorial_literate.jl b/previews/PR41/tutorial_literate.jl new file mode 100644 index 00000000..2f491843 --- /dev/null +++ b/previews/PR41/tutorial_literate.jl @@ -0,0 +1,140 @@ +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_nlinear) +lines!(ax, t, x_linear) +ax.title = "raw data" +fig + +# +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +# +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window. +# This therefore only uses information from `k-width` to `k` at time step `k`. +# Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +# +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + + +# + +# Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2)) +lines!(ax, tfluct, s .- 0.05; color = Cycled(3)) +ax.title = "real signal vs. surrogate(s)" + +# compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin") +lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate") +axislegend() +ax.title = "change metric" + +fig +# + + +n_surrogates = 1_000 +fig = Figure() +axl = Axis(fig[1,1]; title = "linear") +axnl = Axis(fig[1,2]; title = "nonlinear") +axsigl = Axis(fig[2,1]) +axsignl = Axis(fig[2,2]) + +for (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + # Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change; color = Cycled(j)) + lines!(axsig, t_change, pval; color = Cycled(j+2)) +end + +fig + +# %% +# Tutorial short + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_nl_fluct) +ax.title = "input timeseries" +fig + +# These indicators are suitable for Critical Slowing Down +indicators = [var, ar1_whitenoise] +indconfig = IndicatorsConfig(tfluct, last, indicators; width = 400) + + +# use the ridge regression slope for both indicators +change_metrics = [RidgeRegressionSlope()] +sigconfig = SignificanceConfig(indconfig, last, change_metrics; + width = 30, n_surrogates = 1000) + +# perform the full analysis +results = indicators_analysis(tfluct, x_nl_fluct, indconfig, sigconfig) + +# Plot the original timeseries vs. p-value time series +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2), label = "input") +axpval, = lines(fig[2,1], sigconfig.t_change, results.pval[:, 1]; color = Cycled(3), label = "p-value of var") +lines!(axpval, sigconfig.t_change, results.pval[:, 2]; color = Cycled(4), label = "p-value of ar1") +xlims!(ax, (0, 50)) +xlims!(axpval, (0, 50)) +axislegend(axpval) +fig + + +flags_indicators, flags_andicators = transition_flags(results, 0.05) +vlines!(ax, flags_andicators; label = "flags", color = Cycled(3), linestyle = :dash) +axislegend(ax) +fig \ No newline at end of file diff --git a/previews/PR44/api/index.html b/previews/PR44/api/index.html new file mode 100644 index 00000000..7c6cced8 --- /dev/null +++ b/previews/PR44/api/index.html @@ -0,0 +1,20 @@ + +API · TransitionsInTimeseries.jl
                  Edit on GitHub

                  API

                  Main analysis functions

                  TransitionsInTimeseries.WindowedIndicatorConfig — Type
                  WindowedIndicatorConfig(indicators, change_metrics; kwargs...) → config

                  A configuration struct for TransitionsInTimeseries.jl that collects what indicators and corresponding metrics to use in the transitions_analysis.

                  indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                  Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.

                  Keyword arguments

                  • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.

                  • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.

                  • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in transitions_analysis using the keyword whichtime. Options include:

                    • last: use the last timepoint of each window
                    • midpoint: use the mid timepoint of each time window
                    • first: use first timepoint of each window

                    In fact, the indicators time vector is computed simply via

                    t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)

                    so any other function of the time window may be given to extract the time point itself, such as mean or median.

                  • T = Float64: Element type of input timeseries to initialize some computations.

                  source
                  TransitionsInTimeseries.transition_metrics — Function
                  transition_metrics(config::WindowedIndicatorConfig, x [,t]) → output

                  Estimate possible transitions for input timeseries x using a sliding window approach as described by config:

                  1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                  2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                  If t (the time vector of x), is not provided, it is assumed t = eachindex(x).

                  Return the output as WindowedIndicatorResults which can be given to estimate_significance! to deduce which possible transitions are statistically significant using a variety of significance tests.

                  source
                  TransitionsInTimeseries.WindowedIndicatorResults — Type
                  WindowedIndicatorResults

                  A struct containing the output of transition_metrics used with WindowedIndicatorConfig. It can be used for further analysis, visualization, or given to estimate_significance!.

                  It has the following fields that the user may access

                  • x: the input timeseries.

                  • t: the time vector of the input timeseries.

                  • x_indicator, the indicator timeseries (matrix with each column one indicator).

                  • t_indicator, the time vector of the indicator timeseries.

                  • x_change, the change metric timeseries (matrix with each column one change metric).

                  • t_change, the time vector of the change metric timeseries.

                  • wim::WindowedIndicatorConfig, used for the analysis.

                  source

                  Significance testing

                  TransitionsInTimeseries.SurrogatesConfig — Type
                  SurrogatesConfig <: SignificanceConfig
+SurrogatesConfig(; surrogate = RandomFourier(), n = 1_000, tail = :both, rng)

                  A configuration struct for significance testing estimate_significance using timeseries surrogates.

                  Keyword arguments

                  • surromethod = RandomFourier(): method to generate surrogates
                  • n = 1_000: how many surrogates to generate
                  • rng = Random.default_rng(): random number generator for the surrogates
                  • p = 0.05: threshold for significance of the p-value
                  • tail = :both: tail type used, see below
                  • detrend_surro = false: Boolean specifying whether the surrogates are to be

                  detrended by a linear regression. This is sometimes performed in the literature but seldomly impacts the results in a significant way, since the surrogates of the residual should already be largely free of trend.

                  Description

                  When used with WindowedIndicatorResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance, which results in flags. These results are then stored in SurrogatesSignificance.

                  The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowedIndicatorResults.

                  source
                  TransitionsInTimeseries.SurrogatesSignificance — Type
                  SurrogatesSignificance

                  A struct containing the results of estimate_significance based on a SurrogatesConfig, i.e. the p-values and their associated flags. The former gives a continuous value between 0 and 1, with 0 denoting an extremely unlikely and therefore probably significant behavior of the original time series compared to the ensemble of surrogates. The latter is a Boolean matrix which contains true wherever the p-values are below the threshold defined in SurrogatesConfig. Both signif.p_values and signif.flags have the same size as res.x_change, with signif::SurrogatesSignificance and res::WindowedIndicatorResults.

                  source
                  TransitionsInTimeseries.QuantileSignificance — Type

                  QuantileSignificance(; p = 0.95, tail = :right) <: TransitionsSignificance

                  A configuration struct for significance testing significant_transitions. When used with WindowedIndicatorResults, significance is estimated as by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                  source

                  Indicators

                  Value distribution

                  Statistics.mean — Method
                  mean(itr)

                  Compute the mean of all elements in a collection.

                  Note

                  If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

                  Examples

                  julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
                  StatsBase.skewness — Function
                  skewness(v, [wv::AbstractWeights], m=mean(v))

                  Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                  StatsBase.kurtosis — Function
                  kurtosis(v, [wv::AbstractWeights], m=mean(v))

                  Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                  Critical Slowing Down

                  Statistics.var — Method
                  var(itr; corrected::Bool=true, mean=nothing[, dims])

                  Compute the sample variance of collection itr.

                  The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

                  If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

                  A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

                  Note

                  If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

                  TransitionsInTimeseries.ar1_whitenoise — Function
                  ar1_whitenoise(x::AbstractVector)

                  Return the AR1 regression coefficient $θ$ of a time series $x$ by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

                  \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                  source

                  Spectrum

                  TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                  LowfreqPowerSpectrum(; q_lofreq = 0.1)

                  Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                  lfps = precompute( LowfreqPowerSpectrum() )

                  Keyword arguments:

                  • q_lofreq: a number between 0 and 1 that characterises which portion of the

                  frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                  source

                  Nonlinear dynamics

                  Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:

                  function permutation_entropy(; m = 3, τ = 1)
+    est = SymbolicPermutation(; m, τ)
+    return x -> entropy_normalized(est, x)
+end
                  StatsBase.entropy — Function
                  entropy(p, [b])

                  Compute the entropy of a collection of probabilities p, optionally specifying a real number b such that the entropy is scaled by 1/log(b). Elements with probability 0 or 1 add 0 to the entropy.

                  Change metrics

                  Slope

                  TransitionsInTimeseries.kendalltau — Function
                  kendalltau(x::AbstractVector)

                  Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                  source
                  TransitionsInTimeseries.spearman — Function
                  spearman(x::AbstractVector)

                  Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                  source

                  Value distribution differences

                  TransitionsInTimeseries.difference_of_means — Function
                  difference_of_means(x::AbstractArray)

                  Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                  # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                  difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                  source

                  Make your own indicator/metric!

                  The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                  There are situations where you may optimize such a function based on knowledge of input x type and length.

                  TODO: Here explain how to use precomputable functions

                  Missing docstring.

                  Missing docstring for precompute. Check Documenter's build log for details.

                  Surrogates

                  For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                  Sliding windows

                  TransitionsInTimeseries.WindowViewer — Type
                  WindowViewer(x; width, stride)

                  Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                  If not given, the keywords width, stride are taken as default_window_width(x) and 1.

                  source
                  TransitionsInTimeseries.windowmap — Function
                  windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                  A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                  source

                  Load data

                  diff --git a/previews/PR44/assets/documenter.js b/previews/PR44/assets/documenter.js new file mode 100644 index 00000000..6adfbbbf --- /dev/null +++ b/previews/PR44/assets/documenter.js @@ -0,0 +1,331 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fas", "fa-copy"); + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-times"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-times"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); + }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR44/assets/search.js b/previews/PR44/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR44/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
                • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR44/assets/themes/documenter-dark.css b/previews/PR44/assets/themes/documenter-dark.css new file mode 100644 index 00000000..89fbb493 --- /dev/null +++ b/previews/PR44/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ +@keyframes spinAround{from{transform:rotate(0deg)}to{transform:rotate(359deg)}}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark .button,.is-unselectable,html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after,html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after{border:3px solid rgba(0,0,0,0);border-radius:2px;border-right:0;border-top:0;content:" 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kbd.button{background-color:#363636;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#e8e8e8}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content 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kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content 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rgba(37,154,18,0.25)}html.theme--documenter-dark .button.is-success:active,html.theme--documenter-dark .button.is-success.is-active{background-color:#20830f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success{background-color:#259a12;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff 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!important}html.theme--documenter-dark .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark 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.button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#c13930;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(203,60,51,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#b7362e;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-outlined.is-focused{background-color:#cb3c33;border-color:#cb3c33;color:#fff}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:2px;font-size:.75rem}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#fff;border-color:#dbdbdb;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em / 2));top:calc(50% - (1em / 2));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#f5f5f5;border-color:#dbdbdb;color:#7a7a7a;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:290486px;padding-left:1em;padding-right:1em}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:0.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){border-radius:2px;font-size:.75rem}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}html.theme--documenter-dark .container.is-fluid{margin-left:32px;margin-right:32px;max-width:none}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen{max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd{max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container{max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container{max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#cdc3e3;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#f5f5f5;border-left:5px solid #dbdbdb;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #dbdbdb;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#cdc3e3}html.theme--documenter-dark .content table th:not([align]){text-align:left}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 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file mode 100644 index 00000000..c58e993e --- /dev/null +++ b/previews/PR44/assets/themeswap.js @@ -0,0 +1,66 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Intialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if(window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the browser supports user color preference + var darkPreference = false; + // Check if the users preference is for dark color scheme + if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { + darkPreference = true; + } + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; var disabled = []; var darkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if(themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); + // Check if the theme is primary dark theme + var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null); + // If ss is for dark theme then set the value of darkTheme to the name of the theme + if(isDarkTheme) darkTheme = themename; + // If we find a matching theme (and it's not the default), we'll set active to non-null + if(themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if(themename !== theme) disabled.push(ss); + } + if(active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + theme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + else if(darkTheme !== null && darkPreference === true) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + darkTheme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + if (ss.ownerNode.getAttribute("data-theme-name") !== darkTheme) { + ss.disabled = true; + } + }); + } +} +set_theme_from_local_storage(); diff --git a/previews/PR44/assets/warner.js b/previews/PR44/assets/warner.js new file mode 100644 index 00000000..5531c885 --- /dev/null +++ b/previews/PR44/assets/warner.js @@ -0,0 +1,49 @@ +function maybeAddWarning () { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return + }; + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return + }; + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return + }; + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement('meta'); + meta.name = 'robots'; + meta.content = 'noindex'; + + document.getElementsByTagName('head')[0].appendChild(meta); + }; + + const div = document.createElement('div'); + div.classList.add('outdated-warning-overlay'); + const closer = document.createElement('button'); + closer.classList.add('outdated-warning-closer', 'delete'); + closer.addEventListener('click', function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + '/../' + window.DOCUMENTER_STABLE; + div.innerHTML = 'This documentation is not for the latest stable release, but for either the development version or an older release.
                  Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/previews/PR44/examples/do-events.jl b/previews/PR44/examples/do-events.jl new file mode 100644 index 00000000..f01ff852 --- /dev/null +++ b/previews/PR44/examples/do-events.jl @@ -0,0 +1,291 @@ +#= +# Dansgaard-Oescher events + +The $\delta^{18}O$ time series of the North Greenland Ice Core Project ([NGRIP](https://en.wikipedia.org/wiki/North_Greenland_Ice_Core_Project)) are, to this date, the best proxy record for the Dansgaard-Oeschger events ([DO-events](https://en.wikipedia.org/wiki/Dansgaard%E2%80%93Oeschger_event)). DO-events are sudden warming episodes of the North Atlantic, reaching to 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found [here](https://www.iceandclimate.nbi.ku.dk/data/) in its raw format. This analysis has already been done in [^Boers2018] and we here try to reproduce Figure 2.d-f. + +## Preprocessing NGRIP + +Over this example, it will appear that the convenience of TransitionsInTimeseries to leads the bulk of the code to be written for plotting and preprocessing. The latter consists in various steps $i = \lbrace 1,2,3 \rbrace$: +1. Load the data, reverse and offset it to have time vector = time before 2000 AD. +2. Filter non-unique points in time and sort the data. +3. Regrid the data from uneven to even sampling. + +The time and $\delta^{18}O$ vectors resulting from step $i$ are respectively called $t_i$ and $x_i$. The final preprocessing step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. +=# + +using DelimitedFiles, Downloads, DSP, BSplineKit, Loess + +function load_ngrip() + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP.csv") + data, labels = readdlm(tmp, header = true) + return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors +end + +uniqueidx(v) = unique(i -> v[i], eachindex(v)) +function keep_unique(t, x) + unique_idx = uniqueidx(t) + return t[unique_idx], x[unique_idx] +end + +function sort_timeseries!(t, x) + p = sortperm(t) + permute!(t, p) + permute!(x, p) + return nothing +end + +function regrid2evensampling(t, x, dt) + itp = BSplineKit.interpolate(t, x, BSplineOrder(4)) + tspan = (ceil(minimum(t)), floor(maximum(t))) + t_even = collect(tspan[1]:dt:tspan[2]) + x_even = itp.(t_even) + return t_even, x_even +end + +function chebyshev_filter(t, x, fcutoff) + ii = 10 # Chebyshev filtering requires to prune first points of time series. + responsetype = Highpass(fcutoff, fs = 1/dt) + designmethod = Chebyshev1(8, 0.05) + r = filt(digitalfilter(responsetype, designmethod), x) + xtrend = x - r + return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end] +end + +dt, fcutoff = 5.0, 0.95*0.01 # dt = 5 yr and cutoff ≃ 0.01 yr^-1 as in (Boers 2018) +t1, x1 = load_ngrip() +t2, x2 = keep_unique(t1, x1) +sort_timeseries!(t2, x2) +t3, x3 = regrid2evensampling(t2, x2, dt) +t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff) + +#= +Let's now go to the last preprocessing steps and visualize our data in what will become our main figure. To keep the same approach as in [^Boers2018], we hand-code the transition times and highlight them by purple vertical lines: +=# + +using CairoMakie + +function loess_filter(t, x; span = 0.005) + loessmodel = loess(t, x, span = span) + xtrend = Loess.predict(loessmodel, t) + r = x - xtrend + return t, x, xtrend, r +end + +function kyr_xticks(tticks_yr) + tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)] + return (tticks_yr, tticks_kyr) +end + +function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks) + fig = Figure(resolution = (1600, 1200), fontsize = 24) + + ## Original time series with transition marked by vertical lines + ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)", + xaxisposition = :top, xticks = xticks) + lines!(ax1, traw, xraw, color = (:gray70, 0.5)) + lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3) + vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3) + + ## Residual time series + ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + lines!(ax2, t, r, color = :gray50, linewidth = 1) + + ## Axes for variance and AC1 time series + ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$", + xticks = xticks) + + axs = [ax1, ax2, ax3, ax4] + [xlims!(ax, xlims) for ax in axs] + ylims!(axs[1], (-48, -34)) + rowgap!(fig.layout, 10) + return fig, axs +end + +xlims = (-60e3, -10e3) +xticks = kyr_xticks(-60e3:5e3:5e3) +t_transitions = [-59.5e3, -58.2e3, -55.8e3, -54.3e3, -49.35e3, -46.9e3, -43.45e3, + -41.5e3, -40.2e3, -38.25e3, -35.5e3, -33.8e3, -32.55e3, -28.95e3, + -27.85e3, -23.5e3, -14.7e3, -11.7e3] +tloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization + +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_transitions, xlims, xticks) +fig + +#= +## Hindcast on NGRIP data + +As one can see, there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries to study the evolution, measured by the ridge-regression slope, of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including [^Boers2018], the CSD analysis is performed over segments (sometimes only one) of the time series, such that a significance value is obtained for each segment. Dealing with segments can be easily done in TransitionsInTimeseries and is demonstrated here: +=# + +using TransitionsInTimeseries, StatsBase +using Random: Xoshiro + +ac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase +indicators = (var, ac1) +change_metrics = RidgeRegressionSlope() +opts = [(color = Cycled(2), linewidth = 3), # plotting options + (color = :orange, linewidth = 3, linestyle = :dash)] + +function perform_segment_analysis(t, r, indicators, change_metrics, itime, + dt, n, t_transitions, margins) + + ## Initialize results over segment and indicator dimensions + pvalues = fill(Inf, length(t_transitions), length(indicators)) + indicator_results = [fill(Inf, 3, 3) for t in t_transitions] + + for i in eachindex(t_transitions) + ## Select the correct segment limits + if i == 1 + t_start = first(t) + else + t_start = t_transitions[i-1] + margins[1] + end + t_end = t_transitions[i] - margins[2] + i_start, i_end = argmin(abs.(t .- t_start)), argmin(abs.(t .- t_end)) + tseg, rseg = t[i_start:i_end], r[i_start:i_end] + sigconfig = SurrogatesConfig(n = n, tail = :right, rng = Xoshiro(27)) + + if last(tseg) - first(tseg) > itime + 20.0 # only analyze if segment long enough + ## Compute the significance of the transition metrics for the chosen segment + t_indicator = windowmap(last, tseg; width = Int(itime ÷ dt)) + segconfig = WindowedIndicatorConfig(indicators, change_metrics; whichtime = last, + width_ind = Int(itime ÷ dt), width_cha = length(t_indicator)) + segresults = transition_metrics(segconfig, rseg, tseg) + segsignif = estimate_significance(sigconfig, segresults) + + ## Populate the pre-allocated arrays with the results + pvalues[i, :] .= segsignif.pvalues[1, :] + indicator_results[i] = hcat(segresults.t_indicator, segresults.x_indicator) + end + end + return pvalues, indicator_results +end + +function plot_segment_analysis!(axs, pvalues, t_transitions, indicator_results, margins) + for i in eachindex(indicator_results) # loop over the segments + ## Unpack indicator results + tind = indicator_results[i][:, 1] + ind = indicator_results[i][:, 2:end] + + for j in axes(pvalues, 2) # loop over the indicators + if !isinf(pvalues[i, j]) # only plot if enough data points for analysis + ## Plot indicator time series and its linear regression + lines!(axs[j+2], tind, ind[:, j], color = Cycled(1)) + m, p = ridgematrix(tind, 0.0) * ind[:, j] + if pvalues[i, j] < 0.05 + vlines!(axs[1], t_transitions[i] - margins[2]; opts[j]...) + vlines!(axs[j+2], t_transitions[i] - margins[2]; opts[j]...) + lines!(axs[j+2], tind, m .* tind .+ p, color = :gray10, linewidth = 3) + else + lines!(axs[j+2], tind, m .* tind .+ p, color = :gray10, linewidth = 3, + linestyle = :dash) + end + end + end + end + return nothing +end + +margins = [200, 200] # avoid the inclusion of transition data points in the segments +pvalues, indicator_results = perform_segment_analysis(t, r, + indicators, change_metrics, 200.0, dt, 1_000, t_transitions, margins) +plot_segment_analysis!(axs, pvalues, t_transitions, indicator_results, margins) +fig + +#= +In [^Boers2018], 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. Here we respectively find 10/16 true positives for the variance and 4/16 for AC1. The mismatch between [^Boers2018] and the results shown above clearly points out that packages like TransitionsInTimeseries are wishful for research to be reproducible. + +Given that the NGRIP data is sparse, noisy, and presents 16 transitions in total, it appears that the method generates a reasonable rate of true positives, but... + +## Limitations of hindcast + +Finding transition indicators by defining segments, as done above, is arguably misleading when it comes to an operational prediction task. In fact, one does not check for false positives since the analysis is always performed upto time steps shortly before the transition. To make a brief, albeit incomplete check, one can stop the analysis much before the transition and thus check whether CSD indicators would forecast a transition although there is none ahead. +=# + +early_margins = [200, 700] # take "too early" end margin to check for false positives +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_transitions, xlims, xticks) +pvalues, indicator_results = perform_segment_analysis(t, r, + indicators, change_metrics, 200.0, dt, 1_000, t_transitions, early_margins) +plot_segment_analysis!(axs, pvalues, t_transitions, indicator_results, early_margins) +fig + +#= +From 16 predictions which should all be negative, 10 of them are positive for the variance and 3 are positive for AC1. This clearly points out that generating a reasonable amount of true positives comes here at the expense of generating many false positives. We draw attention upon the fact that **checking for false positives is too seldomly performed in literature!** This does not mean that the method are incorrect but rather that the NGRIP data might be too much of a challenge for a CSD analysis. This is not surprising since the $\delta^{18}O$ time series is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. Meh. Is the situation hopeless? Not completely, as we will see in the next section. + +!!! info "Future improvement" + Supporting the computations for uneven time series is a planned improvement of TransitionsInTimeseries. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias. + +## Hindcasting simulated DO-events + +In CLIMBER-X[^Willeit2022], an Earth Model of Intermediate Complexity (EMIC), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. Unlike the segment analysis as the one performed above, the analysis fully relying on sliding windows (as introduced in the [Tutorial](@ref)) is a way to generate true positives while simultaneously checking for false positives, since transition metrics are computed for (almost) all time steps. We run this analysis over two exemplary simulation outputs: +=# + +opts = [(color = (:orange, 0.1), linewidth = 3), + (color = Cycled(2), linewidth = 3, linestyle = :dash)] + +function perform_sliding_analysis(t, r, indicators, change_metrics, itime, ctime, + istride, cstride, dt, n) + config = WindowedIndicatorConfig(indicators, change_metrics; whichtime = last, + width_ind = Int(itime ÷ dt), stride_ind = istride, + width_cha = Int(ctime ÷ dt), stride_cha = cstride) + results = transition_metrics(config, r, t) + sigconfig = SurrogatesConfig(n = n, tail = :right) + signif = estimate_significance(sigconfig, results) + return signif.pvalues, results +end + +function plot_sliding_analysis!(axs, pvalues, results, threshold) + for j in axes(pvalues, 2) + vlines!(axs[1], results.t_change[pvalues[:, j] .< threshold]; opts[j]...) + lines!(axs[2+j], results.t_indicator, results.x_indicator[:, j], color = Cycled(1)) + vlines!(axs[2+j], results.t_change[pvalues[:, j] .< threshold]; opts[j]...) + end + return nothing +end + +t_transitions = [[1850, 2970, 3970, 5070, 5810, 7050, 8050], [3500, 4400, 5790, 7200, 8140]] +figvec = Figure[] +for i in 1:2 + ## Download the data and perform loess filtering on it + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" * + "master/timeseries/climberx-do$(i)-omaxa.csv") + data = readdlm(tmp) + tcx, xcx = data[1, :], data[2, :] + t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02) + + ## Initialize figure + xlims = (0, last(tcx)) + xticks = kyr_xticks(xlims[1]:1e3:xlims[2]) + fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[i], xlims, xticks) + ylims!(axs[1], (5, 40)) + axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$" + + ## Run sliding analysis and update figure with results + dt = mean(diff(tcx)) + pvalues, results = perform_sliding_analysis(t, r, indicators, change_metrics, + 500.0, 20.0, 1, 1, dt, 1_000) + plot_sliding_analysis!(axs, pvalues, results, 0.01) + vlines!(axs[1], t_transitions[i], color = Cycled(1), linewidth = 3) + push!(figvec, fig) +end +figvec[1] + +#= +We here notice that transitions are always preceeded (early enough but not too early) by a significant increase of AC1, sometimes accompanied by the variance. Diagnostics seem to be very reliable, since all transitions lead to both indicators showing significant increases, synchronously and/or subsequently to the transition. False positives continue to arise, however with much lower ratio than on the NGRIP data. It seems like clean data already allows much better results! To make sure we were not simply lucky, let's look at another simulation: +=# + +figvec[2] + +#= +Things look equally good here! Assuming that these simulations capture the DO dynamics well, one can hope that higher resolution data with less noise allows to robustly predict and/or diagnose DO events. We here draw attention upon the fact that even $dt = 1 \, \mathrm{yr}$ is a relatively sparse sampling for a physical, simulated process displaying transitions with a quasi-period of $T \in [1000, 1500] \, \mathrm{yr}$. + +[^Boers2018]: + Niklas Boers (2018): [Early-warning signals for Dansgaard-Oeschger events in a high-resolution ice core record](https://doi.org/10.1038/s41467-018-04881-7) + +[^Willeit2022]: + Matteo Willeit et al. (2022): [The Earth system model CLIMBER-X v1.0 – Part 1: Climate model description and validation​​​​​​​​​​​​​​](https://doi.org/10.5194/gmd-15-5905-2022) +=# \ No newline at end of file diff --git a/previews/PR44/examples/do-events/index.html b/previews/PR44/examples/do-events/index.html new file mode 100644 index 00000000..27c73c28 --- /dev/null +++ b/previews/PR44/examples/do-events/index.html @@ -0,0 +1,222 @@ + +Dansgaard-Oescher events · TransitionsInTimeseries.jl
                  Edit on GitHub

                  Dansgaard-Oescher events

                  The $\delta^{18}O$ time series of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching to 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in [Boers2018] and we here try to reproduce Figure 2.d-f.

                  Preprocessing NGRIP

                  Over this example, it will appear that the convenience of TransitionsInTimeseries to leads the bulk of the code to be written for plotting and preprocessing. The latter consists in various steps $i = \lbrace 1,2,3 \rbrace$:

                  1. Load the data, reverse and offset it to have time vector = time before 2000 AD.
                  2. Filter non-unique points in time and sort the data.
                  3. Regrid the data from uneven to even sampling.

                  The time and $\delta^{18}O$ vectors resulting from step $i$ are respectively called $t_i$ and $x_i$. The final preprocessing step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked.

                  using DelimitedFiles, Downloads, DSP, BSplineKit, Loess
+
+function load_ngrip()
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+        "master/timeseries/NGRIP.csv")
+    data, labels = readdlm(tmp, header = true)
+    return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors
+end
+
+uniqueidx(v) = unique(i -> v[i], eachindex(v))
+function keep_unique(t, x)
+    unique_idx = uniqueidx(t)
+    return t[unique_idx], x[unique_idx]
+end
+
+function sort_timeseries!(t, x)
+    p = sortperm(t)
+    permute!(t, p)
+    permute!(x, p)
+    return nothing
+end
+
+function regrid2evensampling(t, x, dt)
+    itp = BSplineKit.interpolate(t, x, BSplineOrder(4))
+    tspan = (ceil(minimum(t)), floor(maximum(t)))
+    t_even = collect(tspan[1]:dt:tspan[2])
+    x_even = itp.(t_even)
+    return t_even, x_even
+end
+
+function chebyshev_filter(t, x, fcutoff)
+    ii = 10     # Chebyshev filtering requires to prune first points of time series.
+    responsetype = Highpass(fcutoff, fs = 1/dt)
+    designmethod = Chebyshev1(8, 0.05)
+    r = filt(digitalfilter(responsetype, designmethod), x)
+    xtrend = x - r
+    return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]
+end
+
+dt, fcutoff = 5.0, 0.95*0.01    # dt = 5 yr and cutoff ≃ 0.01 yr^-1 as in (Boers 2018)
+t1, x1 = load_ngrip()
+t2, x2 = keep_unique(t1, x1)
+sort_timeseries!(t2, x2)
+t3, x3 = regrid2evensampling(t2, x2, dt)
+t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)
                  ([-59899.0, -59894.0, -59889.0, -59884.0, -59879.0, -59874.0, -59869.0, -59864.0, -59859.0, -59854.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-44.4622612304012, -44.264401428210874, -44.02956767939856, -42.29334237357212, -42.594341674200344, -41.09704877854712, -40.39837540966913, -44.369155046413255, -42.74492506508012, -43.737014520530145  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46], [-43.89287787976461, -48.663435112414156, -51.31169981050155, -51.269094666491796, -49.90310432724566, -47.721430022512344, -44.36050569418247, -43.87556827410048, -43.57802291229893, -41.36870967826094  …  -34.81349114528442, -36.01634453179986, -36.150446802907226, -36.37595639697143, -35.96843653265903, -33.899634243732976, -32.49784036951535, -33.06575312724142, -34.07956188682297, -34.4079080530096], [-0.5693833506365866, 4.399033684203284, 7.282132131102991, 8.975752292919669, 7.308762653045311, 6.624381243965224, 3.9621302845133433, -0.493586772312777, 0.8330978472188112, -2.368304842269206  …  -0.30650885471557926, -0.17365546820014846, 1.0104468029072273, -0.684043603028572, 1.0384365326590237, -0.3303657562670192, -1.0321596304846505, -2.0242468727585807, 0.07956188682296689, -0.05209194699039831])

                  Let's now go to the last preprocessing steps and visualize our data in what will become our main figure. To keep the same approach as in [Boers2018], we hand-code the transition times and highlight them by purple vertical lines:

                  using CairoMakie
+
+function loess_filter(t, x; span = 0.005)
+    loessmodel = loess(t, x, span = span)
+    xtrend = Loess.predict(loessmodel, t)
+    r = x - xtrend
+    return t, x, xtrend, r
+end
+
+function kyr_xticks(tticks_yr)
+    tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)]
+    return (tticks_yr, tticks_kyr)
+end
+
+function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)
+    fig = Figure(resolution = (1600, 1200), fontsize = 24)
+
+    # Original time series with transition marked by vertical lines
+    ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)",
+        xaxisposition = :top, xticks = xticks)
+    lines!(ax1, traw, xraw, color = (:gray70, 0.5))
+    lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)
+    vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)
+
+    # Residual time series
+    ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    lines!(ax2, t, r, color = :gray50, linewidth = 1)
+
+    # Axes for variance and AC1 time series
+    ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$",
+        xticks = xticks)
+
+    axs = [ax1, ax2, ax3, ax4]
+    [xlims!(ax, xlims) for ax in axs]
+    ylims!(axs[1], (-48, -34))
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+
+xlims = (-60e3, -10e3)
+xticks = kyr_xticks(-60e3:5e3:5e3)
+t_transitions = [-59.5e3, -58.2e3, -55.8e3, -54.3e3, -49.35e3, -46.9e3, -43.45e3,
+                 -41.5e3, -40.2e3, -38.25e3, -35.5e3, -33.8e3, -32.55e3, -28.95e3,
+                 -27.85e3, -23.5e3, -14.7e3, -11.7e3]
+tloess, _, xloess, rloess = loess_filter(t3, x3)    # loess-filtered signal for visualization
+
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_transitions, xlims, xticks)
+fig

                  Hindcast on NGRIP data

                  As one can see, there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries to study the evolution, measured by the ridge-regression slope, of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including [Boers2018], the CSD analysis is performed over segments (sometimes only one) of the time series, such that a significance value is obtained for each segment. Dealing with segments can be easily done in TransitionsInTimeseries and is demonstrated here:

                  using TransitionsInTimeseries, StatsBase
+using Random: Xoshiro
+
+ac1(x) = sum(autocor(x, [1]))                   # AC1 from StatsBase
+indicators = (var, ac1)
+change_metrics = RidgeRegressionSlope()
+opts = [(color = Cycled(2), linewidth = 3),     # plotting options
+        (color = :orange, linewidth = 3, linestyle = :dash)]
+
+function perform_segment_analysis(t, r, indicators, change_metrics, itime,
+    dt, n, t_transitions, margins)
+
+    # Initialize results over segment and indicator dimensions
+    pvalues = fill(Inf, length(t_transitions), length(indicators))
+    indicator_results = [fill(Inf, 3, 3) for t in t_transitions]
+
+    for i in eachindex(t_transitions)
+        # Select the correct segment limits
+        if i == 1
+            t_start = first(t)
+        else
+            t_start = t_transitions[i-1] + margins[1]
+        end
+        t_end = t_transitions[i] - margins[2]
+        i_start, i_end = argmin(abs.(t .- t_start)), argmin(abs.(t .- t_end))
+        tseg, rseg = t[i_start:i_end], r[i_start:i_end]
+        sigconfig = SurrogatesConfig(n = n, tail = :right, rng = Xoshiro(27))
+
+        if last(tseg) - first(tseg) > itime + 20.0     # only analyze if segment long enough
+            # Compute the significance of the transition metrics for the chosen segment
+            t_indicator = windowmap(last, tseg; width = Int(itime ÷ dt))
+            segconfig = WindowedIndicatorConfig(indicators, change_metrics; whichtime = last,
+                width_ind = Int(itime ÷ dt), width_cha = length(t_indicator))
+            segresults = transition_metrics(segconfig, rseg, tseg)
+            segsignif = estimate_significance(sigconfig, segresults)
+
+            # Populate the pre-allocated arrays with the results
+            pvalues[i, :] .= segsignif.pvalues[1, :]
+            indicator_results[i] = hcat(segresults.t_indicator, segresults.x_indicator)
+        end
+    end
+    return pvalues, indicator_results
+end
+
+function plot_segment_analysis!(axs, pvalues, t_transitions, indicator_results, margins)
+    for i in eachindex(indicator_results)   # loop over the segments
+        # Unpack indicator results
+        tind = indicator_results[i][:, 1]
+        ind = indicator_results[i][:, 2:end]
+
+        for j in axes(pvalues, 2)           # loop over the indicators
+            if !isinf(pvalues[i, j])        # only plot if enough data points for analysis
+                # Plot indicator time series and its linear regression
+                lines!(axs[j+2], tind, ind[:, j], color = Cycled(1))
+                m, p = ridgematrix(tind, 0.0) * ind[:, j]
+                if pvalues[i, j] < 0.05
+                    vlines!(axs[1], t_transitions[i] - margins[2]; opts[j]...)
+                    vlines!(axs[j+2], t_transitions[i] - margins[2]; opts[j]...)
+                    lines!(axs[j+2], tind, m .* tind .+ p, color = :gray10, linewidth = 3)
+                else
+                    lines!(axs[j+2], tind, m .* tind .+ p, color = :gray10, linewidth = 3,
+                    linestyle = :dash)
+                end
+            end
+        end
+    end
+    return nothing
+end
+
+margins = [200, 200]        # avoid the inclusion of transition data points in the segments
+pvalues, indicator_results = perform_segment_analysis(t, r,
+    indicators, change_metrics, 200.0, dt, 1_000, t_transitions, margins)
+plot_segment_analysis!(axs, pvalues, t_transitions, indicator_results, margins)
+fig

                  In [Boers2018], 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. Here we respectively find 10/16 true positives for the variance and 4/16 for AC1. The mismatch between [Boers2018] and the results shown above clearly points out that packages like TransitionsInTimeseries are wishful for research to be reproducible.

                  Given that the NGRIP data is sparse, noisy, and presents 16 transitions in total, it appears that the method generates a reasonable rate of true positives, but...

                  Limitations of hindcast

                  Finding transition indicators by defining segments, as done above, is arguably misleading when it comes to an operational prediction task. In fact, one does not check for false positives since the analysis is always performed upto time steps shortly before the transition. To make a brief, albeit incomplete check, one can stop the analysis much before the transition and thus check whether CSD indicators would forecast a transition although there is none ahead.

                  early_margins = [200, 700]      # take "too early" end margin to check for false positives
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_transitions, xlims, xticks)
+pvalues, indicator_results = perform_segment_analysis(t, r,
+    indicators, change_metrics, 200.0, dt, 1_000, t_transitions, early_margins)
+plot_segment_analysis!(axs, pvalues, t_transitions, indicator_results, early_margins)
+fig

                  From 16 predictions which should all be negative, 10 of them are positive for the variance and 3 are positive for AC1. This clearly points out that generating a reasonable amount of true positives comes here at the expense of generating many false positives. We draw attention upon the fact that checking for false positives is too seldomly performed in literature! This does not mean that the method are incorrect but rather that the NGRIP data might be too much of a challenge for a CSD analysis. This is not surprising since the $\delta^{18}O$ time series is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. Meh. Is the situation hopeless? Not completely, as we will see in the next section.

                  Future improvement

                  Supporting the computations for uneven time series is a planned improvement of TransitionsInTimeseries. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.

                  Hindcasting simulated DO-events

                  In CLIMBER-X[Willeit2022], an Earth Model of Intermediate Complexity (EMIC), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. Unlike the segment analysis as the one performed above, the analysis fully relying on sliding windows (as introduced in the Tutorial) is a way to generate true positives while simultaneously checking for false positives, since transition metrics are computed for (almost) all time steps. We run this analysis over two exemplary simulation outputs:

                  opts = [(color = (:orange, 0.1), linewidth = 3),
+        (color = Cycled(2), linewidth = 3, linestyle = :dash)]
+
+function perform_sliding_analysis(t, r, indicators, change_metrics, itime, ctime,
+    istride, cstride, dt, n)
+    config = WindowedIndicatorConfig(indicators, change_metrics; whichtime = last,
+        width_ind = Int(itime ÷ dt), stride_ind = istride,
+        width_cha = Int(ctime ÷ dt), stride_cha = cstride)
+    results = transition_metrics(config, r, t)
+    sigconfig = SurrogatesConfig(n = n, tail = :right)
+    signif = estimate_significance(sigconfig, results)
+    return signif.pvalues, results
+end
+
+function plot_sliding_analysis!(axs, pvalues, results, threshold)
+    for j in axes(pvalues, 2)
+        vlines!(axs[1], results.t_change[pvalues[:, j] .< threshold]; opts[j]...)
+        lines!(axs[2+j], results.t_indicator, results.x_indicator[:, j], color = Cycled(1))
+        vlines!(axs[2+j], results.t_change[pvalues[:, j] .< threshold]; opts[j]...)
+    end
+    return nothing
+end
+
+t_transitions = [[1850, 2970, 3970, 5070, 5810, 7050, 8050], [3500, 4400, 5790, 7200, 8140]]
+figvec = Figure[]
+for i in 1:2
+    # Download the data and perform loess filtering on it
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" *
+        "master/timeseries/climberx-do$(i)-omaxa.csv")
+    data = readdlm(tmp)
+    tcx, xcx = data[1, :], data[2, :]
+    t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)
+
+    # Initialize figure
+    xlims = (0, last(tcx))
+    xticks = kyr_xticks(xlims[1]:1e3:xlims[2])
+    fig, axs = plot_do(tcx, xcx,  t, xtrend, t, r, t_transitions[i], xlims, xticks)
+    ylims!(axs[1], (5, 40))
+    axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$"
+
+    # Run sliding analysis and update figure with results
+    dt = mean(diff(tcx))
+    pvalues, results = perform_sliding_analysis(t, r, indicators, change_metrics,
+        500.0, 20.0, 1, 1, dt, 1_000)
+    plot_sliding_analysis!(axs, pvalues, results, 0.01)
+    vlines!(axs[1], t_transitions[i], color = Cycled(1), linewidth = 3)
+    push!(figvec, fig)
+end
+figvec[1]

                  We here notice that transitions are always preceeded (early enough but not too early) by a significant increase of AC1, sometimes accompanied by the variance. Diagnostics seem to be very reliable, since all transitions lead to both indicators showing significant increases, synchronously and/or subsequently to the transition. False positives continue to arise, however with much lower ratio than on the NGRIP data. It seems like clean data already allows much better results! To make sure we were not simply lucky, let's look at another simulation:

                  figvec[2]

                  Things look equally good here! Assuming that these simulations capture the DO dynamics well, one can hope that higher resolution data with less noise allows to robustly predict and/or diagnose DO events. We here draw attention upon the fact that even $dt = 1 \, \mathrm{yr}$ is a relatively sparse sampling for a physical, simulated process displaying transitions with a quasi-period of $T \in [1000, 1500] \, \mathrm{yr}$.

                  diff --git a/previews/PR44/examples/permutation_entropy.jl b/previews/PR44/examples/permutation_entropy.jl new file mode 100644 index 00000000..cac204a7 --- /dev/null +++ b/previews/PR44/examples/permutation_entropy.jl @@ -0,0 +1,190 @@ +# # Examples for TransitionsInTimeseries.jl + +# ## Permutation entropy for dynamic regime changes + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ### Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +logistic_rule(u, p, t) = @inbounds SVector(p[1]*u[1]*(1 - u[1])) +ds = DeterministicIteratedMap(logistic_rule, [0.5], [1.0]) + +r1 = 3.83 +r2 = 3.86[] +N = 2000 +rs = range(r1, r2; length = N) +x = zeros(N) +for (i, r) in enumerate(rs) + set_parameter!(ds, 1, r) + step!(ds) + x[i] = current_state(ds)[1] +end + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ### Using a simpler change metric + +# Now, let's compute and various indicators and their changes, +# focusing on the fourth indicator, the permutation entropy. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries +indicators = (var, ar1_whitenoise, permutation_entropy(m = 4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as `stride_cha` half the `width_cha`. +metric = difference_of_means + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = WindowedIndicatorConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = transition_metrics(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + i < 4 && hidexdecorations!(ax; grid = false) + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ### Significance via random Fourier surrogates +# %% #src + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). +# There are + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 1000, tail = [:both, :both, :right], surrogate = surromethod + ) + pvalues = significant_transitions(results, signif) + flags = pvalues .< 0.05 + + # To make things visually clear, we will plot an example surrogate for each indicator + # and also plot the flags with same color + + for (i, indicator) in enumerate(indicators) + ## generate surrogate change metric timeseries + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surrogate) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric, p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2)) + end + ## Plot the flags with flags + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + label = string(nameof(typeof(surromethod))), color = color, linestyle = :dash, linewidth = 3 + ) + axislegend(content(fig[i+1, 1]); unique = true, position = :lt) + end + +end # function + +surromethod = RandomFourier() +overplot_significance!(fig, surromethod) + +fig + +# ### More appropriate surrogates +# %% #src +# Using random Fourier surrogates does not make much sense in our application. +# Those surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# regarding a sharp transition at some point in the timeseries. +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = BlockShuffle(15) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "red") +fig + +# Here the results do not change because the permutation entropy is an exceptionally well +# suited indicator for this application scenario; But in other cases where things +# are not as clear, or data are contaminated with noise, or we have shorter data, +# choosing a more suitable +# surrogate generator may make the difference between a false positive or not. + +# ### Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be much less strict with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`QuantileSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined quantile of its timeseries. + +fig = plot_change_metrics() +flags = significant_transitions(results, QuantileSignificance() ) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + label = "quantile flags", color = Cycled(3), linestyle = :dash, linewidth = 3 + ) + axislegend(content(fig[i+1, 1]); unique = true, position = :lt) +end +fig diff --git a/previews/PR44/examples/tutorial.jl b/previews/PR44/examples/tutorial.jl new file mode 100644 index 00000000..27d4ca14 --- /dev/null +++ b/previews/PR44/examples/tutorial.jl @@ -0,0 +1,263 @@ +#= + +# Tutorial + +## [Workflow] (@id workflow) + +Computing transition indicators consists of the following steps: + +1. Doing any preprocessing of raw data first, such as detrending (_not part of TransitionsInTimeseries.jl_). This yields the **input timeseries**. +2. Estimating the timeseries of an indicator by sliding a window over the input timeseries. +3. Computing the changes of the indicator by sliding a window over its timeseries. +4. Generating many surrogates that preserve important statistical properties of the original timeseries. +5. Performing step 2 and 3 for the surrogate timeseries. +6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data. + +These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports. + +## [Tutorial -- Educational] (@id example_stepbystep) + +### Raw input data + +Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by: + +```math +\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t) +``` + +with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with [Makie](https://docs.makie.org/stable/)) such prototypical data to test some indicators can be done by simply running: +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_linear) +lines!(ax, t, x_nlinear) +ax.title = "raw data" +fig + +#= +### Preprocessing + +!!! note "Not part of TransitionsInTimeseries.jl" + Any timeseries preprocessing, such as the de-trending step we do here, + is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher. + + +The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1. +=# + +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +#= +At this point, `x_l_fluct` and `x_nl_fluct` are considered the **input timeseries**. + +!!! info "Detrending in Julia" + Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as [Loess.jl](https://github.com/JuliaStats/Loess.jl) or [DSP.jl](https://docs.juliadsp.org/latest/contents/). There the detrending step consists of subtracting the smoothed signal from the original one. + +### Indicator timeseries + +We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the **input timeseries**, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as [`ar1_whitenoise`](@ref): +=# + +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +## By mapping `last::Function` over a windowviewer of the time vector, +## we obtain the last time step of each window. +## This therefore only uses information from `k-width+1` to `k` at time step `k`. +## Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +#= +The lines plotted above are the **indicator timeseries**. + +### Change metric timeseries + +From here, we process the **indicator timeseries** to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the **change metric timeseries**. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a [`RidgeRegressionSlope`](@ref): +=# + +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + +#= +### Timeseries surrogates + +As expected from [Critical Slowing Down](@ref approaches), an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance. + +In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the [TimeseriesSurrogates.jl](https://github.com/JuliaDynamics/TimeseriesSurrogates.jl) Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that `TimeseriesSurrogates` is re-exported by `TransitionsInTimeseries`, so that you don't have to `using` both of them. + +To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries. +=# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) + +function gridfig(nrows, ncols) + fig = Figure() + axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false) + for j in 1:ncols, i in 1:nrows] + rowgap!(fig.layout, 10) + return fig, axs +end +fig, axs = gridfig(2, 1) +lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2)) +lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3)) +axs[1].title = "real signal vs. surrogate(s)" + +## compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2)) +lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3)) +axislegend() +axs[2].title = "change metric" + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +### Quantifying significance + +To quantify the significance of the values of the **change metric timeseries** we perform a standard surrogate test by computing the [p-value](https://en.wikipedia.org/wiki/P-value) w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically `p<0.05`) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time: +=# + +n_surrogates = 1_000 +fig, axs = gridfig(2, 2) +axs[1].title = "linear" +axs[2].title = "nonlinear" + +for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + ## Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change) # ; color = Cycled(j) + lines!(axsig, t_change, pval) # ; color = Cycled(j+2) +end + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar. + +Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section. + +## [Tutorial -- TransitionsInTimeseries.jl] (@id example_fastforward) + +TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go. + +The interface is simple, and directly parallelizes the [Workflow](@ref). It is based on the creation of a [`TransitionsSurrogatesConfig`](@ref), which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate. + +The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +## input timeseries and time +input = x_nl_fluct = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(t, input) +ax.title = "input timeseries" +fig + +#= +To perform all of the above analysis we follow a 2-step process. + +Step 1, we decide what indicators and change metrics to use in [`WindowedIndicatorConfig`](@ref) and apply those via +a sliding window to the input timeseries using [`transition_metrics`](@ref). +=# + +## These indicators are suitable for Critical Slowing Down +indicators = (var, ar1_whitenoise) + +## use the ridge regression slope for both indicators +change_metrics = RidgeRegressionSlope() + +## choices go into a configuration struct +config = WindowedIndicatorConfig(indicators, change_metrics; + width_ind = 400, width_cha = 30, whichtime = last) + +## choices are processed +results = transition_metrics(config, input, t) + +#= +From `result` we can plot the change metric timeseries: +=# + +fig, axs = gridfig(3, 1) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, results.x_change[:, 1]; + label = "var slopes", color = Cycled(3)) +scatter!(axs[3], results.t_change, results.x_change[:, 2]; + label = "ar1 slopes", color = Cycled(4)) +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +Step 2 is to estimate significance using [`SurrogatesConfig`](@ref) +and the function [`estimate_significance!`](@ref). +=# + +sigconfig = SurrogatesConfig(n = 1000, tail = :right) +signif = estimate_significance(sigconfig, results) + +#= +We can now plot the p-values corresponding to each time series of the change metrics. From the `flags` we can additionally obtain the time points where _both_ indicators show significance, via a simple reduction: +=# + +fig, axs = gridfig(2, 1) +lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1)) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 1]; + label = "var p-values", color = Cycled(3)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 2]; + label = "ar1 p-values", color = Cycled(4)) + +flagsboth = vec(reduce(&, signif.flags; dims = 2)) +vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1)) + +[axislegend(ax) for ax in axs] +[xlims!(ax, 0, 50) for ax in axs] +fig \ No newline at end of file diff --git a/previews/PR44/examples/tutorial/index.html b/previews/PR44/examples/tutorial/index.html new file mode 100644 index 00000000..3df77dec --- /dev/null +++ b/previews/PR44/examples/tutorial/index.html @@ -0,0 +1,140 @@ + +Tutorial · TransitionsInTimeseries.jl
                  Edit on GitHub

                  Tutorial

                  Workflow

                  Computing transition indicators consists of the following steps:

                  1. Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                  2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                  3. Computing the changes of the indicator by sliding a window over its timeseries.
                  4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                  5. Performing step 2 and 3 for the surrogate timeseries.
                  6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                  These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                  Tutorial – Educational

                  Raw input data

                  Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                  \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                  with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                  using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig

                  Preprocessing

                  Not part of TransitionsInTimeseries.jl

                  Any timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                  The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                  x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                  At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                  Detrending in Julia

                  Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                  Indicator timeseries

                  We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                  indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector,
+# we obtain the last time step of each window.
+# This therefore only uses information from `k-width+1` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                  The lines plotted above are the indicator timeseries.

                  Change metric timeseries

                  From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                  change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                  Timeseries surrogates

                  As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                  In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                  To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                  # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+
+function gridfig(nrows, ncols)
+    fig = Figure()
+    axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)
+        for j in 1:ncols, i in 1:nrows]
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+fig, axs = gridfig(2, 1)
+lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))
+lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))
+axs[1].title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2))
+lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3))
+axislegend()
+axs[2].title = "change metric"
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                  Quantifying significance

                  To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                  n_surrogates = 1_000
+fig, axs = gridfig(2, 2)
+axs[1].title = "linear"
+axs[2].title = "nonlinear"
+
+for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change)   # ; color = Cycled(j)
+    lines!(axsig, t_change, pval)       # ; color = Cycled(j+2)
+end
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                  As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                  Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                  Tutorial – TransitionsInTimeseries.jl

                  TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                  The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

                  The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

                  using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig

                  To perform all of the above analysis we follow a 2-step process.

                  Step 1, we decide what indicators and change metrics to use in WindowedIndicatorConfig and apply those via a sliding window to the input timeseries using transition_metrics.

                  # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = RidgeRegressionSlope()
+
+# choices go into a configuration struct
+config = WindowedIndicatorConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last)
+
+# choices are processed
+results = transition_metrics(config, input, t)
                  WindowedIndicatorResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                  From result we can plot the change metric timeseries:

                  fig, axs = gridfig(3, 1)
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, results.x_change[:, 1];
+    label = "var slopes", color = Cycled(3))
+scatter!(axs[3], results.t_change, results.x_change[:, 2];
+    label = "ar1 slopes", color = Cycled(4))
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                  Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.

                  sigconfig = SurrogatesConfig(n = 1000, tail = :right)
+signif = estimate_significance(sigconfig, results)
                  SurrogatesSignificance(SurrogatesConfig{RandomFourier, Symbol, Random.TaskLocalRNG}(RandomFourier(true), 1000, :right, Random.TaskLocalRNG(), 0.05, false), [0.511 0.617; 0.565 0.653; … ; 0.804 0.495; 0.754 0.507], Bool[0 0; 0 0; … ; 0 0; 0 0])

                  We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:

                  fig, axs = gridfig(2, 1)
+lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1))
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 1];
+    label = "var p-values", color = Cycled(3))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 2];
+    label = "ar1 p-values", color = Cycled(4))
+
+flagsboth = vec(reduce(&, signif.flags; dims = 2))
+vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1))
+
+[axislegend(ax) for ax in axs]
+[xlims!(ax, 0, 50) for ax in axs]
+fig
                  diff --git a/previews/PR44/index.html b/previews/PR44/index.html new file mode 100644 index 00000000..96a30878 --- /dev/null +++ b/previews/PR44/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
                  Edit on GitHub

                  TransitionsInTimeseries.jl

                  TransitionsInTimeseries.jl

                  TransitionsInTimeseries — Module

                  TransitionsInTimeseries.jl

                  CI codecov Package Downloads

                  A Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                  This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

                  add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

                  All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                  source
                  Star us on GitHub!

                  If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                  Content

                  Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                  • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                  • Makes the surrogate analysis to test for significance under the hub.
                  • Can be easily extended by any user without touching the source code.
                  • Reduces the programming overhead for any researcher willing to benchmark new methods.
                  • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                  • Increases trustworthiness thanks to a large test suite.
                  Similar projects

                  An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                  Approaches

                  Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                  diff --git a/previews/PR44/search/index.html b/previews/PR44/search/index.html new file mode 100644 index 00000000..6c43df97 --- /dev/null +++ b/previews/PR44/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

                  Loading search...

                    diff --git a/previews/PR44/search_index.js b/previews/PR44/search_index.js new file mode 100644 index 00000000..b2091c7c --- /dev/null +++ b/previews/PR44/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowedIndicatorConfig\ntransition_metrics\nWindowedIndicatorResults","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowedIndicatorConfig","page":"API","title":"TransitionsInTimeseries.WindowedIndicatorConfig","text":"WindowedIndicatorConfig(indicators, change_metrics; kwargs...) → config\n\nA configuration struct for TransitionsInTimeseries.jl that collects what indicators and corresponding metrics to use in the transitions_analysis.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in transitions_analysis using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.transition_metrics","page":"API","title":"TransitionsInTimeseries.transition_metrics","text":"transition_metrics(config::WindowedIndicatorConfig, x [,t]) → output\n\nEstimate possible transitions for input timeseries x using a sliding window approach as described by config:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nIf t (the time vector of x), is not provided, it is assumed t = eachindex(x).\n\nReturn the output as WindowedIndicatorResults which can be given to estimate_significance! to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.WindowedIndicatorResults","page":"API","title":"TransitionsInTimeseries.WindowedIndicatorResults","text":"WindowedIndicatorResults\n\nA struct containing the output of transition_metrics used with WindowedIndicatorConfig. It can be used for further analysis, visualization, or given to estimate_significance!.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nwim::WindowedIndicatorConfig, used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"estimate_significance\nSignificanceConfig\nSurrogatesConfig\nTransitionsSignificance\nSurrogatesSignificance\nQuantileSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.estimate_significance","page":"API","title":"TransitionsInTimeseries.estimate_significance","text":"estimate_significance(sigconfig::SignificanceConfig, res::WindowedIndicatorResults)\n\nEstimate the significance of the transition metrics stored in res by using the method described by sigconfig and return the results in TransitionsSignificance.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.SignificanceConfig","page":"API","title":"TransitionsInTimeseries.SignificanceConfig","text":"SignificanceConfig\n\nSupertype used to test for significance in estimate_significance. Valid subtypes are:\n\nSurrogatesConfig.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesConfig","page":"API","title":"TransitionsInTimeseries.SurrogatesConfig","text":"SurrogatesConfig <: SignificanceConfig\nSurrogatesConfig(; surrogate = RandomFourier(), n = 1_000, tail = :both, rng)\n\nA configuration struct for significance testing estimate_significance using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1_000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\ndetrend_surro = false: Boolean specifying whether the surrogates are to be\n\ndetrended by a linear regression. This is sometimes performed in the literature but seldomly impacts the results in a significant way, since the surrogates of the residual should already be largely free of trend.\n\nDescription\n\nWhen used with WindowedIndicatorResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance, which results in flags. These results are then stored in SurrogatesSignificance.\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowedIndicatorResults.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.TransitionsSignificance","page":"API","title":"TransitionsInTimeseries.TransitionsSignificance","text":"TransitionsSignificance\n\nSupertype used to store the results of estimate_significance based on a SignificanceConfig. Valid subtypes are:\n\nSurrogatesSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance\n\nA struct containing the results of estimate_significance based on a SurrogatesConfig, i.e. the p-values and their associated flags. The former gives a continuous value between 0 and 1, with 0 denoting an extremely unlikely and therefore probably significant behavior of the original time series compared to the ensemble of surrogates. The latter is a Boolean matrix which contains true wherever the p-values are below the threshold defined in SurrogatesConfig. Both signif.p_values and signif.flags have the same size as res.x_change, with signif::SurrogatesSignificance and res::WindowedIndicatorResults.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :right) <: TransitionsSignificance\n\nA configuration struct for significance testing significant_transitions. When used with WindowedIndicatorResults, significance is estimated as by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient θ of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:","category":"page"},{"location":"api/","page":"API","title":"API","text":"function permutation_entropy(; m = 3, τ = 1)\n est = SymbolicPermutation(; m, τ)\n return x -> entropy_normalized(est, x)\nend","category":"page"},{"location":"api/","page":"API","title":"API","text":"permutation_entropy\nentropy","category":"page"},{"location":"api/#TransitionsInTimeseries.permutation_entropy","page":"API","title":"TransitionsInTimeseries.permutation_entropy","text":"permutation_entropy(; m = 3, τ = 1) → f\n\nReturn a function that given timeseries x it computes the normalized permutation entropy of order m with time delay τ.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.entropy","page":"API","title":"StatsBase.entropy","text":"entropy(p, [b])\n\nCompute the entropy of a collection of probabilities p, optionally specifying a real number b such that the entropy is scaled by 1/log(b). Elements with probability 0 or 1 add 0 to the entropy.\n\n\n\n\n\n","category":"function"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length.","category":"page"},{"location":"api/","page":"API","title":"API","text":"TODO: Here explain how to use precomputable functions","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"EditURL = \"do-events.jl\"","category":"page"},{"location":"examples/do-events/#Dansgaard-Oescher-events","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"The delta^18O time series of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching to 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in [Boers2018] and we here try to reproduce Figure 2.d-f.","category":"page"},{"location":"examples/do-events/#Preprocessing-NGRIP","page":"Dansgaard-Oescher events","title":"Preprocessing NGRIP","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"Over this example, it will appear that the convenience of TransitionsInTimeseries to leads the bulk of the code to be written for plotting and preprocessing. The latter consists in various steps i = lbrace 123 rbrace:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"Load the data, reverse and offset it to have time vector = time before 2000 AD.\nFilter non-unique points in time and sort the data.\nRegrid the data from uneven to even sampling.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"The time and delta^18O vectors resulting from step i are respectively called t_i and x_i. The final preprocessing step consists in obtaining a residual r, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"using DelimitedFiles, Downloads, DSP, BSplineKit, Loess\n\nfunction load_ngrip()\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP.csv\")\n data, labels = readdlm(tmp, header = true)\n return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors\nend\n\nuniqueidx(v) = unique(i -> v[i], eachindex(v))\nfunction keep_unique(t, x)\n unique_idx = uniqueidx(t)\n return t[unique_idx], x[unique_idx]\nend\n\nfunction sort_timeseries!(t, x)\n p = sortperm(t)\n permute!(t, p)\n permute!(x, p)\n return nothing\nend\n\nfunction regrid2evensampling(t, x, dt)\n itp = BSplineKit.interpolate(t, x, BSplineOrder(4))\n tspan = (ceil(minimum(t)), floor(maximum(t)))\n t_even = collect(tspan[1]:dt:tspan[2])\n x_even = itp.(t_even)\n return t_even, x_even\nend\n\nfunction chebyshev_filter(t, x, fcutoff)\n ii = 10 # Chebyshev filtering requires to prune first points of time series.\n responsetype = Highpass(fcutoff, fs = 1/dt)\n designmethod = Chebyshev1(8, 0.05)\n r = filt(digitalfilter(responsetype, designmethod), x)\n xtrend = x - r\n return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]\nend\n\ndt, fcutoff = 5.0, 0.95*0.01 # dt = 5 yr and cutoff ≃ 0.01 yr^-1 as in (Boers 2018)\nt1, x1 = load_ngrip()\nt2, x2 = keep_unique(t1, x1)\nsort_timeseries!(t2, x2)\nt3, x3 = regrid2evensampling(t2, x2, dt)\nt, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"Let's now go to the last preprocessing steps and visualize our data in what will become our main figure. To keep the same approach as in [Boers2018], we hand-code the transition times and highlight them by purple vertical lines:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"using CairoMakie\n\nfunction loess_filter(t, x; span = 0.005)\n loessmodel = loess(t, x, span = span)\n xtrend = Loess.predict(loessmodel, t)\n r = x - xtrend\n return t, x, xtrend, r\nend\n\nfunction kyr_xticks(tticks_yr)\n tticks_kyr = [\"$t\" for t in Int.(tticks_yr ./ 1e3)]\n return (tticks_yr, tticks_kyr)\nend\n\nfunction plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)\n fig = Figure(resolution = (1600, 1200), fontsize = 24)\n\n # Original time series with transition marked by vertical lines\n ax1 = Axis(fig[1, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"$\\delta^{18}$O (permil)\",\n xaxisposition = :top, xticks = xticks)\n lines!(ax1, traw, xraw, color = (:gray70, 0.5))\n lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)\n vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)\n\n # Residual time series\n ax2 = Axis(fig[2, 1], ylabel = L\"Residual $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n lines!(ax2, t, r, color = :gray50, linewidth = 1)\n\n # Axes for variance and AC1 time series\n ax3 = Axis(fig[3, 1], ylabel = L\"Variance $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n ax4 = Axis(fig[4, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"Lag-1 autocor. $\\,$\",\n xticks = xticks)\n\n axs = [ax1, ax2, ax3, ax4]\n [xlims!(ax, xlims) for ax in axs]\n ylims!(axs[1], (-48, -34))\n rowgap!(fig.layout, 10)\n return fig, axs\nend\n\nxlims = (-60e3, -10e3)\nxticks = kyr_xticks(-60e3:5e3:5e3)\nt_transitions = [-59.5e3, -58.2e3, -55.8e3, -54.3e3, -49.35e3, -46.9e3, -43.45e3,\n -41.5e3, -40.2e3, -38.25e3, -35.5e3, -33.8e3, -32.55e3, -28.95e3,\n -27.85e3, -23.5e3, -14.7e3, -11.7e3]\ntloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization\n\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_transitions, xlims, xticks)\nfig","category":"page"},{"location":"examples/do-events/#Hindcast-on-NGRIP-data","page":"Dansgaard-Oescher events","title":"Hindcast on NGRIP data","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"As one can see, there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries to study the evolution, measured by the ridge-regression slope, of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including [Boers2018], the CSD analysis is performed over segments (sometimes only one) of the time series, such that a significance value is obtained for each segment. Dealing with segments can be easily done in TransitionsInTimeseries and is demonstrated here:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"using TransitionsInTimeseries, StatsBase\nusing Random: Xoshiro\n\nac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase\nindicators = (var, ac1)\nchange_metrics = RidgeRegressionSlope()\nopts = [(color = Cycled(2), linewidth = 3), # plotting options\n (color = :orange, linewidth = 3, linestyle = :dash)]\n\nfunction perform_segment_analysis(t, r, indicators, change_metrics, itime,\n dt, n, t_transitions, margins)\n\n # Initialize results over segment and indicator dimensions\n pvalues = fill(Inf, length(t_transitions), length(indicators))\n indicator_results = [fill(Inf, 3, 3) for t in t_transitions]\n\n for i in eachindex(t_transitions)\n # Select the correct segment limits\n if i == 1\n t_start = first(t)\n else\n t_start = t_transitions[i-1] + margins[1]\n end\n t_end = t_transitions[i] - margins[2]\n i_start, i_end = argmin(abs.(t .- t_start)), argmin(abs.(t .- t_end))\n tseg, rseg = t[i_start:i_end], r[i_start:i_end]\n sigconfig = SurrogatesConfig(n = n, tail = :right, rng = Xoshiro(27))\n\n if last(tseg) - first(tseg) > itime + 20.0 # only analyze if segment long enough\n # Compute the significance of the transition metrics for the chosen segment\n t_indicator = windowmap(last, tseg; width = Int(itime ÷ dt))\n segconfig = WindowedIndicatorConfig(indicators, change_metrics; whichtime = last,\n width_ind = Int(itime ÷ dt), width_cha = length(t_indicator))\n segresults = transition_metrics(segconfig, rseg, tseg)\n segsignif = estimate_significance(sigconfig, segresults)\n\n # Populate the pre-allocated arrays with the results\n pvalues[i, :] .= segsignif.pvalues[1, :]\n indicator_results[i] = hcat(segresults.t_indicator, segresults.x_indicator)\n end\n end\n return pvalues, indicator_results\nend\n\nfunction plot_segment_analysis!(axs, pvalues, t_transitions, indicator_results, margins)\n for i in eachindex(indicator_results) # loop over the segments\n # Unpack indicator results\n tind = indicator_results[i][:, 1]\n ind = indicator_results[i][:, 2:end]\n\n for j in axes(pvalues, 2) # loop over the indicators\n if !isinf(pvalues[i, j]) # only plot if enough data points for analysis\n # Plot indicator time series and its linear regression\n lines!(axs[j+2], tind, ind[:, j], color = Cycled(1))\n m, p = ridgematrix(tind, 0.0) * ind[:, j]\n if pvalues[i, j] < 0.05\n vlines!(axs[1], t_transitions[i] - margins[2]; opts[j]...)\n vlines!(axs[j+2], t_transitions[i] - margins[2]; opts[j]...)\n lines!(axs[j+2], tind, m .* tind .+ p, color = :gray10, linewidth = 3)\n else\n lines!(axs[j+2], tind, m .* tind .+ p, color = :gray10, linewidth = 3,\n linestyle = :dash)\n end\n end\n end\n end\n return nothing\nend\n\nmargins = [200, 200] # avoid the inclusion of transition data points in the segments\npvalues, indicator_results = perform_segment_analysis(t, r,\n indicators, change_metrics, 200.0, dt, 1_000, t_transitions, margins)\nplot_segment_analysis!(axs, pvalues, t_transitions, indicator_results, margins)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"In [Boers2018], 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. Here we respectively find 10/16 true positives for the variance and 4/16 for AC1. The mismatch between [Boers2018] and the results shown above clearly points out that packages like TransitionsInTimeseries are wishful for research to be reproducible.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"Given that the NGRIP data is sparse, noisy, and presents 16 transitions in total, it appears that the method generates a reasonable rate of true positives, but...","category":"page"},{"location":"examples/do-events/#Limitations-of-hindcast","page":"Dansgaard-Oescher events","title":"Limitations of hindcast","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"Finding transition indicators by defining segments, as done above, is arguably misleading when it comes to an operational prediction task. In fact, one does not check for false positives since the analysis is always performed upto time steps shortly before the transition. To make a brief, albeit incomplete check, one can stop the analysis much before the transition and thus check whether CSD indicators would forecast a transition although there is none ahead.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"early_margins = [200, 700] # take \"too early\" end margin to check for false positives\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_transitions, xlims, xticks)\npvalues, indicator_results = perform_segment_analysis(t, r,\n indicators, change_metrics, 200.0, dt, 1_000, t_transitions, early_margins)\nplot_segment_analysis!(axs, pvalues, t_transitions, indicator_results, early_margins)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"From 16 predictions which should all be negative, 10 of them are positive for the variance and 3 are positive for AC1. This clearly points out that generating a reasonable amount of true positives comes here at the expense of generating many false positives. We draw attention upon the fact that checking for false positives is too seldomly performed in literature! This does not mean that the method are incorrect but rather that the NGRIP data might be too much of a challenge for a CSD analysis. This is not surprising since the delta^18O time series is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. Meh. Is the situation hopeless? Not completely, as we will see in the next section.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"info: Future improvement\nSupporting the computations for uneven time series is a planned improvement of TransitionsInTimeseries. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.","category":"page"},{"location":"examples/do-events/#Hindcasting-simulated-DO-events","page":"Dansgaard-Oescher events","title":"Hindcasting simulated DO-events","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"In CLIMBER-X[Willeit2022], an Earth Model of Intermediate Complexity (EMIC), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. Unlike the segment analysis as the one performed above, the analysis fully relying on sliding windows (as introduced in the Tutorial) is a way to generate true positives while simultaneously checking for false positives, since transition metrics are computed for (almost) all time steps. We run this analysis over two exemplary simulation outputs:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"opts = [(color = (:orange, 0.1), linewidth = 3),\n (color = Cycled(2), linewidth = 3, linestyle = :dash)]\n\nfunction perform_sliding_analysis(t, r, indicators, change_metrics, itime, ctime,\n istride, cstride, dt, n)\n config = WindowedIndicatorConfig(indicators, change_metrics; whichtime = last,\n width_ind = Int(itime ÷ dt), stride_ind = istride,\n width_cha = Int(ctime ÷ dt), stride_cha = cstride)\n results = transition_metrics(config, r, t)\n sigconfig = SurrogatesConfig(n = n, tail = :right)\n signif = estimate_significance(sigconfig, results)\n return signif.pvalues, results\nend\n\nfunction plot_sliding_analysis!(axs, pvalues, results, threshold)\n for j in axes(pvalues, 2)\n vlines!(axs[1], results.t_change[pvalues[:, j] .< threshold]; opts[j]...)\n lines!(axs[2+j], results.t_indicator, results.x_indicator[:, j], color = Cycled(1))\n vlines!(axs[2+j], results.t_change[pvalues[:, j] .< threshold]; opts[j]...)\n end\n return nothing\nend\n\nt_transitions = [[1850, 2970, 3970, 5070, 5810, 7050, 8050], [3500, 4400, 5790, 7200, 8140]]\nfigvec = Figure[]\nfor i in 1:2\n # Download the data and perform loess filtering on it\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\" *\n \"master/timeseries/climberx-do$(i)-omaxa.csv\")\n data = readdlm(tmp)\n tcx, xcx = data[1, :], data[2, :]\n t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)\n\n # Initialize figure\n xlims = (0, last(tcx))\n xticks = kyr_xticks(xlims[1]:1e3:xlims[2])\n fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[i], xlims, xticks)\n ylims!(axs[1], (5, 40))\n axs[1].ylabel = L\"Max. Atlantic overturning (Sv) $\\,$\"\n\n # Run sliding analysis and update figure with results\n dt = mean(diff(tcx))\n pvalues, results = perform_sliding_analysis(t, r, indicators, change_metrics,\n 500.0, 20.0, 1, 1, dt, 1_000)\n plot_sliding_analysis!(axs, pvalues, results, 0.01)\n vlines!(axs[1], t_transitions[i], color = Cycled(1), linewidth = 3)\n push!(figvec, fig)\nend\nfigvec[1]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"We here notice that transitions are always preceeded (early enough but not too early) by a significant increase of AC1, sometimes accompanied by the variance. Diagnostics seem to be very reliable, since all transitions lead to both indicators showing significant increases, synchronously and/or subsequently to the transition. False positives continue to arise, however with much lower ratio than on the NGRIP data. It seems like clean data already allows much better results! To make sure we were not simply lucky, let's look at another simulation:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"figvec[2]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"Things look equally good here! Assuming that these simulations capture the DO dynamics well, one can hope that higher resolution data with less noise allows to robustly predict and/or diagnose DO events. We here draw attention upon the fact that even dt = 1 mathrmyr is a relatively sparse sampling for a physical, simulated process displaying transitions with a quasi-period of T in 1000 1500 mathrmyr.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"[Boers2018]: Niklas Boers (2018): Early-warning signals for Dansgaard-Oeschger events in a high-resolution ice core record","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events","title":"Dansgaard-Oescher events","text":"[Willeit2022]: Matteo Willeit et al. (2022): The Earth system model CLIMBER-X v1.0 – Part 1: Climate model description and validation​​​​​​​​​​​​​​","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"EditURL = \"tutorial.jl\"","category":"page"},{"location":"examples/tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"examples/tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"examples/tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"examples/tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"examples/tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"examples/tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector,\n# we obtain the last time step of each window.\n# This therefore only uses information from `k-width+1` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"examples/tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"examples/tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\n\nfunction gridfig(nrows, ncols)\n fig = Figure()\n axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)\n for j in 1:ncols, i in 1:nrows]\n rowgap!(fig.layout, 10)\n return fig, axs\nend\nfig, axs = gridfig(2, 1)\nlines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))\nlines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))\naxs[1].title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nlines!(axs[2], t_change, change_nl, label = \"nonlin\", color = Cycled(2))\nlines!(axs[2], t_change, change_s, label = \"surrogate\", color = Cycled(3))\naxislegend()\naxs[2].title = \"change metric\"\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"examples/tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig, axs = gridfig(2, 2)\naxs[1].title = \"linear\"\naxs[2].title = \"nonlinear\"\n\nfor (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change) # ; color = Cycled(j)\n lines!(axsig, t_change, pval) # ; color = Cycled(j+2)\nend\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"examples/tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in WindowedIndicatorConfig and apply those via a sliding window to the input timeseries using transition_metrics.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = RidgeRegressionSlope()\n\n# choices go into a configuration struct\nconfig = WindowedIndicatorConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last)\n\n# choices are processed\nresults = transition_metrics(config, input, t)","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"From result we can plot the change metric timeseries:","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(3, 1)\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, results.x_change[:, 1];\n label = \"var slopes\", color = Cycled(3))\nscatter!(axs[3], results.t_change, results.x_change[:, 2];\n label = \"ar1 slopes\", color = Cycled(4))\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"sigconfig = SurrogatesConfig(n = 1000, tail = :right)\nsignif = estimate_significance(sigconfig, results)","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:","category":"page"},{"location":"examples/tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(2, 1)\nlines!(axs[1], vcat(0.0, t), x_nlinear; label = \"raw\", color = Cycled(1))\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 1];\n label = \"var p-values\", color = Cycled(3))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 2];\n label = \"ar1 p-values\", color = Cycled(4))\n\nflagsboth = vec(reduce(&, signif.flags; dims = 2))\nvlines!(axs[1], results.t_change[flagsboth]; label = \"flags\", color = (\"black\", 0.1))\n\n[axislegend(ax) for ax in axs]\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"}] +} diff --git a/previews/PR44/siteinfo.js b/previews/PR44/siteinfo.js new file mode 100644 index 00000000..3778f76e --- /dev/null +++ b/previews/PR44/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR44"; diff --git a/previews/PR45/api/index.html b/previews/PR45/api/index.html new file mode 100644 index 00000000..86beb372 --- /dev/null +++ b/previews/PR45/api/index.html @@ -0,0 +1,20 @@ + +API · TransitionsInTimeseries.jl
                    Edit on GitHub

                    API

                    Main analysis functions

                    TransitionsInTimeseries.WindowedIndicatorConfig — Type
                    WindowedIndicatorConfig(indicators, change_metrics; kwargs...) → config

                    A configuration struct for TransitionsInTimeseries.jl that collects what indicators and corresponding metrics to use in the estimate_indicator_changes.

                    indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                    Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.

                    Keyword arguments

                    • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.

                    • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.

                    • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:

                      • last: use the last timepoint of each window
                      • midpoint: use the mid timepoint of each time window
                      • first: use first timepoint of each window

                      In fact, the indicators time vector is computed simply via

                      t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)

                      so any other function of the time window may be given to extract the time point itself, such as mean or median.

                    • T = Float64: Element type of input timeseries to initialize some computations.

                    source
                    TransitionsInTimeseries.estimate_indicator_changes — Function
                    estimate_indicator_changes(config::WindowedIndicatorConfig, x [,t]) → output

                    Estimate possible transitions for input timeseries x using a sliding window approach as described by config:

                    1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                    2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                    If t (the time vector of x), is not provided, it is assumed t = eachindex(x).

                    Return the output as WindowedIndicatorResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                    source
                    TransitionsInTimeseries.WindowedIndicatorResults — Type
                    WindowedIndicatorResults

                    A struct containing the output of estimate_indicator_changes used with WindowedIndicatorConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                    It has the following fields that the user may access

                    • x: the input timeseries.

                    • t: the time vector of the input timeseries.

                    • x_indicator, the indicator timeseries (matrix with each column one indicator).

                    • t_indicator, the time vector of the indicator timeseries.

                    • x_change, the change metric timeseries (matrix with each column one change metric).

                    • t_change, the time vector of the change metric timeseries.

                    • wim::WindowedIndicatorConfig, used for the analysis.

                    source

                    Significance testing

                    TransitionsInTimeseries.significant_transitions — Function
                    significant_transitions(res::WindowedIndicatorResults, signif::TransitionsSignificance)

                    Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.

                    source
                    TransitionsInTimeseries.SurrogatesSignificance — Type
                    SurrogatesSignificance <: TransitionsSignificance
+SurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)

                    A configuration struct for significance testing significant_transitions using timeseries surrogates.

                    Keyword arguments

                    • surromethod = RandomFourier(): method to generate surrogates
                    • n = 1000: how many surrogates to generate
                    • rng = Random.default_rng(): random number generator for the surrogates
                    • p = 0.05: threshold for significance of the p-value
                    • tail = :both: tail type used, see below

                    Description

                    When used with WindowedIndicatorResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

                    The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowedIndicatorResults.

                    Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

                    source
                    TransitionsInTimeseries.QuantileSignificance — Type
                    QuantileSignificance(; p = 0.95, tail = :right) <: TransitionsSignificance

                    A configuration struct for significance testing significant_transitions. When used with WindowedIndicatorResults, significance is estimated as by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                    source

                    Indicators

                    Value distribution

                    Statistics.mean — Method
                    mean(itr)

                    Compute the mean of all elements in a collection.

                    Note

                    If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

                    Examples

                    julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
                    StatsBase.skewness — Function
                    skewness(v, [wv::AbstractWeights], m=mean(v))

                    Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                    StatsBase.kurtosis — Function
                    kurtosis(v, [wv::AbstractWeights], m=mean(v))

                    Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                    Critical Slowing Down

                    Statistics.var — Method
                    var(itr; corrected::Bool=true, mean=nothing[, dims])

                    Compute the sample variance of collection itr.

                    The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

                    If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

                    A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

                    Note

                    If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

                    TransitionsInTimeseries.ar1_whitenoise — Function
                    ar1_whitenoise(x::AbstractVector)

                    Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

                    \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                    source

                    Spectrum

                    TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                    LowfreqPowerSpectrum(; q_lofreq = 0.1)

                    Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                    lfps = precompute( LowfreqPowerSpectrum() )

                    Keyword arguments:

                    • q_lofreq: a number between 0 and 1 that characterises which portion of the

                    frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                    source

                    Nonlinear dynamics

                    Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:

                    function permutation_entropy(; m = 3, τ = 1)
+    est = SymbolicPermutation(; m, τ)
+    return x -> entropy_normalized(est, x)
+end
                    StatsBase.entropy — Function
                    entropy(p, [b])

                    Compute the entropy of a collection of probabilities p, optionally specifying a real number b such that the entropy is scaled by 1/log(b). Elements with probability 0 or 1 add 0 to the entropy.

                    Change metrics

                    Slope

                    TransitionsInTimeseries.kendalltau — Function
                    kendalltau(x::AbstractVector)

                    Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                    source
                    TransitionsInTimeseries.spearman — Function
                    spearman(x::AbstractVector)

                    Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                    source

                    Value distribution differences

                    TransitionsInTimeseries.difference_of_means — Function
                    difference_of_means(x::AbstractArray)

                    Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                    # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                    difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                    source

                    Make your own indicator/metric!

                    The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                    There are situations where you may optimize such a function based on knowledge of input x type and length.

                    TODO: Here explain how to use precomputable functions

                    Missing docstring.

                    Missing docstring for precompute. Check Documenter's build log for details.

                    Surrogates

                    For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                    Sliding windows

                    TransitionsInTimeseries.WindowViewer — Type
                    WindowViewer(x; width, stride)

                    Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                    If not given, the keywords width, stride are taken as default_window_width(x) and 1.

                    source
                    TransitionsInTimeseries.windowmap — Function
                    windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                    A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                    source

                    Load data

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+ } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR45/assets/search.js b/previews/PR45/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR45/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
                  • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR45/assets/themes/documenter-dark.css b/previews/PR45/assets/themes/documenter-dark.css 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rgba(255,255,255,0.25)}html.theme--documenter-dark .button.is-white:active,html.theme--documenter-dark .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white{background-color:#fff;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark 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.button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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rgba(245,245,245,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#f5f5f5;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:#292929}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#2f2f2f;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,54,54,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#292929;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#e8e8e8}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#4eb5de;border-color:#4eb5de;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #4eb5de #4eb5de !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#4eb5de;box-shadow:none;color:#4eb5de}html.theme--documenter-dark 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It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ### Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +logistic_rule(u, p, t) = @inbounds SVector(p[1]*u[1]*(1 - u[1])) +ds = DeterministicIteratedMap(logistic_rule, [0.5], [1.0]) + +r1 = 3.83 +r2 = 3.86 +N = 2000 +rs = range(r1, r2; length = N) +x = zeros(N) +for (i, r) in enumerate(rs) + set_parameter!(ds, 1, r) + step!(ds) + x[i] = current_state(ds)[1] +end + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ### Using a simpler change metric + +# Now, let's compute and various indicators and their changes, +# focusing on the fourth indicator, the permutation entropy. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries +indicators = (var, ar1_whitenoise, permutation_entropy(m = 4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as stride half the window width +metric = difference_of_means + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = WindowedIndicatorConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = estimate_indicator_changes(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + if i < 3 + hidexdecorations!(ax; grid = false) + else + ax.xlabel = "r (time)" + end + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ### Significance via random Fourier surrogates + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 1000, tail = [:both, :both, :right], surromethod + ) + flags = significant_transitions(results, signif) + + ## and also plot the flags with same color + for (i, indicator) in enumerate(indicators) + ## To make things visually clear, we will also plot some example surrogate + ## timeseries for each indicator and change metric pair + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surromethod) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric, p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1) + end + ## Plot the flags as vertical dashed lines + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = color, linestyle = :dash, linewidth = 3 + ) + end + ## add a title to the figure with how we estimate significance + content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod))) +end + +surromethod = RandomFourier() +overplot_surrogate_significance!(fig, surromethod) + +fig + +# ### More appropriate surrogates +# %% #src +# Using random Fourier surrogates does not make much sense in our application. +# Those surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# regarding a sharp transition at some point in the timeseries. +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = BlockShuffle(15) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "red") +fig + +# The results are better for the variance and AR1 indicators. +# For the permutation entropy the results do not change because it already is an +# exceptionally well +# suited indicator for this application scenario. But in other cases where things +# are not as clear, or data are contaminated with noise, or we have shorter data, +# choosing a more suitable +# surrogate generator may make the difference between a false positive or not. + +# ### Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be much less strict with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`QuantileSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined quantile of its timeseries. + +fig = plot_change_metrics() +flags = significant_transitions(results, QuantileSignificance()) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = Cycled(3), linestyle = :dash, linewidth = 3 + ) +end +content(fig[1, 1]).title = "significance from quantile" +fig diff --git a/previews/PR45/examples/index.html b/previews/PR45/examples/index.html new file mode 100644 index 00000000..3023e40a --- /dev/null +++ b/previews/PR45/examples/index.html @@ -0,0 +1,100 @@ + +Examples for TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
                    Edit on GitHub

                    Examples for TransitionsInTimeseries.jl

                    Permutation entropy for dynamic regime changes

                    Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.

                    This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.

                    Logistic map timeseries

                    A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map

                    using DynamicalSystemsBase
+using CairoMakie
+
+logistic_rule(u, p, t) = @inbounds SVector(p[1]*u[1]*(1 - u[1]))
+ds = DeterministicIteratedMap(logistic_rule, [0.5], [1.0])
+
+r1 = 3.83
+r2 = 3.86
+N = 2000
+rs = range(r1, r2; length = N)
+x = zeros(N)
+for (i, r) in enumerate(rs)
+    set_parameter!(ds, 1, r)
+    step!(ds)
+    x[i] = current_state(ds)[1]
+end

                    Plot it, using as time the parameter value (they coincide)

                    fig, ax = lines(rs, x; linewidth = 0.5)
+ax.xlabel = "r (time)"
+ax.ylabel = "x"
+fig

                    In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.

                    Using a simpler change metric

                    Now, let's compute and various indicators and their changes, focusing on the fourth indicator, the permutation entropy. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.

                    using TransitionsInTimeseries
+indicators = (var, ar1_whitenoise, permutation_entropy(m = 4))
+indistrings = ("var", "ar1", "pe")
                    ("var", "ar1", "pe")

                    In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width

                    metric = difference_of_means
+
+width_ind = N÷100
+width_cha = 20
+stride_cha = 10
+
+config = WindowedIndicatorConfig(indicators, metric;
+    width_ind, width_cha, stride_cha,
+)
+
+results = estimate_indicator_changes(config, x, rs)
                    WindowedIndicatorResults
+ input timeseries:              2000-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise, Symbol("#7")]
+ indicator (window, stride):    (20, 1)
+ change metrics:                [:difference_of_means]
+ change metric (window, stride): (20, 10)
+

                    Let's now plot the change metrics of the indicators

                    function plot_change_metrics()
+    fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),))
+    hidexdecorations!(ax; grid = false)
+    # plot all change metrics
+    for (i, c) in enumerate(eachcol(results.x_change))
+        ax, = scatterlines(fig[i+1, 1], results.t_change, c;
+            axis = (ylabel = indistrings[i],), label = "input"
+        )
+        if i < 3
+            hidexdecorations!(ax; grid = false)
+        else
+            ax.xlabel = "r (time)"
+        end
+    end
+    return fig
+end
+
+fig = plot_change_metrics()

                    We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)

                    Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.

                    Significance via random Fourier surrogates

                    One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.

                    Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!

                    surromethod = RandomFourier()
+
+# Define a function because we will re-use later
+function overplot_surrogate_significance!(fig, surromethod, color = "black")
+
+    signif = SurrogatesSignificance(;
+        n = 1000, tail = [:both, :both, :right], surromethod
+    )
+    flags = significant_transitions(results, signif)
+
+    # and also plot the flags with same color
+    for (i, indicator) in enumerate(indicators)
+        # To make things visually clear, we will also plot some example surrogate
+        # timeseries for each indicator and change metric pair
+        for _ in 1:10
+            s = TimeseriesSurrogates.surrogate(x, surromethod)
+            p = windowmap(indicator, s; width = width_ind)
+            q = windowmap(metric, p; width = width_cha, stride = stride_cha)
+            lines!(fig[i+1, 1], results.t_change, q;  color = (color, 0.2), linewidth = 1)
+        end
+        # Plot the flags as vertical dashed lines
+        vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+            color = color, linestyle = :dash, linewidth = 3
+        )
+    end
+    # add a title to the figure with how we estimate significance
+    content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod)))
+end
+
+surromethod = RandomFourier()
+overplot_surrogate_significance!(fig, surromethod)
+
+fig

                    More appropriate surrogates

                    Using random Fourier surrogates does not make much sense in our application. Those surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information regarding a sharp transition at some point in the timeseries. A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

                    surromethod = BlockShuffle(15)
+fig = plot_change_metrics()
+overplot_surrogate_significance!(fig, surromethod, "red")
+fig

                    The results are better for the variance and AR1 indicators. For the permutation entropy the results do not change because it already is an exceptionally well suited indicator for this application scenario. But in other cases where things are not as clear, or data are contaminated with noise, or we have shorter data, choosing a more suitable surrogate generator may make the difference between a false positive or not.

                    Simpler Significance

                    Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be much less strict with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster QuantileSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined quantile of its timeseries.

                    fig = plot_change_metrics()
+flags = significant_transitions(results, QuantileSignificance())
+
+# Plot the flags
+for (i, indicator) in enumerate(indicators)
+    vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+        color = Cycled(3), linestyle = :dash, linewidth = 3
+    )
+end
+content(fig[1, 1]).title = "significance from quantile"
+fig
                    diff --git a/previews/PR45/index.html b/previews/PR45/index.html new file mode 100644 index 00000000..b5826947 --- /dev/null +++ b/previews/PR45/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
                    Edit on GitHub

                    TransitionsInTimeseries.jl

                    TransitionsInTimeseries.jl

                    TransitionsInTimeseries — Module

                    TransitionsInTimeseries.jl

                    CI codecov Package Downloads

                    A Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                    This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

                    add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

                    All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                    source
                    Star us on GitHub!

                    If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                    Content

                    Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                    • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                    • Makes the surrogate analysis to test for significance under the hub.
                    • Can be easily extended by any user without touching the source code.
                    • Reduces the programming overhead for any researcher willing to benchmark new methods.
                    • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                    • Increases trustworthiness thanks to a large test suite.
                    Similar projects

                    An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                    Approaches

                    Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                    diff --git a/previews/PR45/search/index.html b/previews/PR45/search/index.html new file mode 100644 index 00000000..46479607 --- /dev/null +++ b/previews/PR45/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

                    Loading search...

                      diff --git a/previews/PR45/search_index.js b/previews/PR45/search_index.js new file mode 100644 index 00000000..8259a206 --- /dev/null +++ b/previews/PR45/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowedIndicatorConfig\nestimate_indicator_changes\nWindowedIndicatorResults","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowedIndicatorConfig","page":"API","title":"TransitionsInTimeseries.WindowedIndicatorConfig","text":"WindowedIndicatorConfig(indicators, change_metrics; kwargs...) → config\n\nA configuration struct for TransitionsInTimeseries.jl that collects what indicators and corresponding metrics to use in the estimate_indicator_changes.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.estimate_indicator_changes","page":"API","title":"TransitionsInTimeseries.estimate_indicator_changes","text":"estimate_indicator_changes(config::WindowedIndicatorConfig, x [,t]) → output\n\nEstimate possible transitions for input timeseries x using a sliding window approach as described by config:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nIf t (the time vector of x), is not provided, it is assumed t = eachindex(x).\n\nReturn the output as WindowedIndicatorResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.WindowedIndicatorResults","page":"API","title":"TransitionsInTimeseries.WindowedIndicatorResults","text":"WindowedIndicatorResults\n\nA struct containing the output of estimate_indicator_changes used with WindowedIndicatorConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nwim::WindowedIndicatorConfig, used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"significant_transitions\nTransitionsSignificance\nSurrogatesSignificance\nQuantileSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::WindowedIndicatorResults, signif::TransitionsSignificance)\n\nEstimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.TransitionsSignificance","page":"API","title":"TransitionsInTimeseries.TransitionsSignificance","text":"TransitionsSignificance\n\nSupertype used to test for significance in significant_transitions. Valid subtypes are:\n\nSurrogatesSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: TransitionsSignificance\nSurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)\n\nA configuration struct for significance testing significant_transitions using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\n\nDescription\n\nWhen used with WindowedIndicatorResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowedIndicatorResults.\n\nNote that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :right) <: TransitionsSignificance\n\nA configuration struct for significance testing significant_transitions. When used with WindowedIndicatorResults, significance is estimated as by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:","category":"page"},{"location":"api/","page":"API","title":"API","text":"function permutation_entropy(; m = 3, τ = 1)\n est = SymbolicPermutation(; m, τ)\n return x -> entropy_normalized(est, x)\nend","category":"page"},{"location":"api/","page":"API","title":"API","text":"permutation_entropy\nentropy","category":"page"},{"location":"api/#TransitionsInTimeseries.permutation_entropy","page":"API","title":"TransitionsInTimeseries.permutation_entropy","text":"permutation_entropy(; m = 3, τ = 1) → f\n\nReturn a function that given timeseries x it computes the normalized permutation entropy of order m with time delay τ.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.entropy","page":"API","title":"StatsBase.entropy","text":"entropy(p, [b])\n\nCompute the entropy of a collection of probabilities p, optionally specifying a real number b such that the entropy is scaled by 1/log(b). Elements with probability 0 or 1 add 0 to the entropy.\n\n\n\n\n\n","category":"function"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length.","category":"page"},{"location":"api/","page":"API","title":"API","text":"TODO: Here explain how to use precomputable functions","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"EditURL = \"examples.jl\"","category":"page"},{"location":"examples/#Examples-for-TransitionsInTimeseries.jl","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"examples/#Permutation-entropy-for-dynamic-regime-changes","page":"Examples for TransitionsInTimeseries.jl","title":"Permutation entropy for dynamic regime changes","text":"","category":"section"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.","category":"page"},{"location":"examples/#Logistic-map-timeseries","page":"Examples for TransitionsInTimeseries.jl","title":"Logistic map timeseries","text":"","category":"section"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"using DynamicalSystemsBase\nusing CairoMakie\n\nlogistic_rule(u, p, t) = @inbounds SVector(p[1]*u[1]*(1 - u[1]))\nds = DeterministicIteratedMap(logistic_rule, [0.5], [1.0])\n\nr1 = 3.83\nr2 = 3.86\nN = 2000\nrs = range(r1, r2; length = N)\nx = zeros(N)\nfor (i, r) in enumerate(rs)\n set_parameter!(ds, 1, r)\n step!(ds)\n x[i] = current_state(ds)[1]\nend","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"Plot it, using as time the parameter value (they coincide)","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"fig, ax = lines(rs, x; linewidth = 0.5)\nax.xlabel = \"r (time)\"\nax.ylabel = \"x\"\nfig","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.","category":"page"},{"location":"examples/#Using-a-simpler-change-metric","page":"Examples for TransitionsInTimeseries.jl","title":"Using a simpler change metric","text":"","category":"section"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"Now, let's compute and various indicators and their changes, focusing on the fourth indicator, the permutation entropy. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"using TransitionsInTimeseries\nindicators = (var, ar1_whitenoise, permutation_entropy(m = 4))\nindistrings = (\"var\", \"ar1\", \"pe\")","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"metric = difference_of_means\n\nwidth_ind = N÷100\nwidth_cha = 20\nstride_cha = 10\n\nconfig = WindowedIndicatorConfig(indicators, metric;\n width_ind, width_cha, stride_cha,\n)\n\nresults = estimate_indicator_changes(config, x, rs)","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"Let's now plot the change metrics of the indicators","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"function plot_change_metrics()\n fig, ax = lines(rs, x; axis = (ylabel = \"input\",), figure = (resolution = (600, 600),))\n hidexdecorations!(ax; grid = false)\n # plot all change metrics\n for (i, c) in enumerate(eachcol(results.x_change))\n ax, = scatterlines(fig[i+1, 1], results.t_change, c;\n axis = (ylabel = indistrings[i],), label = \"input\"\n )\n if i < 3\n hidexdecorations!(ax; grid = false)\n else\n ax.xlabel = \"r (time)\"\n end\n end\n return fig\nend\n\nfig = plot_change_metrics()","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.","category":"page"},{"location":"examples/#Significance-via-random-Fourier-surrogates","page":"Examples for TransitionsInTimeseries.jl","title":"Significance via random Fourier surrogates","text":"","category":"section"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"surromethod = RandomFourier()\n\n# Define a function because we will re-use later\nfunction overplot_surrogate_significance!(fig, surromethod, color = \"black\")\n\n signif = SurrogatesSignificance(;\n n = 1000, tail = [:both, :both, :right], surromethod\n )\n flags = significant_transitions(results, signif)\n\n # and also plot the flags with same color\n for (i, indicator) in enumerate(indicators)\n # To make things visually clear, we will also plot some example surrogate\n # timeseries for each indicator and change metric pair\n for _ in 1:10\n s = TimeseriesSurrogates.surrogate(x, surromethod)\n p = windowmap(indicator, s; width = width_ind)\n q = windowmap(metric, p; width = width_cha, stride = stride_cha)\n lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1)\n end\n # Plot the flags as vertical dashed lines\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = color, linestyle = :dash, linewidth = 3\n )\n end\n # add a title to the figure with how we estimate significance\n content(fig[1, 1]).title = \"surrogates: \"*string(nameof(typeof(surromethod)))\nend\n\nsurromethod = RandomFourier()\noverplot_surrogate_significance!(fig, surromethod)\n\nfig","category":"page"},{"location":"examples/#More-appropriate-surrogates","page":"Examples for TransitionsInTimeseries.jl","title":"More appropriate surrogates","text":"","category":"section"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"Using random Fourier surrogates does not make much sense in our application. Those surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information regarding a sharp transition at some point in the timeseries. A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"surromethod = BlockShuffle(15)\nfig = plot_change_metrics()\noverplot_surrogate_significance!(fig, surromethod, \"red\")\nfig","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"The results are better for the variance and AR1 indicators. For the permutation entropy the results do not change because it already is an exceptionally well suited indicator for this application scenario. But in other cases where things are not as clear, or data are contaminated with noise, or we have shorter data, choosing a more suitable surrogate generator may make the difference between a false positive or not.","category":"page"},{"location":"examples/#Simpler-Significance","page":"Examples for TransitionsInTimeseries.jl","title":"Simpler Significance","text":"","category":"section"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be much less strict with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster QuantileSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined quantile of its timeseries.","category":"page"},{"location":"examples/","page":"Examples for TransitionsInTimeseries.jl","title":"Examples for TransitionsInTimeseries.jl","text":"fig = plot_change_metrics()\nflags = significant_transitions(results, QuantileSignificance())\n\n# Plot the flags\nfor (i, indicator) in enumerate(indicators)\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = Cycled(3), linestyle = :dash, linewidth = 3\n )\nend\ncontent(fig[1, 1]).title = \"significance from quantile\"\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any pre-processing of raw data first such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_nlinear)\nlines!(ax, t, x_linear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window.\n# This therefore only uses information from `k-width` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\nfig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))\nlines!(ax, tfluct, s .- 0.05; color = Cycled(3))\nax.title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = \"nonlin\")\nlines!(ax, t_change, change_s; color = Cycled(3), label = \"surrogate\")\naxislegend()\nax.title = \"change metric\"\n\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig = Figure()\naxl = Axis(fig[1,1]; title = \"linear\")\naxnl = Axis(fig[1,2]; title = \"nonlinear\")\naxsigl = Axis(fig[2,1])\naxsignl = Axis(fig[2,2])\n\nfor (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change; color = Cycled(j))\n lines!(axsig, t_change, pval; color = Cycled(j+2))\nend\n\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a WindowedIndicatorConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl. First, let's load the timeseries again.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in WindowedIndicatorConfig and apply those via a sliding window to the input timeseries using estimate_indicator_changes.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = RidgeRegressionSlope()\n\n# choices go into a configuration struct\nconfig = WindowedIndicatorConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last\n)\n\n# choices are processed\nresults = estimate_indicator_changes(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From result we can plot the change metric timeseries","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, ax = lines(t, input; color = Cycled(2), label = \"input\")\naxpval, = scatter(fig[2,1], results.t_change, results.x_change[:, 1]; color = Cycled(3), label = \"var slopes\")\naxpval, = scatter(fig[3,1], results.t_change, results.x_change[:, 2]; color = Cycled(4), label = \"ar1 slopes\")","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesSignificance and the function significant_transitions.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = :both)\nflags = significant_transitions(results, signif)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"If we want, we can also plot the p-values corresponding to each timeseries change metric","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, ax = lines(t, input; color = Cycled(2), label = \"input\")\naxpval, = scatter(fig[2,1], results.t_change, signif.pvalues[:, 1]; color = Cycled(3), label = \"var p-values\")\nscatter!(axpval, results.t_change, signif.pvalues[:, 2]; color = Cycled(4), label = \"ar1 p-values\")\naxislegend(axpval)\nxlims!(ax, 0, 50)\nxlims!(axpval, 0, 50)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From the flags we can obtain the time points where both indicators show significance, via a simple reduction","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"flagsboth = vec(reduce(&, flags; dims = 2))\n\nvlines!(ax, results.t_change[flagsboth]; label = \"flags\", color = (\"black\", 0.1))\naxislegend(ax)\nfig","category":"page"}] +} diff --git a/previews/PR45/siteinfo.js b/previews/PR45/siteinfo.js new file mode 100644 index 00000000..dc8e641c --- /dev/null +++ b/previews/PR45/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR45"; diff --git a/previews/PR45/tutorial/index.html b/previews/PR45/tutorial/index.html new file mode 100644 index 00000000..d43c3e0f --- /dev/null +++ b/previews/PR45/tutorial/index.html @@ -0,0 +1,142 @@ + +Tutorial · TransitionsInTimeseries.jl
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                      Tutorial

                      Workflow

                      Computing transition indicators consists of the following steps:

                      1. Doing any pre-processing of raw data first such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                      2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                      3. Computing the changes of the indicator by sliding a window over its timeseries.
                      4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                      5. Performing step 2 and 3 for the surrogate timeseries.
                      6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                      These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                      Tutorial – Educational

                      Raw input data

                      Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                      \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                      with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                      using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_nlinear)
+lines!(ax, t, x_linear)
+ax.title = "raw data"
+fig

                      Preprocessing

                      Not part of TransitionsInTimeseries.jl

                      Any timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                      The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                      x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                      At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                      Detrending in Julia

                      Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                      Indicator timeseries

                      We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                      indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window.
+# This therefore only uses information from `k-width` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                      The lines plotted above are the indicator timeseries.

                      Change metric timeseries

                      From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                      change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                      Timeseries surrogates

                      As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                      In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                      To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                      # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))
+lines!(ax, tfluct, s .- 0.05; color = Cycled(3))
+ax.title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin")
+lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate")
+axislegend()
+ax.title = "change metric"
+
+fig

                      Quantifying significance

                      To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                      n_surrogates = 1_000
+fig = Figure()
+axl = Axis(fig[1,1]; title = "linear")
+axnl = Axis(fig[1,2]; title = "nonlinear")
+axsigl = Axis(fig[2,1])
+axsignl = Axis(fig[2,2])
+
+for (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change; color = Cycled(j))
+    lines!(axsig, t_change, pval; color = Cycled(j+2))
+end
+
+fig

                      As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                      Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                      Tutorial – TransitionsInTimeseries.jl

                      TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                      The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a WindowedIndicatorConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis.

                      The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl. First, let's load the timeseries again.

                      using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig

                      To perform all of the above analysis we follow a 2-step process.

                      Step 1, we decide what indicators and change metrics to use in WindowedIndicatorConfig and apply those via a sliding window to the input timeseries using estimate_indicator_changes.

                      # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = RidgeRegressionSlope()
+
+# choices go into a configuration struct
+config = WindowedIndicatorConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last
+)
+
+# choices are processed
+results = estimate_indicator_changes(config, input, t)
                      WindowedIndicatorResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                      From result we can plot the change metric timeseries

                      fig, ax = lines(t, input; color = Cycled(2), label = "input")
+axpval, = scatter(fig[2,1], results.t_change, results.x_change[:, 1]; color = Cycled(3), label = "var slopes")
+axpval, = scatter(fig[3,1], results.t_change, results.x_change[:, 2]; color = Cycled(4), label = "ar1 slopes")

                      Step 2 is to estimate significance using SurrogatesSignificance and the function significant_transitions.

                      signif = SurrogatesSignificance(n = 1000, tail = :both)
+flags = significant_transitions(results, signif)
                      2072×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ ⋮  
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0

                      If we want, we can also plot the p-values corresponding to each timeseries change metric

                      fig, ax = lines(t, input; color = Cycled(2), label = "input")
+axpval, = scatter(fig[2,1], results.t_change, signif.pvalues[:, 1]; color = Cycled(3), label = "var p-values")
+scatter!(axpval, results.t_change, signif.pvalues[:, 2]; color = Cycled(4), label = "ar1 p-values")
+axislegend(axpval)
+xlims!(ax, 0, 50)
+xlims!(axpval, 0, 50)

                      From the flags we can obtain the time points where both indicators show significance, via a simple reduction

                      flagsboth = vec(reduce(&, flags; dims = 2))
+
+vlines!(ax, results.t_change[flagsboth]; label = "flags", color = ("black", 0.1))
+axislegend(ax)
+fig
                      diff --git a/previews/PR45/tutorial_literate.jl b/previews/PR45/tutorial_literate.jl new file mode 100644 index 00000000..2f491843 --- /dev/null +++ b/previews/PR45/tutorial_literate.jl @@ -0,0 +1,140 @@ +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_nlinear) +lines!(ax, t, x_linear) +ax.title = "raw data" +fig + +# +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +# +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window. +# This therefore only uses information from `k-width` to `k` at time step `k`. +# Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +# +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + + +# + +# Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2)) +lines!(ax, tfluct, s .- 0.05; color = Cycled(3)) +ax.title = "real signal vs. surrogate(s)" + +# compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin") +lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate") +axislegend() +ax.title = "change metric" + +fig +# + + +n_surrogates = 1_000 +fig = Figure() +axl = Axis(fig[1,1]; title = "linear") +axnl = Axis(fig[1,2]; title = "nonlinear") +axsigl = Axis(fig[2,1]) +axsignl = Axis(fig[2,2]) + +for (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + # Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change; color = Cycled(j)) + lines!(axsig, t_change, pval; color = Cycled(j+2)) +end + +fig + +# %% +# Tutorial short + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_nl_fluct) +ax.title = "input timeseries" +fig + +# These indicators are suitable for Critical Slowing Down +indicators = [var, ar1_whitenoise] +indconfig = IndicatorsConfig(tfluct, last, indicators; width = 400) + + +# use the ridge regression slope for both indicators +change_metrics = [RidgeRegressionSlope()] +sigconfig = SignificanceConfig(indconfig, last, change_metrics; + width = 30, n_surrogates = 1000) + +# perform the full analysis +results = indicators_analysis(tfluct, x_nl_fluct, indconfig, sigconfig) + +# Plot the original timeseries vs. p-value time series +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2), label = "input") +axpval, = lines(fig[2,1], sigconfig.t_change, results.pval[:, 1]; color = Cycled(3), label = "p-value of var") +lines!(axpval, sigconfig.t_change, results.pval[:, 2]; color = Cycled(4), label = "p-value of ar1") +xlims!(ax, (0, 50)) +xlims!(axpval, (0, 50)) +axislegend(axpval) +fig + + +flags_indicators, flags_andicators = transition_flags(results, 0.05) +vlines!(ax, flags_andicators; label = "flags", color = Cycled(3), linestyle = :dash) +axislegend(ax) +fig \ No newline at end of file diff --git a/previews/PR46/api/index.html b/previews/PR46/api/index.html new file mode 100644 index 00000000..8138a6bb --- /dev/null +++ b/previews/PR46/api/index.html @@ -0,0 +1,20 @@ + +API · TransitionsInTimeseries.jl
                      Edit on GitHub

                      API

                      Main analysis functions

                      TransitionsInTimeseries.WindowedIndicatorConfig — Type
                      WindowedIndicatorConfig(indicators, change_metrics; kwargs...) → config

                      A configuration struct for TransitionsInTimeseries.jl that collects what indicators and corresponding metrics to use in the estimate_indicator_changes.

                      indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                      Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.

                      Keyword arguments

                      • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.

                      • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.

                      • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:

                        • last: use the last timepoint of each window
                        • midpoint: use the mid timepoint of each time window
                        • first: use first timepoint of each window

                        In fact, the indicators time vector is computed simply via

                        t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)

                        so any other function of the time window may be given to extract the time point itself, such as mean or median.

                      • T = Float64: Element type of input timeseries to initialize some computations.

                      source
                      TransitionsInTimeseries.estimate_indicator_changes — Function
                      estimate_indicator_changes(config::WindowedIndicatorConfig, x [,t]) → output

                      Estimate possible transitions for input timeseries x using a sliding window approach as described by config:

                      1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                      2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                      If t (the time vector of x), is not provided, it is assumed t = eachindex(x).

                      Return the output as WindowedIndicatorResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                      source
                      TransitionsInTimeseries.WindowedIndicatorResults — Type
                      WindowedIndicatorResults

                      A struct containing the output of estimate_indicator_changes used with WindowedIndicatorConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                      It has the following fields that the user may access

                      • x: the input timeseries.

                      • t: the time vector of the input timeseries.

                      • x_indicator, the indicator timeseries (matrix with each column one indicator).

                      • t_indicator, the time vector of the indicator timeseries.

                      • x_change, the change metric timeseries (matrix with each column one change metric).

                      • t_change, the time vector of the change metric timeseries.

                      • wim::WindowedIndicatorConfig, used for the analysis.

                      source

                      Significance testing

                      TransitionsInTimeseries.significant_transitions — Function
                      significant_transitions(res::WindowedIndicatorResults, signif::TransitionsSignificance)

                      Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.

                      source
                      TransitionsInTimeseries.SurrogatesSignificance — Type
                      SurrogatesSignificance <: TransitionsSignificance
+SurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)

                      A configuration struct for significance testing significant_transitions using timeseries surrogates.

                      Keyword arguments

                      • surromethod = RandomFourier(): method to generate surrogates
                      • n = 1000: how many surrogates to generate
                      • rng = Random.default_rng(): random number generator for the surrogates
                      • p = 0.05: threshold for significance of the p-value
                      • tail = :both: tail type used, see below

                      Description

                      When used with WindowedIndicatorResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

                      The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowedIndicatorResults.

                      Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

                      source
                      TransitionsInTimeseries.QuantileSignificance — Type
                      QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance

                      A configuration struct for significance testing significant_transitions. When used with WindowedIndicatorResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                      QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

                      source

                      Indicators

                      Value distribution

                      Statistics.mean — Method
                      mean(itr)

                      Compute the mean of all elements in a collection.

                      Note

                      If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

                      Examples

                      julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
                      StatsBase.skewness — Function
                      skewness(v, [wv::AbstractWeights], m=mean(v))

                      Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                      StatsBase.kurtosis — Function
                      kurtosis(v, [wv::AbstractWeights], m=mean(v))

                      Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                      Critical Slowing Down

                      Statistics.var — Method
                      var(itr; corrected::Bool=true, mean=nothing[, dims])

                      Compute the sample variance of collection itr.

                      The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

                      If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

                      A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

                      Note

                      If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

                      TransitionsInTimeseries.ar1_whitenoise — Function
                      ar1_whitenoise(x::AbstractVector)

                      Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

                      \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                      source

                      Spectrum

                      TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                      LowfreqPowerSpectrum(; q_lofreq = 0.1)

                      Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                      lfps = precompute( LowfreqPowerSpectrum() )

                      Keyword arguments:

                      • q_lofreq: a number between 0 and 1 that characterises which portion of the

                      frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                      source

                      Nonlinear dynamics

                      Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:

                      function permutation_entropy(; m = 3, τ = 1)
+    est = SymbolicPermutation(; m, τ)
+    return x -> entropy_normalized(est, x)
+end
                      StatsBase.entropy — Function
                      entropy(p, [b])

                      Compute the entropy of a collection of probabilities p, optionally specifying a real number b such that the entropy is scaled by 1/log(b). Elements with probability 0 or 1 add 0 to the entropy.

                      Change metrics

                      Slope

                      TransitionsInTimeseries.kendalltau — Function
                      kendalltau(x::AbstractVector)

                      Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                      source
                      TransitionsInTimeseries.spearman — Function
                      spearman(x::AbstractVector)

                      Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                      source

                      Value distribution differences

                      TransitionsInTimeseries.difference_of_means — Function
                      difference_of_means(x::AbstractArray)

                      Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                      # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                      difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                      source

                      Make your own indicator/metric!

                      The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                      There are situations where you may optimize such a function based on knowledge of input x type and length.

                      TODO: Here explain how to use precomputable functions

                      Missing docstring.

                      Missing docstring for precompute. Check Documenter's build log for details.

                      Surrogates

                      For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                      Sliding windows

                      TransitionsInTimeseries.WindowViewer — Type
                      WindowViewer(x; width, stride)

                      Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                      If not given, the keywords width, stride are taken as default_window_width(x) and 1.

                      source
                      TransitionsInTimeseries.windowmap — Function
                      windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                      A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                      source

                      Load data

                      diff --git a/previews/PR46/assets/documenter.js b/previews/PR46/assets/documenter.js new file mode 100644 index 00000000..6adfbbbf --- /dev/null +++ b/previews/PR46/assets/documenter.js @@ -0,0 +1,331 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fas", "fa-copy"); + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-times"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-times"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); + }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR46/assets/search.js b/previews/PR46/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR46/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
                    • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR46/assets/themes/documenter-dark.css 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kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,54,54,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#292929;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#e8e8e8}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#4eb5de;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#43b1dc;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus:not(:active),html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--documenter-dark .button.is-primary.is-focused:not(:active),html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(78,181,222,0.25)}html.theme--documenter-dark .button.is-primary:active,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-active,html.theme--documenter-dark .docstring>section>a.button.is-active.docs-sourcelink{background-color:#39acda;border-color:transparent;color:#fff}html.theme--documenter-dark 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.docstring>section>a.button.is-inverted.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;border-color:transparent;box-shadow:none;color:#4eb5de}html.theme--documenter-dark .button.is-primary.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-loading.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#4eb5de;color:#4eb5de}html.theme--documenter-dark .button.is-primary.is-outlined:hover,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#4eb5de;border-color:#4eb5de;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #4eb5de #4eb5de !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#4eb5de;box-shadow:none;color:#4eb5de}html.theme--documenter-dark 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0.125em rgba(42,215,230,0.25)}html.theme--documenter-dark .button.is-link:active,html.theme--documenter-dark .button.is-link.is-active{background-color:#1acddc;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-link[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link{background-color:#2ad7e6;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-link.is-inverted{background-color:#fff;color:#2ad7e6}html.theme--documenter-dark .button.is-link.is-inverted:hover,html.theme--documenter-dark .button.is-link.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-link.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#2ad7e6}html.theme--documenter-dark .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#2ad7e6;color:#2ad7e6}html.theme--documenter-dark .button.is-link.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-outlined.is-focused{background-color:#2ad7e6;border-color:#2ad7e6;color:#fff}html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #2ad7e6 #2ad7e6 !important}html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark 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rgba(37,154,18,0.25)}html.theme--documenter-dark .button.is-success:active,html.theme--documenter-dark .button.is-success.is-active{background-color:#20830f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success{background-color:#259a12;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff 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.button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:2px;font-size:.75rem}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#fff;border-color:#dbdbdb;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em / 2));top:calc(50% - (1em / 2));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#f5f5f5;border-color:#dbdbdb;color:#7a7a7a;box-shadow:none;pointer-events:none}html.theme--documenter-dark 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.button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}html.theme--documenter-dark .container.is-fluid{margin-left:32px;margin-right:32px;max-width:none}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen{max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd{max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container{max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container{max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#cdc3e3;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#f5f5f5;border-left:5px solid #dbdbdb;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content 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file mode 100644 index 00000000..c58e993e --- /dev/null +++ b/previews/PR46/assets/themeswap.js @@ -0,0 +1,66 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Intialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if(window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the browser supports user color preference + var darkPreference = false; + // Check if the users preference is for dark color scheme + if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { + darkPreference = true; + } + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; var disabled = []; var darkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. 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                      Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/previews/PR46/examples/logistic.jl b/previews/PR46/examples/logistic.jl new file mode 100644 index 00000000..bb629cc1 --- /dev/null +++ b/previews/PR46/examples/logistic.jl @@ -0,0 +1,196 @@ +# # Permutation entropy for dynamic regime changes + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ## Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +## time-dependent logistic map, so that the `r` parameter increases with time +r1 = 3.83 +r2 = 3.86 +N = 2000 +rs = range(r1, r2; length = N) + +function logistic_drifting_rule(u, rs, n) + r = rs[n+1] # time is `n`, starting from 0 + return SVector(r*u[1]*(1 - u[1])) +end + +ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs) +x = trajectory(ds, N-1)[1][:, 1] + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ## Using a simpler change metric + +# Now, let's compute and various indicators and their changes, +# focusing on the fourth indicator, the permutation entropy. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries +indicators = (var, ar1_whitenoise, permutation_entropy(m = 4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as stride half the window width +metric = difference_of_means + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = WindowedIndicatorConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = estimate_indicator_changes(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + if i < 3 + hidexdecorations!(ax; grid = false) + else + ax.xlabel = "r (time)" + end + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ## Significance via random Fourier surrogates + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +using Random: Xoshiro +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42), + ) + flags = significant_transitions(results, signif) + + ## and also plot the flags with same color + for (i, indicator) in enumerate(indicators) + ## To make things visually clear, we will also plot some example surrogate + ## timeseries for each indicator and change metric pair + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surromethod) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric, p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1) + end + ## Plot the flags as vertical dashed lines + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = color, linestyle = :dash, linewidth = 3 + ) + end + ## add a title to the figure with how we estimate significance + content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod))) +end + +surromethod = RandomFourier() +overplot_surrogate_significance!(fig, surromethod) + +fig + +# ## Different surrogates +# %% #src +# Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# highlighting the _local_ dynamics or information that preserves the local +# changes of dynamical behavior. + +# A surrogate type that does a better job in preserving local sharp +# changes in the timeseries (and hence provides **stricter** +# surrogate-based significance) is for example `RelativePartialRandomization`. + +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = RelativePartialRandomization(0.25) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "gray") +fig + +# Our results have improved. In the permutation entropy, we see only two +# transitions detected as significant, which is correct: only two +# real dynamical transitions exist in the data. +# In the other two indicators we also see fewer transitions, but as we +# have already discussed, no results with the other indicators should +# be taken into meaningful consideration, as these indicators +# are simply inappropriate for what we are looking for here. + +# ## Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be less strict and more simple with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`SigmaSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation. + +fig = plot_change_metrics() +flags = significant_transitions(results, SigmaSignificance(factor = 5.0)) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = Cycled(3), linestyle = :dash, linewidth = 3 + ) +end +content(fig[1, 1]).title = "significance from std" +fig diff --git a/previews/PR46/examples/logistic/index.html b/previews/PR46/examples/logistic/index.html new file mode 100644 index 00000000..81cc3568 --- /dev/null +++ b/previews/PR46/examples/logistic/index.html @@ -0,0 +1,121 @@ + +Permutation entropy for dynamic regime changes · TransitionsInTimeseries.jl
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                      Permutation entropy for dynamic regime changes

                      Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.

                      This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.

                      Logistic map timeseries

                      A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map

                      using DynamicalSystemsBase
+using CairoMakie
+
+# time-dependent logistic map, so that the `r` parameter increases with time
+r1 = 3.83
+r2 = 3.86
+N = 2000
+rs = range(r1, r2; length = N)
+
+function logistic_drifting_rule(u, rs, n)
+    r = rs[n+1] # time is `n`, starting from 0
+    return SVector(r*u[1]*(1 - u[1]))
+end
+
+ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)
+x = trajectory(ds, N-1)[1][:, 1]
                      2000-element Vector{Float64}:
+ 0.5
+ 0.9575
+ 0.15585767321160574
+ 0.5039019545917718
+ 0.9574529422362281
+ 0.15602441103002537
+ 0.5043473227583317
+ 0.9574501255597653
+ 0.1560361152301728
+ 0.5043840906474082
+ ⋮
+ 0.4253904015445437
+ 0.9434836074964187
+ 0.20581843730311683
+ 0.6309301050251992
+ 0.8988117342940414
+ 0.3510584545931264
+ 0.8793611090928393
+ 0.40948549063776396
+ 0.9333718681550522

                      Plot it, using as time the parameter value (they coincide)

                      fig, ax = lines(rs, x; linewidth = 0.5)
+ax.xlabel = "r (time)"
+ax.ylabel = "x"
+fig

                      In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.

                      Using a simpler change metric

                      Now, let's compute and various indicators and their changes, focusing on the fourth indicator, the permutation entropy. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.

                      using TransitionsInTimeseries
+indicators = (var, ar1_whitenoise, permutation_entropy(m = 4))
+indistrings = ("var", "ar1", "pe")
                      ("var", "ar1", "pe")

                      In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width

                      metric = difference_of_means
+
+width_ind = N÷100
+width_cha = 20
+stride_cha = 10
+
+config = WindowedIndicatorConfig(indicators, metric;
+    width_ind, width_cha, stride_cha,
+)
+
+results = estimate_indicator_changes(config, x, rs)
                      WindowedIndicatorResults
+ input timeseries:              2000-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise, Symbol("#7")]
+ indicator (window, stride):    (20, 1)
+ change metrics:                [:difference_of_means]
+ change metric (window, stride): (20, 10)
+

                      Let's now plot the change metrics of the indicators

                      function plot_change_metrics()
+    fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),))
+    hidexdecorations!(ax; grid = false)
+    # plot all change metrics
+    for (i, c) in enumerate(eachcol(results.x_change))
+        ax, = scatterlines(fig[i+1, 1], results.t_change, c;
+            axis = (ylabel = indistrings[i],), label = "input"
+        )
+        if i < 3
+            hidexdecorations!(ax; grid = false)
+        else
+            ax.xlabel = "r (time)"
+        end
+    end
+    return fig
+end
+
+fig = plot_change_metrics()

                      We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)

                      Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.

                      Significance via random Fourier surrogates

                      One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.

                      Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!

                      surromethod = RandomFourier()
+
+# Define a function because we will re-use later
+using Random: Xoshiro
+function overplot_surrogate_significance!(fig, surromethod, color = "black")
+
+    signif = SurrogatesSignificance(;
+        n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),
+    )
+    flags = significant_transitions(results, signif)
+
+    # and also plot the flags with same color
+    for (i, indicator) in enumerate(indicators)
+        # To make things visually clear, we will also plot some example surrogate
+        # timeseries for each indicator and change metric pair
+        for _ in 1:10
+            s = TimeseriesSurrogates.surrogate(x, surromethod)
+            p = windowmap(indicator, s; width = width_ind)
+            q = windowmap(metric, p; width = width_cha, stride = stride_cha)
+            lines!(fig[i+1, 1], results.t_change, q;  color = (color, 0.2), linewidth = 1)
+        end
+        # Plot the flags as vertical dashed lines
+        vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+            color = color, linestyle = :dash, linewidth = 3
+        )
+    end
+    # add a title to the figure with how we estimate significance
+    content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod)))
+end
+
+surromethod = RandomFourier()
+overplot_surrogate_significance!(fig, surromethod)
+
+fig

                      Different surrogates

                      Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

                      A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

                      A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

                      surromethod = RelativePartialRandomization(0.25)
+fig = plot_change_metrics()
+overplot_surrogate_significance!(fig, surromethod, "gray")
+fig

                      Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

                      Simpler Significance

                      Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

                      fig = plot_change_metrics()
+flags = significant_transitions(results, SigmaSignificance(factor = 5.0))
+
+# Plot the flags
+for (i, indicator) in enumerate(indicators)
+    vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+        color = Cycled(3), linestyle = :dash, linewidth = 3
+    )
+end
+content(fig[1, 1]).title = "significance from std"
+fig
                      diff --git a/previews/PR46/index.html b/previews/PR46/index.html new file mode 100644 index 00000000..8cc7564a --- /dev/null +++ b/previews/PR46/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
                      Edit on GitHub

                      TransitionsInTimeseries.jl

                      TransitionsInTimeseries.jl

                      TransitionsInTimeseries — Module

                      TransitionsInTimeseries.jl

                      CI codecov Package Downloads

                      A Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                      This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

                      add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

                      All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                      source
                      Star us on GitHub!

                      If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                      Content

                      Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                      • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                      • Makes the surrogate analysis to test for significance under the hub.
                      • Can be easily extended by any user without touching the source code.
                      • Reduces the programming overhead for any researcher willing to benchmark new methods.
                      • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                      • Increases trustworthiness thanks to a large test suite.
                      Similar projects

                      An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                      Approaches

                      Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                      diff --git a/previews/PR46/search/index.html b/previews/PR46/search/index.html new file mode 100644 index 00000000..768b3e15 --- /dev/null +++ b/previews/PR46/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

                      Loading search...

                        diff --git a/previews/PR46/search_index.js b/previews/PR46/search_index.js new file mode 100644 index 00000000..21102f86 --- /dev/null +++ b/previews/PR46/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowedIndicatorConfig\nestimate_indicator_changes\nWindowedIndicatorResults","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowedIndicatorConfig","page":"API","title":"TransitionsInTimeseries.WindowedIndicatorConfig","text":"WindowedIndicatorConfig(indicators, change_metrics; kwargs...) → config\n\nA configuration struct for TransitionsInTimeseries.jl that collects what indicators and corresponding metrics to use in the estimate_indicator_changes.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.estimate_indicator_changes","page":"API","title":"TransitionsInTimeseries.estimate_indicator_changes","text":"estimate_indicator_changes(config::WindowedIndicatorConfig, x [,t]) → output\n\nEstimate possible transitions for input timeseries x using a sliding window approach as described by config:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nIf t (the time vector of x), is not provided, it is assumed t = eachindex(x).\n\nReturn the output as WindowedIndicatorResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.WindowedIndicatorResults","page":"API","title":"TransitionsInTimeseries.WindowedIndicatorResults","text":"WindowedIndicatorResults\n\nA struct containing the output of estimate_indicator_changes used with WindowedIndicatorConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nwim::WindowedIndicatorConfig, used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"significant_transitions\nTransitionsSignificance\nSurrogatesSignificance\nQuantileSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::WindowedIndicatorResults, signif::TransitionsSignificance)\n\nEstimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.TransitionsSignificance","page":"API","title":"TransitionsInTimeseries.TransitionsSignificance","text":"TransitionsSignificance\n\nSupertype used to test for significance in significant_transitions. Valid subtypes are:\n\nSurrogatesSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: TransitionsSignificance\nSurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)\n\nA configuration struct for significance testing significant_transitions using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\n\nDescription\n\nWhen used with WindowedIndicatorResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowedIndicatorResults.\n\nNote that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance\n\nA configuration struct for significance testing significant_transitions. When used with WindowedIndicatorResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\nQuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:","category":"page"},{"location":"api/","page":"API","title":"API","text":"function permutation_entropy(; m = 3, τ = 1)\n est = SymbolicPermutation(; m, τ)\n return x -> entropy_normalized(est, x)\nend","category":"page"},{"location":"api/","page":"API","title":"API","text":"permutation_entropy\nentropy","category":"page"},{"location":"api/#TransitionsInTimeseries.permutation_entropy","page":"API","title":"TransitionsInTimeseries.permutation_entropy","text":"permutation_entropy(; m = 3, τ = 1) → f\n\nReturn a function that given timeseries x it computes the normalized permutation entropy of order m with time delay τ.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.entropy","page":"API","title":"StatsBase.entropy","text":"entropy(p, [b])\n\nCompute the entropy of a collection of probabilities p, optionally specifying a real number b such that the entropy is scaled by 1/log(b). Elements with probability 0 or 1 add 0 to the entropy.\n\n\n\n\n\n","category":"function"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length.","category":"page"},{"location":"api/","page":"API","title":"API","text":"TODO: Here explain how to use precomputable functions","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"EditURL = \"logistic.jl\"","category":"page"},{"location":"examples/logistic/#Permutation-entropy-for-dynamic-regime-changes","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.","category":"page"},{"location":"examples/logistic/#Logistic-map-timeseries","page":"Permutation entropy for dynamic regime changes","title":"Logistic map timeseries","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using DynamicalSystemsBase\nusing CairoMakie\n\n# time-dependent logistic map, so that the `r` parameter increases with time\nr1 = 3.83\nr2 = 3.86\nN = 2000\nrs = range(r1, r2; length = N)\n\nfunction logistic_drifting_rule(u, rs, n)\n r = rs[n+1] # time is `n`, starting from 0\n return SVector(r*u[1]*(1 - u[1]))\nend\n\nds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)\nx = trajectory(ds, N-1)[1][:, 1]","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Plot it, using as time the parameter value (they coincide)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig, ax = lines(rs, x; linewidth = 0.5)\nax.xlabel = \"r (time)\"\nax.ylabel = \"x\"\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.","category":"page"},{"location":"examples/logistic/#Using-a-simpler-change-metric","page":"Permutation entropy for dynamic regime changes","title":"Using a simpler change metric","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Now, let's compute and various indicators and their changes, focusing on the fourth indicator, the permutation entropy. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using TransitionsInTimeseries\nindicators = (var, ar1_whitenoise, permutation_entropy(m = 4))\nindistrings = (\"var\", \"ar1\", \"pe\")","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"metric = difference_of_means\n\nwidth_ind = N÷100\nwidth_cha = 20\nstride_cha = 10\n\nconfig = WindowedIndicatorConfig(indicators, metric;\n width_ind, width_cha, stride_cha,\n)\n\nresults = estimate_indicator_changes(config, x, rs)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's now plot the change metrics of the indicators","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"function plot_change_metrics()\n fig, ax = lines(rs, x; axis = (ylabel = \"input\",), figure = (resolution = (600, 600),))\n hidexdecorations!(ax; grid = false)\n # plot all change metrics\n for (i, c) in enumerate(eachcol(results.x_change))\n ax, = scatterlines(fig[i+1, 1], results.t_change, c;\n axis = (ylabel = indistrings[i],), label = \"input\"\n )\n if i < 3\n hidexdecorations!(ax; grid = false)\n else\n ax.xlabel = \"r (time)\"\n end\n end\n return fig\nend\n\nfig = plot_change_metrics()","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.","category":"page"},{"location":"examples/logistic/#Significance-via-random-Fourier-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Significance via random Fourier surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RandomFourier()\n\n# Define a function because we will re-use later\nusing Random: Xoshiro\nfunction overplot_surrogate_significance!(fig, surromethod, color = \"black\")\n\n signif = SurrogatesSignificance(;\n n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),\n )\n flags = significant_transitions(results, signif)\n\n # and also plot the flags with same color\n for (i, indicator) in enumerate(indicators)\n # To make things visually clear, we will also plot some example surrogate\n # timeseries for each indicator and change metric pair\n for _ in 1:10\n s = TimeseriesSurrogates.surrogate(x, surromethod)\n p = windowmap(indicator, s; width = width_ind)\n q = windowmap(metric, p; width = width_cha, stride = stride_cha)\n lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1)\n end\n # Plot the flags as vertical dashed lines\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = color, linestyle = :dash, linewidth = 3\n )\n end\n # add a title to the figure with how we estimate significance\n content(fig[1, 1]).title = \"surrogates: \"*string(nameof(typeof(surromethod)))\nend\n\nsurromethod = RandomFourier()\noverplot_surrogate_significance!(fig, surromethod)\n\nfig","category":"page"},{"location":"examples/logistic/#Different-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Different surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RelativePartialRandomization(0.25)\nfig = plot_change_metrics()\noverplot_surrogate_significance!(fig, surromethod, \"gray\")\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.","category":"page"},{"location":"examples/logistic/#Simpler-Significance","page":"Permutation entropy for dynamic regime changes","title":"Simpler Significance","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig = plot_change_metrics()\nflags = significant_transitions(results, SigmaSignificance(factor = 5.0))\n\n# Plot the flags\nfor (i, indicator) in enumerate(indicators)\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = Cycled(3), linestyle = :dash, linewidth = 3\n )\nend\ncontent(fig[1, 1]).title = \"significance from std\"\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any pre-processing of raw data first such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_nlinear)\nlines!(ax, t, x_linear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window.\n# This therefore only uses information from `k-width` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\nfig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))\nlines!(ax, tfluct, s .- 0.05; color = Cycled(3))\nax.title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = \"nonlin\")\nlines!(ax, t_change, change_s; color = Cycled(3), label = \"surrogate\")\naxislegend()\nax.title = \"change metric\"\n\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig = Figure()\naxl = Axis(fig[1,1]; title = \"linear\")\naxnl = Axis(fig[1,2]; title = \"nonlinear\")\naxsigl = Axis(fig[2,1])\naxsignl = Axis(fig[2,2])\n\nfor (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change; color = Cycled(j))\n lines!(axsig, t_change, pval; color = Cycled(j+2))\nend\n\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a WindowedIndicatorConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl. First, let's load the timeseries again.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in WindowedIndicatorConfig and apply those via a sliding window to the input timeseries using estimate_indicator_changes.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = RidgeRegressionSlope()\n\n# choices go into a configuration struct\nconfig = WindowedIndicatorConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last\n)\n\n# choices are processed\nresults = estimate_indicator_changes(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From result we can plot the change metric timeseries","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, ax = lines(t, input; color = Cycled(2), label = \"input\")\naxpval, = scatter(fig[2,1], results.t_change, results.x_change[:, 1]; color = Cycled(3), label = \"var slopes\")\naxpval, = scatter(fig[3,1], results.t_change, results.x_change[:, 2]; color = Cycled(4), label = \"ar1 slopes\")","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesSignificance and the function significant_transitions.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = :both)\nflags = significant_transitions(results, signif)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"If we want, we can also plot the p-values corresponding to each timeseries change metric","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, ax = lines(t, input; color = Cycled(2), label = \"input\")\naxpval, = scatter(fig[2,1], results.t_change, signif.pvalues[:, 1]; color = Cycled(3), label = \"var p-values\")\nscatter!(axpval, results.t_change, signif.pvalues[:, 2]; color = Cycled(4), label = \"ar1 p-values\")\naxislegend(axpval)\nxlims!(ax, 0, 50)\nxlims!(axpval, 0, 50)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From the flags we can obtain the time points where both indicators show significance, via a simple reduction","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"flagsboth = vec(reduce(&, flags; dims = 2))\n\nvlines!(ax, results.t_change[flagsboth]; label = \"flags\", color = (\"black\", 0.1))\naxislegend(ax)\nfig","category":"page"}] +} diff --git a/previews/PR46/siteinfo.js b/previews/PR46/siteinfo.js new file mode 100644 index 00000000..7b308b6e --- /dev/null +++ b/previews/PR46/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR46"; diff --git a/previews/PR46/tutorial/index.html b/previews/PR46/tutorial/index.html new file mode 100644 index 00000000..b6b53e39 --- /dev/null +++ b/previews/PR46/tutorial/index.html @@ -0,0 +1,142 @@ + +Tutorial · TransitionsInTimeseries.jl
                        Edit on GitHub

                        Tutorial

                        Workflow

                        Computing transition indicators consists of the following steps:

                        1. Doing any pre-processing of raw data first such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                        2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                        3. Computing the changes of the indicator by sliding a window over its timeseries.
                        4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                        5. Performing step 2 and 3 for the surrogate timeseries.
                        6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                        These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                        Tutorial – Educational

                        Raw input data

                        Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                        \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                        with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                        using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_nlinear)
+lines!(ax, t, x_linear)
+ax.title = "raw data"
+fig

                        Preprocessing

                        Not part of TransitionsInTimeseries.jl

                        Any timeseries pre-processing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                        The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the tracked attractor. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                        x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                        At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                        Detrending in Julia

                        Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                        Indicator timeseries

                        We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                        indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window.
+# This therefore only uses information from `k-width` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                        The lines plotted above are the indicator timeseries.

                        Change metric timeseries

                        From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                        change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                        Timeseries surrogates

                        As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                        In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of flexibility in choosing the surrogate generation method, reproducibility, and automation. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                        To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                        # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2))
+lines!(ax, tfluct, s .- 0.05; color = Cycled(3))
+ax.title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin")
+lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate")
+axislegend()
+ax.title = "change metric"
+
+fig

                        Quantifying significance

                        To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                        n_surrogates = 1_000
+fig = Figure()
+axl = Axis(fig[1,1]; title = "linear")
+axnl = Axis(fig[1,2]; title = "nonlinear")
+axsigl = Axis(fig[2,1])
+axsignl = Axis(fig[2,2])
+
+for (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change; color = Cycled(j))
+    lines!(axsig, t_change, pval; color = Cycled(j+2))
+end
+
+fig

                        As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                        Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                        Tutorial – TransitionsInTimeseries.jl

                        TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                        The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a WindowedIndicatorConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis.

                        The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl. First, let's load the timeseries again.

                        using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig

                        To perform all of the above analysis we follow a 2-step process.

                        Step 1, we decide what indicators and change metrics to use in WindowedIndicatorConfig and apply those via a sliding window to the input timeseries using estimate_indicator_changes.

                        # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = RidgeRegressionSlope()
+
+# choices go into a configuration struct
+config = WindowedIndicatorConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last
+)
+
+# choices are processed
+results = estimate_indicator_changes(config, input, t)
                        WindowedIndicatorResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                        From result we can plot the change metric timeseries

                        fig, ax = lines(t, input; color = Cycled(2), label = "input")
+axpval, = scatter(fig[2,1], results.t_change, results.x_change[:, 1]; color = Cycled(3), label = "var slopes")
+axpval, = scatter(fig[3,1], results.t_change, results.x_change[:, 2]; color = Cycled(4), label = "ar1 slopes")

                        Step 2 is to estimate significance using SurrogatesSignificance and the function significant_transitions.

                        signif = SurrogatesSignificance(n = 1000, tail = :both)
+flags = significant_transitions(results, signif)
                        2072×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ ⋮  
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0

                        If we want, we can also plot the p-values corresponding to each timeseries change metric

                        fig, ax = lines(t, input; color = Cycled(2), label = "input")
+axpval, = scatter(fig[2,1], results.t_change, signif.pvalues[:, 1]; color = Cycled(3), label = "var p-values")
+scatter!(axpval, results.t_change, signif.pvalues[:, 2]; color = Cycled(4), label = "ar1 p-values")
+axislegend(axpval)
+xlims!(ax, 0, 50)
+xlims!(axpval, 0, 50)

                        From the flags we can obtain the time points where both indicators show significance, via a simple reduction

                        flagsboth = vec(reduce(&, flags; dims = 2))
+
+vlines!(ax, results.t_change[flagsboth]; label = "flags", color = ("black", 0.1))
+axislegend(ax)
+fig
                        diff --git a/previews/PR46/tutorial_literate.jl b/previews/PR46/tutorial_literate.jl new file mode 100644 index 00000000..2f491843 --- /dev/null +++ b/previews/PR46/tutorial_literate.jl @@ -0,0 +1,140 @@ +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_nlinear) +lines!(ax, t, x_linear) +ax.title = "raw data" +fig + +# +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +# +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +# By mapping `last::Function` over a windowviewer of the time vector, we obtain the last time step of each window. +# This therefore only uses information from `k-width` to `k` at time step `k`. +# Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +# +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + + +# + +# Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2)) +lines!(ax, tfluct, s .- 0.05; color = Cycled(3)) +ax.title = "real signal vs. surrogate(s)" + +# compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +ax, = lines(fig[1,2], t_change, change_nl; color = Cycled(2), label = "nonlin") +lines!(ax, t_change, change_s; color = Cycled(3), label = "surrogate") +axislegend() +ax.title = "change metric" + +fig +# + + +n_surrogates = 1_000 +fig = Figure() +axl = Axis(fig[1,1]; title = "linear") +axnl = Axis(fig[1,2]; title = "nonlinear") +axsigl = Axis(fig[2,1]) +axsignl = Axis(fig[2,2]) + +for (j, ax, axsig, x) in zip(1:2, (axl, axnl), (axsigl, axsignl), (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + # Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change; color = Cycled(j)) + lines!(axsig, t_change, pval; color = Cycled(j+2)) +end + +fig + +# %% +# Tutorial short + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_nl_fluct) +ax.title = "input timeseries" +fig + +# These indicators are suitable for Critical Slowing Down +indicators = [var, ar1_whitenoise] +indconfig = IndicatorsConfig(tfluct, last, indicators; width = 400) + + +# use the ridge regression slope for both indicators +change_metrics = [RidgeRegressionSlope()] +sigconfig = SignificanceConfig(indconfig, last, change_metrics; + width = 30, n_surrogates = 1000) + +# perform the full analysis +results = indicators_analysis(tfluct, x_nl_fluct, indconfig, sigconfig) + +# Plot the original timeseries vs. p-value time series +fig, ax = lines(tfluct, x_nl_fluct; color = Cycled(2), label = "input") +axpval, = lines(fig[2,1], sigconfig.t_change, results.pval[:, 1]; color = Cycled(3), label = "p-value of var") +lines!(axpval, sigconfig.t_change, results.pval[:, 2]; color = Cycled(4), label = "p-value of ar1") +xlims!(ax, (0, 50)) +xlims!(axpval, (0, 50)) +axislegend(axpval) +fig + + +flags_indicators, flags_andicators = transition_flags(results, 0.05) +vlines!(ax, flags_andicators; label = "flags", color = Cycled(3), linestyle = :dash) +axislegend(ax) +fig \ No newline at end of file diff --git a/previews/PR48/api/index.html b/previews/PR48/api/index.html new file mode 100644 index 00000000..7ff2d146 --- /dev/null +++ b/previews/PR48/api/index.html @@ -0,0 +1,21 @@ + +API · TransitionsInTimeseries.jl
                        Edit on GitHub

                        API

                        Main analysis functions

                        TransitionsInTimeseries.SlidingWindowConfig — Type
                        SlidingWindowConfig(indicators, change_metrics; kwargs...) → config

                        A configuration struct for TransitionsInTimeseries.jl that collects the sliding window parameters, the indicators and the corresponding metrics to use in estimate_indicator_changes.

                        indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                        Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.

                        Keyword arguments

                        • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.

                        • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.

                        • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:

                          • last: use the last timepoint of each window
                          • midpoint: use the mid timepoint of each time window
                          • first: use first timepoint of each window

                          In fact, the indicators time vector is computed simply via

                          t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)

                          so any other function of the time window may be given to extract the time point itself, such as mean or median.

                        • T = Float64: Element type of input timeseries to initialize some computations.

                        source
                        TransitionsInTimeseries.SegmentWindowConfig — Type
                        SegmentWindowConfig(indicators, change_metrics, tseg_start, tseg_end;
+    kwargs...) → config

                        A configuration struct for TransitionsInTimeseries.jl that collects the start and end time of the segments over which the analysis estimate_indicator_changes is to be run, as well as its windowing parameters.

                        indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics. tseg_start and tseg_end are ::Vector of length n, with n the number of segments.

                        Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.

                        Keyword arguments

                        • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.

                        • min_width_cha::Int=50: minimal width required to perform the change metric estimation. If segment not sufficiently long, return Inf.

                        • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:

                          • last: use the last timepoint of each window
                          • midpoint: use the mid timepoint of each time window
                          • first: use first timepoint of each window

                          In fact, the indicators time vector for the k-th segment is computed simply via:

                          t_indicator[k] = windowmap(whichtime, t; width_ind, stride_ind)

                          so any other function of the time window may be given to extract the time point itself, such as mean or median.

                        • T = Float64: Element type of input timeseries to initialize some computations.

                        source
                        TransitionsInTimeseries.estimate_indicator_changes — Function
                        estimate_indicator_changes(config::SlidingWindowConfig, x [,t]) → output

                        Estimate possible transitions for input timeseries x using a sliding window approach as described by config:

                        1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                        2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                        If t (the time vector of x), is not provided, it is assumed t = eachindex(x).

                        Return the output as WindowResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                        source
                        estimate_indicator_changes(config::SegmentWindowConfig, x [,t]) → output

                        Estimate possible transitions for input timeseries x using a segmented window approach as described by config:

                        1. For each segment specified in config, estimate the corresponding indicator timeseries by sliding a window over the input timeseries.
                        2. For each segment of the indicator timeseries, estimate a scalar change metric by applying a window of the size of the indicator segment.

                        If t (the time vector of x), is not provided, it is assumed t = eachindex(x).

                        Return the output as WindowResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                        source
                        TransitionsInTimeseries.SlidingWindowResults — Type
                        SlidingWindowResults

                        A struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                        It has the following fields that the user may access

                        • x: the input timeseries.

                        • t: the time vector of the input timeseries.

                        • x_indicator, the indicator timeseries (matrix with each column one indicator).

                        • t_indicator, the time vector of the indicator timeseries.

                        • x_change, the change metric timeseries (matrix with each column one change metric).

                        • t_change, the time vector of the change metric timeseries.

                        • config::SlidingWindowConfig, used for the analysis.

                        source
                        TransitionsInTimeseries.SegmentWindowResults — Type
                        SegmentWindowResults

                        A struct containing the output of estimate_indicator_changes used with SegmentWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                        It has the following fields that the user may access

                        • x: the input timeseries.

                        • t: the time vector of the input timeseries.

                        • x_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.

                        • t_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.

                        • x_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.

                        • t_change, the time vector of the change metric.

                        • config::SegmentWindowConfig, used for the analysis.

                        source

                        Significance testing

                        TransitionsInTimeseries.significant_transitions — Function
                        significant_transitions(res::WindowResults, signif::TransitionsSignificance)

                        Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.

                        source
                        TransitionsInTimeseries.SurrogatesSignificance — Type
                        SurrogatesSignificance <: TransitionsSignificance
+SurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)

                        A configuration struct for significance testing significant_transitions using timeseries surrogates.

                        Keyword arguments

                        • surromethod = RandomFourier(): method to generate surrogates
                        • n = 1000: how many surrogates to generate
                        • rng = Random.default_rng(): random number generator for the surrogates
                        • p = 0.05: threshold for significance of the p-value
                        • tail = :both: tail type used, see below

                        Description

                        When used with WindowResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

                        The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowResults.

                        Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

                        source
                        TransitionsInTimeseries.QuantileSignificance — Type
                        QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance

                        A configuration struct for significance testing significant_transitions. When used with WindowResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                        QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

                        source

                        Indicators

                        Value distribution

                        Statistics.mean — Method
                        mean(itr)

                        Compute the mean of all elements in a collection.

                        Note

                        If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

                        Examples

                        julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
                        StatsBase.skewness — Function
                        skewness(v, [wv::AbstractWeights], m=mean(v))

                        Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                        StatsBase.kurtosis — Function
                        kurtosis(v, [wv::AbstractWeights], m=mean(v))

                        Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                        Critical Slowing Down

                        Statistics.var — Method
                        var(itr; corrected::Bool=true, mean=nothing[, dims])

                        Compute the sample variance of collection itr.

                        The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

                        If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

                        A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

                        Note

                        If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

                        TransitionsInTimeseries.ar1_whitenoise — Function
                        ar1_whitenoise(x::AbstractVector)

                        Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

                        \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                        source

                        Spectrum

                        TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                        LowfreqPowerSpectrum(; q_lofreq = 0.1)

                        Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                        lfps = precompute( LowfreqPowerSpectrum() )

                        Keyword arguments:

                        • q_lofreq: a number between 0 and 1 that characterises which portion of the

                        frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                        source

                        Nonlinear dynamics

                        Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:

                        function permutation_entropy(; m = 3, τ = 1)
+    est = SymbolicPermutation(; m, τ)
+    return x -> entropy_normalized(est, x)
+end
                        StatsBase.entropy — Function
                        entropy(p, [b])

                        Compute the entropy of a collection of probabilities p, optionally specifying a real number b such that the entropy is scaled by 1/log(b). Elements with probability 0 or 1 add 0 to the entropy.

                        Change metrics

                        Slope

                        TransitionsInTimeseries.kendalltau — Function
                        kendalltau(x::AbstractVector)

                        Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                        source
                        TransitionsInTimeseries.spearman — Function
                        spearman(x::AbstractVector)

                        Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                        source

                        Value distribution differences

                        TransitionsInTimeseries.difference_of_means — Function
                        difference_of_means(x::AbstractArray)

                        Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                        # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                        difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                        source

                        Make your own indicator/metric!

                        The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                        There are situations where you may optimize such a function based on knowledge of input x type and length.

                        TODO: Here explain how to use precomputable functions

                        Missing docstring.

                        Missing docstring for precompute. Check Documenter's build log for details.

                        Surrogates

                        For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                        Sliding windows

                        TransitionsInTimeseries.WindowViewer — Type
                        WindowViewer(x; width, stride)

                        Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                        If not given, the keywords width, stride are taken as default_window_width(x) and 1.

                        source
                        TransitionsInTimeseries.windowmap — Function
                        windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                        A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                        source

                        Load data

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+ + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); + }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR48/assets/search.js b/previews/PR48/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR48/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
                      • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR48/assets/themes/documenter-dark.css b/previews/PR48/assets/themes/documenter-dark.css new file mode 100644 index 00000000..89fbb493 --- /dev/null +++ b/previews/PR48/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ +@keyframes spinAround{from{transform:rotate(0deg)}to{transform:rotate(359deg)}}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark .button,.is-unselectable,html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after,html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after{border:3px solid 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.button.is-warning:focus:not(:active),html.theme--documenter-dark .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(244,199,47,0.25)}html.theme--documenter-dark .button.is-warning:active,html.theme--documenter-dark .button.is-warning.is-active{background-color:#f3c017;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#f4c72f;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark 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.button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:2px;font-size:.75rem}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#fff;border-color:#dbdbdb;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em / 2));top:calc(50% - (1em / 2));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#f5f5f5;border-color:#dbdbdb;color:#7a7a7a;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:290486px;padding-left:1em;padding-right:1em}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:0.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){border-radius:2px;font-size:.75rem}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}html.theme--documenter-dark .container.is-fluid{margin-left:32px;margin-right:32px;max-width:none}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen{max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd{max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container{max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container{max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#cdc3e3;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#f5f5f5;border-left:5px solid #dbdbdb;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #dbdbdb;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#cdc3e3}html.theme--documenter-dark .content table th:not([align]){text-align:left}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#cdc3e3}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#cdc3e3}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:290486px}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 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1055px){html.theme--documenter-dark .columns.is-variable.is-7-tablet-only{--columnGap: 1.75rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-7-touch{--columnGap: 1.75rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-7-desktop{--columnGap: 1.75rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-7-desktop-only{--columnGap: 1.75rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-7-widescreen{--columnGap: 1.75rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only{--columnGap: 1.75rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-7-fullhd{--columnGap: 1.75rem}}html.theme--documenter-dark .columns.is-variable.is-8{--columnGap: 2rem}@media screen and (max-width: 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                        Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/previews/PR48/examples/do-events.jl b/previews/PR48/examples/do-events.jl new file mode 100644 index 00000000..47c06a18 --- /dev/null +++ b/previews/PR48/examples/do-events.jl @@ -0,0 +1,267 @@ +#= +# Dansgaard-Oescher events and Critical Slowing Down + +The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project ([NGRIP](https://en.wikipedia.org/wiki/North_Greenland_Ice_Core_Project)) are, to this date, the best proxy record for the Dansgaard-Oeschger events ([DO-events](https://en.wikipedia.org/wiki/Dansgaard%E2%80%93Oeschger_event)). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found [here](https://www.iceandclimate.nbi.ku.dk/data/) in its raw format. This analysis has already been done in [boers-early-warning-2018](@cite) and we here try to reproduce Figure 2.d-f. + +## Preprocessing NGRIP + +Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps: +1. Load the data, reverse and offset it to have time vector = time before 2000 AD. +2. Filter non-unique points in time and sort the data. +3. Regrid the data from uneven to even sampling. + +The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing. + +### Step 1: +=# + +using DelimitedFiles, Downloads + +function load_ngrip() + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP.csv") + data, labels = readdlm(tmp, header = true) + return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors +end + +t1, x1 = load_ngrip() + +#= +### Step 2 +=# + +uniqueidx(v) = unique(i -> v[i], eachindex(v)) +function keep_unique(t, x) + unique_idx = uniqueidx(t) + return t[unique_idx], x[unique_idx] +end + +function sort_timeseries!(t, x) + p = sortperm(t) + permute!(t, p) + permute!(x, p) + return nothing +end + +t2, x2 = keep_unique(t1, x1) +sort_timeseries!(t2, x2) + +#= +### Step 3 +=# + +using BSplineKit + +function regrid2evensampling(t, x, dt) + itp = BSplineKit.interpolate(t, x, BSplineOrder(4)) + tspan = (ceil(minimum(t)), floor(maximum(t))) + t_even = collect(tspan[1]:dt:tspan[2]) + x_even = itp.(t_even) + return t_even, x_even +end + +dt = 5.0 # dt = 5 yr as in (Boers 2018) +t3, x3 = regrid2evensampling(t2, x2, dt) + +#= +### Step 4 + +For the final step we drop the indices: +=# + +using DSP + +function chebyshev_filter(t, x, fcutoff) + ii = 10 # Chebyshev filtering requires to prune first points of timeseries. + responsetype = Highpass(fcutoff, fs = 1/dt) + designmethod = Chebyshev1(8, 0.05) + r = filt(digitalfilter(responsetype, designmethod), x) + xtrend = x - r + return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end] +end + +fcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018) +t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff) + +#= +Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from [rasmussen-stratigraphic-2014](@cite) (which will soon be available as downloadable): +=# + +using CairoMakie, Loess + +function loess_filter(t, x; span = 0.005) + loessmodel = loess(t, x, span = span) + xtrend = Loess.predict(loessmodel, t) + r = x - xtrend + return t, x, xtrend, r +end + +function kyr_xticks(tticks_yr) + tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)] + return (tticks_yr, tticks_kyr) +end + +function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks) + fig = Figure(resolution = (1600, 1200), fontsize = 24) + + ## Original timeseries with transition marked by vertical lines + ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)", + xaxisposition = :top, xticks = xticks) + lines!(ax1, traw, xraw, color = (:gray70, 0.5)) + lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3) + vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3) + + ## Residual timeseries + ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + lines!(ax2, t, r, color = :gray50, linewidth = 1) + + ## Axes for variance and AC1 timeseries + ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$", + xticks = xticks) + + axs = [ax1, ax2, ax3, ax4] + [xlims!(ax, xlims) for ax in axs] + ylims!(axs[1], (-48, -34)) + rowgap!(fig.layout, 10) + return fig, axs +end + +xlims = (-60e3, -10e3) +xticks = kyr_xticks(-60e3:5e3:5e3) +t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160, + 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703] +tloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +fig + +#= +## Hindcast on NGRIP data + +As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including [boers-early-warning-2018](@cite), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using `SegmentWindowConfig`, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here: +=# + +using TransitionsInTimeseries, StatsBase +using Random: Xoshiro + +ac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase +indicators = (var, ac1) +change_metrics = RidgeRegressionSlope() +tseg_start = t_rasmussen[1:end-1] .+ 200 +tseg_end = t_rasmussen[2:end] .- 200 +config = SegmentWindowConfig(indicators, change_metrics, + tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) # require >=100 data points to estimate change metric +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) + +#= +That's it! We can now visulaise our results with a generic function that we will re-use later: +=# + +function plot_segment_analysis!(axs, results, signif) + (; t_indicator, x_indicator) = results + for k in eachindex(t_indicator) # loop over the segments + for i in axes(signif.pvalues, 2) # loop over the indicators + if !isinf(signif.pvalues[k, i]) # plot if segment long enough + ## Plot indicator timeseries and its linear regression + ti, xi = t_indicator[k], x_indicator[k][:, i] + lines!(axs[i+2], ti, xi, color = Cycled(1)) + m, p = ridgematrix(ti, 0.0) * xi + if signif.pvalues[k, i] < 0.05 + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3) + else + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3) + end + end + end + end +end +plot_segment_analysis!(axs, results, signif) +fig + +#= +In [boers-early-warning-2018](@cite), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in [boers-early-warning-2018](@cite), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of [boers-early-warning-2018](@cite). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media. + +## CSD: only a necessary condition, only in some cases + +For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a **necessary condition** for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is **not a sufficient condition** for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition: +=# + +tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before +config = SegmentWindowConfig(indicators, change_metrics, + tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +plot_segment_analysis!(axs, results, signif) +fig + +#= +For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD. + +We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC). + +!!! warning "Degrees of freedom" + These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice. + +!!! info "Future improvement" + Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias. + +## Hindcasting simulated DO-events + +In CLIMBER-X, the EMIC described in [willeit-earth-2022](@cite), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs: +=# + +t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050], + [1, 3500, 4370, 5790, 7200, 8140]] +t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]] +tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]] +tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50] + +figvec = Figure[] + +for j in 1:2 + ## Download the data and perform loess filtering on it + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" * + "master/timeseries/climberx-do$(j)-omaxa.csv") + data = readdlm(tmp) + tcx, xcx = data[1, 1000:end], data[2, 1000:end] + t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02) + + ## Initialize figure + xlims = (0, last(tcx)) + xticks = kyr_xticks(xlims[1]:1e3:xlims[2]) + fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks) + ylims!(axs[1], (5, 40)) + axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$" + + ## Run sliding analysis and update figure with results + dt = mean(diff(tcx)) + config = SegmentWindowConfig( + indicators, change_metrics, tseg_start[j], tseg_end[j], + whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100) + results = estimate_indicator_changes(config, r, t) + signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995)) + flags = significant_transitions(results, signif) + + plot_segment_analysis!(axs, results, signif) + vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3) + push!(figvec, fig) +end +figvec[1] + +#= +It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case: +=# + +figvec[2] + +#= +Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience. +=# \ No newline at end of file diff --git a/previews/PR48/examples/do-events/index.html b/previews/PR48/examples/do-events/index.html new file mode 100644 index 00000000..ff9a6011 --- /dev/null +++ b/previews/PR48/examples/do-events/index.html @@ -0,0 +1,191 @@ + +Dansgaard-Oescher events and Critical Slowing Down · TransitionsInTimeseries.jl
                        Edit on GitHub

                        Dansgaard-Oescher events and Critical Slowing Down

                        The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.

                        Preprocessing NGRIP

                        Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:

                        1. Load the data, reverse and offset it to have time vector = time before 2000 AD.
                        2. Filter non-unique points in time and sort the data.
                        3. Regrid the data from uneven to even sampling.

                        The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.

                        Step 1:

                        using DelimitedFiles, Downloads
+
+function load_ngrip()
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+        "master/timeseries/NGRIP.csv")
+    data, labels = readdlm(tmp, header = true)
+    return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors
+end
+
+t1, x1 = load_ngrip()
                        ([-59944.5, -59939.6, -59935.9, -59930.5, -59925.0, -59919.0, -59914.3, -59909.4, -59904.5, -59899.7  …  -27.40000000000009, -27.40000000000009, -27.299999999999955, -27.299999999999955, -27.200000000000045, -27.09999999999991, -27.09999999999991, -27.0, -26.90000000000009, -26.799999999999955], [-43.52, -42.94, -42.13, -40.04, -41.09, -43.57, -42.28, -41.2, -44.07, -44.53  …  -35.29, -35.18, -35.51, -36.03, -36.52, -37.12, -37.41, -37.21, -36.62, -35.52])

                        Step 2

                        uniqueidx(v) = unique(i -> v[i], eachindex(v))
+function keep_unique(t, x)
+    unique_idx = uniqueidx(t)
+    return t[unique_idx], x[unique_idx]
+end
+
+function sort_timeseries!(t, x)
+    p = sortperm(t)
+    permute!(t, p)
+    permute!(x, p)
+    return nothing
+end
+
+t2, x2 = keep_unique(t1, x1)
+sort_timeseries!(t2, x2)

                        Step 3

                        using BSplineKit
+
+function regrid2evensampling(t, x, dt)
+    itp = BSplineKit.interpolate(t, x, BSplineOrder(4))
+    tspan = (ceil(minimum(t)), floor(maximum(t)))
+    t_even = collect(tspan[1]:dt:tspan[2])
+    x_even = itp.(t_even)
+    return t_even, x_even
+end
+
+dt = 5.0        # dt = 5 yr as in (Boers 2018)
+t3, x3 = regrid2evensampling(t2, x2, dt)
                        ([-59944.0, -59939.0, -59934.0, -59929.0, -59924.0, -59919.0, -59914.0, -59909.0, -59904.0, -59899.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-43.445268010797946, -42.85408835164853, -41.357360665158936, -39.9365468206892, -41.60554051352076, -43.57000000000001, -42.145558689100454, -41.33160823883399, -44.273597725729985, -44.4622612304012  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46])

                        Step 4

                        For the final step we drop the indices:

                        using DSP
+
+function chebyshev_filter(t, x, fcutoff)
+    ii = 10             # Chebyshev filtering requires to prune first points of timeseries.
+    responsetype = Highpass(fcutoff, fs = 1/dt)
+    designmethod = Chebyshev1(8, 0.05)
+    r = filt(digitalfilter(responsetype, designmethod), x)
+    xtrend = x - r
+    return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]
+end
+
+fcutoff = 0.95 * 0.01   # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)
+t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)
                        ([-59899.0, -59894.0, -59889.0, -59884.0, -59879.0, -59874.0, -59869.0, -59864.0, -59859.0, -59854.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-44.4622612304012, -44.264401428210874, -44.02956767939856, -42.29334237357212, -42.594341674200344, -41.09704877854712, -40.39837540966913, -44.369155046413255, -42.74492506508012, -43.737014520530145  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46], [-43.89287787976461, -48.663435112414156, -51.31169981050155, -51.269094666491796, -49.90310432724566, -47.721430022512344, -44.36050569418247, -43.87556827410048, -43.57802291229893, -41.36870967826094  …  -34.81349114528442, -36.01634453179986, -36.150446802907226, -36.37595639697143, -35.96843653265903, -33.899634243732976, -32.49784036951535, -33.06575312724142, -34.07956188682297, -34.4079080530096], [-0.5693833506365866, 4.399033684203284, 7.282132131102991, 8.975752292919669, 7.308762653045311, 6.624381243965224, 3.9621302845133433, -0.493586772312777, 0.8330978472188112, -2.368304842269206  …  -0.30650885471557926, -0.17365546820014846, 1.0104468029072273, -0.684043603028572, 1.0384365326590237, -0.3303657562670192, -1.0321596304846505, -2.0242468727585807, 0.07956188682296689, -0.05209194699039831])

                        Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):

                        using CairoMakie, Loess
+
+function loess_filter(t, x; span = 0.005)
+    loessmodel = loess(t, x, span = span)
+    xtrend = Loess.predict(loessmodel, t)
+    r = x - xtrend
+    return t, x, xtrend, r
+end
+
+function kyr_xticks(tticks_yr)
+    tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)]
+    return (tticks_yr, tticks_kyr)
+end
+
+function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)
+    fig = Figure(resolution = (1600, 1200), fontsize = 24)
+
+    # Original timeseries with transition marked by vertical lines
+    ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)",
+        xaxisposition = :top, xticks = xticks)
+    lines!(ax1, traw, xraw, color = (:gray70, 0.5))
+    lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)
+    vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)
+
+    # Residual timeseries
+    ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    lines!(ax2, t, r, color = :gray50, linewidth = 1)
+
+    # Axes for variance and AC1 timeseries
+    ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$",
+        xticks = xticks)
+
+    axs = [ax1, ax2, ax3, ax4]
+    [xlims!(ax, xlims) for ax in axs]
+    ylims!(axs[1], (-48, -34))
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+
+xlims = (-60e3, -10e3)
+xticks = kyr_xticks(-60e3:5e3:5e3)
+t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,
+                38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]
+tloess, _, xloess, rloess = loess_filter(t3, x3)    # loess-filtered signal for visualization
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+fig

                        Hindcast on NGRIP data

                        As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:

                        using TransitionsInTimeseries, StatsBase
+using Random: Xoshiro
+
+ac1(x) = sum(autocor(x, [1]))   # AC1 from StatsBase
+indicators = (var, ac1)
+change_metrics = RidgeRegressionSlope()
+tseg_start = t_rasmussen[1:end-1] .+ 200
+tseg_end = t_rasmussen[2:end] .- 200
+config = SegmentWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)        # require >=100 data points to estimate change metric
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
                        18×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 1  0
+ 1  1
+ 1  1
+ 1  1
+ 0  0
+ 1  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 1  0

                        That's it! We can now visulaise our results with a generic function that we will re-use later:

                        function plot_segment_analysis!(axs, results, signif)
+    (; t_indicator, x_indicator) = results
+    for k in eachindex(t_indicator)             # loop over the segments
+        for i in axes(signif.pvalues, 2)        # loop over the indicators
+            if !isinf(signif.pvalues[k, i])     # plot if segment long enough
+                # Plot indicator timeseries and its linear regression
+                ti, xi = t_indicator[k], x_indicator[k][:, i]
+                lines!(axs[i+2], ti, xi, color = Cycled(1))
+                m, p = ridgematrix(ti, 0.0) * xi
+                if signif.pvalues[k, i] < 0.05
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)
+                else
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)
+                end
+            end
+        end
+    end
+end
+plot_segment_analysis!(axs, results, signif)
+fig

                        In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.

                        CSD: only a necessary condition, only in some cases

                        For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:

                        tseg_end = t_rasmussen[2:end] .- 700    # stop analysis 500 years earlier than before
+config = SegmentWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+plot_segment_analysis!(axs, results, signif)
+fig

                        For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD.

                        We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).

                        Degrees of freedom

                        These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.

                        Future improvement

                        Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.

                        Hindcasting simulated DO-events

                        In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:

                        t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],
+                 [1, 3500, 4370, 5790, 7200, 8140]]
+t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]
+tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]
+tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]
+
+figvec = Figure[]
+
+for j in 1:2
+    # Download the data and perform loess filtering on it
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" *
+        "master/timeseries/climberx-do$(j)-omaxa.csv")
+    data = readdlm(tmp)
+    tcx, xcx = data[1, 1000:end], data[2, 1000:end]
+    t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)
+
+    # Initialize figure
+    xlims = (0, last(tcx))
+    xticks = kyr_xticks(xlims[1]:1e3:xlims[2])
+    fig, axs = plot_do(tcx, xcx,  t, xtrend, t, r, t_transitions[j], extrema(t), xticks)
+    ylims!(axs[1], (5, 40))
+    axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$"
+
+    # Run sliding analysis and update figure with results
+    dt = mean(diff(tcx))
+    config = SegmentWindowConfig(
+        indicators, change_metrics, tseg_start[j], tseg_end[j],
+        whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)
+    results = estimate_indicator_changes(config, r, t)
+    signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))
+    flags = significant_transitions(results, signif)
+
+    plot_segment_analysis!(axs, results, signif)
+    vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)
+    push!(figvec, fig)
+end
+figvec[1]

                        It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:

                        figvec[2]

                        Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.

                        diff --git a/previews/PR48/examples/logistic.jl b/previews/PR48/examples/logistic.jl new file mode 100644 index 00000000..fa252a22 --- /dev/null +++ b/previews/PR48/examples/logistic.jl @@ -0,0 +1,196 @@ +# # Permutation entropy for dynamic regime changes + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ## Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +## time-dependent logistic map, so that the `r` parameter increases with time +r1 = 3.83 +r2 = 3.86 +N = 2000 +rs = range(r1, r2; length = N) + +function logistic_drifting_rule(u, rs, n) + r = rs[n+1] # time is `n`, starting from 0 + return SVector(r*u[1]*(1 - u[1])) +end + +ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs) +x = trajectory(ds, N-1)[1][:, 1] + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ## Using a simpler change metric + +# Now, let's compute and various indicators and their changes, +# focusing on the fourth indicator, the permutation entropy. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries +indicators = (var, ar1_whitenoise, permutation_entropy(m = 4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as stride half the window width +metric = difference_of_means + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = SlidingWindowConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = estimate_indicator_changes(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + if i < 3 + hidexdecorations!(ax; grid = false) + else + ax.xlabel = "r (time)" + end + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ## Significance via random Fourier surrogates + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +using Random: Xoshiro +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42), + ) + flags = significant_transitions(results, signif) + + ## and also plot the flags with same color + for (i, indicator) in enumerate(indicators) + ## To make things visually clear, we will also plot some example surrogate + ## timeseries for each indicator and change metric pair + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surromethod) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric, p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1) + end + ## Plot the flags as vertical dashed lines + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = color, linestyle = :dash, linewidth = 3 + ) + end + ## add a title to the figure with how we estimate significance + content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod))) +end + +surromethod = RandomFourier() +overplot_surrogate_significance!(fig, surromethod) + +fig + +# ## Different surrogates +# %% #src +# Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# highlighting the _local_ dynamics or information that preserves the local +# changes of dynamical behavior. + +# A surrogate type that does a better job in preserving local sharp +# changes in the timeseries (and hence provides **stricter** +# surrogate-based significance) is for example `RelativePartialRandomization`. + +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = RelativePartialRandomization(0.25) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "gray") +fig + +# Our results have improved. In the permutation entropy, we see only two +# transitions detected as significant, which is correct: only two +# real dynamical transitions exist in the data. +# In the other two indicators we also see fewer transitions, but as we +# have already discussed, no results with the other indicators should +# be taken into meaningful consideration, as these indicators +# are simply inappropriate for what we are looking for here. + +# ## Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be less strict and more simple with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`SigmaSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation. + +fig = plot_change_metrics() +flags = significant_transitions(results, SigmaSignificance(factor = 5.0)) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = Cycled(3), linestyle = :dash, linewidth = 3 + ) +end +content(fig[1, 1]).title = "significance from std" +fig diff --git a/previews/PR48/examples/logistic/index.html b/previews/PR48/examples/logistic/index.html new file mode 100644 index 00000000..ea326484 --- /dev/null +++ b/previews/PR48/examples/logistic/index.html @@ -0,0 +1,121 @@ + +Permutation entropy for dynamic regime changes · TransitionsInTimeseries.jl
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                        Permutation entropy for dynamic regime changes

                        Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.

                        This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.

                        Logistic map timeseries

                        A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map

                        using DynamicalSystemsBase
+using CairoMakie
+
+# time-dependent logistic map, so that the `r` parameter increases with time
+r1 = 3.83
+r2 = 3.86
+N = 2000
+rs = range(r1, r2; length = N)
+
+function logistic_drifting_rule(u, rs, n)
+    r = rs[n+1] # time is `n`, starting from 0
+    return SVector(r*u[1]*(1 - u[1]))
+end
+
+ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)
+x = trajectory(ds, N-1)[1][:, 1]
                        2000-element Vector{Float64}:
+ 0.5
+ 0.9575
+ 0.15585767321160574
+ 0.5039019545917718
+ 0.9574529422362281
+ 0.15602441103002537
+ 0.5043473227583317
+ 0.9574501255597653
+ 0.1560361152301728
+ 0.5043840906474082
+ ⋮
+ 0.4253904015445437
+ 0.9434836074964187
+ 0.20581843730311683
+ 0.6309301050251992
+ 0.8988117342940414
+ 0.3510584545931264
+ 0.8793611090928393
+ 0.40948549063776396
+ 0.9333718681550522

                        Plot it, using as time the parameter value (they coincide)

                        fig, ax = lines(rs, x; linewidth = 0.5)
+ax.xlabel = "r (time)"
+ax.ylabel = "x"
+fig

                        In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.

                        Using a simpler change metric

                        Now, let's compute and various indicators and their changes, focusing on the fourth indicator, the permutation entropy. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.

                        using TransitionsInTimeseries
+indicators = (var, ar1_whitenoise, permutation_entropy(m = 4))
+indistrings = ("var", "ar1", "pe")
                        ("var", "ar1", "pe")

                        In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width

                        metric = difference_of_means
+
+width_ind = N÷100
+width_cha = 20
+stride_cha = 10
+
+config = SlidingWindowConfig(indicators, metric;
+    width_ind, width_cha, stride_cha,
+)
+
+results = estimate_indicator_changes(config, x, rs)
                        WindowResults
+ input timeseries:              2000-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise, Symbol("#7")]
+ indicator (window, stride):    (20, 1)
+ change metrics:                [:difference_of_means]
+ change metric (window, stride): (20, 10)
+

                        Let's now plot the change metrics of the indicators

                        function plot_change_metrics()
+    fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),))
+    hidexdecorations!(ax; grid = false)
+    # plot all change metrics
+    for (i, c) in enumerate(eachcol(results.x_change))
+        ax, = scatterlines(fig[i+1, 1], results.t_change, c;
+            axis = (ylabel = indistrings[i],), label = "input"
+        )
+        if i < 3
+            hidexdecorations!(ax; grid = false)
+        else
+            ax.xlabel = "r (time)"
+        end
+    end
+    return fig
+end
+
+fig = plot_change_metrics()

                        We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)

                        Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.

                        Significance via random Fourier surrogates

                        One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.

                        Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!

                        surromethod = RandomFourier()
+
+# Define a function because we will re-use later
+using Random: Xoshiro
+function overplot_surrogate_significance!(fig, surromethod, color = "black")
+
+    signif = SurrogatesSignificance(;
+        n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),
+    )
+    flags = significant_transitions(results, signif)
+
+    # and also plot the flags with same color
+    for (i, indicator) in enumerate(indicators)
+        # To make things visually clear, we will also plot some example surrogate
+        # timeseries for each indicator and change metric pair
+        for _ in 1:10
+            s = TimeseriesSurrogates.surrogate(x, surromethod)
+            p = windowmap(indicator, s; width = width_ind)
+            q = windowmap(metric, p; width = width_cha, stride = stride_cha)
+            lines!(fig[i+1, 1], results.t_change, q;  color = (color, 0.2), linewidth = 1)
+        end
+        # Plot the flags as vertical dashed lines
+        vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+            color = color, linestyle = :dash, linewidth = 3
+        )
+    end
+    # add a title to the figure with how we estimate significance
+    content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod)))
+end
+
+surromethod = RandomFourier()
+overplot_surrogate_significance!(fig, surromethod)
+
+fig

                        Different surrogates

                        Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

                        A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

                        A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

                        surromethod = RelativePartialRandomization(0.25)
+fig = plot_change_metrics()
+overplot_surrogate_significance!(fig, surromethod, "gray")
+fig

                        Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

                        Simpler Significance

                        Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

                        fig = plot_change_metrics()
+flags = significant_transitions(results, SigmaSignificance(factor = 5.0))
+
+# Plot the flags
+for (i, indicator) in enumerate(indicators)
+    vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+        color = Cycled(3), linestyle = :dash, linewidth = 3
+    )
+end
+content(fig[1, 1]).title = "significance from std"
+fig
                        diff --git a/previews/PR48/index.html b/previews/PR48/index.html new file mode 100644 index 00000000..5c677740 --- /dev/null +++ b/previews/PR48/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
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                        TransitionsInTimeseries.jl

                        TransitionsInTimeseries.jl

                        TransitionsInTimeseries — Module

                        TransitionsInTimeseries.jl

                        CI codecov Package Downloads

                        A Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                        This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

                        add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

                        All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                        source
                        Star us on GitHub!

                        If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                        Content

                        Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                        • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                        • Makes the surrogate analysis to test for significance under the hub.
                        • Can be easily extended by any user without touching the source code.
                        • Reduces the programming overhead for any researcher willing to benchmark new methods.
                        • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                        • Increases trustworthiness thanks to a large test suite.
                        Similar projects

                        An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                        Approaches

                        Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                        diff --git a/previews/PR48/refs.bib b/previews/PR48/refs.bib new file mode 100644 index 00000000..8010a9d3 --- /dev/null +++ b/previews/PR48/refs.bib @@ -0,0 +1,54 @@ + +@article{willeit-earth-2022, + title = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1: {Climate} model description and validation​​​​​​​​​​​​​​}, + volume = {15}, + issn = {1991-9603}, + shorttitle = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1}, + url = {https://gmd.copernicus.org/articles/15/5905/2022/}, + doi = {10.5194/gmd-15-5905-2022}, + abstract = {The newly developed fast Earth system model CLIMBER-X is presented. The climate component of CLIMBER-X consists of a 2.5-D semi-empirical statistical–dynamical atmosphere model, a 3-D frictional–geostrophic ocean model, a dynamic–thermodynamic sea ice model and a land surface model. All the model components are discretized on a regular lat–long grid with a horizontal resolution of 5 ◦ × 5 ◦. The model has a throughput of ∼ 10 000 simulation years per day on a single node with 16 CPUs on a high-performance computer and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to {\textgreater} 100 000 years. A comprehensive evaluation of the model performance for the present day and the historical period shows that CLIMBER-X is capable of realistically reproducing many observed climate characteristics, with results that generally lie within the range of state-of-theart general circulation models. The analysis of model performance is complemented by a thorough assessment of climate feedbacks and model sensitivities to changes in external forcings and boundary conditions. Limitations and applicability of the model are critically discussed. CLIMBER-X also includes a detailed representation of the global carbon cycle and is coupled to an ice sheet model, which will be described in separate papers. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.}, + language = {en}, + number = {14}, + urldate = {2022-08-11}, + journal = {Geoscientific Model Development}, + author = {Willeit, Matteo and Ganopolski, Andrey and Robinson, Alexander and Edwards, Neil R.}, + month = jul, + year = {2022}, + pages = {5905--5948}, + file = {Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:/home/jan/Zotero/storage/75NKS975/Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:application/pdf}, +} + +@article{boers-early-warning-2018, + title = {Early-warning signals for {Dansgaard}-{Oeschger} events in a high-resolution ice core record}, + volume = {9}, + issn = {2041-1723}, + url = {http://www.nature.com/articles/s41467-018-04881-7}, + doi = {10.1038/s41467-018-04881-7}, + language = {en}, + number = {1}, + urldate = {2022-10-28}, + journal = {Nature Communications}, + author = {Boers, Niklas}, + month = dec, + year = {2018}, + pages = {2556}, + file = {Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:/home/jan/Zotero/storage/DS97Z9UC/Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:application/pdf}, +} + +@article{rasmussen-stratigraphic-2014, + title = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records: refining and extending the {INTIMATE} event stratigraphy}, + volume = {106}, + issn = {02773791}, + shorttitle = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0277379114003485}, + doi = {10.1016/j.quascirev.2014.09.007}, + abstract = {Due to their outstanding resolution and well-constrained chronologies, Greenland ice-core records provide a master record of past climatic changes throughout the Last InterglacialeGlacial cycle in the North Atlantic region. As part of the INTIMATE (INTegration of Ice-core, MArine and TErrestrial records) project, protocols have been proposed to ensure consistent and robust correlation between different records of past climate. A key element of these protocols has been the formal definition and ordinal numbering of the sequence of Greenland Stadials (GS) and Greenland Interstadials (GI) within the most recent glacial period. The GS and GI periods are the Greenland expressions of the characteristic DansgaardeOeschger events that represent cold and warm phases of the North Atlantic region, respectively. We present here a more detailed and extended GS/GI template for the whole of the Last Glacial period. It is based on a synchronization of the NGRIP, GRIP, and GISP2 ice-core records that allows the parallel analysis of all three records on a common time scale. The boundaries of the GS and GI periods are defined based on a combination of stable-oxygen isotope ratios of the ice (d18O, reflecting mainly local temperature) and calcium ion concentrations (reflecting mainly atmospheric dust loading) measured in the ice. The data not only resolve the well-known sequence of DansgaardeOeschger events that were first defined and numbered in the ice-core records more than two decades ago, but also better resolve a number of short-lived climatic oscillations, some defined here for the first time. Using this revised scheme, we propose a consistent approach for discriminating and naming all the significant abrupt climatic events of the Last Glacial period that are represented in the Greenland ice records. The final product constitutes an extended and better resolved Greenland stratotype sequence, against which other proxy records can be compared and correlated. It also provides a more secure basis for investigating the dynamics and fundamental causes of these climatic perturbations.}, + language = {en}, + urldate = {2023-10-04}, + journal = {Quaternary Science Reviews}, + author = {Rasmussen, Sune O. and Bigler, Matthias and Blockley, Simon P. and Blunier, Thomas and Buchardt, Susanne L. and Clausen, Henrik B. and Cvijanovic, Ivana and Dahl-Jensen, Dorthe and Johnsen, Sigfus J. and Fischer, Hubertus and Gkinis, Vasileios and Guillevic, Myriam and Hoek, Wim Z. and Lowe, J. John and Pedro, Joel B. and Popp, Trevor and Seierstad, Inger K. and Steffensen, Jørgen Peder and Svensson, Anders M. and Vallelonga, Paul and Vinther, Bo M. and Walker, Mike J.C. and Wheatley, Joe J. and Winstrup, Mai}, + month = dec, + year = {2014}, + pages = {14--28}, + file = {Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:/home/jan/Zotero/storage/VSUTVWPN/Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:application/pdf}, +} diff --git a/previews/PR48/refs/index.html b/previews/PR48/refs/index.html new file mode 100644 index 00000000..fd7383e3 --- /dev/null +++ b/previews/PR48/refs/index.html @@ -0,0 +1,9 @@ + +References · TransitionsInTimeseries.jl
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                        References

                        diff --git a/previews/PR48/search/index.html b/previews/PR48/search/index.html new file mode 100644 index 00000000..6fb0c177 --- /dev/null +++ b/previews/PR48/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

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                          diff --git a/previews/PR48/search_index.js b/previews/PR48/search_index.js new file mode 100644 index 00000000..e622d8d4 --- /dev/null +++ b/previews/PR48/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowConfig\nSlidingWindowConfig\nSegmentWindowConfig\nestimate_indicator_changes\nWindowResults\nSlidingWindowResults\nSegmentWindowResults","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowConfig","page":"API","title":"TransitionsInTimeseries.WindowConfig","text":"WindowConfig\n\nSupertype used to define the window configuration of estimate_indicator_changes. Valid subtypes are:\n\nSlidingWindowConfig.\nSegmentWindowConfig.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowConfig","page":"API","title":"TransitionsInTimeseries.SlidingWindowConfig","text":"SlidingWindowConfig(indicators, change_metrics; kwargs...) → config\n\nA configuration struct for TransitionsInTimeseries.jl that collects the sliding window parameters, the indicators and the corresponding metrics to use in estimate_indicator_changes.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentWindowConfig","page":"API","title":"TransitionsInTimeseries.SegmentWindowConfig","text":"SegmentWindowConfig(indicators, change_metrics, tseg_start, tseg_end;\n kwargs...) → config\n\nA configuration struct for TransitionsInTimeseries.jl that collects the start and end time of the segments over which the analysis estimate_indicator_changes is to be run, as well as its windowing parameters.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics. tseg_start and tseg_end are ::Vector of length n, with n the number of segments.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any appropriate function may be given and see making custom indicators/change metrics in the documentation for more information.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nmin_width_cha::Int=50: minimal width required to perform the change metric estimation. If segment not sufficiently long, return Inf.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector for the k-th segment is computed simply via:\nt_indicator[k] = windowmap(whichtime, t; width_ind, stride_ind)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.estimate_indicator_changes","page":"API","title":"TransitionsInTimeseries.estimate_indicator_changes","text":"estimate_indicator_changes(config::SlidingWindowConfig, x [,t]) → output\n\nEstimate possible transitions for input timeseries x using a sliding window approach as described by config:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nIf t (the time vector of x), is not provided, it is assumed t = eachindex(x).\n\nReturn the output as WindowResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\nestimate_indicator_changes(config::SegmentWindowConfig, x [,t]) → output\n\nEstimate possible transitions for input timeseries x using a segmented window approach as described by config:\n\nFor each segment specified in config, estimate the corresponding indicator timeseries by sliding a window over the input timeseries.\nFor each segment of the indicator timeseries, estimate a scalar change metric by applying a window of the size of the indicator segment.\n\nIf t (the time vector of x), is not provided, it is assumed t = eachindex(x).\n\nReturn the output as WindowResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.WindowResults","page":"API","title":"TransitionsInTimeseries.WindowResults","text":"WindowResults\n\nSupertype used to gather results of estimate_indicator_changes. Valid subtypes are:\n\nSlidingWindowResults.\nSegmentWindowResults.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowResults","page":"API","title":"TransitionsInTimeseries.SlidingWindowResults","text":"SlidingWindowResults\n\nA struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nconfig::SlidingWindowConfig, used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentWindowResults","page":"API","title":"TransitionsInTimeseries.SegmentWindowResults","text":"SegmentWindowResults\n\nA struct containing the output of estimate_indicator_changes used with SegmentWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.\nt_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.\nx_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.\nt_change, the time vector of the change metric.\nconfig::SegmentWindowConfig, used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"significant_transitions\nTransitionsSignificance\nSurrogatesSignificance\nQuantileSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::WindowResults, signif::TransitionsSignificance)\n\nEstimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.TransitionsSignificance","page":"API","title":"TransitionsInTimeseries.TransitionsSignificance","text":"TransitionsSignificance\n\nSupertype used to test for significance in significant_transitions. Valid subtypes are:\n\nSurrogatesSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: TransitionsSignificance\nSurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)\n\nA configuration struct for significance testing significant_transitions using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\n\nDescription\n\nWhen used with WindowResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowResults.\n\nNote that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance\n\nA configuration struct for significance testing significant_transitions. When used with WindowResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\nQuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis and quantify some entropy-based dynamic quantity in the timeseries. They are provided by the ComplexityMeasures.jl package, that lists 100s of possible such indicators. Here we only provide an indicator out of the box for the permutation entropy, but building something similar is trivial:","category":"page"},{"location":"api/","page":"API","title":"API","text":"function permutation_entropy(; m = 3, τ = 1)\n est = SymbolicPermutation(; m, τ)\n return x -> entropy_normalized(est, x)\nend","category":"page"},{"location":"api/","page":"API","title":"API","text":"permutation_entropy\nentropy","category":"page"},{"location":"api/#TransitionsInTimeseries.permutation_entropy","page":"API","title":"TransitionsInTimeseries.permutation_entropy","text":"permutation_entropy(; m = 3, τ = 1) → f\n\nReturn a function that given timeseries x it computes the normalized permutation entropy of order m with time delay τ.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.entropy","page":"API","title":"StatsBase.entropy","text":"entropy(p, [b])\n\nCompute the entropy of a collection of probabilities p, optionally specifying a real number b such that the entropy is scaled by 1/log(b). Elements with probability 0 or 1 add 0 to the entropy.\n\n\n\n\n\n","category":"function"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length.","category":"page"},{"location":"api/","page":"API","title":"API","text":"TODO: Here explain how to use precomputable functions","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"EditURL = \"do-events.jl\"","category":"page"},{"location":"examples/do-events/#Dansgaard-Oescher-events-and-Critical-Slowing-Down","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The delta^18O timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.","category":"page"},{"location":"examples/do-events/#Preprocessing-NGRIP","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Preprocessing NGRIP","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Load the data, reverse and offset it to have time vector = time before 2000 AD.\nFilter non-unique points in time and sort the data.\nRegrid the data from uneven to even sampling.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The time and delta^18O vectors resulting from the i-th preprocessing step are respectively called t_i and x_i. The final step consists in obtaining a residual r, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.","category":"page"},{"location":"examples/do-events/#Step-1:","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 1:","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DelimitedFiles, Downloads\n\nfunction load_ngrip()\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP.csv\")\n data, labels = readdlm(tmp, header = true)\n return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors\nend\n\nt1, x1 = load_ngrip()","category":"page"},{"location":"examples/do-events/#Step-2","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 2","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"uniqueidx(v) = unique(i -> v[i], eachindex(v))\nfunction keep_unique(t, x)\n unique_idx = uniqueidx(t)\n return t[unique_idx], x[unique_idx]\nend\n\nfunction sort_timeseries!(t, x)\n p = sortperm(t)\n permute!(t, p)\n permute!(x, p)\n return nothing\nend\n\nt2, x2 = keep_unique(t1, x1)\nsort_timeseries!(t2, x2)","category":"page"},{"location":"examples/do-events/#Step-3","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 3","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using BSplineKit\n\nfunction regrid2evensampling(t, x, dt)\n itp = BSplineKit.interpolate(t, x, BSplineOrder(4))\n tspan = (ceil(minimum(t)), floor(maximum(t)))\n t_even = collect(tspan[1]:dt:tspan[2])\n x_even = itp.(t_even)\n return t_even, x_even\nend\n\ndt = 5.0 # dt = 5 yr as in (Boers 2018)\nt3, x3 = regrid2evensampling(t2, x2, dt)","category":"page"},{"location":"examples/do-events/#Step-4","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 4","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the final step we drop the indices:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DSP\n\nfunction chebyshev_filter(t, x, fcutoff)\n ii = 10 # Chebyshev filtering requires to prune first points of timeseries.\n responsetype = Highpass(fcutoff, fs = 1/dt)\n designmethod = Chebyshev1(8, 0.05)\n r = filt(digitalfilter(responsetype, designmethod), x)\n xtrend = x - r\n return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]\nend\n\nfcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)\nt, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using CairoMakie, Loess\n\nfunction loess_filter(t, x; span = 0.005)\n loessmodel = loess(t, x, span = span)\n xtrend = Loess.predict(loessmodel, t)\n r = x - xtrend\n return t, x, xtrend, r\nend\n\nfunction kyr_xticks(tticks_yr)\n tticks_kyr = [\"$t\" for t in Int.(tticks_yr ./ 1e3)]\n return (tticks_yr, tticks_kyr)\nend\n\nfunction plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)\n fig = Figure(resolution = (1600, 1200), fontsize = 24)\n\n # Original timeseries with transition marked by vertical lines\n ax1 = Axis(fig[1, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"$\\delta^{18}$O (permil)\",\n xaxisposition = :top, xticks = xticks)\n lines!(ax1, traw, xraw, color = (:gray70, 0.5))\n lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)\n vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)\n\n # Residual timeseries\n ax2 = Axis(fig[2, 1], ylabel = L\"Residual $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n lines!(ax2, t, r, color = :gray50, linewidth = 1)\n\n # Axes for variance and AC1 timeseries\n ax3 = Axis(fig[3, 1], ylabel = L\"Variance $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n ax4 = Axis(fig[4, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"Lag-1 autocor. $\\,$\",\n xticks = xticks)\n\n axs = [ax1, ax2, ax3, ax4]\n [xlims!(ax, xlims) for ax in axs]\n ylims!(axs[1], (-48, -34))\n rowgap!(fig.layout, 10)\n return fig, axs\nend\n\nxlims = (-60e3, -10e3)\nxticks = kyr_xticks(-60e3:5e3:5e3)\nt_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,\n 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]\ntloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nfig","category":"page"},{"location":"examples/do-events/#Hindcast-on-NGRIP-data","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcast on NGRIP data","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using TransitionsInTimeseries, StatsBase\nusing Random: Xoshiro\n\nac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase\nindicators = (var, ac1)\nchange_metrics = RidgeRegressionSlope()\ntseg_start = t_rasmussen[1:end-1] .+ 200\ntseg_end = t_rasmussen[2:end] .- 200\nconfig = SegmentWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100) # require >=100 data points to estimate change metric\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"That's it! We can now visulaise our results with a generic function that we will re-use later:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"function plot_segment_analysis!(axs, results, signif)\n (; t_indicator, x_indicator) = results\n for k in eachindex(t_indicator) # loop over the segments\n for i in axes(signif.pvalues, 2) # loop over the indicators\n if !isinf(signif.pvalues[k, i]) # plot if segment long enough\n # Plot indicator timeseries and its linear regression\n ti, xi = t_indicator[k], x_indicator[k][:, i]\n lines!(axs[i+2], ti, xi, color = Cycled(1))\n m, p = ridgematrix(ti, 0.0) * xi\n if signif.pvalues[k, i] < 0.05\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)\n else\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)\n end\n end\n end\n end\nend\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.","category":"page"},{"location":"examples/do-events/#CSD:-only-a-necessary-condition,-only-in-some-cases","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"CSD: only a necessary condition, only in some cases","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential U, which defines the deterministic term f = -U of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before\nconfig = SegmentWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100)\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that \"resilience-loss indicators\" is a more accurate name than \"early-warning signals\" when using CSD.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"We draw attention upon the fact that the delta^18O timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"warning: Degrees of freedom\nThese sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"info: Future improvement\nSupporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.","category":"page"},{"location":"examples/do-events/#Hindcasting-simulated-DO-events","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcasting simulated DO-events","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],\n [1, 3500, 4370, 5790, 7200, 8140]]\nt_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]\ntseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]\ntseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]\n\nfigvec = Figure[]\n\nfor j in 1:2\n # Download the data and perform loess filtering on it\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\" *\n \"master/timeseries/climberx-do$(j)-omaxa.csv\")\n data = readdlm(tmp)\n tcx, xcx = data[1, 1000:end], data[2, 1000:end]\n t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)\n\n # Initialize figure\n xlims = (0, last(tcx))\n xticks = kyr_xticks(xlims[1]:1e3:xlims[2])\n fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks)\n ylims!(axs[1], (5, 40))\n axs[1].ylabel = L\"Max. Atlantic overturning (Sv) $\\,$\"\n\n # Run sliding analysis and update figure with results\n dt = mean(diff(tcx))\n config = SegmentWindowConfig(\n indicators, change_metrics, tseg_start[j], tseg_end[j],\n whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)\n results = estimate_indicator_changes(config, r, t)\n signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))\n flags = significant_transitions(results, signif)\n\n plot_segment_analysis!(axs, results, signif)\n vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)\n push!(figvec, fig)\nend\nfigvec[1]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"figvec[2]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"EditURL = \"logistic.jl\"","category":"page"},{"location":"examples/logistic/#Permutation-entropy-for-dynamic-regime-changes","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.","category":"page"},{"location":"examples/logistic/#Logistic-map-timeseries","page":"Permutation entropy for dynamic regime changes","title":"Logistic map timeseries","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using DynamicalSystemsBase\nusing CairoMakie\n\n# time-dependent logistic map, so that the `r` parameter increases with time\nr1 = 3.83\nr2 = 3.86\nN = 2000\nrs = range(r1, r2; length = N)\n\nfunction logistic_drifting_rule(u, rs, n)\n r = rs[n+1] # time is `n`, starting from 0\n return SVector(r*u[1]*(1 - u[1]))\nend\n\nds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)\nx = trajectory(ds, N-1)[1][:, 1]","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Plot it, using as time the parameter value (they coincide)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig, ax = lines(rs, x; linewidth = 0.5)\nax.xlabel = \"r (time)\"\nax.ylabel = \"x\"\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.","category":"page"},{"location":"examples/logistic/#Using-a-simpler-change-metric","page":"Permutation entropy for dynamic regime changes","title":"Using a simpler change metric","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Now, let's compute and various indicators and their changes, focusing on the fourth indicator, the permutation entropy. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using TransitionsInTimeseries\nindicators = (var, ar1_whitenoise, permutation_entropy(m = 4))\nindistrings = (\"var\", \"ar1\", \"pe\")","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"metric = difference_of_means\n\nwidth_ind = N÷100\nwidth_cha = 20\nstride_cha = 10\n\nconfig = SlidingWindowConfig(indicators, metric;\n width_ind, width_cha, stride_cha,\n)\n\nresults = estimate_indicator_changes(config, x, rs)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's now plot the change metrics of the indicators","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"function plot_change_metrics()\n fig, ax = lines(rs, x; axis = (ylabel = \"input\",), figure = (resolution = (600, 600),))\n hidexdecorations!(ax; grid = false)\n # plot all change metrics\n for (i, c) in enumerate(eachcol(results.x_change))\n ax, = scatterlines(fig[i+1, 1], results.t_change, c;\n axis = (ylabel = indistrings[i],), label = \"input\"\n )\n if i < 3\n hidexdecorations!(ax; grid = false)\n else\n ax.xlabel = \"r (time)\"\n end\n end\n return fig\nend\n\nfig = plot_change_metrics()","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.","category":"page"},{"location":"examples/logistic/#Significance-via-random-Fourier-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Significance via random Fourier surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RandomFourier()\n\n# Define a function because we will re-use later\nusing Random: Xoshiro\nfunction overplot_surrogate_significance!(fig, surromethod, color = \"black\")\n\n signif = SurrogatesSignificance(;\n n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),\n )\n flags = significant_transitions(results, signif)\n\n # and also plot the flags with same color\n for (i, indicator) in enumerate(indicators)\n # To make things visually clear, we will also plot some example surrogate\n # timeseries for each indicator and change metric pair\n for _ in 1:10\n s = TimeseriesSurrogates.surrogate(x, surromethod)\n p = windowmap(indicator, s; width = width_ind)\n q = windowmap(metric, p; width = width_cha, stride = stride_cha)\n lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1)\n end\n # Plot the flags as vertical dashed lines\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = color, linestyle = :dash, linewidth = 3\n )\n end\n # add a title to the figure with how we estimate significance\n content(fig[1, 1]).title = \"surrogates: \"*string(nameof(typeof(surromethod)))\nend\n\nsurromethod = RandomFourier()\noverplot_surrogate_significance!(fig, surromethod)\n\nfig","category":"page"},{"location":"examples/logistic/#Different-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Different surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RelativePartialRandomization(0.25)\nfig = plot_change_metrics()\noverplot_surrogate_significance!(fig, surromethod, \"gray\")\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.","category":"page"},{"location":"examples/logistic/#Simpler-Significance","page":"Permutation entropy for dynamic regime changes","title":"Simpler Significance","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig = plot_change_metrics()\nflags = significant_transitions(results, SigmaSignificance(factor = 5.0))\n\n# Plot the flags\nfor (i, indicator) in enumerate(indicators)\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = Cycled(3), linestyle = :dash, linewidth = 3\n )\nend\ncontent(fig[1, 1]).title = \"significance from std\"\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"refs/#References","page":"References","title":"References","text":"","category":"section"},{"location":"refs/","page":"References","title":"References","text":"","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"EditURL = \"tutorial.jl\"","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector,\n# we obtain the last time step of each window.\n# This therefore only uses information from `k-width+1` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\n\nfunction gridfig(nrows, ncols)\n fig = Figure()\n axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)\n for j in 1:ncols, i in 1:nrows]\n rowgap!(fig.layout, 10)\n return fig, axs\nend\nfig, axs = gridfig(2, 1)\nlines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))\nlines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))\naxs[1].title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nlines!(axs[2], t_change, change_nl, label = \"nonlin\", color = Cycled(2))\nlines!(axs[2], t_change, change_s, label = \"surrogate\", color = Cycled(3))\naxislegend()\naxs[2].title = \"change metric\"\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig, axs = gridfig(2, 2)\naxs[1].title = \"linear\"\naxs[2].title = \"nonlinear\"\n\nfor (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change) # ; color = Cycled(j)\n lines!(axsig, t_change, pval) # ; color = Cycled(j+2)\nend\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = RidgeRegressionSlope()\n\n# choices go into a configuration struct\nconfig = SlidingWindowConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last)\n\n# choices are processed\nresults = estimate_indicator_changes(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From result we can plot the change metric timeseries:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(3, 1)\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, results.x_change[:, 1];\n label = \"var slopes\", color = Cycled(3))\nscatter!(axs[3], results.t_change, results.x_change[:, 2];\n label = \"ar1 slopes\", color = Cycled(4))\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = :right)\nflags = significant_transitions(results, signif)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(2, 1)\nlines!(axs[1], vcat(0.0, t), x_nlinear; label = \"raw\", color = Cycled(1))\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 1];\n label = \"var p-values\", color = Cycled(3))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 2];\n label = \"ar1 p-values\", color = Cycled(4))\n\nflagsboth = vec(reduce(&, flags; dims = 2))\nvlines!(axs[1], results.t_change[flagsboth]; label = \"flags\", color = (\"black\", 0.1))\n\n[axislegend(ax) for ax in axs]\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"}] +} diff --git a/previews/PR48/siteinfo.js b/previews/PR48/siteinfo.js new file mode 100644 index 00000000..d4d3f93b --- /dev/null +++ b/previews/PR48/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR48"; diff --git a/previews/PR48/tutorial.jl b/previews/PR48/tutorial.jl new file mode 100644 index 00000000..3f135673 --- /dev/null +++ b/previews/PR48/tutorial.jl @@ -0,0 +1,263 @@ +#= + +# Tutorial + +## [Workflow] (@id workflow) + +Computing transition indicators consists of the following steps: + +1. Doing any preprocessing of raw data first, such as detrending (_not part of TransitionsInTimeseries.jl_). This yields the **input timeseries**. +2. Estimating the timeseries of an indicator by sliding a window over the input timeseries. +3. Computing the changes of the indicator by sliding a window over its timeseries. +4. Generating many surrogates that preserve important statistical properties of the original timeseries. +5. Performing step 2 and 3 for the surrogate timeseries. +6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data. + +These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports. + +## [Tutorial -- Educational] (@id example_stepbystep) + +### Raw input data + +Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by: + +```math +\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t) +``` + +with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with [Makie](https://docs.makie.org/stable/)) such prototypical data to test some indicators can be done by simply running: +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_linear) +lines!(ax, t, x_nlinear) +ax.title = "raw data" +fig + +#= +### Preprocessing + +!!! note "Not part of TransitionsInTimeseries.jl" + Any timeseries preprocessing, such as the de-trending step we do here, + is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher. + + +The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1. +=# + +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +#= +At this point, `x_l_fluct` and `x_nl_fluct` are considered the **input timeseries**. + +!!! info "Detrending in Julia" + Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as [Loess.jl](https://github.com/JuliaStats/Loess.jl) or [DSP.jl](https://docs.juliadsp.org/latest/contents/). There the detrending step consists of subtracting the smoothed signal from the original one. + +### Indicator timeseries + +We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the **input timeseries**, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as [`ar1_whitenoise`](@ref): +=# + +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +## By mapping `last::Function` over a windowviewer of the time vector, +## we obtain the last time step of each window. +## This therefore only uses information from `k-width+1` to `k` at time step `k`. +## Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +#= +The lines plotted above are the **indicator timeseries**. + +### Change metric timeseries + +From here, we process the **indicator timeseries** to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the **change metric timeseries**. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a [`RidgeRegressionSlope`](@ref): +=# + +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + +#= +### Timeseries surrogates + +As expected from [Critical Slowing Down](@ref approaches), an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance. + +In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the [TimeseriesSurrogates.jl](https://github.com/JuliaDynamics/TimeseriesSurrogates.jl) Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that `TimeseriesSurrogates` is re-exported by `TransitionsInTimeseries`, so that you don't have to `using` both of them. + +To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries. +=# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) + +function gridfig(nrows, ncols) + fig = Figure() + axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false) + for j in 1:ncols, i in 1:nrows] + rowgap!(fig.layout, 10) + return fig, axs +end +fig, axs = gridfig(2, 1) +lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2)) +lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3)) +axs[1].title = "real signal vs. surrogate(s)" + +## compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2)) +lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3)) +axislegend() +axs[2].title = "change metric" + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +### Quantifying significance + +To quantify the significance of the values of the **change metric timeseries** we perform a standard surrogate test by computing the [p-value](https://en.wikipedia.org/wiki/P-value) w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically `p<0.05`) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time: +=# + +n_surrogates = 1_000 +fig, axs = gridfig(2, 2) +axs[1].title = "linear" +axs[2].title = "nonlinear" + +for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + ## Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change) # ; color = Cycled(j) + lines!(axsig, t_change, pval) # ; color = Cycled(j+2) +end + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar. + +Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section. + +## [Tutorial -- TransitionsInTimeseries.jl] (@id example_fastforward) + +TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go. + +The interface is simple, and directly parallelizes the [Workflow](@ref). It is based on the creation of a [`TransitionsSurrogatesConfig`](@ref), which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate. + +The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +## input timeseries and time +input = x_nl_fluct = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(t, input) +ax.title = "input timeseries" +fig + +#= +To perform all of the above analysis we follow a 2-step process. + +Step 1, we decide what indicators and change metrics to use in [`SlidingWindowConfig`](@ref) and apply those via +a sliding window to the input timeseries using [`transition_metrics`](@ref). +=# + +## These indicators are suitable for Critical Slowing Down +indicators = (var, ar1_whitenoise) + +## use the ridge regression slope for both indicators +change_metrics = RidgeRegressionSlope() + +## choices go into a configuration struct +config = SlidingWindowConfig(indicators, change_metrics; + width_ind = 400, width_cha = 30, whichtime = last) + +## choices are processed +results = estimate_indicator_changes(config, input, t) + +#= +From `result` we can plot the change metric timeseries: +=# + +fig, axs = gridfig(3, 1) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, results.x_change[:, 1]; + label = "var slopes", color = Cycled(3)) +scatter!(axs[3], results.t_change, results.x_change[:, 2]; + label = "ar1 slopes", color = Cycled(4)) +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +Step 2 is to estimate significance using [`SurrogatesConfig`](@ref) +and the function [`estimate_significance!`](@ref). +=# + +signif = SurrogatesSignificance(n = 1000, tail = :right) +flags = significant_transitions(results, signif) + +#= +We can now plot the p-values corresponding to each time series of the change metrics. From the `flags` we can additionally obtain the time points where _both_ indicators show significance, via a simple reduction: +=# + +fig, axs = gridfig(2, 1) +lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1)) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 1]; + label = "var p-values", color = Cycled(3)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 2]; + label = "ar1 p-values", color = Cycled(4)) + +flagsboth = vec(reduce(&, flags; dims = 2)) +vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1)) + +[axislegend(ax) for ax in axs] +[xlims!(ax, 0, 50) for ax in axs] +fig \ No newline at end of file diff --git a/previews/PR48/tutorial/index.html b/previews/PR48/tutorial/index.html new file mode 100644 index 00000000..09b2c71b --- /dev/null +++ b/previews/PR48/tutorial/index.html @@ -0,0 +1,160 @@ + +Tutorial · TransitionsInTimeseries.jl
                          Edit on GitHub

                          Tutorial

                          Workflow

                          Computing transition indicators consists of the following steps:

                          1. Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                          2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                          3. Computing the changes of the indicator by sliding a window over its timeseries.
                          4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                          5. Performing step 2 and 3 for the surrogate timeseries.
                          6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                          These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                          Tutorial – Educational

                          Raw input data

                          Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                          \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                          with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                          using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig

                          Preprocessing

                          Not part of TransitionsInTimeseries.jl

                          Any timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                          The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                          x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                          At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                          Detrending in Julia

                          Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                          Indicator timeseries

                          We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                          indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector,
+# we obtain the last time step of each window.
+# This therefore only uses information from `k-width+1` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                          The lines plotted above are the indicator timeseries.

                          Change metric timeseries

                          From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                          change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                          Timeseries surrogates

                          As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                          In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                          To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                          # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+
+function gridfig(nrows, ncols)
+    fig = Figure()
+    axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)
+        for j in 1:ncols, i in 1:nrows]
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+fig, axs = gridfig(2, 1)
+lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))
+lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))
+axs[1].title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2))
+lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3))
+axislegend()
+axs[2].title = "change metric"
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                          Quantifying significance

                          To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                          n_surrogates = 1_000
+fig, axs = gridfig(2, 2)
+axs[1].title = "linear"
+axs[2].title = "nonlinear"
+
+for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change)   # ; color = Cycled(j)
+    lines!(axsig, t_change, pval)       # ; color = Cycled(j+2)
+end
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                          As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                          Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                          Tutorial – TransitionsInTimeseries.jl

                          TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                          The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

                          The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

                          using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig

                          To perform all of the above analysis we follow a 2-step process.

                          Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.

                          # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = RidgeRegressionSlope()
+
+# choices go into a configuration struct
+config = SlidingWindowConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last)
+
+# choices are processed
+results = estimate_indicator_changes(config, input, t)
                          WindowResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                          From result we can plot the change metric timeseries:

                          fig, axs = gridfig(3, 1)
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, results.x_change[:, 1];
+    label = "var slopes", color = Cycled(3))
+scatter!(axs[3], results.t_change, results.x_change[:, 2];
+    label = "ar1 slopes", color = Cycled(4))
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                          Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.

                          signif = SurrogatesSignificance(n = 1000, tail = :right)
+flags = significant_transitions(results, signif)
                          2072×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ ⋮  
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0

                          We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:

                          fig, axs = gridfig(2, 1)
+lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1))
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 1];
+    label = "var p-values", color = Cycled(3))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 2];
+    label = "ar1 p-values", color = Cycled(4))
+
+flagsboth = vec(reduce(&, flags; dims = 2))
+vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1))
+
+[axislegend(ax) for ax in axs]
+[xlims!(ax, 0, 50) for ax in axs]
+fig
                          diff --git a/previews/PR49/api/index.html b/previews/PR49/api/index.html new file mode 100644 index 00000000..4a2ec2a8 --- /dev/null +++ b/previews/PR49/api/index.html @@ -0,0 +1,22 @@ + +API · TransitionsInTimeseries.jl
                          Edit on GitHub

                          API

                          Main analysis functions

                          TransitionsInTimeseries.SlidingWindowConfig — Type
                          SlidingWindowConfig <: IndicatorsChangesConfig
+SlidingWindowConfig(indicators, change_metrics; kwargs...)

                          A configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:

                          1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                          2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                          indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                          Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.

                          Keyword arguments

                          • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.
                          • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.
                          • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:
                            • last: use the last timepoint of each window
                            • midpoint: use the mid timepoint of each time window
                            • first: use first timepoint of each window
                            In fact, the indicators time vector is computed simply via
                            t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)
                            so any other function of the time window may be given to extract the time point itself, such as mean or median.
                          • T = Float64: Element type of input timeseries to initialize some computations.
                          source
                          TransitionsInTimeseries.SegmentedWindowConfig — Type
                          SegmentedWindowConfig <: IndicatorsChangeConfig
+SegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)

                          A configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:

                          1. For each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).
                          2. For each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d

                          tseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.

                          Keyword arguments

                          • width_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.
                          • min_width_cha::Int=50: minimal width required to perform the change metric estimation. If segment not sufficiently long, return NaN.
                          source
                          TransitionsInTimeseries.estimate_indicator_changes — Function
                          estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → output

                          Estimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).

                          Return the output as WindowResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                          source
                          TransitionsInTimeseries.SlidingWindowResults — Type
                          SlidingWindowResults

                          A struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                          It has the following fields that the user may access

                          • x: the input timeseries.

                          • t: the time vector of the input timeseries.

                          • x_indicator, the indicator timeseries (matrix with each column one indicator).

                          • t_indicator, the time vector of the indicator timeseries.

                          • x_change, the change metric timeseries (matrix with each column one change metric).

                          • t_change, the time vector of the change metric timeseries.

                          • config::SlidingWindowConfig, used for the analysis.

                          source
                          TransitionsInTimeseries.SegmentWindowResults — Type
                          SegmentWindowResults

                          A struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                          It has the following fields that the user may access

                          • x: the input timeseries.

                          • t: the time vector of the input timeseries.

                          • x_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.

                          • t_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.

                          • x_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.

                          • t_change, the time vector of the change metric.

                          • config::SegmentedWindowConfig, used for the analysis.

                          source

                          Significance testing

                          TransitionsInTimeseries.significant_transitions — Function
                          significant_transitions(res::WindowResults, signif::TransitionsSignificance)

                          Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.

                          source
                          TransitionsInTimeseries.SurrogatesSignificance — Type
                          SurrogatesSignificance <: TransitionsSignificance
+SurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)

                          A configuration struct for significance testing significant_transitions using timeseries surrogates.

                          Keyword arguments

                          • surromethod = RandomFourier(): method to generate surrogates
                          • n = 1000: how many surrogates to generate
                          • rng = Random.default_rng(): random number generator for the surrogates
                          • p = 0.05: threshold for significance of the p-value
                          • tail = :both: tail type used, see below

                          Description

                          When used with WindowResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

                          The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowResults.

                          Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

                          source
                          TransitionsInTimeseries.QuantileSignificance — Type
                          QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance

                          A configuration struct for significance testing significant_transitions. When used with WindowResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                          QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

                          source

                          Indicators

                          Value distribution

                          Statistics.mean — Method
                          mean(itr)

                          Compute the mean of all elements in a collection.

                          Note

                          If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

                          Examples

                          julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
                          StatsBase.skewness — Function
                          skewness(v, [wv::AbstractWeights], m=mean(v))

                          Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                          StatsBase.kurtosis — Function
                          kurtosis(v, [wv::AbstractWeights], m=mean(v))

                          Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                          Critical Slowing Down

                          Statistics.var — Method
                          var(itr; corrected::Bool=true, mean=nothing[, dims])

                          Compute the sample variance of collection itr.

                          The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

                          If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

                          A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

                          Note

                          If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

                          TransitionsInTimeseries.ar1_whitenoise — Function
                          ar1_whitenoise(x::AbstractVector)

                          Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

                          \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                          source

                          Spectrum

                          TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                          LowfreqPowerSpectrum(; q_lofreq = 0.1)

                          Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                          lfps = precompute( LowfreqPowerSpectrum() )

                          Keyword arguments:

                          • q_lofreq: a number between 0 and 1 that characterises which portion of the

                          frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                          source

                          Nonlinear dynamics

                          Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.

                          For example, using the permutation entropy as an indicator is as simple as doing

                          using ComplexityMeasures
+est = OrdinalPatterns(; m = 3) # order 3
+# create a function that given timeseries returns permutation entropy
+indicator = x -> entropy_normalized(est, x)

                          and giving the created indicator to e.g., SlidingWindowConfig.

                          Change metrics

                          Slope

                          TransitionsInTimeseries.kendalltau — Function
                          kendalltau(x::AbstractVector)

                          Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                          source
                          TransitionsInTimeseries.spearman — Function
                          spearman(x::AbstractVector)

                          Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                          source

                          Value distribution differences

                          TransitionsInTimeseries.difference_of_means — Function
                          difference_of_means(x::AbstractArray)

                          Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                          # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                          difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                          source

                          Make your own indicator/metric!

                          The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                          There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:

                          Missing docstring.

                          Missing docstring for precompute. Check Documenter's build log for details.

                          Surrogates

                          For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                          Sliding windows

                          TransitionsInTimeseries.WindowViewer — Type
                          WindowViewer(x; width, stride)

                          Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                          If not given, the keywords width, stride are taken as default_window_width(x) and 1.

                          source
                          TransitionsInTimeseries.windowmap — Function
                          windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                          A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                          source

                          Load data

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+ } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR49/assets/search.js b/previews/PR49/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR49/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
                        • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR49/assets/themes/documenter-dark.css 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rgba(255,255,255,0.25)}html.theme--documenter-dark .button.is-white:active,html.theme--documenter-dark .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white{background-color:#fff;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark 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.button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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rgba(245,245,245,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#f5f5f5;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:#292929}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#2f2f2f;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,54,54,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#292929;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#e8e8e8}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#4eb5de;border-color:#4eb5de;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #4eb5de #4eb5de !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#4eb5de;box-shadow:none;color:#4eb5de}html.theme--documenter-dark 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They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found [here](https://www.iceandclimate.nbi.ku.dk/data/) in its raw format. This analysis has already been done in [boers-early-warning-2018](@cite) and we here try to reproduce Figure 2.d-f. + +## Preprocessing NGRIP + +Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps: +1. Load the data, reverse and offset it to have time vector = time before 2000 AD. +2. Filter non-unique points in time and sort the data. +3. Regrid the data from uneven to even sampling. + +The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing. + +### Step 1: +=# + +using DelimitedFiles, Downloads + +function load_ngrip() + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP.csv") + data, labels = readdlm(tmp, header = true) + return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors +end + +t1, x1 = load_ngrip() + +#= +### Step 2 +=# + +uniqueidx(v) = unique(i -> v[i], eachindex(v)) +function keep_unique(t, x) + unique_idx = uniqueidx(t) + return t[unique_idx], x[unique_idx] +end + +function sort_timeseries!(t, x) + p = sortperm(t) + permute!(t, p) + permute!(x, p) + return nothing +end + +t2, x2 = keep_unique(t1, x1) +sort_timeseries!(t2, x2) + +#= +### Step 3 +=# + +using BSplineKit + +function regrid2evensampling(t, x, dt) + itp = BSplineKit.interpolate(t, x, BSplineOrder(4)) + tspan = (ceil(minimum(t)), floor(maximum(t))) + t_even = collect(tspan[1]:dt:tspan[2]) + x_even = itp.(t_even) + return t_even, x_even +end + +dt = 5.0 # dt = 5 yr as in (Boers 2018) +t3, x3 = regrid2evensampling(t2, x2, dt) + +#= +### Step 4 + +For the final step we drop the indices: +=# + +using DSP + +function chebyshev_filter(t, x, fcutoff) + ii = 10 # Chebyshev filtering requires to prune first points of timeseries. + responsetype = Highpass(fcutoff, fs = 1/dt) + designmethod = Chebyshev1(8, 0.05) + r = filt(digitalfilter(responsetype, designmethod), x) + xtrend = x - r + return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end] +end + +fcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018) +t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff) + +#= +Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from [rasmussen-stratigraphic-2014](@cite) (which will soon be available as downloadable): +=# + +using CairoMakie, Loess + +function loess_filter(t, x; span = 0.005) + loessmodel = loess(t, x, span = span) + xtrend = Loess.predict(loessmodel, t) + r = x - xtrend + return t, x, xtrend, r +end + +function kyr_xticks(tticks_yr) + tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)] + return (tticks_yr, tticks_kyr) +end + +function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks) + fig = Figure(resolution = (1600, 1200), fontsize = 24) + + ## Original timeseries with transition marked by vertical lines + ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)", + xaxisposition = :top, xticks = xticks) + lines!(ax1, traw, xraw, color = (:gray70, 0.5)) + lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3) + vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3) + + ## Residual timeseries + ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + lines!(ax2, t, r, color = :gray50, linewidth = 1) + + ## Axes for variance and AC1 timeseries + ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$", + xticks = xticks) + + axs = [ax1, ax2, ax3, ax4] + [xlims!(ax, xlims) for ax in axs] + ylims!(axs[1], (-48, -34)) + rowgap!(fig.layout, 10) + return fig, axs +end + +xlims = (-60e3, -10e3) +xticks = kyr_xticks(-60e3:5e3:5e3) +t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160, + 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703] +tloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +fig + +#= +## Hindcast on NGRIP data + +As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including [boers-early-warning-2018](@cite), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using `SegmentedWindowConfig`, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here: +=# + +using TransitionsInTimeseries, StatsBase +using Random: Xoshiro + +ac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase +indicators = (var, ac1) +change_metrics = RidgeRegressionSlope() +tseg_start = t_rasmussen[1:end-1] .+ 200 +tseg_end = t_rasmussen[2:end] .- 200 +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) # require >=100 data points to estimate change metric +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) + +#= +That's it! We can now visulaise our results with a generic function that we will re-use later: +=# + +function plot_segment_analysis!(axs, results, signif) + (; t_indicator, x_indicator) = results + for k in eachindex(t_indicator) # loop over the segments + for i in axes(signif.pvalues, 2) # loop over the indicators + if !isinf(signif.pvalues[k, i]) # plot if segment long enough + ## Plot indicator timeseries and its linear regression + ti, xi = t_indicator[k], x_indicator[k][:, i] + lines!(axs[i+2], ti, xi, color = Cycled(1)) + m, p = ridgematrix(ti, 0.0) * xi + if signif.pvalues[k, i] < 0.05 + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3) + else + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3) + end + end + end + end +end +plot_segment_analysis!(axs, results, signif) +fig + +#= +In [boers-early-warning-2018](@cite), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in [boers-early-warning-2018](@cite), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of [boers-early-warning-2018](@cite). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media. + +## CSD: only a necessary condition, only in some cases + +For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a **necessary condition** for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is **not a sufficient condition** for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition: +=# + +tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +plot_segment_analysis!(axs, results, signif) +fig + +#= +For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD. + +We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC). + +!!! warning "Degrees of freedom" + These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice. + +!!! info "Future improvement" + Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias. + +## Hindcasting simulated DO-events + +In CLIMBER-X, the EMIC described in [willeit-earth-2022](@cite), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs: +=# + +t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050], + [1, 3500, 4370, 5790, 7200, 8140]] +t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]] +tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]] +tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50] + +figvec = Figure[] + +for j in 1:2 + ## Download the data and perform loess filtering on it + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" * + "master/timeseries/climberx-do$(j)-omaxa.csv") + data = readdlm(tmp) + tcx, xcx = data[1, 1000:end], data[2, 1000:end] + t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02) + + ## Initialize figure + xlims = (0, last(tcx)) + xticks = kyr_xticks(xlims[1]:1e3:xlims[2]) + fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks) + ylims!(axs[1], (5, 40)) + axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$" + + ## Run sliding analysis and update figure with results + dt = mean(diff(tcx)) + config = SegmentedWindowConfig( + indicators, change_metrics, tseg_start[j], tseg_end[j], + whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100) + results = estimate_indicator_changes(config, r, t) + signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995)) + flags = significant_transitions(results, signif) + + plot_segment_analysis!(axs, results, signif) + vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3) + push!(figvec, fig) +end +figvec[1] + +#= +It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case: +=# + +figvec[2] + +#= +Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience. +=# \ No newline at end of file diff --git a/previews/PR49/examples/do-events/index.html b/previews/PR49/examples/do-events/index.html new file mode 100644 index 00000000..19cc0325 --- /dev/null +++ b/previews/PR49/examples/do-events/index.html @@ -0,0 +1,191 @@ + +Dansgaard-Oescher events and Critical Slowing Down · TransitionsInTimeseries.jl
                          Edit on GitHub

                          Dansgaard-Oescher events and Critical Slowing Down

                          The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.

                          Preprocessing NGRIP

                          Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:

                          1. Load the data, reverse and offset it to have time vector = time before 2000 AD.
                          2. Filter non-unique points in time and sort the data.
                          3. Regrid the data from uneven to even sampling.

                          The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.

                          Step 1:

                          using DelimitedFiles, Downloads
+
+function load_ngrip()
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+        "master/timeseries/NGRIP.csv")
+    data, labels = readdlm(tmp, header = true)
+    return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors
+end
+
+t1, x1 = load_ngrip()
                          ([-59944.5, -59939.6, -59935.9, -59930.5, -59925.0, -59919.0, -59914.3, -59909.4, -59904.5, -59899.7  …  -27.40000000000009, -27.40000000000009, -27.299999999999955, -27.299999999999955, -27.200000000000045, -27.09999999999991, -27.09999999999991, -27.0, -26.90000000000009, -26.799999999999955], [-43.52, -42.94, -42.13, -40.04, -41.09, -43.57, -42.28, -41.2, -44.07, -44.53  …  -35.29, -35.18, -35.51, -36.03, -36.52, -37.12, -37.41, -37.21, -36.62, -35.52])

                          Step 2

                          uniqueidx(v) = unique(i -> v[i], eachindex(v))
+function keep_unique(t, x)
+    unique_idx = uniqueidx(t)
+    return t[unique_idx], x[unique_idx]
+end
+
+function sort_timeseries!(t, x)
+    p = sortperm(t)
+    permute!(t, p)
+    permute!(x, p)
+    return nothing
+end
+
+t2, x2 = keep_unique(t1, x1)
+sort_timeseries!(t2, x2)

                          Step 3

                          using BSplineKit
+
+function regrid2evensampling(t, x, dt)
+    itp = BSplineKit.interpolate(t, x, BSplineOrder(4))
+    tspan = (ceil(minimum(t)), floor(maximum(t)))
+    t_even = collect(tspan[1]:dt:tspan[2])
+    x_even = itp.(t_even)
+    return t_even, x_even
+end
+
+dt = 5.0        # dt = 5 yr as in (Boers 2018)
+t3, x3 = regrid2evensampling(t2, x2, dt)
                          ([-59944.0, -59939.0, -59934.0, -59929.0, -59924.0, -59919.0, -59914.0, -59909.0, -59904.0, -59899.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-43.445268010797946, -42.85408835164853, -41.357360665158936, -39.9365468206892, -41.60554051352076, -43.57000000000001, -42.145558689100454, -41.33160823883399, -44.273597725729985, -44.4622612304012  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46])

                          Step 4

                          For the final step we drop the indices:

                          using DSP
+
+function chebyshev_filter(t, x, fcutoff)
+    ii = 10             # Chebyshev filtering requires to prune first points of timeseries.
+    responsetype = Highpass(fcutoff, fs = 1/dt)
+    designmethod = Chebyshev1(8, 0.05)
+    r = filt(digitalfilter(responsetype, designmethod), x)
+    xtrend = x - r
+    return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]
+end
+
+fcutoff = 0.95 * 0.01   # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)
+t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)
                          ([-59899.0, -59894.0, -59889.0, -59884.0, -59879.0, -59874.0, -59869.0, -59864.0, -59859.0, -59854.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-44.4622612304012, -44.264401428210874, -44.02956767939856, -42.29334237357212, -42.594341674200344, -41.09704877854712, -40.39837540966913, -44.369155046413255, -42.74492506508012, -43.737014520530145  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46], [-43.89287787976461, -48.663435112414156, -51.31169981050155, -51.269094666491796, -49.90310432724566, -47.721430022512344, -44.36050569418247, -43.87556827410048, -43.57802291229893, -41.36870967826094  …  -34.81349114528442, -36.01634453179986, -36.150446802907226, -36.37595639697143, -35.96843653265903, -33.899634243732976, -32.49784036951535, -33.06575312724142, -34.07956188682297, -34.4079080530096], [-0.5693833506365866, 4.399033684203284, 7.282132131102991, 8.975752292919669, 7.308762653045311, 6.624381243965224, 3.9621302845133433, -0.493586772312777, 0.8330978472188112, -2.368304842269206  …  -0.30650885471557926, -0.17365546820014846, 1.0104468029072273, -0.684043603028572, 1.0384365326590237, -0.3303657562670192, -1.0321596304846505, -2.0242468727585807, 0.07956188682296689, -0.05209194699039831])

                          Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):

                          using CairoMakie, Loess
+
+function loess_filter(t, x; span = 0.005)
+    loessmodel = loess(t, x, span = span)
+    xtrend = Loess.predict(loessmodel, t)
+    r = x - xtrend
+    return t, x, xtrend, r
+end
+
+function kyr_xticks(tticks_yr)
+    tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)]
+    return (tticks_yr, tticks_kyr)
+end
+
+function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)
+    fig = Figure(resolution = (1600, 1200), fontsize = 24)
+
+    # Original timeseries with transition marked by vertical lines
+    ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)",
+        xaxisposition = :top, xticks = xticks)
+    lines!(ax1, traw, xraw, color = (:gray70, 0.5))
+    lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)
+    vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)
+
+    # Residual timeseries
+    ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    lines!(ax2, t, r, color = :gray50, linewidth = 1)
+
+    # Axes for variance and AC1 timeseries
+    ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$",
+        xticks = xticks)
+
+    axs = [ax1, ax2, ax3, ax4]
+    [xlims!(ax, xlims) for ax in axs]
+    ylims!(axs[1], (-48, -34))
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+
+xlims = (-60e3, -10e3)
+xticks = kyr_xticks(-60e3:5e3:5e3)
+t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,
+                38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]
+tloess, _, xloess, rloess = loess_filter(t3, x3)    # loess-filtered signal for visualization
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+fig

                          Hindcast on NGRIP data

                          As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:

                          using TransitionsInTimeseries, StatsBase
+using Random: Xoshiro
+
+ac1(x) = sum(autocor(x, [1]))   # AC1 from StatsBase
+indicators = (var, ac1)
+change_metrics = RidgeRegressionSlope()
+tseg_start = t_rasmussen[1:end-1] .+ 200
+tseg_end = t_rasmussen[2:end] .- 200
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)        # require >=100 data points to estimate change metric
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
                          18×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 1  0
+ 1  1
+ 1  1
+ 1  1
+ 0  0
+ 1  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 1  0

                          That's it! We can now visulaise our results with a generic function that we will re-use later:

                          function plot_segment_analysis!(axs, results, signif)
+    (; t_indicator, x_indicator) = results
+    for k in eachindex(t_indicator)             # loop over the segments
+        for i in axes(signif.pvalues, 2)        # loop over the indicators
+            if !isinf(signif.pvalues[k, i])     # plot if segment long enough
+                # Plot indicator timeseries and its linear regression
+                ti, xi = t_indicator[k], x_indicator[k][:, i]
+                lines!(axs[i+2], ti, xi, color = Cycled(1))
+                m, p = ridgematrix(ti, 0.0) * xi
+                if signif.pvalues[k, i] < 0.05
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)
+                else
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)
+                end
+            end
+        end
+    end
+end
+plot_segment_analysis!(axs, results, signif)
+fig

                          In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.

                          CSD: only a necessary condition, only in some cases

                          For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:

                          tseg_end = t_rasmussen[2:end] .- 700    # stop analysis 500 years earlier than before
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+plot_segment_analysis!(axs, results, signif)
+fig

                          For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD.

                          We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).

                          Degrees of freedom

                          These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.

                          Future improvement

                          Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.

                          Hindcasting simulated DO-events

                          In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:

                          t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],
+                 [1, 3500, 4370, 5790, 7200, 8140]]
+t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]
+tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]
+tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]
+
+figvec = Figure[]
+
+for j in 1:2
+    # Download the data and perform loess filtering on it
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" *
+        "master/timeseries/climberx-do$(j)-omaxa.csv")
+    data = readdlm(tmp)
+    tcx, xcx = data[1, 1000:end], data[2, 1000:end]
+    t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)
+
+    # Initialize figure
+    xlims = (0, last(tcx))
+    xticks = kyr_xticks(xlims[1]:1e3:xlims[2])
+    fig, axs = plot_do(tcx, xcx,  t, xtrend, t, r, t_transitions[j], extrema(t), xticks)
+    ylims!(axs[1], (5, 40))
+    axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$"
+
+    # Run sliding analysis and update figure with results
+    dt = mean(diff(tcx))
+    config = SegmentedWindowConfig(
+        indicators, change_metrics, tseg_start[j], tseg_end[j],
+        whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)
+    results = estimate_indicator_changes(config, r, t)
+    signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))
+    flags = significant_transitions(results, signif)
+
+    plot_segment_analysis!(axs, results, signif)
+    vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)
+    push!(figvec, fig)
+end
+figvec[1]

                          It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:

                          figvec[2]

                          Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.

                          diff --git a/previews/PR49/examples/logistic.jl b/previews/PR49/examples/logistic.jl new file mode 100644 index 00000000..a2894fbd --- /dev/null +++ b/previews/PR49/examples/logistic.jl @@ -0,0 +1,203 @@ +# # Permutation entropy for dynamic regime changes + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ## Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +## time-dependent logistic map, so that the `r` parameter increases with time +r1 = 3.83 +r2 = 3.86 +N = 2000 +rs = range(r1, r2; length = N) + +function logistic_drifting_rule(u, rs, n) + r = rs[n+1] # time is `n`, starting from 0 + return SVector(r*u[1]*(1 - u[1])) +end + +ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs) +x = trajectory(ds, N-1)[1][:, 1] + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ## Using a simpler change metric + +# Now, let's compute and various indicators and their changes, +# focusing on the permutation entropy as an indicator. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries, ComplexityMeasures + +function permutation_entropy(m) + est = SymbolicPermutation(; m) # order 3 + indicator = x -> entropy_normalized(est, x) + return indicator +end + +indicators = (var, ar1_whitenoise, permutation_entropy(4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as stride half the window width +metric = difference_of_means + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = SlidingWindowConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = estimate_indicator_changes(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + if i < 3 + hidexdecorations!(ax; grid = false) + else + ax.xlabel = "r (time)" + end + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ## Significance via random Fourier surrogates + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +using Random: Xoshiro +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42), + ) + flags = significant_transitions(results, signif) + + ## and also plot the flags with same color + for (i, indicator) in enumerate(indicators) + ## To make things visually clear, we will also plot some example surrogate + ## timeseries for each indicator and change metric pair + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surromethod) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric, p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1) + end + ## Plot the flags as vertical dashed lines + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = color, linestyle = :dash, linewidth = 3 + ) + end + ## add a title to the figure with how we estimate significance + content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod))) +end + +surromethod = RandomFourier() +overplot_surrogate_significance!(fig, surromethod) + +fig + +# ## Different surrogates +# %% #src +# Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# highlighting the _local_ dynamics or information that preserves the local +# changes of dynamical behavior. + +# A surrogate type that does a better job in preserving local sharp +# changes in the timeseries (and hence provides **stricter** +# surrogate-based significance) is for example `RelativePartialRandomization`. + +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = RelativePartialRandomization(0.25) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "gray") +fig + +# Our results have improved. In the permutation entropy, we see only two +# transitions detected as significant, which is correct: only two +# real dynamical transitions exist in the data. +# In the other two indicators we also see fewer transitions, but as we +# have already discussed, no results with the other indicators should +# be taken into meaningful consideration, as these indicators +# are simply inappropriate for what we are looking for here. + +# ## Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be less strict and more simple with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`SigmaSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation. + +fig = plot_change_metrics() +flags = significant_transitions(results, SigmaSignificance(factor = 5.0)) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = Cycled(3), linestyle = :dash, linewidth = 3 + ) +end +content(fig[1, 1]).title = "significance from std" +fig diff --git a/previews/PR49/examples/logistic/index.html b/previews/PR49/examples/logistic/index.html new file mode 100644 index 00000000..55538f15 --- /dev/null +++ b/previews/PR49/examples/logistic/index.html @@ -0,0 +1,128 @@ + +Permutation entropy for dynamic regime changes · TransitionsInTimeseries.jl
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                          Permutation entropy for dynamic regime changes

                          Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.

                          This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.

                          Logistic map timeseries

                          A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map

                          using DynamicalSystemsBase
+using CairoMakie
+
+# time-dependent logistic map, so that the `r` parameter increases with time
+r1 = 3.83
+r2 = 3.86
+N = 2000
+rs = range(r1, r2; length = N)
+
+function logistic_drifting_rule(u, rs, n)
+    r = rs[n+1] # time is `n`, starting from 0
+    return SVector(r*u[1]*(1 - u[1]))
+end
+
+ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)
+x = trajectory(ds, N-1)[1][:, 1]
                          2000-element Vector{Float64}:
+ 0.5
+ 0.9575
+ 0.15585767321160574
+ 0.5039019545917718
+ 0.9574529422362281
+ 0.15602441103002537
+ 0.5043473227583317
+ 0.9574501255597653
+ 0.1560361152301728
+ 0.5043840906474082
+ ⋮
+ 0.4253904015445437
+ 0.9434836074964187
+ 0.20581843730311683
+ 0.6309301050251992
+ 0.8988117342940414
+ 0.3510584545931264
+ 0.8793611090928393
+ 0.40948549063776396
+ 0.9333718681550522

                          Plot it, using as time the parameter value (they coincide)

                          fig, ax = lines(rs, x; linewidth = 0.5)
+ax.xlabel = "r (time)"
+ax.ylabel = "x"
+fig

                          In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.

                          Using a simpler change metric

                          Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.

                          using TransitionsInTimeseries, ComplexityMeasures
+
+function permutation_entropy(m)
+    est = SymbolicPermutation(; m) # order 3
+    indicator = x -> entropy_normalized(est, x)
+    return indicator
+end
+
+indicators = (var, ar1_whitenoise, permutation_entropy(4))
+indistrings = ("var", "ar1", "pe")
                          ("var", "ar1", "pe")

                          In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width

                          metric = difference_of_means
+
+width_ind = N÷100
+width_cha = 20
+stride_cha = 10
+
+config = SlidingWindowConfig(indicators, metric;
+    width_ind, width_cha, stride_cha,
+)
+
+results = estimate_indicator_changes(config, x, rs)
                          WindowResults
+ input timeseries:              2000-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise, Symbol("#1")]
+ indicator (window, stride):    (20, 1)
+ change metrics:                [:difference_of_means]
+ change metric (window, stride): (20, 10)
+

                          Let's now plot the change metrics of the indicators

                          function plot_change_metrics()
+    fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),))
+    hidexdecorations!(ax; grid = false)
+    # plot all change metrics
+    for (i, c) in enumerate(eachcol(results.x_change))
+        ax, = scatterlines(fig[i+1, 1], results.t_change, c;
+            axis = (ylabel = indistrings[i],), label = "input"
+        )
+        if i < 3
+            hidexdecorations!(ax; grid = false)
+        else
+            ax.xlabel = "r (time)"
+        end
+    end
+    return fig
+end
+
+fig = plot_change_metrics()

                          We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)

                          Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.

                          Significance via random Fourier surrogates

                          One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.

                          Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!

                          surromethod = RandomFourier()
+
+# Define a function because we will re-use later
+using Random: Xoshiro
+function overplot_surrogate_significance!(fig, surromethod, color = "black")
+
+    signif = SurrogatesSignificance(;
+        n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),
+    )
+    flags = significant_transitions(results, signif)
+
+    # and also plot the flags with same color
+    for (i, indicator) in enumerate(indicators)
+        # To make things visually clear, we will also plot some example surrogate
+        # timeseries for each indicator and change metric pair
+        for _ in 1:10
+            s = TimeseriesSurrogates.surrogate(x, surromethod)
+            p = windowmap(indicator, s; width = width_ind)
+            q = windowmap(metric, p; width = width_cha, stride = stride_cha)
+            lines!(fig[i+1, 1], results.t_change, q;  color = (color, 0.2), linewidth = 1)
+        end
+        # Plot the flags as vertical dashed lines
+        vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+            color = color, linestyle = :dash, linewidth = 3
+        )
+    end
+    # add a title to the figure with how we estimate significance
+    content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod)))
+end
+
+surromethod = RandomFourier()
+overplot_surrogate_significance!(fig, surromethod)
+
+fig

                          Different surrogates

                          Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

                          A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

                          A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

                          surromethod = RelativePartialRandomization(0.25)
+fig = plot_change_metrics()
+overplot_surrogate_significance!(fig, surromethod, "gray")
+fig

                          Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

                          Simpler Significance

                          Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

                          fig = plot_change_metrics()
+flags = significant_transitions(results, SigmaSignificance(factor = 5.0))
+
+# Plot the flags
+for (i, indicator) in enumerate(indicators)
+    vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+        color = Cycled(3), linestyle = :dash, linewidth = 3
+    )
+end
+content(fig[1, 1]).title = "significance from std"
+fig
                          diff --git a/previews/PR49/index.html b/previews/PR49/index.html new file mode 100644 index 00000000..9b85412b --- /dev/null +++ b/previews/PR49/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
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                          TransitionsInTimeseries.jl

                          TransitionsInTimeseries.jl

                          TransitionsInTimeseries — Module

                          TransitionsInTimeseries.jl

                          CI codecov Package Downloads

                          A Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                          This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

                          add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

                          All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                          source
                          Star us on GitHub!

                          If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                          Content

                          Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                          • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                          • Makes the surrogate analysis to test for significance under the hub.
                          • Can be easily extended by any user without touching the source code.
                          • Reduces the programming overhead for any researcher willing to benchmark new methods.
                          • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                          • Increases trustworthiness thanks to a large test suite.
                          Similar projects

                          An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                          Approaches

                          Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                          diff --git a/previews/PR49/refs.bib b/previews/PR49/refs.bib new file mode 100644 index 00000000..8010a9d3 --- /dev/null +++ b/previews/PR49/refs.bib @@ -0,0 +1,54 @@ + +@article{willeit-earth-2022, + title = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1: {Climate} model description and validation​​​​​​​​​​​​​​}, + volume = {15}, + issn = {1991-9603}, + shorttitle = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1}, + url = {https://gmd.copernicus.org/articles/15/5905/2022/}, + doi = {10.5194/gmd-15-5905-2022}, + abstract = {The newly developed fast Earth system model CLIMBER-X is presented. The climate component of CLIMBER-X consists of a 2.5-D semi-empirical statistical–dynamical atmosphere model, a 3-D frictional–geostrophic ocean model, a dynamic–thermodynamic sea ice model and a land surface model. All the model components are discretized on a regular lat–long grid with a horizontal resolution of 5 ◦ × 5 ◦. The model has a throughput of ∼ 10 000 simulation years per day on a single node with 16 CPUs on a high-performance computer and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to {\textgreater} 100 000 years. A comprehensive evaluation of the model performance for the present day and the historical period shows that CLIMBER-X is capable of realistically reproducing many observed climate characteristics, with results that generally lie within the range of state-of-theart general circulation models. The analysis of model performance is complemented by a thorough assessment of climate feedbacks and model sensitivities to changes in external forcings and boundary conditions. Limitations and applicability of the model are critically discussed. CLIMBER-X also includes a detailed representation of the global carbon cycle and is coupled to an ice sheet model, which will be described in separate papers. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.}, + language = {en}, + number = {14}, + urldate = {2022-08-11}, + journal = {Geoscientific Model Development}, + author = {Willeit, Matteo and Ganopolski, Andrey and Robinson, Alexander and Edwards, Neil R.}, + month = jul, + year = {2022}, + pages = {5905--5948}, + file = {Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:/home/jan/Zotero/storage/75NKS975/Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:application/pdf}, +} + +@article{boers-early-warning-2018, + title = {Early-warning signals for {Dansgaard}-{Oeschger} events in a high-resolution ice core record}, + volume = {9}, + issn = {2041-1723}, + url = {http://www.nature.com/articles/s41467-018-04881-7}, + doi = {10.1038/s41467-018-04881-7}, + language = {en}, + number = {1}, + urldate = {2022-10-28}, + journal = {Nature Communications}, + author = {Boers, Niklas}, + month = dec, + year = {2018}, + pages = {2556}, + file = {Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:/home/jan/Zotero/storage/DS97Z9UC/Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:application/pdf}, +} + +@article{rasmussen-stratigraphic-2014, + title = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records: refining and extending the {INTIMATE} event stratigraphy}, + volume = {106}, + issn = {02773791}, + shorttitle = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0277379114003485}, + doi = {10.1016/j.quascirev.2014.09.007}, + abstract = {Due to their outstanding resolution and well-constrained chronologies, Greenland ice-core records provide a master record of past climatic changes throughout the Last InterglacialeGlacial cycle in the North Atlantic region. As part of the INTIMATE (INTegration of Ice-core, MArine and TErrestrial records) project, protocols have been proposed to ensure consistent and robust correlation between different records of past climate. A key element of these protocols has been the formal definition and ordinal numbering of the sequence of Greenland Stadials (GS) and Greenland Interstadials (GI) within the most recent glacial period. The GS and GI periods are the Greenland expressions of the characteristic DansgaardeOeschger events that represent cold and warm phases of the North Atlantic region, respectively. We present here a more detailed and extended GS/GI template for the whole of the Last Glacial period. It is based on a synchronization of the NGRIP, GRIP, and GISP2 ice-core records that allows the parallel analysis of all three records on a common time scale. The boundaries of the GS and GI periods are defined based on a combination of stable-oxygen isotope ratios of the ice (d18O, reflecting mainly local temperature) and calcium ion concentrations (reflecting mainly atmospheric dust loading) measured in the ice. The data not only resolve the well-known sequence of DansgaardeOeschger events that were first defined and numbered in the ice-core records more than two decades ago, but also better resolve a number of short-lived climatic oscillations, some defined here for the first time. Using this revised scheme, we propose a consistent approach for discriminating and naming all the significant abrupt climatic events of the Last Glacial period that are represented in the Greenland ice records. The final product constitutes an extended and better resolved Greenland stratotype sequence, against which other proxy records can be compared and correlated. It also provides a more secure basis for investigating the dynamics and fundamental causes of these climatic perturbations.}, + language = {en}, + urldate = {2023-10-04}, + journal = {Quaternary Science Reviews}, + author = {Rasmussen, Sune O. and Bigler, Matthias and Blockley, Simon P. and Blunier, Thomas and Buchardt, Susanne L. and Clausen, Henrik B. and Cvijanovic, Ivana and Dahl-Jensen, Dorthe and Johnsen, Sigfus J. and Fischer, Hubertus and Gkinis, Vasileios and Guillevic, Myriam and Hoek, Wim Z. and Lowe, J. John and Pedro, Joel B. and Popp, Trevor and Seierstad, Inger K. and Steffensen, Jørgen Peder and Svensson, Anders M. and Vallelonga, Paul and Vinther, Bo M. and Walker, Mike J.C. and Wheatley, Joe J. and Winstrup, Mai}, + month = dec, + year = {2014}, + pages = {14--28}, + file = {Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:/home/jan/Zotero/storage/VSUTVWPN/Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:application/pdf}, +} diff --git a/previews/PR49/refs/index.html b/previews/PR49/refs/index.html new file mode 100644 index 00000000..4be5248f --- /dev/null +++ b/previews/PR49/refs/index.html @@ -0,0 +1,9 @@ + +References · TransitionsInTimeseries.jl
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                          References

                          diff --git a/previews/PR49/search/index.html b/previews/PR49/search/index.html new file mode 100644 index 00000000..e7a8bb39 --- /dev/null +++ b/previews/PR49/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

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                            diff --git a/previews/PR49/search_index.js b/previews/PR49/search_index.js new file mode 100644 index 00000000..674815c8 --- /dev/null +++ b/previews/PR49/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"IndicatorsChangesConfig\nSlidingWindowConfig\nSegmentedWindowConfig\nestimate_indicator_changes\nWindowResults\nSlidingWindowResults\nSegmentWindowResults","category":"page"},{"location":"api/#TransitionsInTimeseries.IndicatorsChangesConfig","page":"API","title":"TransitionsInTimeseries.IndicatorsChangesConfig","text":"IndicatorsChangesConfig\n\nSupertype used to define how indicators and their changes are estimated in estimate_indicator_changes. Valid subtypes are:\n\nSlidingWindowConfig.\nSegmentedWindowConfig.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowConfig","page":"API","title":"TransitionsInTimeseries.SlidingWindowConfig","text":"SlidingWindowConfig <: IndicatorsChangesConfig\nSlidingWindowConfig(indicators, change_metrics; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowConfig","page":"API","title":"TransitionsInTimeseries.SegmentedWindowConfig","text":"SegmentedWindowConfig <: IndicatorsChangeConfig\nSegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:\n\nFor each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).\nFor each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d\n\ntseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.\n\nKeyword arguments\n\n\nwidth_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.\nmin_width_cha::Int=50: minimal width required to perform the change metric estimation. If segment not sufficiently long, return NaN.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.estimate_indicator_changes","page":"API","title":"TransitionsInTimeseries.estimate_indicator_changes","text":"estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → output\n\nEstimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).\n\nReturn the output as WindowResults which can be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.WindowResults","page":"API","title":"TransitionsInTimeseries.WindowResults","text":"WindowResults\n\nSupertype used to gather results of estimate_indicator_changes. Valid subtypes are:\n\nSlidingWindowResults.\nSegmentWindowResults.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowResults","page":"API","title":"TransitionsInTimeseries.SlidingWindowResults","text":"SlidingWindowResults\n\nA struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nconfig::SlidingWindowConfig, used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentWindowResults","page":"API","title":"TransitionsInTimeseries.SegmentWindowResults","text":"SegmentWindowResults\n\nA struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.\nt_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.\nx_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.\nt_change, the time vector of the change metric.\nconfig::SegmentedWindowConfig, used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"significant_transitions\nTransitionsSignificance\nSurrogatesSignificance\nQuantileSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::WindowResults, signif::TransitionsSignificance)\n\nEstimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.TransitionsSignificance","page":"API","title":"TransitionsInTimeseries.TransitionsSignificance","text":"TransitionsSignificance\n\nSupertype used to test for significance in significant_transitions. Valid subtypes are:\n\nSurrogatesSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: TransitionsSignificance\nSurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)\n\nA configuration struct for significance testing significant_transitions using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\n\nDescription\n\nWhen used with WindowResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in WindowResults.\n\nNote that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance\n\nA configuration struct for significance testing significant_transitions. When used with WindowResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\nQuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.","category":"page"},{"location":"api/","page":"API","title":"API","text":"For example, using the permutation entropy as an indicator is as simple as doing","category":"page"},{"location":"api/","page":"API","title":"API","text":"using ComplexityMeasures\nest = OrdinalPatterns(; m = 3) # order 3\n# create a function that given timeseries returns permutation entropy\nindicator = x -> entropy_normalized(est, x)","category":"page"},{"location":"api/","page":"API","title":"API","text":"and giving the created indicator to e.g., SlidingWindowConfig.","category":"page"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"EditURL = \"do-events.jl\"","category":"page"},{"location":"examples/do-events/#Dansgaard-Oescher-events-and-Critical-Slowing-Down","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The delta^18O timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.","category":"page"},{"location":"examples/do-events/#Preprocessing-NGRIP","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Preprocessing NGRIP","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Load the data, reverse and offset it to have time vector = time before 2000 AD.\nFilter non-unique points in time and sort the data.\nRegrid the data from uneven to even sampling.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The time and delta^18O vectors resulting from the i-th preprocessing step are respectively called t_i and x_i. The final step consists in obtaining a residual r, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.","category":"page"},{"location":"examples/do-events/#Step-1:","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 1:","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DelimitedFiles, Downloads\n\nfunction load_ngrip()\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP.csv\")\n data, labels = readdlm(tmp, header = true)\n return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors\nend\n\nt1, x1 = load_ngrip()","category":"page"},{"location":"examples/do-events/#Step-2","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 2","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"uniqueidx(v) = unique(i -> v[i], eachindex(v))\nfunction keep_unique(t, x)\n unique_idx = uniqueidx(t)\n return t[unique_idx], x[unique_idx]\nend\n\nfunction sort_timeseries!(t, x)\n p = sortperm(t)\n permute!(t, p)\n permute!(x, p)\n return nothing\nend\n\nt2, x2 = keep_unique(t1, x1)\nsort_timeseries!(t2, x2)","category":"page"},{"location":"examples/do-events/#Step-3","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 3","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using BSplineKit\n\nfunction regrid2evensampling(t, x, dt)\n itp = BSplineKit.interpolate(t, x, BSplineOrder(4))\n tspan = (ceil(minimum(t)), floor(maximum(t)))\n t_even = collect(tspan[1]:dt:tspan[2])\n x_even = itp.(t_even)\n return t_even, x_even\nend\n\ndt = 5.0 # dt = 5 yr as in (Boers 2018)\nt3, x3 = regrid2evensampling(t2, x2, dt)","category":"page"},{"location":"examples/do-events/#Step-4","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 4","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the final step we drop the indices:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DSP\n\nfunction chebyshev_filter(t, x, fcutoff)\n ii = 10 # Chebyshev filtering requires to prune first points of timeseries.\n responsetype = Highpass(fcutoff, fs = 1/dt)\n designmethod = Chebyshev1(8, 0.05)\n r = filt(digitalfilter(responsetype, designmethod), x)\n xtrend = x - r\n return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]\nend\n\nfcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)\nt, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using CairoMakie, Loess\n\nfunction loess_filter(t, x; span = 0.005)\n loessmodel = loess(t, x, span = span)\n xtrend = Loess.predict(loessmodel, t)\n r = x - xtrend\n return t, x, xtrend, r\nend\n\nfunction kyr_xticks(tticks_yr)\n tticks_kyr = [\"$t\" for t in Int.(tticks_yr ./ 1e3)]\n return (tticks_yr, tticks_kyr)\nend\n\nfunction plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)\n fig = Figure(resolution = (1600, 1200), fontsize = 24)\n\n # Original timeseries with transition marked by vertical lines\n ax1 = Axis(fig[1, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"$\\delta^{18}$O (permil)\",\n xaxisposition = :top, xticks = xticks)\n lines!(ax1, traw, xraw, color = (:gray70, 0.5))\n lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)\n vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)\n\n # Residual timeseries\n ax2 = Axis(fig[2, 1], ylabel = L\"Residual $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n lines!(ax2, t, r, color = :gray50, linewidth = 1)\n\n # Axes for variance and AC1 timeseries\n ax3 = Axis(fig[3, 1], ylabel = L\"Variance $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n ax4 = Axis(fig[4, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"Lag-1 autocor. $\\,$\",\n xticks = xticks)\n\n axs = [ax1, ax2, ax3, ax4]\n [xlims!(ax, xlims) for ax in axs]\n ylims!(axs[1], (-48, -34))\n rowgap!(fig.layout, 10)\n return fig, axs\nend\n\nxlims = (-60e3, -10e3)\nxticks = kyr_xticks(-60e3:5e3:5e3)\nt_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,\n 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]\ntloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nfig","category":"page"},{"location":"examples/do-events/#Hindcast-on-NGRIP-data","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcast on NGRIP data","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using TransitionsInTimeseries, StatsBase\nusing Random: Xoshiro\n\nac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase\nindicators = (var, ac1)\nchange_metrics = RidgeRegressionSlope()\ntseg_start = t_rasmussen[1:end-1] .+ 200\ntseg_end = t_rasmussen[2:end] .- 200\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100) # require >=100 data points to estimate change metric\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"That's it! We can now visulaise our results with a generic function that we will re-use later:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"function plot_segment_analysis!(axs, results, signif)\n (; t_indicator, x_indicator) = results\n for k in eachindex(t_indicator) # loop over the segments\n for i in axes(signif.pvalues, 2) # loop over the indicators\n if !isinf(signif.pvalues[k, i]) # plot if segment long enough\n # Plot indicator timeseries and its linear regression\n ti, xi = t_indicator[k], x_indicator[k][:, i]\n lines!(axs[i+2], ti, xi, color = Cycled(1))\n m, p = ridgematrix(ti, 0.0) * xi\n if signif.pvalues[k, i] < 0.05\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)\n else\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)\n end\n end\n end\n end\nend\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.","category":"page"},{"location":"examples/do-events/#CSD:-only-a-necessary-condition,-only-in-some-cases","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"CSD: only a necessary condition, only in some cases","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential U, which defines the deterministic term f = -U of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100)\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that \"resilience-loss indicators\" is a more accurate name than \"early-warning signals\" when using CSD.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"We draw attention upon the fact that the delta^18O timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"warning: Degrees of freedom\nThese sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"info: Future improvement\nSupporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.","category":"page"},{"location":"examples/do-events/#Hindcasting-simulated-DO-events","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcasting simulated DO-events","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],\n [1, 3500, 4370, 5790, 7200, 8140]]\nt_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]\ntseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]\ntseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]\n\nfigvec = Figure[]\n\nfor j in 1:2\n # Download the data and perform loess filtering on it\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\" *\n \"master/timeseries/climberx-do$(j)-omaxa.csv\")\n data = readdlm(tmp)\n tcx, xcx = data[1, 1000:end], data[2, 1000:end]\n t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)\n\n # Initialize figure\n xlims = (0, last(tcx))\n xticks = kyr_xticks(xlims[1]:1e3:xlims[2])\n fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks)\n ylims!(axs[1], (5, 40))\n axs[1].ylabel = L\"Max. Atlantic overturning (Sv) $\\,$\"\n\n # Run sliding analysis and update figure with results\n dt = mean(diff(tcx))\n config = SegmentedWindowConfig(\n indicators, change_metrics, tseg_start[j], tseg_end[j],\n whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)\n results = estimate_indicator_changes(config, r, t)\n signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))\n flags = significant_transitions(results, signif)\n\n plot_segment_analysis!(axs, results, signif)\n vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)\n push!(figvec, fig)\nend\nfigvec[1]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"figvec[2]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"EditURL = \"logistic.jl\"","category":"page"},{"location":"examples/logistic/#Permutation-entropy-for-dynamic-regime-changes","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.","category":"page"},{"location":"examples/logistic/#Logistic-map-timeseries","page":"Permutation entropy for dynamic regime changes","title":"Logistic map timeseries","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using DynamicalSystemsBase\nusing CairoMakie\n\n# time-dependent logistic map, so that the `r` parameter increases with time\nr1 = 3.83\nr2 = 3.86\nN = 2000\nrs = range(r1, r2; length = N)\n\nfunction logistic_drifting_rule(u, rs, n)\n r = rs[n+1] # time is `n`, starting from 0\n return SVector(r*u[1]*(1 - u[1]))\nend\n\nds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)\nx = trajectory(ds, N-1)[1][:, 1]","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Plot it, using as time the parameter value (they coincide)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig, ax = lines(rs, x; linewidth = 0.5)\nax.xlabel = \"r (time)\"\nax.ylabel = \"x\"\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.","category":"page"},{"location":"examples/logistic/#Using-a-simpler-change-metric","page":"Permutation entropy for dynamic regime changes","title":"Using a simpler change metric","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using TransitionsInTimeseries, ComplexityMeasures\n\nfunction permutation_entropy(m)\n est = SymbolicPermutation(; m) # order 3\n indicator = x -> entropy_normalized(est, x)\n return indicator\nend\n\nindicators = (var, ar1_whitenoise, permutation_entropy(4))\nindistrings = (\"var\", \"ar1\", \"pe\")","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"metric = difference_of_means\n\nwidth_ind = N÷100\nwidth_cha = 20\nstride_cha = 10\n\nconfig = SlidingWindowConfig(indicators, metric;\n width_ind, width_cha, stride_cha,\n)\n\nresults = estimate_indicator_changes(config, x, rs)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's now plot the change metrics of the indicators","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"function plot_change_metrics()\n fig, ax = lines(rs, x; axis = (ylabel = \"input\",), figure = (resolution = (600, 600),))\n hidexdecorations!(ax; grid = false)\n # plot all change metrics\n for (i, c) in enumerate(eachcol(results.x_change))\n ax, = scatterlines(fig[i+1, 1], results.t_change, c;\n axis = (ylabel = indistrings[i],), label = \"input\"\n )\n if i < 3\n hidexdecorations!(ax; grid = false)\n else\n ax.xlabel = \"r (time)\"\n end\n end\n return fig\nend\n\nfig = plot_change_metrics()","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.","category":"page"},{"location":"examples/logistic/#Significance-via-random-Fourier-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Significance via random Fourier surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RandomFourier()\n\n# Define a function because we will re-use later\nusing Random: Xoshiro\nfunction overplot_surrogate_significance!(fig, surromethod, color = \"black\")\n\n signif = SurrogatesSignificance(;\n n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),\n )\n flags = significant_transitions(results, signif)\n\n # and also plot the flags with same color\n for (i, indicator) in enumerate(indicators)\n # To make things visually clear, we will also plot some example surrogate\n # timeseries for each indicator and change metric pair\n for _ in 1:10\n s = TimeseriesSurrogates.surrogate(x, surromethod)\n p = windowmap(indicator, s; width = width_ind)\n q = windowmap(metric, p; width = width_cha, stride = stride_cha)\n lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1)\n end\n # Plot the flags as vertical dashed lines\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = color, linestyle = :dash, linewidth = 3\n )\n end\n # add a title to the figure with how we estimate significance\n content(fig[1, 1]).title = \"surrogates: \"*string(nameof(typeof(surromethod)))\nend\n\nsurromethod = RandomFourier()\noverplot_surrogate_significance!(fig, surromethod)\n\nfig","category":"page"},{"location":"examples/logistic/#Different-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Different surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RelativePartialRandomization(0.25)\nfig = plot_change_metrics()\noverplot_surrogate_significance!(fig, surromethod, \"gray\")\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.","category":"page"},{"location":"examples/logistic/#Simpler-Significance","page":"Permutation entropy for dynamic regime changes","title":"Simpler Significance","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig = plot_change_metrics()\nflags = significant_transitions(results, SigmaSignificance(factor = 5.0))\n\n# Plot the flags\nfor (i, indicator) in enumerate(indicators)\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = Cycled(3), linestyle = :dash, linewidth = 3\n )\nend\ncontent(fig[1, 1]).title = \"significance from std\"\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"refs/#References","page":"References","title":"References","text":"","category":"section"},{"location":"refs/","page":"References","title":"References","text":"","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"EditURL = \"tutorial.jl\"","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector,\n# we obtain the last time step of each window.\n# This therefore only uses information from `k-width+1` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\n\nfunction gridfig(nrows, ncols)\n fig = Figure()\n axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)\n for j in 1:ncols, i in 1:nrows]\n rowgap!(fig.layout, 10)\n return fig, axs\nend\nfig, axs = gridfig(2, 1)\nlines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))\nlines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))\naxs[1].title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nlines!(axs[2], t_change, change_nl, label = \"nonlin\", color = Cycled(2))\nlines!(axs[2], t_change, change_s, label = \"surrogate\", color = Cycled(3))\naxislegend()\naxs[2].title = \"change metric\"\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig, axs = gridfig(2, 2)\naxs[1].title = \"linear\"\naxs[2].title = \"nonlinear\"\n\nfor (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change) # ; color = Cycled(j)\n lines!(axsig, t_change, pval) # ; color = Cycled(j+2)\nend\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = RidgeRegressionSlope()\n\n# choices go into a configuration struct\nconfig = SlidingWindowConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last)\n\n# choices are processed\nresults = estimate_indicator_changes(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From result we can plot the change metric timeseries:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(3, 1)\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, results.x_change[:, 1];\n label = \"var slopes\", color = Cycled(3))\nscatter!(axs[3], results.t_change, results.x_change[:, 2];\n label = \"ar1 slopes\", color = Cycled(4))\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = :right)\nflags = significant_transitions(results, signif)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(2, 1)\nlines!(axs[1], vcat(0.0, t), x_nlinear; label = \"raw\", color = Cycled(1))\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 1];\n label = \"var p-values\", color = Cycled(3))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 2];\n label = \"ar1 p-values\", color = Cycled(4))\n\nflagsboth = vec(reduce(&, flags; dims = 2))\nvlines!(axs[1], results.t_change[flagsboth]; label = \"flags\", color = (\"black\", 0.1))\n\n[axislegend(ax) for ax in axs]\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"}] +} diff --git a/previews/PR49/siteinfo.js b/previews/PR49/siteinfo.js new file mode 100644 index 00000000..a04ef74a --- /dev/null +++ b/previews/PR49/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR49"; diff --git a/previews/PR49/tutorial.jl b/previews/PR49/tutorial.jl new file mode 100644 index 00000000..3f135673 --- /dev/null +++ b/previews/PR49/tutorial.jl @@ -0,0 +1,263 @@ +#= + +# Tutorial + +## [Workflow] (@id workflow) + +Computing transition indicators consists of the following steps: + +1. Doing any preprocessing of raw data first, such as detrending (_not part of TransitionsInTimeseries.jl_). This yields the **input timeseries**. +2. Estimating the timeseries of an indicator by sliding a window over the input timeseries. +3. Computing the changes of the indicator by sliding a window over its timeseries. +4. Generating many surrogates that preserve important statistical properties of the original timeseries. +5. Performing step 2 and 3 for the surrogate timeseries. +6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data. + +These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports. + +## [Tutorial -- Educational] (@id example_stepbystep) + +### Raw input data + +Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by: + +```math +\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t) +``` + +with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with [Makie](https://docs.makie.org/stable/)) such prototypical data to test some indicators can be done by simply running: +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_linear) +lines!(ax, t, x_nlinear) +ax.title = "raw data" +fig + +#= +### Preprocessing + +!!! note "Not part of TransitionsInTimeseries.jl" + Any timeseries preprocessing, such as the de-trending step we do here, + is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher. + + +The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1. +=# + +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +#= +At this point, `x_l_fluct` and `x_nl_fluct` are considered the **input timeseries**. + +!!! info "Detrending in Julia" + Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as [Loess.jl](https://github.com/JuliaStats/Loess.jl) or [DSP.jl](https://docs.juliadsp.org/latest/contents/). There the detrending step consists of subtracting the smoothed signal from the original one. + +### Indicator timeseries + +We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the **input timeseries**, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as [`ar1_whitenoise`](@ref): +=# + +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +## By mapping `last::Function` over a windowviewer of the time vector, +## we obtain the last time step of each window. +## This therefore only uses information from `k-width+1` to `k` at time step `k`. +## Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +#= +The lines plotted above are the **indicator timeseries**. + +### Change metric timeseries + +From here, we process the **indicator timeseries** to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the **change metric timeseries**. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a [`RidgeRegressionSlope`](@ref): +=# + +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + +#= +### Timeseries surrogates + +As expected from [Critical Slowing Down](@ref approaches), an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance. + +In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the [TimeseriesSurrogates.jl](https://github.com/JuliaDynamics/TimeseriesSurrogates.jl) Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that `TimeseriesSurrogates` is re-exported by `TransitionsInTimeseries`, so that you don't have to `using` both of them. + +To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries. +=# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) + +function gridfig(nrows, ncols) + fig = Figure() + axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false) + for j in 1:ncols, i in 1:nrows] + rowgap!(fig.layout, 10) + return fig, axs +end +fig, axs = gridfig(2, 1) +lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2)) +lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3)) +axs[1].title = "real signal vs. surrogate(s)" + +## compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2)) +lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3)) +axislegend() +axs[2].title = "change metric" + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +### Quantifying significance + +To quantify the significance of the values of the **change metric timeseries** we perform a standard surrogate test by computing the [p-value](https://en.wikipedia.org/wiki/P-value) w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically `p<0.05`) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time: +=# + +n_surrogates = 1_000 +fig, axs = gridfig(2, 2) +axs[1].title = "linear" +axs[2].title = "nonlinear" + +for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + ## Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change) # ; color = Cycled(j) + lines!(axsig, t_change, pval) # ; color = Cycled(j+2) +end + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar. + +Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section. + +## [Tutorial -- TransitionsInTimeseries.jl] (@id example_fastforward) + +TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go. + +The interface is simple, and directly parallelizes the [Workflow](@ref). It is based on the creation of a [`TransitionsSurrogatesConfig`](@ref), which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate. + +The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +## input timeseries and time +input = x_nl_fluct = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(t, input) +ax.title = "input timeseries" +fig + +#= +To perform all of the above analysis we follow a 2-step process. + +Step 1, we decide what indicators and change metrics to use in [`SlidingWindowConfig`](@ref) and apply those via +a sliding window to the input timeseries using [`transition_metrics`](@ref). +=# + +## These indicators are suitable for Critical Slowing Down +indicators = (var, ar1_whitenoise) + +## use the ridge regression slope for both indicators +change_metrics = RidgeRegressionSlope() + +## choices go into a configuration struct +config = SlidingWindowConfig(indicators, change_metrics; + width_ind = 400, width_cha = 30, whichtime = last) + +## choices are processed +results = estimate_indicator_changes(config, input, t) + +#= +From `result` we can plot the change metric timeseries: +=# + +fig, axs = gridfig(3, 1) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, results.x_change[:, 1]; + label = "var slopes", color = Cycled(3)) +scatter!(axs[3], results.t_change, results.x_change[:, 2]; + label = "ar1 slopes", color = Cycled(4)) +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +Step 2 is to estimate significance using [`SurrogatesConfig`](@ref) +and the function [`estimate_significance!`](@ref). +=# + +signif = SurrogatesSignificance(n = 1000, tail = :right) +flags = significant_transitions(results, signif) + +#= +We can now plot the p-values corresponding to each time series of the change metrics. From the `flags` we can additionally obtain the time points where _both_ indicators show significance, via a simple reduction: +=# + +fig, axs = gridfig(2, 1) +lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1)) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 1]; + label = "var p-values", color = Cycled(3)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 2]; + label = "ar1 p-values", color = Cycled(4)) + +flagsboth = vec(reduce(&, flags; dims = 2)) +vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1)) + +[axislegend(ax) for ax in axs] +[xlims!(ax, 0, 50) for ax in axs] +fig \ No newline at end of file diff --git a/previews/PR49/tutorial/index.html b/previews/PR49/tutorial/index.html new file mode 100644 index 00000000..f7a8f4ec --- /dev/null +++ b/previews/PR49/tutorial/index.html @@ -0,0 +1,160 @@ + +Tutorial · TransitionsInTimeseries.jl
                            Edit on GitHub

                            Tutorial

                            Workflow

                            Computing transition indicators consists of the following steps:

                            1. Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                            2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                            3. Computing the changes of the indicator by sliding a window over its timeseries.
                            4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                            5. Performing step 2 and 3 for the surrogate timeseries.
                            6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                            These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                            Tutorial – Educational

                            Raw input data

                            Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                            \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                            with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                            using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig

                            Preprocessing

                            Not part of TransitionsInTimeseries.jl

                            Any timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                            The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                            x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                            At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                            Detrending in Julia

                            Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                            Indicator timeseries

                            We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                            indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector,
+# we obtain the last time step of each window.
+# This therefore only uses information from `k-width+1` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                            The lines plotted above are the indicator timeseries.

                            Change metric timeseries

                            From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                            change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                            Timeseries surrogates

                            As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                            In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                            To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                            # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+
+function gridfig(nrows, ncols)
+    fig = Figure()
+    axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)
+        for j in 1:ncols, i in 1:nrows]
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+fig, axs = gridfig(2, 1)
+lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))
+lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))
+axs[1].title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2))
+lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3))
+axislegend()
+axs[2].title = "change metric"
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                            Quantifying significance

                            To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                            n_surrogates = 1_000
+fig, axs = gridfig(2, 2)
+axs[1].title = "linear"
+axs[2].title = "nonlinear"
+
+for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change)   # ; color = Cycled(j)
+    lines!(axsig, t_change, pval)       # ; color = Cycled(j+2)
+end
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                            As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                            Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                            Tutorial – TransitionsInTimeseries.jl

                            TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                            The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

                            The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

                            using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig

                            To perform all of the above analysis we follow a 2-step process.

                            Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.

                            # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = RidgeRegressionSlope()
+
+# choices go into a configuration struct
+config = SlidingWindowConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last)
+
+# choices are processed
+results = estimate_indicator_changes(config, input, t)
                            WindowResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                            From result we can plot the change metric timeseries:

                            fig, axs = gridfig(3, 1)
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, results.x_change[:, 1];
+    label = "var slopes", color = Cycled(3))
+scatter!(axs[3], results.t_change, results.x_change[:, 2];
+    label = "ar1 slopes", color = Cycled(4))
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                            Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.

                            signif = SurrogatesSignificance(n = 1000, tail = :right)
+flags = significant_transitions(results, signif)
                            2072×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ ⋮  
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0

                            We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:

                            fig, axs = gridfig(2, 1)
+lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1))
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 1];
+    label = "var p-values", color = Cycled(3))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 2];
+    label = "ar1 p-values", color = Cycled(4))
+
+flagsboth = vec(reduce(&, flags; dims = 2))
+vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1))
+
+[axislegend(ax) for ax in axs]
+[xlims!(ax, 0, 50) for ax in axs]
+fig
                            diff --git a/previews/PR50/api/index.html b/previews/PR50/api/index.html new file mode 100644 index 00000000..3070eaf2 --- /dev/null +++ b/previews/PR50/api/index.html @@ -0,0 +1,22 @@ + +API · TransitionsInTimeseries.jl
                            Edit on GitHub

                            API

                            Main analysis functions

                            TransitionsInTimeseries.SlidingWindowConfig — Type
                            SlidingWindowConfig <: IndicatorsChangesConfig
+SlidingWindowConfig(indicators, change_metrics; kwargs...)

                            A configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:

                            1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                            2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                            indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                            Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.

                            The results output corresponding to SlidingWindowConfig is SlidingWindowResults.

                            Keyword arguments

                            • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.
                            • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.
                            • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:
                              • last: use the last timepoint of each window
                              • midpoint: use the mid timepoint of each time window
                              • first: use first timepoint of each window
                              In fact, the indicators time vector is computed simply via
                              t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)
                              so any other function of the time window may be given to extract the time point itself, such as mean or median.
                            • T = Float64: Element type of input timeseries to initialize some computations.
                            source
                            TransitionsInTimeseries.SegmentedWindowConfig — Type
                            SegmentedWindowConfig <: IndicatorsChangeConfig
+SegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)

                            A configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:

                            1. For each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).
                            2. For each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d

                            tseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.

                            The results output corresponding to SlidingWindowConfig is SegmentedWindowResults.

                            Keyword arguments

                            • width_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.
                            • min_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.
                            source
                            TransitionsInTimeseries.estimate_indicator_changes — Function
                            estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → result

                            Estimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).

                            Return the output as subtype of IndicatorsChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                            source
                            TransitionsInTimeseries.SlidingWindowResults — Type
                            SlidingWindowResults <: IndicatorsChangesResults

                            A struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                            It has the following fields that the user may access

                            • x: the input timeseries.

                            • t: the time vector of the input timeseries.

                            • x_indicator, the indicator timeseries (matrix with each column one indicator).

                            • t_indicator, the time vector of the indicator timeseries.

                            • x_change, the change metric timeseries (matrix with each column one change metric).

                            • t_change, the time vector of the change metric timeseries.

                            • config::SlidingWindowConfig, what was used for the analysis.

                            source
                            TransitionsInTimeseries.SegmentedWindowResults — Type
                            SegmentedWindowResults <: IndicatorsChangesResults

                            A struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                            It has the following fields that the user may access

                            • x: the input timeseries.

                            • t: the time vector of the input timeseries.

                            • x_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.

                            • t_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.

                            • x_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.

                            • t_change, the time vector of the change metric.

                            • config::SegmentedWindowConfig, what was used for the analysis.

                            source

                            Significance testing

                            TransitionsInTimeseries.significant_transitions — Function
                            significant_transitions(res::IndicatorsChangesResults, signif::TransitionsSignificance)

                            Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.

                            source
                            TransitionsInTimeseries.SurrogatesSignificance — Type
                            SurrogatesSignificance <: TransitionsSignificance
+SurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)

                            A configuration struct for significance testing significant_transitions using timeseries surrogates.

                            Keyword arguments

                            • surromethod = RandomFourier(): method to generate surrogates
                            • n = 1000: how many surrogates to generate
                            • rng = Random.default_rng(): random number generator for the surrogates
                            • p = 0.05: threshold for significance of the p-value
                            • tail = :both: tail type used, see below

                            Description

                            When used with IndicatorsChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

                            The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in IndicatorsChangesResults.

                            Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

                            source
                            TransitionsInTimeseries.QuantileSignificance — Type
                            QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance

                            A configuration struct for significance testing significant_transitions. When used with IndicatorsChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                            QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

                            source

                            Indicators

                            Value distribution

                            Statistics.mean — Method
                            mean(itr)

                            Compute the mean of all elements in a collection.

                            Note

                            If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

                            Examples

                            julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
                            StatsBase.skewness — Function
                            skewness(v, [wv::AbstractWeights], m=mean(v))

                            Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                            StatsBase.kurtosis — Function
                            kurtosis(v, [wv::AbstractWeights], m=mean(v))

                            Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                            Critical Slowing Down

                            Statistics.var — Method
                            var(itr; corrected::Bool=true, mean=nothing[, dims])

                            Compute the sample variance of collection itr.

                            The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

                            If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

                            A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

                            Note

                            If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

                            TransitionsInTimeseries.ar1_whitenoise — Function
                            ar1_whitenoise(x::AbstractVector)

                            Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

                            \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                            source

                            Spectrum

                            TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                            LowfreqPowerSpectrum(; q_lofreq = 0.1)

                            Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                            lfps = precompute( LowfreqPowerSpectrum() )

                            Keyword arguments:

                            • q_lofreq: a number between 0 and 1 that characterises which portion of the

                            frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                            source

                            Nonlinear dynamics

                            Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.

                            For example, using the permutation entropy as an indicator is as simple as doing

                            using ComplexityMeasures
+est = OrdinalPatterns(; m = 3) # order 3
+# create a function that given timeseries returns permutation entropy
+indicator = x -> entropy_normalized(est, x)

                            and giving the created indicator to e.g., SlidingWindowConfig.

                            Change metrics

                            Slope

                            TransitionsInTimeseries.kendalltau — Function
                            kendalltau(x::AbstractVector)

                            Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                            source
                            TransitionsInTimeseries.spearman — Function
                            spearman(x::AbstractVector)

                            Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                            source

                            Value distribution differences

                            TransitionsInTimeseries.difference_of_means — Function
                            difference_of_means(x::AbstractArray)

                            Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                            # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                            difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                            source

                            Make your own indicator/metric!

                            The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                            There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:

                            Missing docstring.

                            Missing docstring for precompute. Check Documenter's build log for details.

                            Surrogates

                            For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                            Sliding windows

                            TransitionsInTimeseries.WindowViewer — Type
                            WindowViewer(x; width, stride)

                            Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                            If not given, the keywords width, stride are taken as default_window_width(x) and 1.

                            source
                            TransitionsInTimeseries.windowmap — Function
                            windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                            A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                            source

                            Load data

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+ } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR50/assets/search.js b/previews/PR50/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR50/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
                          • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR50/assets/themes/documenter-dark.css 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rgba(255,255,255,0.25)}html.theme--documenter-dark .button.is-white:active,html.theme--documenter-dark .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white{background-color:#fff;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark 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.button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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rgba(245,245,245,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#f5f5f5;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:#292929}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#2f2f2f;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,54,54,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#292929;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#e8e8e8}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#4eb5de;border-color:#4eb5de;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #4eb5de #4eb5de !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#4eb5de;box-shadow:none;color:#4eb5de}html.theme--documenter-dark 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They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found [here](https://www.iceandclimate.nbi.ku.dk/data/) in its raw format. This analysis has already been done in [boers-early-warning-2018](@cite) and we here try to reproduce Figure 2.d-f. + +## Preprocessing NGRIP + +Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps: +1. Load the data, reverse and offset it to have time vector = time before 2000 AD. +2. Filter non-unique points in time and sort the data. +3. Regrid the data from uneven to even sampling. + +The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing. + +### Step 1: +=# + +using DelimitedFiles, Downloads + +function load_ngrip() + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP.csv") + data, labels = readdlm(tmp, header = true) + return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors +end + +t1, x1 = load_ngrip() + +#= +### Step 2 +=# + +uniqueidx(v) = unique(i -> v[i], eachindex(v)) +function keep_unique(t, x) + unique_idx = uniqueidx(t) + return t[unique_idx], x[unique_idx] +end + +function sort_timeseries!(t, x) + p = sortperm(t) + permute!(t, p) + permute!(x, p) + return nothing +end + +t2, x2 = keep_unique(t1, x1) +sort_timeseries!(t2, x2) + +#= +### Step 3 +=# + +using BSplineKit + +function regrid2evensampling(t, x, dt) + itp = BSplineKit.interpolate(t, x, BSplineOrder(4)) + tspan = (ceil(minimum(t)), floor(maximum(t))) + t_even = collect(tspan[1]:dt:tspan[2]) + x_even = itp.(t_even) + return t_even, x_even +end + +dt = 5.0 # dt = 5 yr as in (Boers 2018) +t3, x3 = regrid2evensampling(t2, x2, dt) + +#= +### Step 4 + +For the final step we drop the indices: +=# + +using DSP + +function chebyshev_filter(t, x, fcutoff) + ii = 10 # Chebyshev filtering requires to prune first points of timeseries. + responsetype = Highpass(fcutoff, fs = 1/dt) + designmethod = Chebyshev1(8, 0.05) + r = filt(digitalfilter(responsetype, designmethod), x) + xtrend = x - r + return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end] +end + +fcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018) +t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff) + +#= +Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from [rasmussen-stratigraphic-2014](@cite) (which will soon be available as downloadable): +=# + +using CairoMakie, Loess + +function loess_filter(t, x; span = 0.005) + loessmodel = loess(t, x, span = span) + xtrend = Loess.predict(loessmodel, t) + r = x - xtrend + return t, x, xtrend, r +end + +function kyr_xticks(tticks_yr) + tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)] + return (tticks_yr, tticks_kyr) +end + +function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks) + fig = Figure(resolution = (1600, 1200), fontsize = 24) + + ## Original timeseries with transition marked by vertical lines + ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)", + xaxisposition = :top, xticks = xticks) + lines!(ax1, traw, xraw, color = (:gray70, 0.5)) + lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3) + vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3) + + ## Residual timeseries + ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + lines!(ax2, t, r, color = :gray50, linewidth = 1) + + ## Axes for variance and AC1 timeseries + ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$", + xticks = xticks) + + axs = [ax1, ax2, ax3, ax4] + [xlims!(ax, xlims) for ax in axs] + ylims!(axs[1], (-48, -34)) + rowgap!(fig.layout, 10) + return fig, axs +end + +xlims = (-60e3, -10e3) +xticks = kyr_xticks(-60e3:5e3:5e3) +t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160, + 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703] +tloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +fig + +#= +## Hindcast on NGRIP data + +As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including [boers-early-warning-2018](@cite), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using `SegmentedWindowConfig`, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here: +=# + +using TransitionsInTimeseries, StatsBase +using Random: Xoshiro + +ac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase +indicators = (var, ac1) +change_metrics = RidgeRegressionSlope() +tseg_start = t_rasmussen[1:end-1] .+ 200 +tseg_end = t_rasmussen[2:end] .- 200 +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) # require >=100 data points to estimate change metric +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) + +#= +That's it! We can now visulaise our results with a generic function that we will re-use later: +=# + +function plot_segment_analysis!(axs, results, signif) + (; t_indicator, x_indicator) = results + for k in eachindex(t_indicator) # loop over the segments + for i in axes(signif.pvalues, 2) # loop over the indicators + if !isinf(signif.pvalues[k, i]) # plot if segment long enough + ## Plot indicator timeseries and its linear regression + ti, xi = t_indicator[k], x_indicator[k][:, i] + lines!(axs[i+2], ti, xi, color = Cycled(1)) + m, p = ridgematrix(ti, 0.0) * xi + if signif.pvalues[k, i] < 0.05 + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3) + else + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3) + end + end + end + end +end +plot_segment_analysis!(axs, results, signif) +fig + +#= +In [boers-early-warning-2018](@cite), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in [boers-early-warning-2018](@cite), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of [boers-early-warning-2018](@cite). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media. + +## CSD: only a necessary condition, only in some cases + +For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a **necessary condition** for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is **not a sufficient condition** for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition: +=# + +tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +plot_segment_analysis!(axs, results, signif) +fig + +#= +For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD. + +We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC). + +!!! warning "Degrees of freedom" + These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice. + +!!! info "Future improvement" + Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias. + +## Hindcasting simulated DO-events + +In CLIMBER-X, the EMIC described in [willeit-earth-2022](@cite), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs: +=# + +t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050], + [1, 3500, 4370, 5790, 7200, 8140]] +t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]] +tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]] +tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50] + +figvec = Figure[] + +for j in 1:2 + ## Download the data and perform loess filtering on it + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" * + "master/timeseries/climberx-do$(j)-omaxa.csv") + data = readdlm(tmp) + tcx, xcx = data[1, 1000:end], data[2, 1000:end] + t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02) + + ## Initialize figure + xlims = (0, last(tcx)) + xticks = kyr_xticks(xlims[1]:1e3:xlims[2]) + fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks) + ylims!(axs[1], (5, 40)) + axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$" + + ## Run sliding analysis and update figure with results + dt = mean(diff(tcx)) + config = SegmentedWindowConfig( + indicators, change_metrics, tseg_start[j], tseg_end[j], + whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100) + results = estimate_indicator_changes(config, r, t) + signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995)) + flags = significant_transitions(results, signif) + + plot_segment_analysis!(axs, results, signif) + vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3) + push!(figvec, fig) +end +figvec[1] + +#= +It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case: +=# + +figvec[2] + +#= +Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience. +=# \ No newline at end of file diff --git a/previews/PR50/examples/do-events/index.html b/previews/PR50/examples/do-events/index.html new file mode 100644 index 00000000..a0cfcacc --- /dev/null +++ b/previews/PR50/examples/do-events/index.html @@ -0,0 +1,191 @@ + +Dansgaard-Oescher events and Critical Slowing Down · TransitionsInTimeseries.jl
                            Edit on GitHub

                            Dansgaard-Oescher events and Critical Slowing Down

                            The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.

                            Preprocessing NGRIP

                            Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:

                            1. Load the data, reverse and offset it to have time vector = time before 2000 AD.
                            2. Filter non-unique points in time and sort the data.
                            3. Regrid the data from uneven to even sampling.

                            The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.

                            Step 1:

                            using DelimitedFiles, Downloads
+
+function load_ngrip()
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+        "master/timeseries/NGRIP.csv")
+    data, labels = readdlm(tmp, header = true)
+    return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors
+end
+
+t1, x1 = load_ngrip()
                            ([-59944.5, -59939.6, -59935.9, -59930.5, -59925.0, -59919.0, -59914.3, -59909.4, -59904.5, -59899.7  …  -27.40000000000009, -27.40000000000009, -27.299999999999955, -27.299999999999955, -27.200000000000045, -27.09999999999991, -27.09999999999991, -27.0, -26.90000000000009, -26.799999999999955], [-43.52, -42.94, -42.13, -40.04, -41.09, -43.57, -42.28, -41.2, -44.07, -44.53  …  -35.29, -35.18, -35.51, -36.03, -36.52, -37.12, -37.41, -37.21, -36.62, -35.52])

                            Step 2

                            uniqueidx(v) = unique(i -> v[i], eachindex(v))
+function keep_unique(t, x)
+    unique_idx = uniqueidx(t)
+    return t[unique_idx], x[unique_idx]
+end
+
+function sort_timeseries!(t, x)
+    p = sortperm(t)
+    permute!(t, p)
+    permute!(x, p)
+    return nothing
+end
+
+t2, x2 = keep_unique(t1, x1)
+sort_timeseries!(t2, x2)

                            Step 3

                            using BSplineKit
+
+function regrid2evensampling(t, x, dt)
+    itp = BSplineKit.interpolate(t, x, BSplineOrder(4))
+    tspan = (ceil(minimum(t)), floor(maximum(t)))
+    t_even = collect(tspan[1]:dt:tspan[2])
+    x_even = itp.(t_even)
+    return t_even, x_even
+end
+
+dt = 5.0        # dt = 5 yr as in (Boers 2018)
+t3, x3 = regrid2evensampling(t2, x2, dt)
                            ([-59944.0, -59939.0, -59934.0, -59929.0, -59924.0, -59919.0, -59914.0, -59909.0, -59904.0, -59899.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-43.445268010797946, -42.85408835164853, -41.357360665158936, -39.9365468206892, -41.60554051352076, -43.57000000000001, -42.145558689100454, -41.33160823883399, -44.273597725729985, -44.4622612304012  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46])

                            Step 4

                            For the final step we drop the indices:

                            using DSP
+
+function chebyshev_filter(t, x, fcutoff)
+    ii = 10             # Chebyshev filtering requires to prune first points of timeseries.
+    responsetype = Highpass(fcutoff, fs = 1/dt)
+    designmethod = Chebyshev1(8, 0.05)
+    r = filt(digitalfilter(responsetype, designmethod), x)
+    xtrend = x - r
+    return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]
+end
+
+fcutoff = 0.95 * 0.01   # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)
+t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)
                            ([-59899.0, -59894.0, -59889.0, -59884.0, -59879.0, -59874.0, -59869.0, -59864.0, -59859.0, -59854.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-44.4622612304012, -44.264401428210874, -44.02956767939856, -42.29334237357212, -42.594341674200344, -41.09704877854712, -40.39837540966913, -44.369155046413255, -42.74492506508012, -43.737014520530145  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46], [-43.89287787976461, -48.663435112414156, -51.31169981050155, -51.269094666491796, -49.90310432724566, -47.721430022512344, -44.36050569418247, -43.87556827410048, -43.57802291229893, -41.36870967826094  …  -34.81349114528442, -36.01634453179986, -36.150446802907226, -36.37595639697143, -35.96843653265903, -33.899634243732976, -32.49784036951535, -33.06575312724142, -34.07956188682297, -34.4079080530096], [-0.5693833506365866, 4.399033684203284, 7.282132131102991, 8.975752292919669, 7.308762653045311, 6.624381243965224, 3.9621302845133433, -0.493586772312777, 0.8330978472188112, -2.368304842269206  …  -0.30650885471557926, -0.17365546820014846, 1.0104468029072273, -0.684043603028572, 1.0384365326590237, -0.3303657562670192, -1.0321596304846505, -2.0242468727585807, 0.07956188682296689, -0.05209194699039831])

                            Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):

                            using CairoMakie, Loess
+
+function loess_filter(t, x; span = 0.005)
+    loessmodel = loess(t, x, span = span)
+    xtrend = Loess.predict(loessmodel, t)
+    r = x - xtrend
+    return t, x, xtrend, r
+end
+
+function kyr_xticks(tticks_yr)
+    tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)]
+    return (tticks_yr, tticks_kyr)
+end
+
+function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)
+    fig = Figure(resolution = (1600, 1200), fontsize = 24)
+
+    # Original timeseries with transition marked by vertical lines
+    ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)",
+        xaxisposition = :top, xticks = xticks)
+    lines!(ax1, traw, xraw, color = (:gray70, 0.5))
+    lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)
+    vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)
+
+    # Residual timeseries
+    ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    lines!(ax2, t, r, color = :gray50, linewidth = 1)
+
+    # Axes for variance and AC1 timeseries
+    ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$",
+        xticks = xticks)
+
+    axs = [ax1, ax2, ax3, ax4]
+    [xlims!(ax, xlims) for ax in axs]
+    ylims!(axs[1], (-48, -34))
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+
+xlims = (-60e3, -10e3)
+xticks = kyr_xticks(-60e3:5e3:5e3)
+t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,
+                38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]
+tloess, _, xloess, rloess = loess_filter(t3, x3)    # loess-filtered signal for visualization
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+fig

                            Hindcast on NGRIP data

                            As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:

                            using TransitionsInTimeseries, StatsBase
+using Random: Xoshiro
+
+ac1(x) = sum(autocor(x, [1]))   # AC1 from StatsBase
+indicators = (var, ac1)
+change_metrics = RidgeRegressionSlope()
+tseg_start = t_rasmussen[1:end-1] .+ 200
+tseg_end = t_rasmussen[2:end] .- 200
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)        # require >=100 data points to estimate change metric
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
                            18×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 1  0
+ 1  1
+ 1  1
+ 1  1
+ 0  0
+ 1  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 1  0

                            That's it! We can now visulaise our results with a generic function that we will re-use later:

                            function plot_segment_analysis!(axs, results, signif)
+    (; t_indicator, x_indicator) = results
+    for k in eachindex(t_indicator)             # loop over the segments
+        for i in axes(signif.pvalues, 2)        # loop over the indicators
+            if !isinf(signif.pvalues[k, i])     # plot if segment long enough
+                # Plot indicator timeseries and its linear regression
+                ti, xi = t_indicator[k], x_indicator[k][:, i]
+                lines!(axs[i+2], ti, xi, color = Cycled(1))
+                m, p = ridgematrix(ti, 0.0) * xi
+                if signif.pvalues[k, i] < 0.05
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)
+                else
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)
+                end
+            end
+        end
+    end
+end
+plot_segment_analysis!(axs, results, signif)
+fig

                            In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.

                            CSD: only a necessary condition, only in some cases

                            For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:

                            tseg_end = t_rasmussen[2:end] .- 700    # stop analysis 500 years earlier than before
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+plot_segment_analysis!(axs, results, signif)
+fig

                            For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD.

                            We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).

                            Degrees of freedom

                            These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.

                            Future improvement

                            Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.

                            Hindcasting simulated DO-events

                            In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:

                            t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],
+                 [1, 3500, 4370, 5790, 7200, 8140]]
+t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]
+tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]
+tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]
+
+figvec = Figure[]
+
+for j in 1:2
+    # Download the data and perform loess filtering on it
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" *
+        "master/timeseries/climberx-do$(j)-omaxa.csv")
+    data = readdlm(tmp)
+    tcx, xcx = data[1, 1000:end], data[2, 1000:end]
+    t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)
+
+    # Initialize figure
+    xlims = (0, last(tcx))
+    xticks = kyr_xticks(xlims[1]:1e3:xlims[2])
+    fig, axs = plot_do(tcx, xcx,  t, xtrend, t, r, t_transitions[j], extrema(t), xticks)
+    ylims!(axs[1], (5, 40))
+    axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$"
+
+    # Run sliding analysis and update figure with results
+    dt = mean(diff(tcx))
+    config = SegmentedWindowConfig(
+        indicators, change_metrics, tseg_start[j], tseg_end[j],
+        whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)
+    results = estimate_indicator_changes(config, r, t)
+    signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))
+    flags = significant_transitions(results, signif)
+
+    plot_segment_analysis!(axs, results, signif)
+    vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)
+    push!(figvec, fig)
+end
+figvec[1]

                            It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:

                            figvec[2]

                            Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.

                            diff --git a/previews/PR50/examples/logistic.jl b/previews/PR50/examples/logistic.jl new file mode 100644 index 00000000..a2894fbd --- /dev/null +++ b/previews/PR50/examples/logistic.jl @@ -0,0 +1,203 @@ +# # Permutation entropy for dynamic regime changes + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ## Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +## time-dependent logistic map, so that the `r` parameter increases with time +r1 = 3.83 +r2 = 3.86 +N = 2000 +rs = range(r1, r2; length = N) + +function logistic_drifting_rule(u, rs, n) + r = rs[n+1] # time is `n`, starting from 0 + return SVector(r*u[1]*(1 - u[1])) +end + +ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs) +x = trajectory(ds, N-1)[1][:, 1] + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ## Using a simpler change metric + +# Now, let's compute and various indicators and their changes, +# focusing on the permutation entropy as an indicator. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries, ComplexityMeasures + +function permutation_entropy(m) + est = SymbolicPermutation(; m) # order 3 + indicator = x -> entropy_normalized(est, x) + return indicator +end + +indicators = (var, ar1_whitenoise, permutation_entropy(4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as stride half the window width +metric = difference_of_means + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = SlidingWindowConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = estimate_indicator_changes(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + if i < 3 + hidexdecorations!(ax; grid = false) + else + ax.xlabel = "r (time)" + end + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ## Significance via random Fourier surrogates + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +using Random: Xoshiro +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42), + ) + flags = significant_transitions(results, signif) + + ## and also plot the flags with same color + for (i, indicator) in enumerate(indicators) + ## To make things visually clear, we will also plot some example surrogate + ## timeseries for each indicator and change metric pair + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surromethod) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric, p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1) + end + ## Plot the flags as vertical dashed lines + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = color, linestyle = :dash, linewidth = 3 + ) + end + ## add a title to the figure with how we estimate significance + content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod))) +end + +surromethod = RandomFourier() +overplot_surrogate_significance!(fig, surromethod) + +fig + +# ## Different surrogates +# %% #src +# Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# highlighting the _local_ dynamics or information that preserves the local +# changes of dynamical behavior. + +# A surrogate type that does a better job in preserving local sharp +# changes in the timeseries (and hence provides **stricter** +# surrogate-based significance) is for example `RelativePartialRandomization`. + +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = RelativePartialRandomization(0.25) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "gray") +fig + +# Our results have improved. In the permutation entropy, we see only two +# transitions detected as significant, which is correct: only two +# real dynamical transitions exist in the data. +# In the other two indicators we also see fewer transitions, but as we +# have already discussed, no results with the other indicators should +# be taken into meaningful consideration, as these indicators +# are simply inappropriate for what we are looking for here. + +# ## Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be less strict and more simple with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`SigmaSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation. + +fig = plot_change_metrics() +flags = significant_transitions(results, SigmaSignificance(factor = 5.0)) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = Cycled(3), linestyle = :dash, linewidth = 3 + ) +end +content(fig[1, 1]).title = "significance from std" +fig diff --git a/previews/PR50/examples/logistic/index.html b/previews/PR50/examples/logistic/index.html new file mode 100644 index 00000000..1e3375b0 --- /dev/null +++ b/previews/PR50/examples/logistic/index.html @@ -0,0 +1,128 @@ + +Permutation entropy for dynamic regime changes · TransitionsInTimeseries.jl
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                            Permutation entropy for dynamic regime changes

                            Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.

                            This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.

                            Logistic map timeseries

                            A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map

                            using DynamicalSystemsBase
+using CairoMakie
+
+# time-dependent logistic map, so that the `r` parameter increases with time
+r1 = 3.83
+r2 = 3.86
+N = 2000
+rs = range(r1, r2; length = N)
+
+function logistic_drifting_rule(u, rs, n)
+    r = rs[n+1] # time is `n`, starting from 0
+    return SVector(r*u[1]*(1 - u[1]))
+end
+
+ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)
+x = trajectory(ds, N-1)[1][:, 1]
                            2000-element Vector{Float64}:
+ 0.5
+ 0.9575
+ 0.15585767321160574
+ 0.5039019545917718
+ 0.9574529422362281
+ 0.15602441103002537
+ 0.5043473227583317
+ 0.9574501255597653
+ 0.1560361152301728
+ 0.5043840906474082
+ ⋮
+ 0.4253904015445437
+ 0.9434836074964187
+ 0.20581843730311683
+ 0.6309301050251992
+ 0.8988117342940414
+ 0.3510584545931264
+ 0.8793611090928393
+ 0.40948549063776396
+ 0.9333718681550522

                            Plot it, using as time the parameter value (they coincide)

                            fig, ax = lines(rs, x; linewidth = 0.5)
+ax.xlabel = "r (time)"
+ax.ylabel = "x"
+fig

                            In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.

                            Using a simpler change metric

                            Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.

                            using TransitionsInTimeseries, ComplexityMeasures
+
+function permutation_entropy(m)
+    est = SymbolicPermutation(; m) # order 3
+    indicator = x -> entropy_normalized(est, x)
+    return indicator
+end
+
+indicators = (var, ar1_whitenoise, permutation_entropy(4))
+indistrings = ("var", "ar1", "pe")
                            ("var", "ar1", "pe")

                            In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width

                            metric = difference_of_means
+
+width_ind = N÷100
+width_cha = 20
+stride_cha = 10
+
+config = SlidingWindowConfig(indicators, metric;
+    width_ind, width_cha, stride_cha,
+)
+
+results = estimate_indicator_changes(config, x, rs)
                            IndicatorsChangesResults
+ input timeseries:              2000-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise, Symbol("#1")]
+ indicator (window, stride):    (20, 1)
+ change metrics:                [:difference_of_means]
+ change metric (window, stride): (20, 10)
+

                            Let's now plot the change metrics of the indicators

                            function plot_change_metrics()
+    fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),))
+    hidexdecorations!(ax; grid = false)
+    # plot all change metrics
+    for (i, c) in enumerate(eachcol(results.x_change))
+        ax, = scatterlines(fig[i+1, 1], results.t_change, c;
+            axis = (ylabel = indistrings[i],), label = "input"
+        )
+        if i < 3
+            hidexdecorations!(ax; grid = false)
+        else
+            ax.xlabel = "r (time)"
+        end
+    end
+    return fig
+end
+
+fig = plot_change_metrics()

                            We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)

                            Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.

                            Significance via random Fourier surrogates

                            One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.

                            Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!

                            surromethod = RandomFourier()
+
+# Define a function because we will re-use later
+using Random: Xoshiro
+function overplot_surrogate_significance!(fig, surromethod, color = "black")
+
+    signif = SurrogatesSignificance(;
+        n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),
+    )
+    flags = significant_transitions(results, signif)
+
+    # and also plot the flags with same color
+    for (i, indicator) in enumerate(indicators)
+        # To make things visually clear, we will also plot some example surrogate
+        # timeseries for each indicator and change metric pair
+        for _ in 1:10
+            s = TimeseriesSurrogates.surrogate(x, surromethod)
+            p = windowmap(indicator, s; width = width_ind)
+            q = windowmap(metric, p; width = width_cha, stride = stride_cha)
+            lines!(fig[i+1, 1], results.t_change, q;  color = (color, 0.2), linewidth = 1)
+        end
+        # Plot the flags as vertical dashed lines
+        vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+            color = color, linestyle = :dash, linewidth = 3
+        )
+    end
+    # add a title to the figure with how we estimate significance
+    content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod)))
+end
+
+surromethod = RandomFourier()
+overplot_surrogate_significance!(fig, surromethod)
+
+fig

                            Different surrogates

                            Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

                            A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

                            A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

                            surromethod = RelativePartialRandomization(0.25)
+fig = plot_change_metrics()
+overplot_surrogate_significance!(fig, surromethod, "gray")
+fig

                            Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

                            Simpler Significance

                            Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

                            fig = plot_change_metrics()
+flags = significant_transitions(results, SigmaSignificance(factor = 5.0))
+
+# Plot the flags
+for (i, indicator) in enumerate(indicators)
+    vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+        color = Cycled(3), linestyle = :dash, linewidth = 3
+    )
+end
+content(fig[1, 1]).title = "significance from std"
+fig
                            diff --git a/previews/PR50/index.html b/previews/PR50/index.html new file mode 100644 index 00000000..4fb0edb7 --- /dev/null +++ b/previews/PR50/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
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                            TransitionsInTimeseries.jl

                            TransitionsInTimeseries.jl

                            TransitionsInTimeseries — Module

                            TransitionsInTimeseries.jl

                            CI codecov Package Downloads

                            A Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                            This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

                            add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

                            All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                            source
                            Star us on GitHub!

                            If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                            Content

                            Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                            • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                            • Makes the surrogate analysis to test for significance under the hub.
                            • Can be easily extended by any user without touching the source code.
                            • Reduces the programming overhead for any researcher willing to benchmark new methods.
                            • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                            • Increases trustworthiness thanks to a large test suite.
                            Similar projects

                            An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                            Approaches

                            Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                            diff --git a/previews/PR50/refs.bib b/previews/PR50/refs.bib new file mode 100644 index 00000000..8010a9d3 --- /dev/null +++ b/previews/PR50/refs.bib @@ -0,0 +1,54 @@ + +@article{willeit-earth-2022, + title = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1: {Climate} model description and validation​​​​​​​​​​​​​​}, + volume = {15}, + issn = {1991-9603}, + shorttitle = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1}, + url = {https://gmd.copernicus.org/articles/15/5905/2022/}, + doi = {10.5194/gmd-15-5905-2022}, + abstract = {The newly developed fast Earth system model CLIMBER-X is presented. The climate component of CLIMBER-X consists of a 2.5-D semi-empirical statistical–dynamical atmosphere model, a 3-D frictional–geostrophic ocean model, a dynamic–thermodynamic sea ice model and a land surface model. All the model components are discretized on a regular lat–long grid with a horizontal resolution of 5 ◦ × 5 ◦. The model has a throughput of ∼ 10 000 simulation years per day on a single node with 16 CPUs on a high-performance computer and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to {\textgreater} 100 000 years. A comprehensive evaluation of the model performance for the present day and the historical period shows that CLIMBER-X is capable of realistically reproducing many observed climate characteristics, with results that generally lie within the range of state-of-theart general circulation models. The analysis of model performance is complemented by a thorough assessment of climate feedbacks and model sensitivities to changes in external forcings and boundary conditions. Limitations and applicability of the model are critically discussed. CLIMBER-X also includes a detailed representation of the global carbon cycle and is coupled to an ice sheet model, which will be described in separate papers. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.}, + language = {en}, + number = {14}, + urldate = {2022-08-11}, + journal = {Geoscientific Model Development}, + author = {Willeit, Matteo and Ganopolski, Andrey and Robinson, Alexander and Edwards, Neil R.}, + month = jul, + year = {2022}, + pages = {5905--5948}, + file = {Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:/home/jan/Zotero/storage/75NKS975/Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:application/pdf}, +} + +@article{boers-early-warning-2018, + title = {Early-warning signals for {Dansgaard}-{Oeschger} events in a high-resolution ice core record}, + volume = {9}, + issn = {2041-1723}, + url = {http://www.nature.com/articles/s41467-018-04881-7}, + doi = {10.1038/s41467-018-04881-7}, + language = {en}, + number = {1}, + urldate = {2022-10-28}, + journal = {Nature Communications}, + author = {Boers, Niklas}, + month = dec, + year = {2018}, + pages = {2556}, + file = {Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:/home/jan/Zotero/storage/DS97Z9UC/Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:application/pdf}, +} + +@article{rasmussen-stratigraphic-2014, + title = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records: refining and extending the {INTIMATE} event stratigraphy}, + volume = {106}, + issn = {02773791}, + shorttitle = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0277379114003485}, + doi = {10.1016/j.quascirev.2014.09.007}, + abstract = {Due to their outstanding resolution and well-constrained chronologies, Greenland ice-core records provide a master record of past climatic changes throughout the Last InterglacialeGlacial cycle in the North Atlantic region. As part of the INTIMATE (INTegration of Ice-core, MArine and TErrestrial records) project, protocols have been proposed to ensure consistent and robust correlation between different records of past climate. A key element of these protocols has been the formal definition and ordinal numbering of the sequence of Greenland Stadials (GS) and Greenland Interstadials (GI) within the most recent glacial period. The GS and GI periods are the Greenland expressions of the characteristic DansgaardeOeschger events that represent cold and warm phases of the North Atlantic region, respectively. We present here a more detailed and extended GS/GI template for the whole of the Last Glacial period. It is based on a synchronization of the NGRIP, GRIP, and GISP2 ice-core records that allows the parallel analysis of all three records on a common time scale. The boundaries of the GS and GI periods are defined based on a combination of stable-oxygen isotope ratios of the ice (d18O, reflecting mainly local temperature) and calcium ion concentrations (reflecting mainly atmospheric dust loading) measured in the ice. The data not only resolve the well-known sequence of DansgaardeOeschger events that were first defined and numbered in the ice-core records more than two decades ago, but also better resolve a number of short-lived climatic oscillations, some defined here for the first time. Using this revised scheme, we propose a consistent approach for discriminating and naming all the significant abrupt climatic events of the Last Glacial period that are represented in the Greenland ice records. The final product constitutes an extended and better resolved Greenland stratotype sequence, against which other proxy records can be compared and correlated. It also provides a more secure basis for investigating the dynamics and fundamental causes of these climatic perturbations.}, + language = {en}, + urldate = {2023-10-04}, + journal = {Quaternary Science Reviews}, + author = {Rasmussen, Sune O. and Bigler, Matthias and Blockley, Simon P. and Blunier, Thomas and Buchardt, Susanne L. and Clausen, Henrik B. and Cvijanovic, Ivana and Dahl-Jensen, Dorthe and Johnsen, Sigfus J. and Fischer, Hubertus and Gkinis, Vasileios and Guillevic, Myriam and Hoek, Wim Z. and Lowe, J. John and Pedro, Joel B. and Popp, Trevor and Seierstad, Inger K. and Steffensen, Jørgen Peder and Svensson, Anders M. and Vallelonga, Paul and Vinther, Bo M. and Walker, Mike J.C. and Wheatley, Joe J. and Winstrup, Mai}, + month = dec, + year = {2014}, + pages = {14--28}, + file = {Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:/home/jan/Zotero/storage/VSUTVWPN/Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:application/pdf}, +} diff --git a/previews/PR50/refs/index.html b/previews/PR50/refs/index.html new file mode 100644 index 00000000..92916a3d --- /dev/null +++ b/previews/PR50/refs/index.html @@ -0,0 +1,9 @@ + +References · TransitionsInTimeseries.jl
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                            References

                            diff --git a/previews/PR50/search/index.html b/previews/PR50/search/index.html new file mode 100644 index 00000000..9578dafa --- /dev/null +++ b/previews/PR50/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

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                              diff --git a/previews/PR50/search_index.js b/previews/PR50/search_index.js new file mode 100644 index 00000000..fff84e9c --- /dev/null +++ b/previews/PR50/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"IndicatorsChangesConfig\nSlidingWindowConfig\nSegmentedWindowConfig\nestimate_indicator_changes\nIndicatorsChangesResults\nSlidingWindowResults\nSegmentedWindowResults","category":"page"},{"location":"api/#TransitionsInTimeseries.IndicatorsChangesConfig","page":"API","title":"TransitionsInTimeseries.IndicatorsChangesConfig","text":"IndicatorsChangesConfig\n\nSupertype used to define how indicators and their changes are estimated in estimate_indicator_changes. Valid subtypes are:\n\nSlidingWindowConfig.\nSegmentedWindowConfig.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowConfig","page":"API","title":"TransitionsInTimeseries.SlidingWindowConfig","text":"SlidingWindowConfig <: IndicatorsChangesConfig\nSlidingWindowConfig(indicators, change_metrics; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.\n\nThe results output corresponding to SlidingWindowConfig is SlidingWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowConfig","page":"API","title":"TransitionsInTimeseries.SegmentedWindowConfig","text":"SegmentedWindowConfig <: IndicatorsChangeConfig\nSegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:\n\nFor each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).\nFor each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d\n\ntseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.\n\nThe results output corresponding to SlidingWindowConfig is SegmentedWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.\nmin_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.estimate_indicator_changes","page":"API","title":"TransitionsInTimeseries.estimate_indicator_changes","text":"estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → result\n\nEstimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).\n\nReturn the output as subtype of IndicatorsChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.IndicatorsChangesResults","page":"API","title":"TransitionsInTimeseries.IndicatorsChangesResults","text":"IndicatorsChangesResults\n\nSupertype used to gather results of estimate_indicator_changes. The concrete subtype instances are described in the docstrings of configuration types.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowResults","page":"API","title":"TransitionsInTimeseries.SlidingWindowResults","text":"SlidingWindowResults <: IndicatorsChangesResults\n\nA struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nconfig::SlidingWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowResults","page":"API","title":"TransitionsInTimeseries.SegmentedWindowResults","text":"SegmentedWindowResults <: IndicatorsChangesResults\n\nA struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.\nt_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.\nx_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.\nt_change, the time vector of the change metric.\nconfig::SegmentedWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"significant_transitions\nTransitionsSignificance\nSurrogatesSignificance\nQuantileSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::IndicatorsChangesResults, signif::TransitionsSignificance)\n\nEstimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.TransitionsSignificance","page":"API","title":"TransitionsInTimeseries.TransitionsSignificance","text":"TransitionsSignificance\n\nSupertype used to test for significance in significant_transitions. Valid subtypes are:\n\nSurrogatesSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: TransitionsSignificance\nSurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)\n\nA configuration struct for significance testing significant_transitions using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\n\nDescription\n\nWhen used with IndicatorsChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in IndicatorsChangesResults.\n\nNote that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance\n\nA configuration struct for significance testing significant_transitions. When used with IndicatorsChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\nQuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.","category":"page"},{"location":"api/","page":"API","title":"API","text":"For example, using the permutation entropy as an indicator is as simple as doing","category":"page"},{"location":"api/","page":"API","title":"API","text":"using ComplexityMeasures\nest = OrdinalPatterns(; m = 3) # order 3\n# create a function that given timeseries returns permutation entropy\nindicator = x -> entropy_normalized(est, x)","category":"page"},{"location":"api/","page":"API","title":"API","text":"and giving the created indicator to e.g., SlidingWindowConfig.","category":"page"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"EditURL = \"do-events.jl\"","category":"page"},{"location":"examples/do-events/#Dansgaard-Oescher-events-and-Critical-Slowing-Down","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The delta^18O timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.","category":"page"},{"location":"examples/do-events/#Preprocessing-NGRIP","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Preprocessing NGRIP","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Load the data, reverse and offset it to have time vector = time before 2000 AD.\nFilter non-unique points in time and sort the data.\nRegrid the data from uneven to even sampling.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The time and delta^18O vectors resulting from the i-th preprocessing step are respectively called t_i and x_i. The final step consists in obtaining a residual r, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.","category":"page"},{"location":"examples/do-events/#Step-1:","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 1:","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DelimitedFiles, Downloads\n\nfunction load_ngrip()\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP.csv\")\n data, labels = readdlm(tmp, header = true)\n return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors\nend\n\nt1, x1 = load_ngrip()","category":"page"},{"location":"examples/do-events/#Step-2","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 2","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"uniqueidx(v) = unique(i -> v[i], eachindex(v))\nfunction keep_unique(t, x)\n unique_idx = uniqueidx(t)\n return t[unique_idx], x[unique_idx]\nend\n\nfunction sort_timeseries!(t, x)\n p = sortperm(t)\n permute!(t, p)\n permute!(x, p)\n return nothing\nend\n\nt2, x2 = keep_unique(t1, x1)\nsort_timeseries!(t2, x2)","category":"page"},{"location":"examples/do-events/#Step-3","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 3","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using BSplineKit\n\nfunction regrid2evensampling(t, x, dt)\n itp = BSplineKit.interpolate(t, x, BSplineOrder(4))\n tspan = (ceil(minimum(t)), floor(maximum(t)))\n t_even = collect(tspan[1]:dt:tspan[2])\n x_even = itp.(t_even)\n return t_even, x_even\nend\n\ndt = 5.0 # dt = 5 yr as in (Boers 2018)\nt3, x3 = regrid2evensampling(t2, x2, dt)","category":"page"},{"location":"examples/do-events/#Step-4","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 4","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the final step we drop the indices:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DSP\n\nfunction chebyshev_filter(t, x, fcutoff)\n ii = 10 # Chebyshev filtering requires to prune first points of timeseries.\n responsetype = Highpass(fcutoff, fs = 1/dt)\n designmethod = Chebyshev1(8, 0.05)\n r = filt(digitalfilter(responsetype, designmethod), x)\n xtrend = x - r\n return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]\nend\n\nfcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)\nt, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using CairoMakie, Loess\n\nfunction loess_filter(t, x; span = 0.005)\n loessmodel = loess(t, x, span = span)\n xtrend = Loess.predict(loessmodel, t)\n r = x - xtrend\n return t, x, xtrend, r\nend\n\nfunction kyr_xticks(tticks_yr)\n tticks_kyr = [\"$t\" for t in Int.(tticks_yr ./ 1e3)]\n return (tticks_yr, tticks_kyr)\nend\n\nfunction plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)\n fig = Figure(resolution = (1600, 1200), fontsize = 24)\n\n # Original timeseries with transition marked by vertical lines\n ax1 = Axis(fig[1, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"$\\delta^{18}$O (permil)\",\n xaxisposition = :top, xticks = xticks)\n lines!(ax1, traw, xraw, color = (:gray70, 0.5))\n lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)\n vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)\n\n # Residual timeseries\n ax2 = Axis(fig[2, 1], ylabel = L\"Residual $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n lines!(ax2, t, r, color = :gray50, linewidth = 1)\n\n # Axes for variance and AC1 timeseries\n ax3 = Axis(fig[3, 1], ylabel = L\"Variance $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n ax4 = Axis(fig[4, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"Lag-1 autocor. $\\,$\",\n xticks = xticks)\n\n axs = [ax1, ax2, ax3, ax4]\n [xlims!(ax, xlims) for ax in axs]\n ylims!(axs[1], (-48, -34))\n rowgap!(fig.layout, 10)\n return fig, axs\nend\n\nxlims = (-60e3, -10e3)\nxticks = kyr_xticks(-60e3:5e3:5e3)\nt_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,\n 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]\ntloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nfig","category":"page"},{"location":"examples/do-events/#Hindcast-on-NGRIP-data","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcast on NGRIP data","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using TransitionsInTimeseries, StatsBase\nusing Random: Xoshiro\n\nac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase\nindicators = (var, ac1)\nchange_metrics = RidgeRegressionSlope()\ntseg_start = t_rasmussen[1:end-1] .+ 200\ntseg_end = t_rasmussen[2:end] .- 200\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100) # require >=100 data points to estimate change metric\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"That's it! We can now visulaise our results with a generic function that we will re-use later:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"function plot_segment_analysis!(axs, results, signif)\n (; t_indicator, x_indicator) = results\n for k in eachindex(t_indicator) # loop over the segments\n for i in axes(signif.pvalues, 2) # loop over the indicators\n if !isinf(signif.pvalues[k, i]) # plot if segment long enough\n # Plot indicator timeseries and its linear regression\n ti, xi = t_indicator[k], x_indicator[k][:, i]\n lines!(axs[i+2], ti, xi, color = Cycled(1))\n m, p = ridgematrix(ti, 0.0) * xi\n if signif.pvalues[k, i] < 0.05\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)\n else\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)\n end\n end\n end\n end\nend\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.","category":"page"},{"location":"examples/do-events/#CSD:-only-a-necessary-condition,-only-in-some-cases","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"CSD: only a necessary condition, only in some cases","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential U, which defines the deterministic term f = -U of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100)\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that \"resilience-loss indicators\" is a more accurate name than \"early-warning signals\" when using CSD.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"We draw attention upon the fact that the delta^18O timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"warning: Degrees of freedom\nThese sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"info: Future improvement\nSupporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.","category":"page"},{"location":"examples/do-events/#Hindcasting-simulated-DO-events","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcasting simulated DO-events","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],\n [1, 3500, 4370, 5790, 7200, 8140]]\nt_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]\ntseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]\ntseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]\n\nfigvec = Figure[]\n\nfor j in 1:2\n # Download the data and perform loess filtering on it\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\" *\n \"master/timeseries/climberx-do$(j)-omaxa.csv\")\n data = readdlm(tmp)\n tcx, xcx = data[1, 1000:end], data[2, 1000:end]\n t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)\n\n # Initialize figure\n xlims = (0, last(tcx))\n xticks = kyr_xticks(xlims[1]:1e3:xlims[2])\n fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks)\n ylims!(axs[1], (5, 40))\n axs[1].ylabel = L\"Max. Atlantic overturning (Sv) $\\,$\"\n\n # Run sliding analysis and update figure with results\n dt = mean(diff(tcx))\n config = SegmentedWindowConfig(\n indicators, change_metrics, tseg_start[j], tseg_end[j],\n whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)\n results = estimate_indicator_changes(config, r, t)\n signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))\n flags = significant_transitions(results, signif)\n\n plot_segment_analysis!(axs, results, signif)\n vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)\n push!(figvec, fig)\nend\nfigvec[1]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"figvec[2]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"EditURL = \"logistic.jl\"","category":"page"},{"location":"examples/logistic/#Permutation-entropy-for-dynamic-regime-changes","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.","category":"page"},{"location":"examples/logistic/#Logistic-map-timeseries","page":"Permutation entropy for dynamic regime changes","title":"Logistic map timeseries","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using DynamicalSystemsBase\nusing CairoMakie\n\n# time-dependent logistic map, so that the `r` parameter increases with time\nr1 = 3.83\nr2 = 3.86\nN = 2000\nrs = range(r1, r2; length = N)\n\nfunction logistic_drifting_rule(u, rs, n)\n r = rs[n+1] # time is `n`, starting from 0\n return SVector(r*u[1]*(1 - u[1]))\nend\n\nds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)\nx = trajectory(ds, N-1)[1][:, 1]","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Plot it, using as time the parameter value (they coincide)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig, ax = lines(rs, x; linewidth = 0.5)\nax.xlabel = \"r (time)\"\nax.ylabel = \"x\"\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.","category":"page"},{"location":"examples/logistic/#Using-a-simpler-change-metric","page":"Permutation entropy for dynamic regime changes","title":"Using a simpler change metric","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using TransitionsInTimeseries, ComplexityMeasures\n\nfunction permutation_entropy(m)\n est = SymbolicPermutation(; m) # order 3\n indicator = x -> entropy_normalized(est, x)\n return indicator\nend\n\nindicators = (var, ar1_whitenoise, permutation_entropy(4))\nindistrings = (\"var\", \"ar1\", \"pe\")","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"metric = difference_of_means\n\nwidth_ind = N÷100\nwidth_cha = 20\nstride_cha = 10\n\nconfig = SlidingWindowConfig(indicators, metric;\n width_ind, width_cha, stride_cha,\n)\n\nresults = estimate_indicator_changes(config, x, rs)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's now plot the change metrics of the indicators","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"function plot_change_metrics()\n fig, ax = lines(rs, x; axis = (ylabel = \"input\",), figure = (resolution = (600, 600),))\n hidexdecorations!(ax; grid = false)\n # plot all change metrics\n for (i, c) in enumerate(eachcol(results.x_change))\n ax, = scatterlines(fig[i+1, 1], results.t_change, c;\n axis = (ylabel = indistrings[i],), label = \"input\"\n )\n if i < 3\n hidexdecorations!(ax; grid = false)\n else\n ax.xlabel = \"r (time)\"\n end\n end\n return fig\nend\n\nfig = plot_change_metrics()","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.","category":"page"},{"location":"examples/logistic/#Significance-via-random-Fourier-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Significance via random Fourier surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RandomFourier()\n\n# Define a function because we will re-use later\nusing Random: Xoshiro\nfunction overplot_surrogate_significance!(fig, surromethod, color = \"black\")\n\n signif = SurrogatesSignificance(;\n n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),\n )\n flags = significant_transitions(results, signif)\n\n # and also plot the flags with same color\n for (i, indicator) in enumerate(indicators)\n # To make things visually clear, we will also plot some example surrogate\n # timeseries for each indicator and change metric pair\n for _ in 1:10\n s = TimeseriesSurrogates.surrogate(x, surromethod)\n p = windowmap(indicator, s; width = width_ind)\n q = windowmap(metric, p; width = width_cha, stride = stride_cha)\n lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1)\n end\n # Plot the flags as vertical dashed lines\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = color, linestyle = :dash, linewidth = 3\n )\n end\n # add a title to the figure with how we estimate significance\n content(fig[1, 1]).title = \"surrogates: \"*string(nameof(typeof(surromethod)))\nend\n\nsurromethod = RandomFourier()\noverplot_surrogate_significance!(fig, surromethod)\n\nfig","category":"page"},{"location":"examples/logistic/#Different-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Different surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RelativePartialRandomization(0.25)\nfig = plot_change_metrics()\noverplot_surrogate_significance!(fig, surromethod, \"gray\")\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.","category":"page"},{"location":"examples/logistic/#Simpler-Significance","page":"Permutation entropy for dynamic regime changes","title":"Simpler Significance","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig = plot_change_metrics()\nflags = significant_transitions(results, SigmaSignificance(factor = 5.0))\n\n# Plot the flags\nfor (i, indicator) in enumerate(indicators)\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = Cycled(3), linestyle = :dash, linewidth = 3\n )\nend\ncontent(fig[1, 1]).title = \"significance from std\"\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package that can estimate indicators of transitions (from one dynamic regime or stable state to another) in timeseries. Also bundles the indicators with significance testing via surrogate analysis using TimeseriesSurrogates.jl. Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"refs/#References","page":"References","title":"References","text":"","category":"section"},{"location":"refs/","page":"References","title":"References","text":"","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"EditURL = \"tutorial.jl\"","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector,\n# we obtain the last time step of each window.\n# This therefore only uses information from `k-width+1` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\n\nfunction gridfig(nrows, ncols)\n fig = Figure()\n axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)\n for j in 1:ncols, i in 1:nrows]\n rowgap!(fig.layout, 10)\n return fig, axs\nend\nfig, axs = gridfig(2, 1)\nlines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))\nlines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))\naxs[1].title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nlines!(axs[2], t_change, change_nl, label = \"nonlin\", color = Cycled(2))\nlines!(axs[2], t_change, change_s, label = \"surrogate\", color = Cycled(3))\naxislegend()\naxs[2].title = \"change metric\"\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig, axs = gridfig(2, 2)\naxs[1].title = \"linear\"\naxs[2].title = \"nonlinear\"\n\nfor (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change) # ; color = Cycled(j)\n lines!(axsig, t_change, pval) # ; color = Cycled(j+2)\nend\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = RidgeRegressionSlope()\n\n# choices go into a configuration struct\nconfig = SlidingWindowConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last)\n\n# choices are processed\nresults = estimate_indicator_changes(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From result we can plot the change metric timeseries:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(3, 1)\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, results.x_change[:, 1];\n label = \"var slopes\", color = Cycled(3))\nscatter!(axs[3], results.t_change, results.x_change[:, 2];\n label = \"ar1 slopes\", color = Cycled(4))\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = :right)\nflags = significant_transitions(results, signif)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(2, 1)\nlines!(axs[1], vcat(0.0, t), x_nlinear; label = \"raw\", color = Cycled(1))\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 1];\n label = \"var p-values\", color = Cycled(3))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 2];\n label = \"ar1 p-values\", color = Cycled(4))\n\nflagsboth = vec(reduce(&, flags; dims = 2))\nvlines!(axs[1], results.t_change[flagsboth]; label = \"flags\", color = (\"black\", 0.1))\n\n[axislegend(ax) for ax in axs]\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"}] +} diff --git a/previews/PR50/siteinfo.js b/previews/PR50/siteinfo.js new file mode 100644 index 00000000..7cde162d --- /dev/null +++ b/previews/PR50/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR50"; diff --git a/previews/PR50/tutorial.jl b/previews/PR50/tutorial.jl new file mode 100644 index 00000000..3f135673 --- /dev/null +++ b/previews/PR50/tutorial.jl @@ -0,0 +1,263 @@ +#= + +# Tutorial + +## [Workflow] (@id workflow) + +Computing transition indicators consists of the following steps: + +1. Doing any preprocessing of raw data first, such as detrending (_not part of TransitionsInTimeseries.jl_). This yields the **input timeseries**. +2. Estimating the timeseries of an indicator by sliding a window over the input timeseries. +3. Computing the changes of the indicator by sliding a window over its timeseries. +4. Generating many surrogates that preserve important statistical properties of the original timeseries. +5. Performing step 2 and 3 for the surrogate timeseries. +6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data. + +These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports. + +## [Tutorial -- Educational] (@id example_stepbystep) + +### Raw input data + +Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by: + +```math +\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t) +``` + +with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with [Makie](https://docs.makie.org/stable/)) such prototypical data to test some indicators can be done by simply running: +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_linear) +lines!(ax, t, x_nlinear) +ax.title = "raw data" +fig + +#= +### Preprocessing + +!!! note "Not part of TransitionsInTimeseries.jl" + Any timeseries preprocessing, such as the de-trending step we do here, + is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher. + + +The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1. +=# + +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +#= +At this point, `x_l_fluct` and `x_nl_fluct` are considered the **input timeseries**. + +!!! info "Detrending in Julia" + Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as [Loess.jl](https://github.com/JuliaStats/Loess.jl) or [DSP.jl](https://docs.juliadsp.org/latest/contents/). There the detrending step consists of subtracting the smoothed signal from the original one. + +### Indicator timeseries + +We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the **input timeseries**, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as [`ar1_whitenoise`](@ref): +=# + +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +## By mapping `last::Function` over a windowviewer of the time vector, +## we obtain the last time step of each window. +## This therefore only uses information from `k-width+1` to `k` at time step `k`. +## Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +#= +The lines plotted above are the **indicator timeseries**. + +### Change metric timeseries + +From here, we process the **indicator timeseries** to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the **change metric timeseries**. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a [`RidgeRegressionSlope`](@ref): +=# + +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + +#= +### Timeseries surrogates + +As expected from [Critical Slowing Down](@ref approaches), an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance. + +In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the [TimeseriesSurrogates.jl](https://github.com/JuliaDynamics/TimeseriesSurrogates.jl) Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that `TimeseriesSurrogates` is re-exported by `TransitionsInTimeseries`, so that you don't have to `using` both of them. + +To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries. +=# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) + +function gridfig(nrows, ncols) + fig = Figure() + axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false) + for j in 1:ncols, i in 1:nrows] + rowgap!(fig.layout, 10) + return fig, axs +end +fig, axs = gridfig(2, 1) +lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2)) +lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3)) +axs[1].title = "real signal vs. surrogate(s)" + +## compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2)) +lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3)) +axislegend() +axs[2].title = "change metric" + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +### Quantifying significance + +To quantify the significance of the values of the **change metric timeseries** we perform a standard surrogate test by computing the [p-value](https://en.wikipedia.org/wiki/P-value) w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically `p<0.05`) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time: +=# + +n_surrogates = 1_000 +fig, axs = gridfig(2, 2) +axs[1].title = "linear" +axs[2].title = "nonlinear" + +for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + ## Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change) # ; color = Cycled(j) + lines!(axsig, t_change, pval) # ; color = Cycled(j+2) +end + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar. + +Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section. + +## [Tutorial -- TransitionsInTimeseries.jl] (@id example_fastforward) + +TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go. + +The interface is simple, and directly parallelizes the [Workflow](@ref). It is based on the creation of a [`TransitionsSurrogatesConfig`](@ref), which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate. + +The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +## input timeseries and time +input = x_nl_fluct = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(t, input) +ax.title = "input timeseries" +fig + +#= +To perform all of the above analysis we follow a 2-step process. + +Step 1, we decide what indicators and change metrics to use in [`SlidingWindowConfig`](@ref) and apply those via +a sliding window to the input timeseries using [`transition_metrics`](@ref). +=# + +## These indicators are suitable for Critical Slowing Down +indicators = (var, ar1_whitenoise) + +## use the ridge regression slope for both indicators +change_metrics = RidgeRegressionSlope() + +## choices go into a configuration struct +config = SlidingWindowConfig(indicators, change_metrics; + width_ind = 400, width_cha = 30, whichtime = last) + +## choices are processed +results = estimate_indicator_changes(config, input, t) + +#= +From `result` we can plot the change metric timeseries: +=# + +fig, axs = gridfig(3, 1) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, results.x_change[:, 1]; + label = "var slopes", color = Cycled(3)) +scatter!(axs[3], results.t_change, results.x_change[:, 2]; + label = "ar1 slopes", color = Cycled(4)) +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +Step 2 is to estimate significance using [`SurrogatesConfig`](@ref) +and the function [`estimate_significance!`](@ref). +=# + +signif = SurrogatesSignificance(n = 1000, tail = :right) +flags = significant_transitions(results, signif) + +#= +We can now plot the p-values corresponding to each time series of the change metrics. From the `flags` we can additionally obtain the time points where _both_ indicators show significance, via a simple reduction: +=# + +fig, axs = gridfig(2, 1) +lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1)) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 1]; + label = "var p-values", color = Cycled(3)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 2]; + label = "ar1 p-values", color = Cycled(4)) + +flagsboth = vec(reduce(&, flags; dims = 2)) +vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1)) + +[axislegend(ax) for ax in axs] +[xlims!(ax, 0, 50) for ax in axs] +fig \ No newline at end of file diff --git a/previews/PR50/tutorial/index.html b/previews/PR50/tutorial/index.html new file mode 100644 index 00000000..c7a029e6 --- /dev/null +++ b/previews/PR50/tutorial/index.html @@ -0,0 +1,160 @@ + +Tutorial · TransitionsInTimeseries.jl
                              Edit on GitHub

                              Tutorial

                              Workflow

                              Computing transition indicators consists of the following steps:

                              1. Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                              2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                              3. Computing the changes of the indicator by sliding a window over its timeseries.
                              4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                              5. Performing step 2 and 3 for the surrogate timeseries.
                              6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                              These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                              Tutorial – Educational

                              Raw input data

                              Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                              \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                              with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                              using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig

                              Preprocessing

                              Not part of TransitionsInTimeseries.jl

                              Any timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                              The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                              x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                              At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                              Detrending in Julia

                              Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                              Indicator timeseries

                              We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                              indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector,
+# we obtain the last time step of each window.
+# This therefore only uses information from `k-width+1` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                              The lines plotted above are the indicator timeseries.

                              Change metric timeseries

                              From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                              change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                              Timeseries surrogates

                              As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                              In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                              To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                              # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+
+function gridfig(nrows, ncols)
+    fig = Figure()
+    axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)
+        for j in 1:ncols, i in 1:nrows]
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+fig, axs = gridfig(2, 1)
+lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))
+lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))
+axs[1].title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2))
+lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3))
+axislegend()
+axs[2].title = "change metric"
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                              Quantifying significance

                              To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                              n_surrogates = 1_000
+fig, axs = gridfig(2, 2)
+axs[1].title = "linear"
+axs[2].title = "nonlinear"
+
+for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change)   # ; color = Cycled(j)
+    lines!(axsig, t_change, pval)       # ; color = Cycled(j+2)
+end
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                              As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                              Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                              Tutorial – TransitionsInTimeseries.jl

                              TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                              The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

                              The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

                              using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig

                              To perform all of the above analysis we follow a 2-step process.

                              Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.

                              # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = RidgeRegressionSlope()
+
+# choices go into a configuration struct
+config = SlidingWindowConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last)
+
+# choices are processed
+results = estimate_indicator_changes(config, input, t)
                              IndicatorsChangesResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                              From result we can plot the change metric timeseries:

                              fig, axs = gridfig(3, 1)
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, results.x_change[:, 1];
+    label = "var slopes", color = Cycled(3))
+scatter!(axs[3], results.t_change, results.x_change[:, 2];
+    label = "ar1 slopes", color = Cycled(4))
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                              Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.

                              signif = SurrogatesSignificance(n = 1000, tail = :right)
+flags = significant_transitions(results, signif)
                              2072×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ ⋮  
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0

                              We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:

                              fig, axs = gridfig(2, 1)
+lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1))
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 1];
+    label = "var p-values", color = Cycled(3))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 2];
+    label = "ar1 p-values", color = Cycled(4))
+
+flagsboth = vec(reduce(&, flags; dims = 2))
+vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1))
+
+[axislegend(ax) for ax in axs]
+[xlims!(ax, 0, 50) for ax in axs]
+fig
                              diff --git a/previews/PR51/api/index.html b/previews/PR51/api/index.html new file mode 100644 index 00000000..d39b0990 --- /dev/null +++ b/previews/PR51/api/index.html @@ -0,0 +1,22 @@ + +API · TransitionsInTimeseries.jl
                              Edit on GitHub

                              API

                              Main analysis functions

                              TransitionsInTimeseries.SlidingWindowConfig — Type
                              SlidingWindowConfig <: IndicatorsChangesConfig
+SlidingWindowConfig(indicators, change_metrics; kwargs...)

                              A configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:

                              1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                              2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                              indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                              Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.

                              The results output corresponding to SlidingWindowConfig is SlidingWindowResults.

                              Keyword arguments

                              • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.
                              • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.
                              • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:
                                • last: use the last timepoint of each window
                                • midpoint: use the mid timepoint of each time window
                                • first: use first timepoint of each window
                                In fact, the indicators time vector is computed simply via
                                t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)
                                so any other function of the time window may be given to extract the time point itself, such as mean or median.
                              • T = Float64: Element type of input timeseries to initialize some computations.
                              source
                              TransitionsInTimeseries.SegmentedWindowConfig — Type
                              SegmentedWindowConfig <: IndicatorsChangeConfig
+SegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)

                              A configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:

                              1. For each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).
                              2. For each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d

                              tseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.

                              The results output corresponding to SlidingWindowConfig is SegmentedWindowResults.

                              Keyword arguments

                              • width_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.
                              • min_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.
                              source
                              TransitionsInTimeseries.estimate_indicator_changes — Function
                              estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → result

                              Estimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).

                              Return the output as subtype of IndicatorsChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                              source
                              TransitionsInTimeseries.SlidingWindowResults — Type
                              SlidingWindowResults <: IndicatorsChangesResults

                              A struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                              It has the following fields that the user may access

                              • x: the input timeseries.

                              • t: the time vector of the input timeseries.

                              • x_indicator, the indicator timeseries (matrix with each column one indicator).

                              • t_indicator, the time vector of the indicator timeseries.

                              • x_change, the change metric timeseries (matrix with each column one change metric).

                              • t_change, the time vector of the change metric timeseries.

                              • config::SlidingWindowConfig, what was used for the analysis.

                              source
                              TransitionsInTimeseries.SegmentedWindowResults — Type
                              SegmentedWindowResults <: IndicatorsChangesResults

                              A struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                              It has the following fields that the user may access

                              • x: the input timeseries.

                              • t: the time vector of the input timeseries.

                              • x_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.

                              • t_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.

                              • x_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.

                              • t_change, the time vector of the change metric.

                              • config::SegmentedWindowConfig, what was used for the analysis.

                              source

                              Significance testing

                              TransitionsInTimeseries.significant_transitions — Function
                              significant_transitions(res::IndicatorsChangesResults, signif::TransitionsSignificance)

                              Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.

                              source
                              TransitionsInTimeseries.SurrogatesSignificance — Type
                              SurrogatesSignificance <: TransitionsSignificance
+SurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)

                              A configuration struct for significance testing significant_transitions using timeseries surrogates.

                              Keyword arguments

                              • surromethod = RandomFourier(): method to generate surrogates
                              • n = 1000: how many surrogates to generate
                              • rng = Random.default_rng(): random number generator for the surrogates
                              • p = 0.05: threshold for significance of the p-value
                              • tail = :both: tail type used, see below

                              Description

                              When used with IndicatorsChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

                              The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in IndicatorsChangesResults.

                              Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

                              source
                              TransitionsInTimeseries.QuantileSignificance — Type
                              QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance

                              A configuration struct for significance testing significant_transitions. When used with IndicatorsChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                              QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

                              source

                              Indicators

                              Value distribution

                              Statistics.mean — Method
                              mean(itr)

                              Compute the mean of all elements in a collection.

                              Note

                              If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

                              Examples

                              julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
                              StatsBase.skewness — Function
                              skewness(v, [wv::AbstractWeights], m=mean(v))

                              Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                              StatsBase.kurtosis — Function
                              kurtosis(v, [wv::AbstractWeights], m=mean(v))

                              Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                              Critical Slowing Down

                              Statistics.var — Method
                              var(itr; corrected::Bool=true, mean=nothing[, dims])

                              Compute the sample variance of collection itr.

                              The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

                              If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

                              A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

                              Note

                              If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

                              TransitionsInTimeseries.ar1_whitenoise — Function
                              ar1_whitenoise(x::AbstractVector)

                              Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

                              \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                              source

                              Spectrum

                              TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                              LowfreqPowerSpectrum(; q_lofreq = 0.1)

                              Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                              lfps = precompute( LowfreqPowerSpectrum() )

                              Keyword arguments:

                              • q_lofreq: a number between 0 and 1 that characterises which portion of the

                              frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                              source

                              Nonlinear dynamics

                              Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.

                              For example, using the permutation entropy as an indicator is as simple as doing

                              using ComplexityMeasures
+est = OrdinalPatterns(; m = 3) # order 3
+# create a function that given timeseries returns permutation entropy
+indicator = x -> entropy_normalized(est, x)

                              and giving the created indicator to e.g., SlidingWindowConfig.

                              Change metrics

                              Slope

                              TransitionsInTimeseries.kendalltau — Function
                              kendalltau(x::AbstractVector)

                              Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                              source
                              TransitionsInTimeseries.spearman — Function
                              spearman(x::AbstractVector)

                              Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                              source

                              Value distribution differences

                              TransitionsInTimeseries.difference_of_means — Function
                              difference_of_means(x::AbstractArray)

                              Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                              # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                              difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                              source

                              Make your own indicator/metric!

                              The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                              There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:

                              Missing docstring.

                              Missing docstring for precompute. Check Documenter's build log for details.

                              Surrogates

                              For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                              Sliding windows

                              TransitionsInTimeseries.WindowViewer — Type
                              WindowViewer(x; width, stride)

                              Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                              If not given, the keywords width, stride are taken as default_window_width(x) and 1.

                              source
                              TransitionsInTimeseries.windowmap — Function
                              windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                              A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                              source

                              Load data

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+ } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR51/assets/search.js b/previews/PR51/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR51/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
                            • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR51/assets/themes/documenter-dark.css 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rgba(255,255,255,0.25)}html.theme--documenter-dark .button.is-white:active,html.theme--documenter-dark .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white{background-color:#fff;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark 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.button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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rgba(245,245,245,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#f5f5f5;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:#292929}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#2f2f2f;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,54,54,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#292929;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#e8e8e8}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#4eb5de;border-color:#4eb5de;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #4eb5de #4eb5de !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#4eb5de;box-shadow:none;color:#4eb5de}html.theme--documenter-dark 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They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found [here](https://www.iceandclimate.nbi.ku.dk/data/) in its raw format. This analysis has already been done in [boers-early-warning-2018](@cite) and we here try to reproduce Figure 2.d-f. + +## Preprocessing NGRIP + +Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps: +1. Load the data, reverse and offset it to have time vector = time before 2000 AD. +2. Filter non-unique points in time and sort the data. +3. Regrid the data from uneven to even sampling. + +The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing. + +### Step 1: +=# + +using DelimitedFiles, Downloads + +function load_ngrip() + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP.csv") + data, labels = readdlm(tmp, header = true) + return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors +end + +t1, x1 = load_ngrip() + +#= +### Step 2 +=# + +uniqueidx(v) = unique(i -> v[i], eachindex(v)) +function keep_unique(t, x) + unique_idx = uniqueidx(t) + return t[unique_idx], x[unique_idx] +end + +function sort_timeseries!(t, x) + p = sortperm(t) + permute!(t, p) + permute!(x, p) + return nothing +end + +t2, x2 = keep_unique(t1, x1) +sort_timeseries!(t2, x2) + +#= +### Step 3 +=# + +using BSplineKit + +function regrid2evensampling(t, x, dt) + itp = BSplineKit.interpolate(t, x, BSplineOrder(4)) + tspan = (ceil(minimum(t)), floor(maximum(t))) + t_even = collect(tspan[1]:dt:tspan[2]) + x_even = itp.(t_even) + return t_even, x_even +end + +dt = 5.0 # dt = 5 yr as in (Boers 2018) +t3, x3 = regrid2evensampling(t2, x2, dt) + +#= +### Step 4 + +For the final step we drop the indices: +=# + +using DSP + +function chebyshev_filter(t, x, fcutoff) + ii = 10 # Chebyshev filtering requires to prune first points of timeseries. + responsetype = Highpass(fcutoff, fs = 1/dt) + designmethod = Chebyshev1(8, 0.05) + r = filt(digitalfilter(responsetype, designmethod), x) + xtrend = x - r + return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end] +end + +fcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018) +t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff) + +#= +Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from [rasmussen-stratigraphic-2014](@cite) (which will soon be available as downloadable): +=# + +using CairoMakie, Loess + +function loess_filter(t, x; span = 0.005) + loessmodel = loess(t, x, span = span) + xtrend = Loess.predict(loessmodel, t) + r = x - xtrend + return t, x, xtrend, r +end + +function kyr_xticks(tticks_yr) + tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)] + return (tticks_yr, tticks_kyr) +end + +function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks) + fig = Figure(resolution = (1600, 1200), fontsize = 24) + + ## Original timeseries with transition marked by vertical lines + ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)", + xaxisposition = :top, xticks = xticks) + lines!(ax1, traw, xraw, color = (:gray70, 0.5)) + lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3) + vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3) + + ## Residual timeseries + ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + lines!(ax2, t, r, color = :gray50, linewidth = 1) + + ## Axes for variance and AC1 timeseries + ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$", + xticks = xticks) + + axs = [ax1, ax2, ax3, ax4] + [xlims!(ax, xlims) for ax in axs] + ylims!(axs[1], (-48, -34)) + rowgap!(fig.layout, 10) + return fig, axs +end + +xlims = (-60e3, -10e3) +xticks = kyr_xticks(-60e3:5e3:5e3) +t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160, + 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703] +tloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +fig + +#= +## Hindcast on NGRIP data + +As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including [boers-early-warning-2018](@cite), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using `SegmentedWindowConfig`, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here: +=# + +using TransitionsInTimeseries, StatsBase +using Random: Xoshiro + +ac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase +indicators = (var, ac1) +change_metrics = RidgeRegressionSlope() +tseg_start = t_rasmussen[1:end-1] .+ 200 +tseg_end = t_rasmussen[2:end] .- 200 +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) # require >=100 data points to estimate change metric +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) + +#= +That's it! We can now visulaise our results with a generic function that we will re-use later: +=# + +function plot_segment_analysis!(axs, results, signif) + (; t_indicator, x_indicator) = results + for k in eachindex(t_indicator) # loop over the segments + for i in axes(signif.pvalues, 2) # loop over the indicators + if !isinf(signif.pvalues[k, i]) # plot if segment long enough + ## Plot indicator timeseries and its linear regression + ti, xi = t_indicator[k], x_indicator[k][:, i] + lines!(axs[i+2], ti, xi, color = Cycled(1)) + m, p = ridgematrix(ti, 0.0) * xi + if signif.pvalues[k, i] < 0.05 + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3) + else + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3) + end + end + end + end +end +plot_segment_analysis!(axs, results, signif) +fig + +#= +In [boers-early-warning-2018](@cite), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in [boers-early-warning-2018](@cite), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of [boers-early-warning-2018](@cite). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media. + +## CSD: only a necessary condition, only in some cases + +For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a **necessary condition** for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is **not a sufficient condition** for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition: +=# + +tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +plot_segment_analysis!(axs, results, signif) +fig + +#= +For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD. + +We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC). + +!!! warning "Degrees of freedom" + These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice. + +!!! info "Future improvement" + Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias. + +## Hindcasting simulated DO-events + +In CLIMBER-X, the EMIC described in [willeit-earth-2022](@cite), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs: +=# + +t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050], + [1, 3500, 4370, 5790, 7200, 8140]] +t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]] +tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]] +tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50] + +figvec = Figure[] + +for j in 1:2 + ## Download the data and perform loess filtering on it + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" * + "master/timeseries/climberx-do$(j)-omaxa.csv") + data = readdlm(tmp) + tcx, xcx = data[1, 1000:end], data[2, 1000:end] + t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02) + + ## Initialize figure + xlims = (0, last(tcx)) + xticks = kyr_xticks(xlims[1]:1e3:xlims[2]) + fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks) + ylims!(axs[1], (5, 40)) + axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$" + + ## Run sliding analysis and update figure with results + dt = mean(diff(tcx)) + config = SegmentedWindowConfig( + indicators, change_metrics, tseg_start[j], tseg_end[j], + whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100) + results = estimate_indicator_changes(config, r, t) + signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995)) + flags = significant_transitions(results, signif) + + plot_segment_analysis!(axs, results, signif) + vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3) + push!(figvec, fig) +end +figvec[1] + +#= +It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case: +=# + +figvec[2] + +#= +Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience. +=# \ No newline at end of file diff --git a/previews/PR51/examples/do-events/index.html b/previews/PR51/examples/do-events/index.html new file mode 100644 index 00000000..dcb9aca6 --- /dev/null +++ b/previews/PR51/examples/do-events/index.html @@ -0,0 +1,191 @@ + +Dansgaard-Oescher events and Critical Slowing Down · TransitionsInTimeseries.jl
                              Edit on GitHub

                              Dansgaard-Oescher events and Critical Slowing Down

                              The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.

                              Preprocessing NGRIP

                              Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:

                              1. Load the data, reverse and offset it to have time vector = time before 2000 AD.
                              2. Filter non-unique points in time and sort the data.
                              3. Regrid the data from uneven to even sampling.

                              The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.

                              Step 1:

                              using DelimitedFiles, Downloads
+
+function load_ngrip()
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+        "master/timeseries/NGRIP.csv")
+    data, labels = readdlm(tmp, header = true)
+    return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors
+end
+
+t1, x1 = load_ngrip()
                              ([-59944.5, -59939.6, -59935.9, -59930.5, -59925.0, -59919.0, -59914.3, -59909.4, -59904.5, -59899.7  …  -27.40000000000009, -27.40000000000009, -27.299999999999955, -27.299999999999955, -27.200000000000045, -27.09999999999991, -27.09999999999991, -27.0, -26.90000000000009, -26.799999999999955], [-43.52, -42.94, -42.13, -40.04, -41.09, -43.57, -42.28, -41.2, -44.07, -44.53  …  -35.29, -35.18, -35.51, -36.03, -36.52, -37.12, -37.41, -37.21, -36.62, -35.52])

                              Step 2

                              uniqueidx(v) = unique(i -> v[i], eachindex(v))
+function keep_unique(t, x)
+    unique_idx = uniqueidx(t)
+    return t[unique_idx], x[unique_idx]
+end
+
+function sort_timeseries!(t, x)
+    p = sortperm(t)
+    permute!(t, p)
+    permute!(x, p)
+    return nothing
+end
+
+t2, x2 = keep_unique(t1, x1)
+sort_timeseries!(t2, x2)

                              Step 3

                              using BSplineKit
+
+function regrid2evensampling(t, x, dt)
+    itp = BSplineKit.interpolate(t, x, BSplineOrder(4))
+    tspan = (ceil(minimum(t)), floor(maximum(t)))
+    t_even = collect(tspan[1]:dt:tspan[2])
+    x_even = itp.(t_even)
+    return t_even, x_even
+end
+
+dt = 5.0        # dt = 5 yr as in (Boers 2018)
+t3, x3 = regrid2evensampling(t2, x2, dt)
                              ([-59944.0, -59939.0, -59934.0, -59929.0, -59924.0, -59919.0, -59914.0, -59909.0, -59904.0, -59899.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-43.445268010797946, -42.85408835164853, -41.357360665158936, -39.9365468206892, -41.60554051352076, -43.57000000000001, -42.145558689100454, -41.33160823883399, -44.273597725729985, -44.4622612304012  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46])

                              Step 4

                              For the final step we drop the indices:

                              using DSP
+
+function chebyshev_filter(t, x, fcutoff)
+    ii = 10             # Chebyshev filtering requires to prune first points of timeseries.
+    responsetype = Highpass(fcutoff, fs = 1/dt)
+    designmethod = Chebyshev1(8, 0.05)
+    r = filt(digitalfilter(responsetype, designmethod), x)
+    xtrend = x - r
+    return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]
+end
+
+fcutoff = 0.95 * 0.01   # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)
+t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)
                              ([-59899.0, -59894.0, -59889.0, -59884.0, -59879.0, -59874.0, -59869.0, -59864.0, -59859.0, -59854.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-44.4622612304012, -44.264401428210874, -44.02956767939856, -42.29334237357212, -42.594341674200344, -41.09704877854712, -40.39837540966913, -44.369155046413255, -42.74492506508012, -43.737014520530145  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46], [-43.89287787976461, -48.663435112414156, -51.31169981050155, -51.269094666491796, -49.90310432724566, -47.721430022512344, -44.36050569418247, -43.87556827410048, -43.57802291229893, -41.36870967826094  …  -34.81349114528442, -36.01634453179986, -36.150446802907226, -36.37595639697143, -35.96843653265903, -33.899634243732976, -32.49784036951535, -33.06575312724142, -34.07956188682297, -34.4079080530096], [-0.5693833506365866, 4.399033684203284, 7.282132131102991, 8.975752292919669, 7.308762653045311, 6.624381243965224, 3.9621302845133433, -0.493586772312777, 0.8330978472188112, -2.368304842269206  …  -0.30650885471557926, -0.17365546820014846, 1.0104468029072273, -0.684043603028572, 1.0384365326590237, -0.3303657562670192, -1.0321596304846505, -2.0242468727585807, 0.07956188682296689, -0.05209194699039831])

                              Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):

                              using CairoMakie, Loess
+
+function loess_filter(t, x; span = 0.005)
+    loessmodel = loess(t, x, span = span)
+    xtrend = Loess.predict(loessmodel, t)
+    r = x - xtrend
+    return t, x, xtrend, r
+end
+
+function kyr_xticks(tticks_yr)
+    tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)]
+    return (tticks_yr, tticks_kyr)
+end
+
+function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)
+    fig = Figure(resolution = (1600, 1200), fontsize = 24)
+
+    # Original timeseries with transition marked by vertical lines
+    ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)",
+        xaxisposition = :top, xticks = xticks)
+    lines!(ax1, traw, xraw, color = (:gray70, 0.5))
+    lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)
+    vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)
+
+    # Residual timeseries
+    ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    lines!(ax2, t, r, color = :gray50, linewidth = 1)
+
+    # Axes for variance and AC1 timeseries
+    ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$",
+        xticks = xticks)
+
+    axs = [ax1, ax2, ax3, ax4]
+    [xlims!(ax, xlims) for ax in axs]
+    ylims!(axs[1], (-48, -34))
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+
+xlims = (-60e3, -10e3)
+xticks = kyr_xticks(-60e3:5e3:5e3)
+t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,
+                38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]
+tloess, _, xloess, rloess = loess_filter(t3, x3)    # loess-filtered signal for visualization
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+fig

                              Hindcast on NGRIP data

                              As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:

                              using TransitionsInTimeseries, StatsBase
+using Random: Xoshiro
+
+ac1(x) = sum(autocor(x, [1]))   # AC1 from StatsBase
+indicators = (var, ac1)
+change_metrics = RidgeRegressionSlope()
+tseg_start = t_rasmussen[1:end-1] .+ 200
+tseg_end = t_rasmussen[2:end] .- 200
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)        # require >=100 data points to estimate change metric
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
                              18×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 1  0
+ 1  1
+ 1  1
+ 1  1
+ 0  0
+ 1  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 1  0

                              That's it! We can now visulaise our results with a generic function that we will re-use later:

                              function plot_segment_analysis!(axs, results, signif)
+    (; t_indicator, x_indicator) = results
+    for k in eachindex(t_indicator)             # loop over the segments
+        for i in axes(signif.pvalues, 2)        # loop over the indicators
+            if !isinf(signif.pvalues[k, i])     # plot if segment long enough
+                # Plot indicator timeseries and its linear regression
+                ti, xi = t_indicator[k], x_indicator[k][:, i]
+                lines!(axs[i+2], ti, xi, color = Cycled(1))
+                m, p = ridgematrix(ti, 0.0) * xi
+                if signif.pvalues[k, i] < 0.05
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)
+                else
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)
+                end
+            end
+        end
+    end
+end
+plot_segment_analysis!(axs, results, signif)
+fig

                              In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.

                              CSD: only a necessary condition, only in some cases

                              For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:

                              tseg_end = t_rasmussen[2:end] .- 700    # stop analysis 500 years earlier than before
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+plot_segment_analysis!(axs, results, signif)
+fig

                              For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD.

                              We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).

                              Degrees of freedom

                              These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.

                              Future improvement

                              Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.

                              Hindcasting simulated DO-events

                              In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:

                              t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],
+                 [1, 3500, 4370, 5790, 7200, 8140]]
+t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]
+tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]
+tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]
+
+figvec = Figure[]
+
+for j in 1:2
+    # Download the data and perform loess filtering on it
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" *
+        "master/timeseries/climberx-do$(j)-omaxa.csv")
+    data = readdlm(tmp)
+    tcx, xcx = data[1, 1000:end], data[2, 1000:end]
+    t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)
+
+    # Initialize figure
+    xlims = (0, last(tcx))
+    xticks = kyr_xticks(xlims[1]:1e3:xlims[2])
+    fig, axs = plot_do(tcx, xcx,  t, xtrend, t, r, t_transitions[j], extrema(t), xticks)
+    ylims!(axs[1], (5, 40))
+    axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$"
+
+    # Run sliding analysis and update figure with results
+    dt = mean(diff(tcx))
+    config = SegmentedWindowConfig(
+        indicators, change_metrics, tseg_start[j], tseg_end[j],
+        whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)
+    results = estimate_indicator_changes(config, r, t)
+    signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))
+    flags = significant_transitions(results, signif)
+
+    plot_segment_analysis!(axs, results, signif)
+    vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)
+    push!(figvec, fig)
+end
+figvec[1]

                              It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:

                              figvec[2]

                              Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.

                              diff --git a/previews/PR51/examples/logistic.jl b/previews/PR51/examples/logistic.jl new file mode 100644 index 00000000..a2894fbd --- /dev/null +++ b/previews/PR51/examples/logistic.jl @@ -0,0 +1,203 @@ +# # Permutation entropy for dynamic regime changes + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ## Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +## time-dependent logistic map, so that the `r` parameter increases with time +r1 = 3.83 +r2 = 3.86 +N = 2000 +rs = range(r1, r2; length = N) + +function logistic_drifting_rule(u, rs, n) + r = rs[n+1] # time is `n`, starting from 0 + return SVector(r*u[1]*(1 - u[1])) +end + +ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs) +x = trajectory(ds, N-1)[1][:, 1] + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ## Using a simpler change metric + +# Now, let's compute and various indicators and their changes, +# focusing on the permutation entropy as an indicator. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries, ComplexityMeasures + +function permutation_entropy(m) + est = SymbolicPermutation(; m) # order 3 + indicator = x -> entropy_normalized(est, x) + return indicator +end + +indicators = (var, ar1_whitenoise, permutation_entropy(4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as stride half the window width +metric = difference_of_means + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = SlidingWindowConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = estimate_indicator_changes(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + if i < 3 + hidexdecorations!(ax; grid = false) + else + ax.xlabel = "r (time)" + end + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ## Significance via random Fourier surrogates + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +using Random: Xoshiro +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42), + ) + flags = significant_transitions(results, signif) + + ## and also plot the flags with same color + for (i, indicator) in enumerate(indicators) + ## To make things visually clear, we will also plot some example surrogate + ## timeseries for each indicator and change metric pair + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surromethod) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric, p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1) + end + ## Plot the flags as vertical dashed lines + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = color, linestyle = :dash, linewidth = 3 + ) + end + ## add a title to the figure with how we estimate significance + content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod))) +end + +surromethod = RandomFourier() +overplot_surrogate_significance!(fig, surromethod) + +fig + +# ## Different surrogates +# %% #src +# Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# highlighting the _local_ dynamics or information that preserves the local +# changes of dynamical behavior. + +# A surrogate type that does a better job in preserving local sharp +# changes in the timeseries (and hence provides **stricter** +# surrogate-based significance) is for example `RelativePartialRandomization`. + +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = RelativePartialRandomization(0.25) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "gray") +fig + +# Our results have improved. In the permutation entropy, we see only two +# transitions detected as significant, which is correct: only two +# real dynamical transitions exist in the data. +# In the other two indicators we also see fewer transitions, but as we +# have already discussed, no results with the other indicators should +# be taken into meaningful consideration, as these indicators +# are simply inappropriate for what we are looking for here. + +# ## Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be less strict and more simple with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`SigmaSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation. + +fig = plot_change_metrics() +flags = significant_transitions(results, SigmaSignificance(factor = 5.0)) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = Cycled(3), linestyle = :dash, linewidth = 3 + ) +end +content(fig[1, 1]).title = "significance from std" +fig diff --git a/previews/PR51/examples/logistic/index.html b/previews/PR51/examples/logistic/index.html new file mode 100644 index 00000000..639c97d5 --- /dev/null +++ b/previews/PR51/examples/logistic/index.html @@ -0,0 +1,128 @@ + +Permutation entropy for dynamic regime changes · TransitionsInTimeseries.jl
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                              Permutation entropy for dynamic regime changes

                              Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.

                              This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.

                              Logistic map timeseries

                              A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map

                              using DynamicalSystemsBase
+using CairoMakie
+
+# time-dependent logistic map, so that the `r` parameter increases with time
+r1 = 3.83
+r2 = 3.86
+N = 2000
+rs = range(r1, r2; length = N)
+
+function logistic_drifting_rule(u, rs, n)
+    r = rs[n+1] # time is `n`, starting from 0
+    return SVector(r*u[1]*(1 - u[1]))
+end
+
+ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)
+x = trajectory(ds, N-1)[1][:, 1]
                              2000-element Vector{Float64}:
+ 0.5
+ 0.9575
+ 0.15585767321160574
+ 0.5039019545917718
+ 0.9574529422362281
+ 0.15602441103002537
+ 0.5043473227583317
+ 0.9574501255597653
+ 0.1560361152301728
+ 0.5043840906474082
+ ⋮
+ 0.4253904015445437
+ 0.9434836074964187
+ 0.20581843730311683
+ 0.6309301050251992
+ 0.8988117342940414
+ 0.3510584545931264
+ 0.8793611090928393
+ 0.40948549063776396
+ 0.9333718681550522

                              Plot it, using as time the parameter value (they coincide)

                              fig, ax = lines(rs, x; linewidth = 0.5)
+ax.xlabel = "r (time)"
+ax.ylabel = "x"
+fig

                              In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.

                              Using a simpler change metric

                              Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.

                              using TransitionsInTimeseries, ComplexityMeasures
+
+function permutation_entropy(m)
+    est = SymbolicPermutation(; m) # order 3
+    indicator = x -> entropy_normalized(est, x)
+    return indicator
+end
+
+indicators = (var, ar1_whitenoise, permutation_entropy(4))
+indistrings = ("var", "ar1", "pe")
                              ("var", "ar1", "pe")

                              In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width

                              metric = difference_of_means
+
+width_ind = N÷100
+width_cha = 20
+stride_cha = 10
+
+config = SlidingWindowConfig(indicators, metric;
+    width_ind, width_cha, stride_cha,
+)
+
+results = estimate_indicator_changes(config, x, rs)
                              IndicatorsChangesResults
+ input timeseries:              2000-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise, Symbol("#1")]
+ indicator (window, stride):    (20, 1)
+ change metrics:                [:difference_of_means]
+ change metric (window, stride): (20, 10)
+

                              Let's now plot the change metrics of the indicators

                              function plot_change_metrics()
+    fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),))
+    hidexdecorations!(ax; grid = false)
+    # plot all change metrics
+    for (i, c) in enumerate(eachcol(results.x_change))
+        ax, = scatterlines(fig[i+1, 1], results.t_change, c;
+            axis = (ylabel = indistrings[i],), label = "input"
+        )
+        if i < 3
+            hidexdecorations!(ax; grid = false)
+        else
+            ax.xlabel = "r (time)"
+        end
+    end
+    return fig
+end
+
+fig = plot_change_metrics()

                              We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)

                              Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.

                              Significance via random Fourier surrogates

                              One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.

                              Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!

                              surromethod = RandomFourier()
+
+# Define a function because we will re-use later
+using Random: Xoshiro
+function overplot_surrogate_significance!(fig, surromethod, color = "black")
+
+    signif = SurrogatesSignificance(;
+        n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),
+    )
+    flags = significant_transitions(results, signif)
+
+    # and also plot the flags with same color
+    for (i, indicator) in enumerate(indicators)
+        # To make things visually clear, we will also plot some example surrogate
+        # timeseries for each indicator and change metric pair
+        for _ in 1:10
+            s = TimeseriesSurrogates.surrogate(x, surromethod)
+            p = windowmap(indicator, s; width = width_ind)
+            q = windowmap(metric, p; width = width_cha, stride = stride_cha)
+            lines!(fig[i+1, 1], results.t_change, q;  color = (color, 0.2), linewidth = 1)
+        end
+        # Plot the flags as vertical dashed lines
+        vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+            color = color, linestyle = :dash, linewidth = 3
+        )
+    end
+    # add a title to the figure with how we estimate significance
+    content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod)))
+end
+
+surromethod = RandomFourier()
+overplot_surrogate_significance!(fig, surromethod)
+
+fig

                              Different surrogates

                              Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

                              A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

                              A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

                              surromethod = RelativePartialRandomization(0.25)
+fig = plot_change_metrics()
+overplot_surrogate_significance!(fig, surromethod, "gray")
+fig

                              Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

                              Simpler Significance

                              Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

                              fig = plot_change_metrics()
+flags = significant_transitions(results, SigmaSignificance(factor = 5.0))
+
+# Plot the flags
+for (i, indicator) in enumerate(indicators)
+    vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+        color = Cycled(3), linestyle = :dash, linewidth = 3
+    )
+end
+content(fig[1, 1]).title = "significance from std"
+fig
                              diff --git a/previews/PR51/index.html b/previews/PR51/index.html new file mode 100644 index 00000000..21f36f4f --- /dev/null +++ b/previews/PR51/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
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                              TransitionsInTimeseries.jl

                              TransitionsInTimeseries.jl

                              TransitionsInTimeseries — Module

                              TransitionsInTimeseries.jl

                              CI codecov Package Downloads

                              A Julia package for estimating transitions (from one dynamic regime or stable state to another) in timeseries and testing the statistical significance of found transitions. It integrates with the entire Julia ecosystem of timeseries analysis, and hence offers thousands of metrics that can indicate transitions right out of the box. It also offers a variety of analysis pipelines for identifying transitions and a variety of statistical pipelines for testing for significance.

                              In contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:

                              1. Add new indicators that work with the existing analysis pipelines for finding transitions
                              2. Add new analysis pipelines for finding transitions
                              3. Add new ways for testing whether already found transitions are significant

                              This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

                              add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

                              All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                              Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                              source
                              Star us on GitHub!

                              If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                              Content

                              Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                              • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                              • Makes the surrogate analysis to test for significance under the hub.
                              • Can be easily extended by any user without touching the source code.
                              • Reduces the programming overhead for any researcher willing to benchmark new methods.
                              • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                              • Increases trustworthiness thanks to a large test suite.
                              Similar projects

                              An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                              Approaches

                              Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                              diff --git a/previews/PR51/refs.bib b/previews/PR51/refs.bib new file mode 100644 index 00000000..8010a9d3 --- /dev/null +++ b/previews/PR51/refs.bib @@ -0,0 +1,54 @@ + +@article{willeit-earth-2022, + title = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1: {Climate} model description and validation​​​​​​​​​​​​​​}, + volume = {15}, + issn = {1991-9603}, + shorttitle = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1}, + url = {https://gmd.copernicus.org/articles/15/5905/2022/}, + doi = {10.5194/gmd-15-5905-2022}, + abstract = {The newly developed fast Earth system model CLIMBER-X is presented. The climate component of CLIMBER-X consists of a 2.5-D semi-empirical statistical–dynamical atmosphere model, a 3-D frictional–geostrophic ocean model, a dynamic–thermodynamic sea ice model and a land surface model. All the model components are discretized on a regular lat–long grid with a horizontal resolution of 5 ◦ × 5 ◦. The model has a throughput of ∼ 10 000 simulation years per day on a single node with 16 CPUs on a high-performance computer and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to {\textgreater} 100 000 years. A comprehensive evaluation of the model performance for the present day and the historical period shows that CLIMBER-X is capable of realistically reproducing many observed climate characteristics, with results that generally lie within the range of state-of-theart general circulation models. The analysis of model performance is complemented by a thorough assessment of climate feedbacks and model sensitivities to changes in external forcings and boundary conditions. Limitations and applicability of the model are critically discussed. CLIMBER-X also includes a detailed representation of the global carbon cycle and is coupled to an ice sheet model, which will be described in separate papers. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.}, + language = {en}, + number = {14}, + urldate = {2022-08-11}, + journal = {Geoscientific Model Development}, + author = {Willeit, Matteo and Ganopolski, Andrey and Robinson, Alexander and Edwards, Neil R.}, + month = jul, + year = {2022}, + pages = {5905--5948}, + file = {Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:/home/jan/Zotero/storage/75NKS975/Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:application/pdf}, +} + +@article{boers-early-warning-2018, + title = {Early-warning signals for {Dansgaard}-{Oeschger} events in a high-resolution ice core record}, + volume = {9}, + issn = {2041-1723}, + url = {http://www.nature.com/articles/s41467-018-04881-7}, + doi = {10.1038/s41467-018-04881-7}, + language = {en}, + number = {1}, + urldate = {2022-10-28}, + journal = {Nature Communications}, + author = {Boers, Niklas}, + month = dec, + year = {2018}, + pages = {2556}, + file = {Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:/home/jan/Zotero/storage/DS97Z9UC/Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:application/pdf}, +} + +@article{rasmussen-stratigraphic-2014, + title = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records: refining and extending the {INTIMATE} event stratigraphy}, + volume = {106}, + issn = {02773791}, + shorttitle = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0277379114003485}, + doi = {10.1016/j.quascirev.2014.09.007}, + abstract = {Due to their outstanding resolution and well-constrained chronologies, Greenland ice-core records provide a master record of past climatic changes throughout the Last InterglacialeGlacial cycle in the North Atlantic region. As part of the INTIMATE (INTegration of Ice-core, MArine and TErrestrial records) project, protocols have been proposed to ensure consistent and robust correlation between different records of past climate. A key element of these protocols has been the formal definition and ordinal numbering of the sequence of Greenland Stadials (GS) and Greenland Interstadials (GI) within the most recent glacial period. The GS and GI periods are the Greenland expressions of the characteristic DansgaardeOeschger events that represent cold and warm phases of the North Atlantic region, respectively. We present here a more detailed and extended GS/GI template for the whole of the Last Glacial period. It is based on a synchronization of the NGRIP, GRIP, and GISP2 ice-core records that allows the parallel analysis of all three records on a common time scale. The boundaries of the GS and GI periods are defined based on a combination of stable-oxygen isotope ratios of the ice (d18O, reflecting mainly local temperature) and calcium ion concentrations (reflecting mainly atmospheric dust loading) measured in the ice. The data not only resolve the well-known sequence of DansgaardeOeschger events that were first defined and numbered in the ice-core records more than two decades ago, but also better resolve a number of short-lived climatic oscillations, some defined here for the first time. Using this revised scheme, we propose a consistent approach for discriminating and naming all the significant abrupt climatic events of the Last Glacial period that are represented in the Greenland ice records. The final product constitutes an extended and better resolved Greenland stratotype sequence, against which other proxy records can be compared and correlated. It also provides a more secure basis for investigating the dynamics and fundamental causes of these climatic perturbations.}, + language = {en}, + urldate = {2023-10-04}, + journal = {Quaternary Science Reviews}, + author = {Rasmussen, Sune O. and Bigler, Matthias and Blockley, Simon P. and Blunier, Thomas and Buchardt, Susanne L. and Clausen, Henrik B. and Cvijanovic, Ivana and Dahl-Jensen, Dorthe and Johnsen, Sigfus J. and Fischer, Hubertus and Gkinis, Vasileios and Guillevic, Myriam and Hoek, Wim Z. and Lowe, J. John and Pedro, Joel B. and Popp, Trevor and Seierstad, Inger K. and Steffensen, Jørgen Peder and Svensson, Anders M. and Vallelonga, Paul and Vinther, Bo M. and Walker, Mike J.C. and Wheatley, Joe J. and Winstrup, Mai}, + month = dec, + year = {2014}, + pages = {14--28}, + file = {Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:/home/jan/Zotero/storage/VSUTVWPN/Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:application/pdf}, +} diff --git a/previews/PR51/refs/index.html b/previews/PR51/refs/index.html new file mode 100644 index 00000000..5bb73286 --- /dev/null +++ b/previews/PR51/refs/index.html @@ -0,0 +1,9 @@ + +References · TransitionsInTimeseries.jl
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                              References

                              diff --git a/previews/PR51/search/index.html b/previews/PR51/search/index.html new file mode 100644 index 00000000..e928e902 --- /dev/null +++ b/previews/PR51/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

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                                diff --git a/previews/PR51/search_index.js b/previews/PR51/search_index.js new file mode 100644 index 00000000..0396ea47 --- /dev/null +++ b/previews/PR51/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"IndicatorsChangesConfig\nSlidingWindowConfig\nSegmentedWindowConfig\nestimate_indicator_changes\nIndicatorsChangesResults\nSlidingWindowResults\nSegmentedWindowResults","category":"page"},{"location":"api/#TransitionsInTimeseries.IndicatorsChangesConfig","page":"API","title":"TransitionsInTimeseries.IndicatorsChangesConfig","text":"IndicatorsChangesConfig\n\nSupertype used to define how indicators and their changes are estimated in estimate_indicator_changes. Valid subtypes are:\n\nSlidingWindowConfig.\nSegmentedWindowConfig.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowConfig","page":"API","title":"TransitionsInTimeseries.SlidingWindowConfig","text":"SlidingWindowConfig <: IndicatorsChangesConfig\nSlidingWindowConfig(indicators, change_metrics; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.\n\nThe results output corresponding to SlidingWindowConfig is SlidingWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowConfig","page":"API","title":"TransitionsInTimeseries.SegmentedWindowConfig","text":"SegmentedWindowConfig <: IndicatorsChangeConfig\nSegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:\n\nFor each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).\nFor each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d\n\ntseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.\n\nThe results output corresponding to SlidingWindowConfig is SegmentedWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.\nmin_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.estimate_indicator_changes","page":"API","title":"TransitionsInTimeseries.estimate_indicator_changes","text":"estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → result\n\nEstimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).\n\nReturn the output as subtype of IndicatorsChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.IndicatorsChangesResults","page":"API","title":"TransitionsInTimeseries.IndicatorsChangesResults","text":"IndicatorsChangesResults\n\nSupertype used to gather results of estimate_indicator_changes. The concrete subtype instances are described in the docstrings of configuration types.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowResults","page":"API","title":"TransitionsInTimeseries.SlidingWindowResults","text":"SlidingWindowResults <: IndicatorsChangesResults\n\nA struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nconfig::SlidingWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowResults","page":"API","title":"TransitionsInTimeseries.SegmentedWindowResults","text":"SegmentedWindowResults <: IndicatorsChangesResults\n\nA struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.\nt_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.\nx_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.\nt_change, the time vector of the change metric.\nconfig::SegmentedWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"significant_transitions\nTransitionsSignificance\nSurrogatesSignificance\nQuantileSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::IndicatorsChangesResults, signif::TransitionsSignificance)\n\nEstimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.TransitionsSignificance","page":"API","title":"TransitionsInTimeseries.TransitionsSignificance","text":"TransitionsSignificance\n\nSupertype used to test for significance in significant_transitions. Valid subtypes are:\n\nSurrogatesSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: TransitionsSignificance\nSurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)\n\nA configuration struct for significance testing significant_transitions using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\n\nDescription\n\nWhen used with IndicatorsChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in IndicatorsChangesResults.\n\nNote that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance\n\nA configuration struct for significance testing significant_transitions. When used with IndicatorsChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\nQuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.","category":"page"},{"location":"api/","page":"API","title":"API","text":"For example, using the permutation entropy as an indicator is as simple as doing","category":"page"},{"location":"api/","page":"API","title":"API","text":"using ComplexityMeasures\nest = OrdinalPatterns(; m = 3) # order 3\n# create a function that given timeseries returns permutation entropy\nindicator = x -> entropy_normalized(est, x)","category":"page"},{"location":"api/","page":"API","title":"API","text":"and giving the created indicator to e.g., SlidingWindowConfig.","category":"page"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"EditURL = \"do-events.jl\"","category":"page"},{"location":"examples/do-events/#Dansgaard-Oescher-events-and-Critical-Slowing-Down","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The delta^18O timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.","category":"page"},{"location":"examples/do-events/#Preprocessing-NGRIP","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Preprocessing NGRIP","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Load the data, reverse and offset it to have time vector = time before 2000 AD.\nFilter non-unique points in time and sort the data.\nRegrid the data from uneven to even sampling.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The time and delta^18O vectors resulting from the i-th preprocessing step are respectively called t_i and x_i. The final step consists in obtaining a residual r, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.","category":"page"},{"location":"examples/do-events/#Step-1:","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 1:","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DelimitedFiles, Downloads\n\nfunction load_ngrip()\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP.csv\")\n data, labels = readdlm(tmp, header = true)\n return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors\nend\n\nt1, x1 = load_ngrip()","category":"page"},{"location":"examples/do-events/#Step-2","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 2","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"uniqueidx(v) = unique(i -> v[i], eachindex(v))\nfunction keep_unique(t, x)\n unique_idx = uniqueidx(t)\n return t[unique_idx], x[unique_idx]\nend\n\nfunction sort_timeseries!(t, x)\n p = sortperm(t)\n permute!(t, p)\n permute!(x, p)\n return nothing\nend\n\nt2, x2 = keep_unique(t1, x1)\nsort_timeseries!(t2, x2)","category":"page"},{"location":"examples/do-events/#Step-3","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 3","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using BSplineKit\n\nfunction regrid2evensampling(t, x, dt)\n itp = BSplineKit.interpolate(t, x, BSplineOrder(4))\n tspan = (ceil(minimum(t)), floor(maximum(t)))\n t_even = collect(tspan[1]:dt:tspan[2])\n x_even = itp.(t_even)\n return t_even, x_even\nend\n\ndt = 5.0 # dt = 5 yr as in (Boers 2018)\nt3, x3 = regrid2evensampling(t2, x2, dt)","category":"page"},{"location":"examples/do-events/#Step-4","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 4","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the final step we drop the indices:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DSP\n\nfunction chebyshev_filter(t, x, fcutoff)\n ii = 10 # Chebyshev filtering requires to prune first points of timeseries.\n responsetype = Highpass(fcutoff, fs = 1/dt)\n designmethod = Chebyshev1(8, 0.05)\n r = filt(digitalfilter(responsetype, designmethod), x)\n xtrend = x - r\n return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]\nend\n\nfcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)\nt, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using CairoMakie, Loess\n\nfunction loess_filter(t, x; span = 0.005)\n loessmodel = loess(t, x, span = span)\n xtrend = Loess.predict(loessmodel, t)\n r = x - xtrend\n return t, x, xtrend, r\nend\n\nfunction kyr_xticks(tticks_yr)\n tticks_kyr = [\"$t\" for t in Int.(tticks_yr ./ 1e3)]\n return (tticks_yr, tticks_kyr)\nend\n\nfunction plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)\n fig = Figure(resolution = (1600, 1200), fontsize = 24)\n\n # Original timeseries with transition marked by vertical lines\n ax1 = Axis(fig[1, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"$\\delta^{18}$O (permil)\",\n xaxisposition = :top, xticks = xticks)\n lines!(ax1, traw, xraw, color = (:gray70, 0.5))\n lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)\n vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)\n\n # Residual timeseries\n ax2 = Axis(fig[2, 1], ylabel = L\"Residual $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n lines!(ax2, t, r, color = :gray50, linewidth = 1)\n\n # Axes for variance and AC1 timeseries\n ax3 = Axis(fig[3, 1], ylabel = L\"Variance $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n ax4 = Axis(fig[4, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"Lag-1 autocor. $\\,$\",\n xticks = xticks)\n\n axs = [ax1, ax2, ax3, ax4]\n [xlims!(ax, xlims) for ax in axs]\n ylims!(axs[1], (-48, -34))\n rowgap!(fig.layout, 10)\n return fig, axs\nend\n\nxlims = (-60e3, -10e3)\nxticks = kyr_xticks(-60e3:5e3:5e3)\nt_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,\n 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]\ntloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nfig","category":"page"},{"location":"examples/do-events/#Hindcast-on-NGRIP-data","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcast on NGRIP data","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using TransitionsInTimeseries, StatsBase\nusing Random: Xoshiro\n\nac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase\nindicators = (var, ac1)\nchange_metrics = RidgeRegressionSlope()\ntseg_start = t_rasmussen[1:end-1] .+ 200\ntseg_end = t_rasmussen[2:end] .- 200\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100) # require >=100 data points to estimate change metric\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"That's it! We can now visulaise our results with a generic function that we will re-use later:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"function plot_segment_analysis!(axs, results, signif)\n (; t_indicator, x_indicator) = results\n for k in eachindex(t_indicator) # loop over the segments\n for i in axes(signif.pvalues, 2) # loop over the indicators\n if !isinf(signif.pvalues[k, i]) # plot if segment long enough\n # Plot indicator timeseries and its linear regression\n ti, xi = t_indicator[k], x_indicator[k][:, i]\n lines!(axs[i+2], ti, xi, color = Cycled(1))\n m, p = ridgematrix(ti, 0.0) * xi\n if signif.pvalues[k, i] < 0.05\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)\n else\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)\n end\n end\n end\n end\nend\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.","category":"page"},{"location":"examples/do-events/#CSD:-only-a-necessary-condition,-only-in-some-cases","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"CSD: only a necessary condition, only in some cases","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential U, which defines the deterministic term f = -U of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100)\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that \"resilience-loss indicators\" is a more accurate name than \"early-warning signals\" when using CSD.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"We draw attention upon the fact that the delta^18O timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"warning: Degrees of freedom\nThese sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"info: Future improvement\nSupporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.","category":"page"},{"location":"examples/do-events/#Hindcasting-simulated-DO-events","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcasting simulated DO-events","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],\n [1, 3500, 4370, 5790, 7200, 8140]]\nt_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]\ntseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]\ntseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]\n\nfigvec = Figure[]\n\nfor j in 1:2\n # Download the data and perform loess filtering on it\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\" *\n \"master/timeseries/climberx-do$(j)-omaxa.csv\")\n data = readdlm(tmp)\n tcx, xcx = data[1, 1000:end], data[2, 1000:end]\n t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)\n\n # Initialize figure\n xlims = (0, last(tcx))\n xticks = kyr_xticks(xlims[1]:1e3:xlims[2])\n fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks)\n ylims!(axs[1], (5, 40))\n axs[1].ylabel = L\"Max. Atlantic overturning (Sv) $\\,$\"\n\n # Run sliding analysis and update figure with results\n dt = mean(diff(tcx))\n config = SegmentedWindowConfig(\n indicators, change_metrics, tseg_start[j], tseg_end[j],\n whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)\n results = estimate_indicator_changes(config, r, t)\n signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))\n flags = significant_transitions(results, signif)\n\n plot_segment_analysis!(axs, results, signif)\n vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)\n push!(figvec, fig)\nend\nfigvec[1]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"figvec[2]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"EditURL = \"logistic.jl\"","category":"page"},{"location":"examples/logistic/#Permutation-entropy-for-dynamic-regime-changes","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.","category":"page"},{"location":"examples/logistic/#Logistic-map-timeseries","page":"Permutation entropy for dynamic regime changes","title":"Logistic map timeseries","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using DynamicalSystemsBase\nusing CairoMakie\n\n# time-dependent logistic map, so that the `r` parameter increases with time\nr1 = 3.83\nr2 = 3.86\nN = 2000\nrs = range(r1, r2; length = N)\n\nfunction logistic_drifting_rule(u, rs, n)\n r = rs[n+1] # time is `n`, starting from 0\n return SVector(r*u[1]*(1 - u[1]))\nend\n\nds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)\nx = trajectory(ds, N-1)[1][:, 1]","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Plot it, using as time the parameter value (they coincide)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig, ax = lines(rs, x; linewidth = 0.5)\nax.xlabel = \"r (time)\"\nax.ylabel = \"x\"\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.","category":"page"},{"location":"examples/logistic/#Using-a-simpler-change-metric","page":"Permutation entropy for dynamic regime changes","title":"Using a simpler change metric","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using TransitionsInTimeseries, ComplexityMeasures\n\nfunction permutation_entropy(m)\n est = SymbolicPermutation(; m) # order 3\n indicator = x -> entropy_normalized(est, x)\n return indicator\nend\n\nindicators = (var, ar1_whitenoise, permutation_entropy(4))\nindistrings = (\"var\", \"ar1\", \"pe\")","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"metric = difference_of_means\n\nwidth_ind = N÷100\nwidth_cha = 20\nstride_cha = 10\n\nconfig = SlidingWindowConfig(indicators, metric;\n width_ind, width_cha, stride_cha,\n)\n\nresults = estimate_indicator_changes(config, x, rs)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's now plot the change metrics of the indicators","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"function plot_change_metrics()\n fig, ax = lines(rs, x; axis = (ylabel = \"input\",), figure = (resolution = (600, 600),))\n hidexdecorations!(ax; grid = false)\n # plot all change metrics\n for (i, c) in enumerate(eachcol(results.x_change))\n ax, = scatterlines(fig[i+1, 1], results.t_change, c;\n axis = (ylabel = indistrings[i],), label = \"input\"\n )\n if i < 3\n hidexdecorations!(ax; grid = false)\n else\n ax.xlabel = \"r (time)\"\n end\n end\n return fig\nend\n\nfig = plot_change_metrics()","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.","category":"page"},{"location":"examples/logistic/#Significance-via-random-Fourier-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Significance via random Fourier surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RandomFourier()\n\n# Define a function because we will re-use later\nusing Random: Xoshiro\nfunction overplot_surrogate_significance!(fig, surromethod, color = \"black\")\n\n signif = SurrogatesSignificance(;\n n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),\n )\n flags = significant_transitions(results, signif)\n\n # and also plot the flags with same color\n for (i, indicator) in enumerate(indicators)\n # To make things visually clear, we will also plot some example surrogate\n # timeseries for each indicator and change metric pair\n for _ in 1:10\n s = TimeseriesSurrogates.surrogate(x, surromethod)\n p = windowmap(indicator, s; width = width_ind)\n q = windowmap(metric, p; width = width_cha, stride = stride_cha)\n lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1)\n end\n # Plot the flags as vertical dashed lines\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = color, linestyle = :dash, linewidth = 3\n )\n end\n # add a title to the figure with how we estimate significance\n content(fig[1, 1]).title = \"surrogates: \"*string(nameof(typeof(surromethod)))\nend\n\nsurromethod = RandomFourier()\noverplot_surrogate_significance!(fig, surromethod)\n\nfig","category":"page"},{"location":"examples/logistic/#Different-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Different surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RelativePartialRandomization(0.25)\nfig = plot_change_metrics()\noverplot_surrogate_significance!(fig, surromethod, \"gray\")\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.","category":"page"},{"location":"examples/logistic/#Simpler-Significance","page":"Permutation entropy for dynamic regime changes","title":"Simpler Significance","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig = plot_change_metrics()\nflags = significant_transitions(results, SigmaSignificance(factor = 5.0))\n\n# Plot the flags\nfor (i, indicator) in enumerate(indicators)\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = Cycled(3), linestyle = :dash, linewidth = 3\n )\nend\ncontent(fig[1, 1]).title = \"significance from std\"\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package for estimating transitions (from one dynamic regime or stable state to another) in timeseries and testing the statistical significance of found transitions. It integrates with the entire Julia ecosystem of timeseries analysis, and hence offers thousands of metrics that can indicate transitions right out of the box. It also offers a variety of analysis pipelines for identifying transitions and a variety of statistical pipelines for testing for significance.\n\nIn contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:\n\nAdd new indicators that work with the existing analysis pipelines for finding transitions\nAdd new analysis pipelines for finding transitions\nAdd new ways for testing whether already found transitions are significant\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\nAlternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"refs/#References","page":"References","title":"References","text":"","category":"section"},{"location":"refs/","page":"References","title":"References","text":"","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"EditURL = \"tutorial.jl\"","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector,\n# we obtain the last time step of each window.\n# This therefore only uses information from `k-width+1` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\n\nfunction gridfig(nrows, ncols)\n fig = Figure()\n axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)\n for j in 1:ncols, i in 1:nrows]\n rowgap!(fig.layout, 10)\n return fig, axs\nend\nfig, axs = gridfig(2, 1)\nlines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))\nlines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))\naxs[1].title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nlines!(axs[2], t_change, change_nl, label = \"nonlin\", color = Cycled(2))\nlines!(axs[2], t_change, change_s, label = \"surrogate\", color = Cycled(3))\naxislegend()\naxs[2].title = \"change metric\"\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig, axs = gridfig(2, 2)\naxs[1].title = \"linear\"\naxs[2].title = \"nonlinear\"\n\nfor (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change) # ; color = Cycled(j)\n lines!(axsig, t_change, pval) # ; color = Cycled(j+2)\nend\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = RidgeRegressionSlope()\n\n# choices go into a configuration struct\nconfig = SlidingWindowConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last)\n\n# choices are processed\nresults = estimate_indicator_changes(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From result we can plot the change metric timeseries:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(3, 1)\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, results.x_change[:, 1];\n label = \"var slopes\", color = Cycled(3))\nscatter!(axs[3], results.t_change, results.x_change[:, 2];\n label = \"ar1 slopes\", color = Cycled(4))\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = :right)\nflags = significant_transitions(results, signif)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(2, 1)\nlines!(axs[1], vcat(0.0, t), x_nlinear; label = \"raw\", color = Cycled(1))\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 1];\n label = \"var p-values\", color = Cycled(3))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 2];\n label = \"ar1 p-values\", color = Cycled(4))\n\nflagsboth = vec(reduce(&, flags; dims = 2))\nvlines!(axs[1], results.t_change[flagsboth]; label = \"flags\", color = (\"black\", 0.1))\n\n[axislegend(ax) for ax in axs]\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"}] +} diff --git a/previews/PR51/siteinfo.js b/previews/PR51/siteinfo.js new file mode 100644 index 00000000..51c6badb --- /dev/null +++ b/previews/PR51/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR51"; diff --git a/previews/PR51/tutorial.jl b/previews/PR51/tutorial.jl new file mode 100644 index 00000000..3f135673 --- /dev/null +++ b/previews/PR51/tutorial.jl @@ -0,0 +1,263 @@ +#= + +# Tutorial + +## [Workflow] (@id workflow) + +Computing transition indicators consists of the following steps: + +1. Doing any preprocessing of raw data first, such as detrending (_not part of TransitionsInTimeseries.jl_). This yields the **input timeseries**. +2. Estimating the timeseries of an indicator by sliding a window over the input timeseries. +3. Computing the changes of the indicator by sliding a window over its timeseries. +4. Generating many surrogates that preserve important statistical properties of the original timeseries. +5. Performing step 2 and 3 for the surrogate timeseries. +6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data. + +These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports. + +## [Tutorial -- Educational] (@id example_stepbystep) + +### Raw input data + +Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by: + +```math +\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t) +``` + +with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with [Makie](https://docs.makie.org/stable/)) such prototypical data to test some indicators can be done by simply running: +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_linear) +lines!(ax, t, x_nlinear) +ax.title = "raw data" +fig + +#= +### Preprocessing + +!!! note "Not part of TransitionsInTimeseries.jl" + Any timeseries preprocessing, such as the de-trending step we do here, + is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher. + + +The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1. +=# + +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +#= +At this point, `x_l_fluct` and `x_nl_fluct` are considered the **input timeseries**. + +!!! info "Detrending in Julia" + Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as [Loess.jl](https://github.com/JuliaStats/Loess.jl) or [DSP.jl](https://docs.juliadsp.org/latest/contents/). There the detrending step consists of subtracting the smoothed signal from the original one. + +### Indicator timeseries + +We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the **input timeseries**, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as [`ar1_whitenoise`](@ref): +=# + +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +## By mapping `last::Function` over a windowviewer of the time vector, +## we obtain the last time step of each window. +## This therefore only uses information from `k-width+1` to `k` at time step `k`. +## Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +#= +The lines plotted above are the **indicator timeseries**. + +### Change metric timeseries + +From here, we process the **indicator timeseries** to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the **change metric timeseries**. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a [`RidgeRegressionSlope`](@ref): +=# + +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + +#= +### Timeseries surrogates + +As expected from [Critical Slowing Down](@ref approaches), an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance. + +In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the [TimeseriesSurrogates.jl](https://github.com/JuliaDynamics/TimeseriesSurrogates.jl) Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that `TimeseriesSurrogates` is re-exported by `TransitionsInTimeseries`, so that you don't have to `using` both of them. + +To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries. +=# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) + +function gridfig(nrows, ncols) + fig = Figure() + axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false) + for j in 1:ncols, i in 1:nrows] + rowgap!(fig.layout, 10) + return fig, axs +end +fig, axs = gridfig(2, 1) +lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2)) +lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3)) +axs[1].title = "real signal vs. surrogate(s)" + +## compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2)) +lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3)) +axislegend() +axs[2].title = "change metric" + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +### Quantifying significance + +To quantify the significance of the values of the **change metric timeseries** we perform a standard surrogate test by computing the [p-value](https://en.wikipedia.org/wiki/P-value) w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically `p<0.05`) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time: +=# + +n_surrogates = 1_000 +fig, axs = gridfig(2, 2) +axs[1].title = "linear" +axs[2].title = "nonlinear" + +for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + ## Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change) # ; color = Cycled(j) + lines!(axsig, t_change, pval) # ; color = Cycled(j+2) +end + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar. + +Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section. + +## [Tutorial -- TransitionsInTimeseries.jl] (@id example_fastforward) + +TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go. + +The interface is simple, and directly parallelizes the [Workflow](@ref). It is based on the creation of a [`TransitionsSurrogatesConfig`](@ref), which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate. + +The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +## input timeseries and time +input = x_nl_fluct = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(t, input) +ax.title = "input timeseries" +fig + +#= +To perform all of the above analysis we follow a 2-step process. + +Step 1, we decide what indicators and change metrics to use in [`SlidingWindowConfig`](@ref) and apply those via +a sliding window to the input timeseries using [`transition_metrics`](@ref). +=# + +## These indicators are suitable for Critical Slowing Down +indicators = (var, ar1_whitenoise) + +## use the ridge regression slope for both indicators +change_metrics = RidgeRegressionSlope() + +## choices go into a configuration struct +config = SlidingWindowConfig(indicators, change_metrics; + width_ind = 400, width_cha = 30, whichtime = last) + +## choices are processed +results = estimate_indicator_changes(config, input, t) + +#= +From `result` we can plot the change metric timeseries: +=# + +fig, axs = gridfig(3, 1) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, results.x_change[:, 1]; + label = "var slopes", color = Cycled(3)) +scatter!(axs[3], results.t_change, results.x_change[:, 2]; + label = "ar1 slopes", color = Cycled(4)) +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +Step 2 is to estimate significance using [`SurrogatesConfig`](@ref) +and the function [`estimate_significance!`](@ref). +=# + +signif = SurrogatesSignificance(n = 1000, tail = :right) +flags = significant_transitions(results, signif) + +#= +We can now plot the p-values corresponding to each time series of the change metrics. From the `flags` we can additionally obtain the time points where _both_ indicators show significance, via a simple reduction: +=# + +fig, axs = gridfig(2, 1) +lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1)) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 1]; + label = "var p-values", color = Cycled(3)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 2]; + label = "ar1 p-values", color = Cycled(4)) + +flagsboth = vec(reduce(&, flags; dims = 2)) +vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1)) + +[axislegend(ax) for ax in axs] +[xlims!(ax, 0, 50) for ax in axs] +fig \ No newline at end of file diff --git a/previews/PR51/tutorial/index.html b/previews/PR51/tutorial/index.html new file mode 100644 index 00000000..852e838c --- /dev/null +++ b/previews/PR51/tutorial/index.html @@ -0,0 +1,160 @@ + +Tutorial · TransitionsInTimeseries.jl
                                Edit on GitHub

                                Tutorial

                                Workflow

                                Computing transition indicators consists of the following steps:

                                1. Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                                2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                                3. Computing the changes of the indicator by sliding a window over its timeseries.
                                4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                                5. Performing step 2 and 3 for the surrogate timeseries.
                                6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                                These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                                Tutorial – Educational

                                Raw input data

                                Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                                \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                                with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                                using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig

                                Preprocessing

                                Not part of TransitionsInTimeseries.jl

                                Any timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                                The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                                x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                                At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                                Detrending in Julia

                                Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                                Indicator timeseries

                                We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                                indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector,
+# we obtain the last time step of each window.
+# This therefore only uses information from `k-width+1` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                                The lines plotted above are the indicator timeseries.

                                Change metric timeseries

                                From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                                change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                                Timeseries surrogates

                                As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                                In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                                To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                                # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+
+function gridfig(nrows, ncols)
+    fig = Figure()
+    axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)
+        for j in 1:ncols, i in 1:nrows]
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+fig, axs = gridfig(2, 1)
+lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))
+lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))
+axs[1].title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2))
+lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3))
+axislegend()
+axs[2].title = "change metric"
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                Quantifying significance

                                To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                                n_surrogates = 1_000
+fig, axs = gridfig(2, 2)
+axs[1].title = "linear"
+axs[2].title = "nonlinear"
+
+for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change)   # ; color = Cycled(j)
+    lines!(axsig, t_change, pval)       # ; color = Cycled(j+2)
+end
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                                Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                                Tutorial – TransitionsInTimeseries.jl

                                TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                                The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

                                The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

                                using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig

                                To perform all of the above analysis we follow a 2-step process.

                                Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.

                                # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = RidgeRegressionSlope()
+
+# choices go into a configuration struct
+config = SlidingWindowConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last)
+
+# choices are processed
+results = estimate_indicator_changes(config, input, t)
                                IndicatorsChangesResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                                From result we can plot the change metric timeseries:

                                fig, axs = gridfig(3, 1)
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, results.x_change[:, 1];
+    label = "var slopes", color = Cycled(3))
+scatter!(axs[3], results.t_change, results.x_change[:, 2];
+    label = "ar1 slopes", color = Cycled(4))
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.

                                signif = SurrogatesSignificance(n = 1000, tail = :right)
+flags = significant_transitions(results, signif)
                                2072×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ ⋮  
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0

                                We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:

                                fig, axs = gridfig(2, 1)
+lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1))
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 1];
+    label = "var p-values", color = Cycled(3))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 2];
+    label = "ar1 p-values", color = Cycled(4))
+
+flagsboth = vec(reduce(&, flags; dims = 2))
+vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1))
+
+[axislegend(ax) for ax in axs]
+[xlims!(ax, 0, 50) for ax in axs]
+fig
                                diff --git a/previews/PR54/api/index.html b/previews/PR54/api/index.html new file mode 100644 index 00000000..b52218e1 --- /dev/null +++ b/previews/PR54/api/index.html @@ -0,0 +1,22 @@ + +API · TransitionsInTimeseries.jl
                                Edit on GitHub

                                API

                                Main analysis functions

                                TransitionsInTimeseries.SlidingWindowConfig — Type
                                SlidingWindowConfig <: IndicatorsChangesConfig
+SlidingWindowConfig(indicators, change_metrics; kwargs...)

                                A configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:

                                1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                                2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                                indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                                Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.

                                The results output corresponding to SlidingWindowConfig is SlidingWindowResults.

                                Keyword arguments

                                • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.
                                • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.
                                • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:
                                  • last: use the last timepoint of each window
                                  • midpoint: use the mid timepoint of each time window
                                  • first: use first timepoint of each window
                                  In fact, the indicators time vector is computed simply via
                                  t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)
                                  so any other function of the time window may be given to extract the time point itself, such as mean or median.
                                • T = Float64: Element type of input timeseries to initialize some computations.
                                source
                                TransitionsInTimeseries.SegmentedWindowConfig — Type
                                SegmentedWindowConfig <: IndicatorsChangeConfig
+SegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)

                                A configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:

                                1. For each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).
                                2. For each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d

                                tseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.

                                The results output corresponding to SlidingWindowConfig is SegmentedWindowResults.

                                Keyword arguments

                                • width_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.
                                • min_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.
                                source
                                TransitionsInTimeseries.estimate_indicator_changes — Function
                                estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → result

                                Estimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).

                                Return the output as subtype of IndicatorsChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                                source
                                TransitionsInTimeseries.SlidingWindowResults — Type
                                SlidingWindowResults <: IndicatorsChangesResults

                                A struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                                It has the following fields that the user may access

                                • x: the input timeseries.

                                • t: the time vector of the input timeseries.

                                • x_indicator, the indicator timeseries (matrix with each column one indicator).

                                • t_indicator, the time vector of the indicator timeseries.

                                • x_change, the change metric timeseries (matrix with each column one change metric).

                                • t_change, the time vector of the change metric timeseries.

                                • config::SlidingWindowConfig, what was used for the analysis.

                                source
                                TransitionsInTimeseries.SegmentedWindowResults — Type
                                SegmentedWindowResults <: IndicatorsChangesResults

                                A struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                                It has the following fields that the user may access

                                • x: the input timeseries.

                                • t: the time vector of the input timeseries.

                                • x_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.

                                • t_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.

                                • x_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.

                                • t_change, the time vector of the change metric.

                                • config::SegmentedWindowConfig, what was used for the analysis.

                                source

                                Significance testing

                                TransitionsInTimeseries.significant_transitions — Function
                                significant_transitions(res::IndicatorsChangesResults, signif::TransitionsSignificance)

                                Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.

                                source
                                TransitionsInTimeseries.SurrogatesSignificance — Type
                                SurrogatesSignificance <: TransitionsSignificance
+SurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)

                                A configuration struct for significance testing significant_transitions using timeseries surrogates.

                                Keyword arguments

                                • surromethod = RandomFourier(): method to generate surrogates
                                • n = 1000: how many surrogates to generate
                                • rng = Random.default_rng(): random number generator for the surrogates
                                • p = 0.05: threshold for significance of the p-value
                                • tail = :both: tail type used, see below

                                Description

                                When used with IndicatorsChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

                                The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in IndicatorsChangesResults.

                                Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

                                source
                                TransitionsInTimeseries.QuantileSignificance — Type
                                QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance

                                A configuration struct for significance testing significant_transitions. When used with IndicatorsChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                                QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

                                source

                                Indicators

                                Value distribution

                                Statistics.mean — Method
                                mean(itr)

                                Compute the mean of all elements in a collection.

                                Note

                                If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

                                Examples

                                julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
                                StatsBase.skewness — Function
                                skewness(v, [wv::AbstractWeights], m=mean(v))

                                Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                                StatsBase.kurtosis — Function
                                kurtosis(v, [wv::AbstractWeights], m=mean(v))

                                Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                                Critical Slowing Down

                                Statistics.var — Method
                                var(itr; corrected::Bool=true, mean=nothing[, dims])

                                Compute the sample variance of collection itr.

                                The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

                                If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

                                A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

                                Note

                                If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

                                TransitionsInTimeseries.ar1_whitenoise — Function
                                ar1_whitenoise(x::AbstractVector)

                                Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

                                \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                                source

                                Spectrum

                                TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                                LowfreqPowerSpectrum(; q_lofreq = 0.1)

                                Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                                lfps = precompute( LowfreqPowerSpectrum() )

                                Keyword arguments:

                                • q_lofreq: a number between 0 and 1 that characterises which portion of the

                                frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                                source

                                Nonlinear dynamics

                                Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.

                                For example, using the permutation entropy as an indicator is as simple as doing

                                using ComplexityMeasures
+est = OrdinalPatterns(; m = 3) # order 3
+# create a function that given timeseries returns permutation entropy
+indicator = x -> entropy_normalized(est, x)

                                and giving the created indicator to e.g., SlidingWindowConfig.

                                Change metrics

                                Slope

                                TransitionsInTimeseries.kendalltau — Function
                                kendalltau(x::AbstractVector)

                                Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                                source
                                TransitionsInTimeseries.spearman — Function
                                spearman(x::AbstractVector)

                                Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                                source

                                Value distribution differences

                                TransitionsInTimeseries.difference_of_means — Function
                                difference_of_means(x::AbstractArray)

                                Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                                # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                                difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                                source

                                Make your own indicator/metric!

                                The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                                There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:

                                Missing docstring.

                                Missing docstring for precompute. Check Documenter's build log for details.

                                Surrogates

                                For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                                Sliding windows

                                TransitionsInTimeseries.WindowViewer — Type
                                WindowViewer(x; width, stride)

                                Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                                If not given, the keywords width, stride are taken as default_window_width(x) and 1.

                                source
                                TransitionsInTimeseries.windowmap — Function
                                windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                                A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                                source

                                Load data

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+ } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR54/assets/search.js b/previews/PR54/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR54/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
                              • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR54/assets/themes/documenter-dark.css 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rgba(255,255,255,0.25)}html.theme--documenter-dark .button.is-white:active,html.theme--documenter-dark .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white{background-color:#fff;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark 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.button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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rgba(245,245,245,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#f5f5f5;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:#292929}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#2f2f2f;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,54,54,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#292929;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#e8e8e8}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#4eb5de;border-color:#4eb5de;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #4eb5de #4eb5de !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#4eb5de;box-shadow:none;color:#4eb5de}html.theme--documenter-dark 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They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found [here](https://www.iceandclimate.nbi.ku.dk/data/) in its raw format. This analysis has already been done in [boers-early-warning-2018](@cite) and we here try to reproduce Figure 2.d-f. + +## Preprocessing NGRIP + +Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps: +1. Load the data, reverse and offset it to have time vector = time before 2000 AD. +2. Filter non-unique points in time and sort the data. +3. Regrid the data from uneven to even sampling. + +The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing. + +### Step 1: +=# + +using DelimitedFiles, Downloads + +function load_ngrip() + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP.csv") + data, labels = readdlm(tmp, header = true) + return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors +end + +t1, x1 = load_ngrip() + +#= +### Step 2 +=# + +uniqueidx(v) = unique(i -> v[i], eachindex(v)) +function keep_unique(t, x) + unique_idx = uniqueidx(t) + return t[unique_idx], x[unique_idx] +end + +function sort_timeseries!(t, x) + p = sortperm(t) + permute!(t, p) + permute!(x, p) + return nothing +end + +t2, x2 = keep_unique(t1, x1) +sort_timeseries!(t2, x2) + +#= +### Step 3 +=# + +using BSplineKit + +function regrid2evensampling(t, x, dt) + itp = BSplineKit.interpolate(t, x, BSplineOrder(4)) + tspan = (ceil(minimum(t)), floor(maximum(t))) + t_even = collect(tspan[1]:dt:tspan[2]) + x_even = itp.(t_even) + return t_even, x_even +end + +dt = 5.0 # dt = 5 yr as in (Boers 2018) +t3, x3 = regrid2evensampling(t2, x2, dt) + +#= +### Step 4 + +For the final step we drop the indices: +=# + +using DSP + +function chebyshev_filter(t, x, fcutoff) + ii = 10 # Chebyshev filtering requires to prune first points of timeseries. + responsetype = Highpass(fcutoff, fs = 1/dt) + designmethod = Chebyshev1(8, 0.05) + r = filt(digitalfilter(responsetype, designmethod), x) + xtrend = x - r + return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end] +end + +fcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018) +t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff) + +#= +Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from [rasmussen-stratigraphic-2014](@cite) (which will soon be available as downloadable): +=# + +using CairoMakie, Loess + +function loess_filter(t, x; span = 0.005) + loessmodel = loess(t, x, span = span) + xtrend = Loess.predict(loessmodel, t) + r = x - xtrend + return t, x, xtrend, r +end + +function kyr_xticks(tticks_yr) + tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)] + return (tticks_yr, tticks_kyr) +end + +function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks) + fig = Figure(resolution = (1600, 1200), fontsize = 24) + + ## Original timeseries with transition marked by vertical lines + ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)", + xaxisposition = :top, xticks = xticks) + lines!(ax1, traw, xraw, color = (:gray70, 0.5)) + lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3) + vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3) + + ## Residual timeseries + ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + lines!(ax2, t, r, color = :gray50, linewidth = 1) + + ## Axes for variance and AC1 timeseries + ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$", + xticks = xticks) + + axs = [ax1, ax2, ax3, ax4] + [xlims!(ax, xlims) for ax in axs] + ylims!(axs[1], (-48, -34)) + rowgap!(fig.layout, 10) + return fig, axs +end + +xlims = (-60e3, -10e3) +xticks = kyr_xticks(-60e3:5e3:5e3) +t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160, + 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703] +tloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +fig + +#= +## Hindcast on NGRIP data + +As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including [boers-early-warning-2018](@cite), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using `SegmentedWindowConfig`, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here: +=# + +using TransitionsInTimeseries, StatsBase +using Random: Xoshiro + +ac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase +indicators = (var, ac1) +change_metrics = RidgeRegressionSlope() +tseg_start = t_rasmussen[1:end-1] .+ 200 +tseg_end = t_rasmussen[2:end] .- 200 +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) # require >=100 data points to estimate change metric +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) + +#= +That's it! We can now visulaise our results with a generic function that we will re-use later: +=# + +function plot_segment_analysis!(axs, results, signif) + (; t_indicator, x_indicator) = results + for k in eachindex(t_indicator) # loop over the segments + for i in axes(signif.pvalues, 2) # loop over the indicators + if !isinf(signif.pvalues[k, i]) # plot if segment long enough + ## Plot indicator timeseries and its linear regression + ti, xi = t_indicator[k], x_indicator[k][:, i] + lines!(axs[i+2], ti, xi, color = Cycled(1)) + m, p = ridgematrix(ti, 0.0) * xi + if signif.pvalues[k, i] < 0.05 + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3) + else + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3) + end + end + end + end +end +plot_segment_analysis!(axs, results, signif) +fig + +#= +In [boers-early-warning-2018](@cite), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in [boers-early-warning-2018](@cite), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of [boers-early-warning-2018](@cite). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media. + +## CSD: only a necessary condition, only in some cases + +For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a **necessary condition** for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is **not a sufficient condition** for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition: +=# + +tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +plot_segment_analysis!(axs, results, signif) +fig + +#= +For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD. + +We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC). + +!!! warning "Degrees of freedom" + These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice. + +!!! info "Future improvement" + Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias. + +## Hindcasting simulated DO-events + +In CLIMBER-X, the EMIC described in [willeit-earth-2022](@cite), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs: +=# + +t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050], + [1, 3500, 4370, 5790, 7200, 8140]] +t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]] +tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]] +tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50] + +figvec = Figure[] + +for j in 1:2 + ## Download the data and perform loess filtering on it + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" * + "master/timeseries/climberx-do$(j)-omaxa.csv") + data = readdlm(tmp) + tcx, xcx = data[1, 1000:end], data[2, 1000:end] + t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02) + + ## Initialize figure + xlims = (0, last(tcx)) + xticks = kyr_xticks(xlims[1]:1e3:xlims[2]) + fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks) + ylims!(axs[1], (5, 40)) + axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$" + + ## Run sliding analysis and update figure with results + dt = mean(diff(tcx)) + config = SegmentedWindowConfig( + indicators, change_metrics, tseg_start[j], tseg_end[j], + whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100) + results = estimate_indicator_changes(config, r, t) + signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995)) + flags = significant_transitions(results, signif) + + plot_segment_analysis!(axs, results, signif) + vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3) + push!(figvec, fig) +end +figvec[1] + +#= +It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case: +=# + +figvec[2] + +#= +Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience. +=# \ No newline at end of file diff --git a/previews/PR54/examples/do-events/index.html b/previews/PR54/examples/do-events/index.html new file mode 100644 index 00000000..b323492d --- /dev/null +++ b/previews/PR54/examples/do-events/index.html @@ -0,0 +1,191 @@ + +Dansgaard-Oescher events and Critical Slowing Down · TransitionsInTimeseries.jl
                                Edit on GitHub

                                Dansgaard-Oescher events and Critical Slowing Down

                                The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.

                                Preprocessing NGRIP

                                Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:

                                1. Load the data, reverse and offset it to have time vector = time before 2000 AD.
                                2. Filter non-unique points in time and sort the data.
                                3. Regrid the data from uneven to even sampling.

                                The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.

                                Step 1:

                                using DelimitedFiles, Downloads
+
+function load_ngrip()
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+        "master/timeseries/NGRIP.csv")
+    data, labels = readdlm(tmp, header = true)
+    return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors
+end
+
+t1, x1 = load_ngrip()
                                ([-59944.5, -59939.6, -59935.9, -59930.5, -59925.0, -59919.0, -59914.3, -59909.4, -59904.5, -59899.7  …  -27.40000000000009, -27.40000000000009, -27.299999999999955, -27.299999999999955, -27.200000000000045, -27.09999999999991, -27.09999999999991, -27.0, -26.90000000000009, -26.799999999999955], [-43.52, -42.94, -42.13, -40.04, -41.09, -43.57, -42.28, -41.2, -44.07, -44.53  …  -35.29, -35.18, -35.51, -36.03, -36.52, -37.12, -37.41, -37.21, -36.62, -35.52])

                                Step 2

                                uniqueidx(v) = unique(i -> v[i], eachindex(v))
+function keep_unique(t, x)
+    unique_idx = uniqueidx(t)
+    return t[unique_idx], x[unique_idx]
+end
+
+function sort_timeseries!(t, x)
+    p = sortperm(t)
+    permute!(t, p)
+    permute!(x, p)
+    return nothing
+end
+
+t2, x2 = keep_unique(t1, x1)
+sort_timeseries!(t2, x2)

                                Step 3

                                using BSplineKit
+
+function regrid2evensampling(t, x, dt)
+    itp = BSplineKit.interpolate(t, x, BSplineOrder(4))
+    tspan = (ceil(minimum(t)), floor(maximum(t)))
+    t_even = collect(tspan[1]:dt:tspan[2])
+    x_even = itp.(t_even)
+    return t_even, x_even
+end
+
+dt = 5.0        # dt = 5 yr as in (Boers 2018)
+t3, x3 = regrid2evensampling(t2, x2, dt)
                                ([-59944.0, -59939.0, -59934.0, -59929.0, -59924.0, -59919.0, -59914.0, -59909.0, -59904.0, -59899.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-43.445268010797946, -42.85408835164853, -41.357360665158936, -39.9365468206892, -41.60554051352076, -43.57000000000001, -42.145558689100454, -41.33160823883399, -44.273597725729985, -44.4622612304012  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46])

                                Step 4

                                For the final step we drop the indices:

                                using DSP
+
+function chebyshev_filter(t, x, fcutoff)
+    ii = 10             # Chebyshev filtering requires to prune first points of timeseries.
+    responsetype = Highpass(fcutoff, fs = 1/dt)
+    designmethod = Chebyshev1(8, 0.05)
+    r = filt(digitalfilter(responsetype, designmethod), x)
+    xtrend = x - r
+    return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]
+end
+
+fcutoff = 0.95 * 0.01   # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)
+t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)
                                ([-59899.0, -59894.0, -59889.0, -59884.0, -59879.0, -59874.0, -59869.0, -59864.0, -59859.0, -59854.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-44.4622612304012, -44.264401428210874, -44.02956767939856, -42.29334237357212, -42.594341674200344, -41.09704877854712, -40.39837540966913, -44.369155046413255, -42.74492506508012, -43.737014520530145  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46], [-43.89287787976461, -48.663435112414156, -51.31169981050155, -51.269094666491796, -49.90310432724566, -47.721430022512344, -44.36050569418247, -43.87556827410048, -43.57802291229893, -41.36870967826094  …  -34.81349114528442, -36.01634453179986, -36.150446802907226, -36.37595639697143, -35.96843653265903, -33.899634243732976, -32.49784036951535, -33.06575312724142, -34.07956188682297, -34.4079080530096], [-0.5693833506365866, 4.399033684203284, 7.282132131102991, 8.975752292919669, 7.308762653045311, 6.624381243965224, 3.9621302845133433, -0.493586772312777, 0.8330978472188112, -2.368304842269206  …  -0.30650885471557926, -0.17365546820014846, 1.0104468029072273, -0.684043603028572, 1.0384365326590237, -0.3303657562670192, -1.0321596304846505, -2.0242468727585807, 0.07956188682296689, -0.05209194699039831])

                                Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):

                                using CairoMakie, Loess
+
+function loess_filter(t, x; span = 0.005)
+    loessmodel = loess(t, x, span = span)
+    xtrend = Loess.predict(loessmodel, t)
+    r = x - xtrend
+    return t, x, xtrend, r
+end
+
+function kyr_xticks(tticks_yr)
+    tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)]
+    return (tticks_yr, tticks_kyr)
+end
+
+function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)
+    fig = Figure(resolution = (1600, 1200), fontsize = 24)
+
+    # Original timeseries with transition marked by vertical lines
+    ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)",
+        xaxisposition = :top, xticks = xticks)
+    lines!(ax1, traw, xraw, color = (:gray70, 0.5))
+    lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)
+    vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)
+
+    # Residual timeseries
+    ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    lines!(ax2, t, r, color = :gray50, linewidth = 1)
+
+    # Axes for variance and AC1 timeseries
+    ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$",
+        xticks = xticks)
+
+    axs = [ax1, ax2, ax3, ax4]
+    [xlims!(ax, xlims) for ax in axs]
+    ylims!(axs[1], (-48, -34))
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+
+xlims = (-60e3, -10e3)
+xticks = kyr_xticks(-60e3:5e3:5e3)
+t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,
+                38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]
+tloess, _, xloess, rloess = loess_filter(t3, x3)    # loess-filtered signal for visualization
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+fig

                                Hindcast on NGRIP data

                                As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:

                                using TransitionsInTimeseries, StatsBase
+using Random: Xoshiro
+
+ac1(x) = sum(autocor(x, [1]))   # AC1 from StatsBase
+indicators = (var, ac1)
+change_metrics = RidgeRegressionSlope()
+tseg_start = t_rasmussen[1:end-1] .+ 200
+tseg_end = t_rasmussen[2:end] .- 200
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)        # require >=100 data points to estimate change metric
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
                                18×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 1  0
+ 1  1
+ 1  1
+ 1  1
+ 0  0
+ 1  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 1  0

                                That's it! We can now visulaise our results with a generic function that we will re-use later:

                                function plot_segment_analysis!(axs, results, signif)
+    (; t_indicator, x_indicator) = results
+    for k in eachindex(t_indicator)             # loop over the segments
+        for i in axes(signif.pvalues, 2)        # loop over the indicators
+            if !isinf(signif.pvalues[k, i])     # plot if segment long enough
+                # Plot indicator timeseries and its linear regression
+                ti, xi = t_indicator[k], x_indicator[k][:, i]
+                lines!(axs[i+2], ti, xi, color = Cycled(1))
+                m, p = ridgematrix(ti, 0.0) * xi
+                if signif.pvalues[k, i] < 0.05
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)
+                else
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)
+                end
+            end
+        end
+    end
+end
+plot_segment_analysis!(axs, results, signif)
+fig

                                In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.

                                CSD: only a necessary condition, only in some cases

                                For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:

                                tseg_end = t_rasmussen[2:end] .- 700    # stop analysis 500 years earlier than before
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+plot_segment_analysis!(axs, results, signif)
+fig

                                For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD.

                                We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).

                                Degrees of freedom

                                These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.

                                Future improvement

                                Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.

                                Hindcasting simulated DO-events

                                In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:

                                t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],
+                 [1, 3500, 4370, 5790, 7200, 8140]]
+t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]
+tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]
+tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]
+
+figvec = Figure[]
+
+for j in 1:2
+    # Download the data and perform loess filtering on it
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" *
+        "master/timeseries/climberx-do$(j)-omaxa.csv")
+    data = readdlm(tmp)
+    tcx, xcx = data[1, 1000:end], data[2, 1000:end]
+    t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)
+
+    # Initialize figure
+    xlims = (0, last(tcx))
+    xticks = kyr_xticks(xlims[1]:1e3:xlims[2])
+    fig, axs = plot_do(tcx, xcx,  t, xtrend, t, r, t_transitions[j], extrema(t), xticks)
+    ylims!(axs[1], (5, 40))
+    axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$"
+
+    # Run sliding analysis and update figure with results
+    dt = mean(diff(tcx))
+    config = SegmentedWindowConfig(
+        indicators, change_metrics, tseg_start[j], tseg_end[j],
+        whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)
+    results = estimate_indicator_changes(config, r, t)
+    signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))
+    flags = significant_transitions(results, signif)
+
+    plot_segment_analysis!(axs, results, signif)
+    vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)
+    push!(figvec, fig)
+end
+figvec[1]

                                It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:

                                figvec[2]

                                Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.

                                diff --git a/previews/PR54/examples/logistic.jl b/previews/PR54/examples/logistic.jl new file mode 100644 index 00000000..a2894fbd --- /dev/null +++ b/previews/PR54/examples/logistic.jl @@ -0,0 +1,203 @@ +# # Permutation entropy for dynamic regime changes + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ## Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +## time-dependent logistic map, so that the `r` parameter increases with time +r1 = 3.83 +r2 = 3.86 +N = 2000 +rs = range(r1, r2; length = N) + +function logistic_drifting_rule(u, rs, n) + r = rs[n+1] # time is `n`, starting from 0 + return SVector(r*u[1]*(1 - u[1])) +end + +ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs) +x = trajectory(ds, N-1)[1][:, 1] + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ## Using a simpler change metric + +# Now, let's compute and various indicators and their changes, +# focusing on the permutation entropy as an indicator. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries, ComplexityMeasures + +function permutation_entropy(m) + est = SymbolicPermutation(; m) # order 3 + indicator = x -> entropy_normalized(est, x) + return indicator +end + +indicators = (var, ar1_whitenoise, permutation_entropy(4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as stride half the window width +metric = difference_of_means + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = SlidingWindowConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = estimate_indicator_changes(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + if i < 3 + hidexdecorations!(ax; grid = false) + else + ax.xlabel = "r (time)" + end + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ## Significance via random Fourier surrogates + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +using Random: Xoshiro +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42), + ) + flags = significant_transitions(results, signif) + + ## and also plot the flags with same color + for (i, indicator) in enumerate(indicators) + ## To make things visually clear, we will also plot some example surrogate + ## timeseries for each indicator and change metric pair + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surromethod) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric, p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1) + end + ## Plot the flags as vertical dashed lines + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = color, linestyle = :dash, linewidth = 3 + ) + end + ## add a title to the figure with how we estimate significance + content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod))) +end + +surromethod = RandomFourier() +overplot_surrogate_significance!(fig, surromethod) + +fig + +# ## Different surrogates +# %% #src +# Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# highlighting the _local_ dynamics or information that preserves the local +# changes of dynamical behavior. + +# A surrogate type that does a better job in preserving local sharp +# changes in the timeseries (and hence provides **stricter** +# surrogate-based significance) is for example `RelativePartialRandomization`. + +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = RelativePartialRandomization(0.25) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "gray") +fig + +# Our results have improved. In the permutation entropy, we see only two +# transitions detected as significant, which is correct: only two +# real dynamical transitions exist in the data. +# In the other two indicators we also see fewer transitions, but as we +# have already discussed, no results with the other indicators should +# be taken into meaningful consideration, as these indicators +# are simply inappropriate for what we are looking for here. + +# ## Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be less strict and more simple with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`SigmaSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation. + +fig = plot_change_metrics() +flags = significant_transitions(results, SigmaSignificance(factor = 5.0)) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = Cycled(3), linestyle = :dash, linewidth = 3 + ) +end +content(fig[1, 1]).title = "significance from std" +fig diff --git a/previews/PR54/examples/logistic/index.html b/previews/PR54/examples/logistic/index.html new file mode 100644 index 00000000..9a08b286 --- /dev/null +++ b/previews/PR54/examples/logistic/index.html @@ -0,0 +1,128 @@ + +Permutation entropy for dynamic regime changes · TransitionsInTimeseries.jl
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                                Permutation entropy for dynamic regime changes

                                Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.

                                This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.

                                Logistic map timeseries

                                A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map

                                using DynamicalSystemsBase
+using CairoMakie
+
+# time-dependent logistic map, so that the `r` parameter increases with time
+r1 = 3.83
+r2 = 3.86
+N = 2000
+rs = range(r1, r2; length = N)
+
+function logistic_drifting_rule(u, rs, n)
+    r = rs[n+1] # time is `n`, starting from 0
+    return SVector(r*u[1]*(1 - u[1]))
+end
+
+ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)
+x = trajectory(ds, N-1)[1][:, 1]
                                2000-element Vector{Float64}:
+ 0.5
+ 0.9575
+ 0.15585767321160574
+ 0.5039019545917718
+ 0.9574529422362281
+ 0.15602441103002537
+ 0.5043473227583317
+ 0.9574501255597653
+ 0.1560361152301728
+ 0.5043840906474082
+ ⋮
+ 0.4253904015445437
+ 0.9434836074964187
+ 0.20581843730311683
+ 0.6309301050251992
+ 0.8988117342940414
+ 0.3510584545931264
+ 0.8793611090928393
+ 0.40948549063776396
+ 0.9333718681550522

                                Plot it, using as time the parameter value (they coincide)

                                fig, ax = lines(rs, x; linewidth = 0.5)
+ax.xlabel = "r (time)"
+ax.ylabel = "x"
+fig

                                In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.

                                Using a simpler change metric

                                Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.

                                using TransitionsInTimeseries, ComplexityMeasures
+
+function permutation_entropy(m)
+    est = SymbolicPermutation(; m) # order 3
+    indicator = x -> entropy_normalized(est, x)
+    return indicator
+end
+
+indicators = (var, ar1_whitenoise, permutation_entropy(4))
+indistrings = ("var", "ar1", "pe")
                                ("var", "ar1", "pe")

                                In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width

                                metric = difference_of_means
+
+width_ind = N÷100
+width_cha = 20
+stride_cha = 10
+
+config = SlidingWindowConfig(indicators, metric;
+    width_ind, width_cha, stride_cha,
+)
+
+results = estimate_indicator_changes(config, x, rs)
                                IndicatorsChangesResults
+ input timeseries:              2000-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise, Symbol("#1")]
+ indicator (window, stride):    (20, 1)
+ change metrics:                [:difference_of_means]
+ change metric (window, stride): (20, 10)
+

                                Let's now plot the change metrics of the indicators

                                function plot_change_metrics()
+    fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),))
+    hidexdecorations!(ax; grid = false)
+    # plot all change metrics
+    for (i, c) in enumerate(eachcol(results.x_change))
+        ax, = scatterlines(fig[i+1, 1], results.t_change, c;
+            axis = (ylabel = indistrings[i],), label = "input"
+        )
+        if i < 3
+            hidexdecorations!(ax; grid = false)
+        else
+            ax.xlabel = "r (time)"
+        end
+    end
+    return fig
+end
+
+fig = plot_change_metrics()

                                We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)

                                Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.

                                Significance via random Fourier surrogates

                                One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.

                                Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!

                                surromethod = RandomFourier()
+
+# Define a function because we will re-use later
+using Random: Xoshiro
+function overplot_surrogate_significance!(fig, surromethod, color = "black")
+
+    signif = SurrogatesSignificance(;
+        n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),
+    )
+    flags = significant_transitions(results, signif)
+
+    # and also plot the flags with same color
+    for (i, indicator) in enumerate(indicators)
+        # To make things visually clear, we will also plot some example surrogate
+        # timeseries for each indicator and change metric pair
+        for _ in 1:10
+            s = TimeseriesSurrogates.surrogate(x, surromethod)
+            p = windowmap(indicator, s; width = width_ind)
+            q = windowmap(metric, p; width = width_cha, stride = stride_cha)
+            lines!(fig[i+1, 1], results.t_change, q;  color = (color, 0.2), linewidth = 1)
+        end
+        # Plot the flags as vertical dashed lines
+        vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+            color = color, linestyle = :dash, linewidth = 3
+        )
+    end
+    # add a title to the figure with how we estimate significance
+    content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod)))
+end
+
+surromethod = RandomFourier()
+overplot_surrogate_significance!(fig, surromethod)
+
+fig

                                Different surrogates

                                Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

                                A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

                                A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

                                surromethod = RelativePartialRandomization(0.25)
+fig = plot_change_metrics()
+overplot_surrogate_significance!(fig, surromethod, "gray")
+fig

                                Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

                                Simpler Significance

                                Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

                                fig = plot_change_metrics()
+flags = significant_transitions(results, SigmaSignificance(factor = 5.0))
+
+# Plot the flags
+for (i, indicator) in enumerate(indicators)
+    vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+        color = Cycled(3), linestyle = :dash, linewidth = 3
+    )
+end
+content(fig[1, 1]).title = "significance from std"
+fig
                                diff --git a/previews/PR54/index.html b/previews/PR54/index.html new file mode 100644 index 00000000..dd4be49b --- /dev/null +++ b/previews/PR54/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
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                                TransitionsInTimeseries.jl

                                TransitionsInTimeseries.jl

                                TransitionsInTimeseries — Module

                                TransitionsInTimeseries.jl

                                CI codecov Package Downloads

                                A Julia package for estimating transitions (from one dynamic regime or stable state to another) in timeseries and testing the statistical significance of found transitions. It integrates with the entire Julia ecosystem of timeseries analysis, and hence offers thousands of metrics that can indicate transitions right out of the box. It also offers a variety of analysis pipelines for identifying transitions and a variety of statistical pipelines for testing for significance.

                                In contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:

                                1. Add new indicators that work with the existing analysis pipelines for finding transitions
                                2. Add new analysis pipelines for finding transitions
                                3. Add new ways for testing whether already found transitions are significant

                                This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

                                add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

                                All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                                Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                                source
                                Star us on GitHub!

                                If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                                Content

                                Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                                • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                                • Makes the surrogate analysis to test for significance under the hub.
                                • Can be easily extended by any user without touching the source code.
                                • Reduces the programming overhead for any researcher willing to benchmark new methods.
                                • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                                • Increases trustworthiness thanks to a large test suite.
                                Similar projects

                                An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                                Approaches

                                Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                                diff --git a/previews/PR54/refs.bib b/previews/PR54/refs.bib new file mode 100644 index 00000000..8010a9d3 --- /dev/null +++ b/previews/PR54/refs.bib @@ -0,0 +1,54 @@ + +@article{willeit-earth-2022, + title = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1: {Climate} model description and validation​​​​​​​​​​​​​​}, + volume = {15}, + issn = {1991-9603}, + shorttitle = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1}, + url = {https://gmd.copernicus.org/articles/15/5905/2022/}, + doi = {10.5194/gmd-15-5905-2022}, + abstract = {The newly developed fast Earth system model CLIMBER-X is presented. The climate component of CLIMBER-X consists of a 2.5-D semi-empirical statistical–dynamical atmosphere model, a 3-D frictional–geostrophic ocean model, a dynamic–thermodynamic sea ice model and a land surface model. All the model components are discretized on a regular lat–long grid with a horizontal resolution of 5 ◦ × 5 ◦. The model has a throughput of ∼ 10 000 simulation years per day on a single node with 16 CPUs on a high-performance computer and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to {\textgreater} 100 000 years. A comprehensive evaluation of the model performance for the present day and the historical period shows that CLIMBER-X is capable of realistically reproducing many observed climate characteristics, with results that generally lie within the range of state-of-theart general circulation models. The analysis of model performance is complemented by a thorough assessment of climate feedbacks and model sensitivities to changes in external forcings and boundary conditions. Limitations and applicability of the model are critically discussed. CLIMBER-X also includes a detailed representation of the global carbon cycle and is coupled to an ice sheet model, which will be described in separate papers. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.}, + language = {en}, + number = {14}, + urldate = {2022-08-11}, + journal = {Geoscientific Model Development}, + author = {Willeit, Matteo and Ganopolski, Andrey and Robinson, Alexander and Edwards, Neil R.}, + month = jul, + year = {2022}, + pages = {5905--5948}, + file = {Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:/home/jan/Zotero/storage/75NKS975/Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:application/pdf}, +} + +@article{boers-early-warning-2018, + title = {Early-warning signals for {Dansgaard}-{Oeschger} events in a high-resolution ice core record}, + volume = {9}, + issn = {2041-1723}, + url = {http://www.nature.com/articles/s41467-018-04881-7}, + doi = {10.1038/s41467-018-04881-7}, + language = {en}, + number = {1}, + urldate = {2022-10-28}, + journal = {Nature Communications}, + author = {Boers, Niklas}, + month = dec, + year = {2018}, + pages = {2556}, + file = {Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:/home/jan/Zotero/storage/DS97Z9UC/Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:application/pdf}, +} + +@article{rasmussen-stratigraphic-2014, + title = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records: refining and extending the {INTIMATE} event stratigraphy}, + volume = {106}, + issn = {02773791}, + shorttitle = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0277379114003485}, + doi = {10.1016/j.quascirev.2014.09.007}, + abstract = {Due to their outstanding resolution and well-constrained chronologies, Greenland ice-core records provide a master record of past climatic changes throughout the Last InterglacialeGlacial cycle in the North Atlantic region. As part of the INTIMATE (INTegration of Ice-core, MArine and TErrestrial records) project, protocols have been proposed to ensure consistent and robust correlation between different records of past climate. A key element of these protocols has been the formal definition and ordinal numbering of the sequence of Greenland Stadials (GS) and Greenland Interstadials (GI) within the most recent glacial period. The GS and GI periods are the Greenland expressions of the characteristic DansgaardeOeschger events that represent cold and warm phases of the North Atlantic region, respectively. We present here a more detailed and extended GS/GI template for the whole of the Last Glacial period. It is based on a synchronization of the NGRIP, GRIP, and GISP2 ice-core records that allows the parallel analysis of all three records on a common time scale. The boundaries of the GS and GI periods are defined based on a combination of stable-oxygen isotope ratios of the ice (d18O, reflecting mainly local temperature) and calcium ion concentrations (reflecting mainly atmospheric dust loading) measured in the ice. The data not only resolve the well-known sequence of DansgaardeOeschger events that were first defined and numbered in the ice-core records more than two decades ago, but also better resolve a number of short-lived climatic oscillations, some defined here for the first time. Using this revised scheme, we propose a consistent approach for discriminating and naming all the significant abrupt climatic events of the Last Glacial period that are represented in the Greenland ice records. The final product constitutes an extended and better resolved Greenland stratotype sequence, against which other proxy records can be compared and correlated. It also provides a more secure basis for investigating the dynamics and fundamental causes of these climatic perturbations.}, + language = {en}, + urldate = {2023-10-04}, + journal = {Quaternary Science Reviews}, + author = {Rasmussen, Sune O. and Bigler, Matthias and Blockley, Simon P. and Blunier, Thomas and Buchardt, Susanne L. and Clausen, Henrik B. and Cvijanovic, Ivana and Dahl-Jensen, Dorthe and Johnsen, Sigfus J. and Fischer, Hubertus and Gkinis, Vasileios and Guillevic, Myriam and Hoek, Wim Z. and Lowe, J. John and Pedro, Joel B. and Popp, Trevor and Seierstad, Inger K. and Steffensen, Jørgen Peder and Svensson, Anders M. and Vallelonga, Paul and Vinther, Bo M. and Walker, Mike J.C. and Wheatley, Joe J. and Winstrup, Mai}, + month = dec, + year = {2014}, + pages = {14--28}, + file = {Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:/home/jan/Zotero/storage/VSUTVWPN/Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:application/pdf}, +} diff --git a/previews/PR54/refs/index.html b/previews/PR54/refs/index.html new file mode 100644 index 00000000..7020bc13 --- /dev/null +++ b/previews/PR54/refs/index.html @@ -0,0 +1,9 @@ + +References · TransitionsInTimeseries.jl
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                                References

                                diff --git a/previews/PR54/search/index.html b/previews/PR54/search/index.html new file mode 100644 index 00000000..8630a7f7 --- /dev/null +++ b/previews/PR54/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

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                                  diff --git a/previews/PR54/search_index.js b/previews/PR54/search_index.js new file mode 100644 index 00000000..0396ea47 --- /dev/null +++ b/previews/PR54/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"IndicatorsChangesConfig\nSlidingWindowConfig\nSegmentedWindowConfig\nestimate_indicator_changes\nIndicatorsChangesResults\nSlidingWindowResults\nSegmentedWindowResults","category":"page"},{"location":"api/#TransitionsInTimeseries.IndicatorsChangesConfig","page":"API","title":"TransitionsInTimeseries.IndicatorsChangesConfig","text":"IndicatorsChangesConfig\n\nSupertype used to define how indicators and their changes are estimated in estimate_indicator_changes. Valid subtypes are:\n\nSlidingWindowConfig.\nSegmentedWindowConfig.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowConfig","page":"API","title":"TransitionsInTimeseries.SlidingWindowConfig","text":"SlidingWindowConfig <: IndicatorsChangesConfig\nSlidingWindowConfig(indicators, change_metrics; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.\n\nThe results output corresponding to SlidingWindowConfig is SlidingWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowConfig","page":"API","title":"TransitionsInTimeseries.SegmentedWindowConfig","text":"SegmentedWindowConfig <: IndicatorsChangeConfig\nSegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:\n\nFor each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).\nFor each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d\n\ntseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.\n\nThe results output corresponding to SlidingWindowConfig is SegmentedWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.\nmin_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.estimate_indicator_changes","page":"API","title":"TransitionsInTimeseries.estimate_indicator_changes","text":"estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → result\n\nEstimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).\n\nReturn the output as subtype of IndicatorsChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.IndicatorsChangesResults","page":"API","title":"TransitionsInTimeseries.IndicatorsChangesResults","text":"IndicatorsChangesResults\n\nSupertype used to gather results of estimate_indicator_changes. The concrete subtype instances are described in the docstrings of configuration types.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowResults","page":"API","title":"TransitionsInTimeseries.SlidingWindowResults","text":"SlidingWindowResults <: IndicatorsChangesResults\n\nA struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nconfig::SlidingWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowResults","page":"API","title":"TransitionsInTimeseries.SegmentedWindowResults","text":"SegmentedWindowResults <: IndicatorsChangesResults\n\nA struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.\nt_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.\nx_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.\nt_change, the time vector of the change metric.\nconfig::SegmentedWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"significant_transitions\nTransitionsSignificance\nSurrogatesSignificance\nQuantileSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::IndicatorsChangesResults, signif::TransitionsSignificance)\n\nEstimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.TransitionsSignificance","page":"API","title":"TransitionsInTimeseries.TransitionsSignificance","text":"TransitionsSignificance\n\nSupertype used to test for significance in significant_transitions. Valid subtypes are:\n\nSurrogatesSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: TransitionsSignificance\nSurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)\n\nA configuration struct for significance testing significant_transitions using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\n\nDescription\n\nWhen used with IndicatorsChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in IndicatorsChangesResults.\n\nNote that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance\n\nA configuration struct for significance testing significant_transitions. When used with IndicatorsChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\nQuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.","category":"page"},{"location":"api/","page":"API","title":"API","text":"For example, using the permutation entropy as an indicator is as simple as doing","category":"page"},{"location":"api/","page":"API","title":"API","text":"using ComplexityMeasures\nest = OrdinalPatterns(; m = 3) # order 3\n# create a function that given timeseries returns permutation entropy\nindicator = x -> entropy_normalized(est, x)","category":"page"},{"location":"api/","page":"API","title":"API","text":"and giving the created indicator to e.g., SlidingWindowConfig.","category":"page"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"EditURL = \"do-events.jl\"","category":"page"},{"location":"examples/do-events/#Dansgaard-Oescher-events-and-Critical-Slowing-Down","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The delta^18O timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.","category":"page"},{"location":"examples/do-events/#Preprocessing-NGRIP","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Preprocessing NGRIP","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Load the data, reverse and offset it to have time vector = time before 2000 AD.\nFilter non-unique points in time and sort the data.\nRegrid the data from uneven to even sampling.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The time and delta^18O vectors resulting from the i-th preprocessing step are respectively called t_i and x_i. The final step consists in obtaining a residual r, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.","category":"page"},{"location":"examples/do-events/#Step-1:","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 1:","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DelimitedFiles, Downloads\n\nfunction load_ngrip()\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP.csv\")\n data, labels = readdlm(tmp, header = true)\n return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors\nend\n\nt1, x1 = load_ngrip()","category":"page"},{"location":"examples/do-events/#Step-2","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 2","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"uniqueidx(v) = unique(i -> v[i], eachindex(v))\nfunction keep_unique(t, x)\n unique_idx = uniqueidx(t)\n return t[unique_idx], x[unique_idx]\nend\n\nfunction sort_timeseries!(t, x)\n p = sortperm(t)\n permute!(t, p)\n permute!(x, p)\n return nothing\nend\n\nt2, x2 = keep_unique(t1, x1)\nsort_timeseries!(t2, x2)","category":"page"},{"location":"examples/do-events/#Step-3","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 3","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using BSplineKit\n\nfunction regrid2evensampling(t, x, dt)\n itp = BSplineKit.interpolate(t, x, BSplineOrder(4))\n tspan = (ceil(minimum(t)), floor(maximum(t)))\n t_even = collect(tspan[1]:dt:tspan[2])\n x_even = itp.(t_even)\n return t_even, x_even\nend\n\ndt = 5.0 # dt = 5 yr as in (Boers 2018)\nt3, x3 = regrid2evensampling(t2, x2, dt)","category":"page"},{"location":"examples/do-events/#Step-4","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 4","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the final step we drop the indices:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DSP\n\nfunction chebyshev_filter(t, x, fcutoff)\n ii = 10 # Chebyshev filtering requires to prune first points of timeseries.\n responsetype = Highpass(fcutoff, fs = 1/dt)\n designmethod = Chebyshev1(8, 0.05)\n r = filt(digitalfilter(responsetype, designmethod), x)\n xtrend = x - r\n return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]\nend\n\nfcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)\nt, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using CairoMakie, Loess\n\nfunction loess_filter(t, x; span = 0.005)\n loessmodel = loess(t, x, span = span)\n xtrend = Loess.predict(loessmodel, t)\n r = x - xtrend\n return t, x, xtrend, r\nend\n\nfunction kyr_xticks(tticks_yr)\n tticks_kyr = [\"$t\" for t in Int.(tticks_yr ./ 1e3)]\n return (tticks_yr, tticks_kyr)\nend\n\nfunction plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)\n fig = Figure(resolution = (1600, 1200), fontsize = 24)\n\n # Original timeseries with transition marked by vertical lines\n ax1 = Axis(fig[1, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"$\\delta^{18}$O (permil)\",\n xaxisposition = :top, xticks = xticks)\n lines!(ax1, traw, xraw, color = (:gray70, 0.5))\n lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)\n vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)\n\n # Residual timeseries\n ax2 = Axis(fig[2, 1], ylabel = L\"Residual $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n lines!(ax2, t, r, color = :gray50, linewidth = 1)\n\n # Axes for variance and AC1 timeseries\n ax3 = Axis(fig[3, 1], ylabel = L\"Variance $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n ax4 = Axis(fig[4, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"Lag-1 autocor. $\\,$\",\n xticks = xticks)\n\n axs = [ax1, ax2, ax3, ax4]\n [xlims!(ax, xlims) for ax in axs]\n ylims!(axs[1], (-48, -34))\n rowgap!(fig.layout, 10)\n return fig, axs\nend\n\nxlims = (-60e3, -10e3)\nxticks = kyr_xticks(-60e3:5e3:5e3)\nt_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,\n 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]\ntloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nfig","category":"page"},{"location":"examples/do-events/#Hindcast-on-NGRIP-data","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcast on NGRIP data","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using TransitionsInTimeseries, StatsBase\nusing Random: Xoshiro\n\nac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase\nindicators = (var, ac1)\nchange_metrics = RidgeRegressionSlope()\ntseg_start = t_rasmussen[1:end-1] .+ 200\ntseg_end = t_rasmussen[2:end] .- 200\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100) # require >=100 data points to estimate change metric\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"That's it! We can now visulaise our results with a generic function that we will re-use later:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"function plot_segment_analysis!(axs, results, signif)\n (; t_indicator, x_indicator) = results\n for k in eachindex(t_indicator) # loop over the segments\n for i in axes(signif.pvalues, 2) # loop over the indicators\n if !isinf(signif.pvalues[k, i]) # plot if segment long enough\n # Plot indicator timeseries and its linear regression\n ti, xi = t_indicator[k], x_indicator[k][:, i]\n lines!(axs[i+2], ti, xi, color = Cycled(1))\n m, p = ridgematrix(ti, 0.0) * xi\n if signif.pvalues[k, i] < 0.05\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)\n else\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)\n end\n end\n end\n end\nend\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.","category":"page"},{"location":"examples/do-events/#CSD:-only-a-necessary-condition,-only-in-some-cases","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"CSD: only a necessary condition, only in some cases","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential U, which defines the deterministic term f = -U of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100)\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that \"resilience-loss indicators\" is a more accurate name than \"early-warning signals\" when using CSD.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"We draw attention upon the fact that the delta^18O timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"warning: Degrees of freedom\nThese sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"info: Future improvement\nSupporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.","category":"page"},{"location":"examples/do-events/#Hindcasting-simulated-DO-events","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcasting simulated DO-events","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],\n [1, 3500, 4370, 5790, 7200, 8140]]\nt_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]\ntseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]\ntseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]\n\nfigvec = Figure[]\n\nfor j in 1:2\n # Download the data and perform loess filtering on it\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\" *\n \"master/timeseries/climberx-do$(j)-omaxa.csv\")\n data = readdlm(tmp)\n tcx, xcx = data[1, 1000:end], data[2, 1000:end]\n t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)\n\n # Initialize figure\n xlims = (0, last(tcx))\n xticks = kyr_xticks(xlims[1]:1e3:xlims[2])\n fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks)\n ylims!(axs[1], (5, 40))\n axs[1].ylabel = L\"Max. Atlantic overturning (Sv) $\\,$\"\n\n # Run sliding analysis and update figure with results\n dt = mean(diff(tcx))\n config = SegmentedWindowConfig(\n indicators, change_metrics, tseg_start[j], tseg_end[j],\n whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)\n results = estimate_indicator_changes(config, r, t)\n signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))\n flags = significant_transitions(results, signif)\n\n plot_segment_analysis!(axs, results, signif)\n vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)\n push!(figvec, fig)\nend\nfigvec[1]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"figvec[2]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"EditURL = \"logistic.jl\"","category":"page"},{"location":"examples/logistic/#Permutation-entropy-for-dynamic-regime-changes","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.","category":"page"},{"location":"examples/logistic/#Logistic-map-timeseries","page":"Permutation entropy for dynamic regime changes","title":"Logistic map timeseries","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using DynamicalSystemsBase\nusing CairoMakie\n\n# time-dependent logistic map, so that the `r` parameter increases with time\nr1 = 3.83\nr2 = 3.86\nN = 2000\nrs = range(r1, r2; length = N)\n\nfunction logistic_drifting_rule(u, rs, n)\n r = rs[n+1] # time is `n`, starting from 0\n return SVector(r*u[1]*(1 - u[1]))\nend\n\nds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)\nx = trajectory(ds, N-1)[1][:, 1]","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Plot it, using as time the parameter value (they coincide)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig, ax = lines(rs, x; linewidth = 0.5)\nax.xlabel = \"r (time)\"\nax.ylabel = \"x\"\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.","category":"page"},{"location":"examples/logistic/#Using-a-simpler-change-metric","page":"Permutation entropy for dynamic regime changes","title":"Using a simpler change metric","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using TransitionsInTimeseries, ComplexityMeasures\n\nfunction permutation_entropy(m)\n est = SymbolicPermutation(; m) # order 3\n indicator = x -> entropy_normalized(est, x)\n return indicator\nend\n\nindicators = (var, ar1_whitenoise, permutation_entropy(4))\nindistrings = (\"var\", \"ar1\", \"pe\")","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"metric = difference_of_means\n\nwidth_ind = N÷100\nwidth_cha = 20\nstride_cha = 10\n\nconfig = SlidingWindowConfig(indicators, metric;\n width_ind, width_cha, stride_cha,\n)\n\nresults = estimate_indicator_changes(config, x, rs)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's now plot the change metrics of the indicators","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"function plot_change_metrics()\n fig, ax = lines(rs, x; axis = (ylabel = \"input\",), figure = (resolution = (600, 600),))\n hidexdecorations!(ax; grid = false)\n # plot all change metrics\n for (i, c) in enumerate(eachcol(results.x_change))\n ax, = scatterlines(fig[i+1, 1], results.t_change, c;\n axis = (ylabel = indistrings[i],), label = \"input\"\n )\n if i < 3\n hidexdecorations!(ax; grid = false)\n else\n ax.xlabel = \"r (time)\"\n end\n end\n return fig\nend\n\nfig = plot_change_metrics()","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.","category":"page"},{"location":"examples/logistic/#Significance-via-random-Fourier-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Significance via random Fourier surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RandomFourier()\n\n# Define a function because we will re-use later\nusing Random: Xoshiro\nfunction overplot_surrogate_significance!(fig, surromethod, color = \"black\")\n\n signif = SurrogatesSignificance(;\n n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),\n )\n flags = significant_transitions(results, signif)\n\n # and also plot the flags with same color\n for (i, indicator) in enumerate(indicators)\n # To make things visually clear, we will also plot some example surrogate\n # timeseries for each indicator and change metric pair\n for _ in 1:10\n s = TimeseriesSurrogates.surrogate(x, surromethod)\n p = windowmap(indicator, s; width = width_ind)\n q = windowmap(metric, p; width = width_cha, stride = stride_cha)\n lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1)\n end\n # Plot the flags as vertical dashed lines\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = color, linestyle = :dash, linewidth = 3\n )\n end\n # add a title to the figure with how we estimate significance\n content(fig[1, 1]).title = \"surrogates: \"*string(nameof(typeof(surromethod)))\nend\n\nsurromethod = RandomFourier()\noverplot_surrogate_significance!(fig, surromethod)\n\nfig","category":"page"},{"location":"examples/logistic/#Different-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Different surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RelativePartialRandomization(0.25)\nfig = plot_change_metrics()\noverplot_surrogate_significance!(fig, surromethod, \"gray\")\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.","category":"page"},{"location":"examples/logistic/#Simpler-Significance","page":"Permutation entropy for dynamic regime changes","title":"Simpler Significance","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig = plot_change_metrics()\nflags = significant_transitions(results, SigmaSignificance(factor = 5.0))\n\n# Plot the flags\nfor (i, indicator) in enumerate(indicators)\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = Cycled(3), linestyle = :dash, linewidth = 3\n )\nend\ncontent(fig[1, 1]).title = \"significance from std\"\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package for estimating transitions (from one dynamic regime or stable state to another) in timeseries and testing the statistical significance of found transitions. It integrates with the entire Julia ecosystem of timeseries analysis, and hence offers thousands of metrics that can indicate transitions right out of the box. It also offers a variety of analysis pipelines for identifying transitions and a variety of statistical pipelines for testing for significance.\n\nIn contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:\n\nAdd new indicators that work with the existing analysis pipelines for finding transitions\nAdd new analysis pipelines for finding transitions\nAdd new ways for testing whether already found transitions are significant\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\nAlternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"refs/#References","page":"References","title":"References","text":"","category":"section"},{"location":"refs/","page":"References","title":"References","text":"","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"EditURL = \"tutorial.jl\"","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector,\n# we obtain the last time step of each window.\n# This therefore only uses information from `k-width+1` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\n\nfunction gridfig(nrows, ncols)\n fig = Figure()\n axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)\n for j in 1:ncols, i in 1:nrows]\n rowgap!(fig.layout, 10)\n return fig, axs\nend\nfig, axs = gridfig(2, 1)\nlines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))\nlines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))\naxs[1].title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nlines!(axs[2], t_change, change_nl, label = \"nonlin\", color = Cycled(2))\nlines!(axs[2], t_change, change_s, label = \"surrogate\", color = Cycled(3))\naxislegend()\naxs[2].title = \"change metric\"\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig, axs = gridfig(2, 2)\naxs[1].title = \"linear\"\naxs[2].title = \"nonlinear\"\n\nfor (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change) # ; color = Cycled(j)\n lines!(axsig, t_change, pval) # ; color = Cycled(j+2)\nend\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = RidgeRegressionSlope()\n\n# choices go into a configuration struct\nconfig = SlidingWindowConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last)\n\n# choices are processed\nresults = estimate_indicator_changes(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From result we can plot the change metric timeseries:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(3, 1)\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, results.x_change[:, 1];\n label = \"var slopes\", color = Cycled(3))\nscatter!(axs[3], results.t_change, results.x_change[:, 2];\n label = \"ar1 slopes\", color = Cycled(4))\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = :right)\nflags = significant_transitions(results, signif)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(2, 1)\nlines!(axs[1], vcat(0.0, t), x_nlinear; label = \"raw\", color = Cycled(1))\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 1];\n label = \"var p-values\", color = Cycled(3))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 2];\n label = \"ar1 p-values\", color = Cycled(4))\n\nflagsboth = vec(reduce(&, flags; dims = 2))\nvlines!(axs[1], results.t_change[flagsboth]; label = \"flags\", color = (\"black\", 0.1))\n\n[axislegend(ax) for ax in axs]\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"}] +} diff --git a/previews/PR54/siteinfo.js b/previews/PR54/siteinfo.js new file mode 100644 index 00000000..31333f8d --- /dev/null +++ b/previews/PR54/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR54"; diff --git a/previews/PR54/tutorial.jl b/previews/PR54/tutorial.jl new file mode 100644 index 00000000..3f135673 --- /dev/null +++ b/previews/PR54/tutorial.jl @@ -0,0 +1,263 @@ +#= + +# Tutorial + +## [Workflow] (@id workflow) + +Computing transition indicators consists of the following steps: + +1. Doing any preprocessing of raw data first, such as detrending (_not part of TransitionsInTimeseries.jl_). This yields the **input timeseries**. +2. Estimating the timeseries of an indicator by sliding a window over the input timeseries. +3. Computing the changes of the indicator by sliding a window over its timeseries. +4. Generating many surrogates that preserve important statistical properties of the original timeseries. +5. Performing step 2 and 3 for the surrogate timeseries. +6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data. + +These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports. + +## [Tutorial -- Educational] (@id example_stepbystep) + +### Raw input data + +Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by: + +```math +\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t) +``` + +with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with [Makie](https://docs.makie.org/stable/)) such prototypical data to test some indicators can be done by simply running: +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_linear) +lines!(ax, t, x_nlinear) +ax.title = "raw data" +fig + +#= +### Preprocessing + +!!! note "Not part of TransitionsInTimeseries.jl" + Any timeseries preprocessing, such as the de-trending step we do here, + is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher. + + +The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1. +=# + +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +#= +At this point, `x_l_fluct` and `x_nl_fluct` are considered the **input timeseries**. + +!!! info "Detrending in Julia" + Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as [Loess.jl](https://github.com/JuliaStats/Loess.jl) or [DSP.jl](https://docs.juliadsp.org/latest/contents/). There the detrending step consists of subtracting the smoothed signal from the original one. + +### Indicator timeseries + +We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the **input timeseries**, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as [`ar1_whitenoise`](@ref): +=# + +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +## By mapping `last::Function` over a windowviewer of the time vector, +## we obtain the last time step of each window. +## This therefore only uses information from `k-width+1` to `k` at time step `k`. +## Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +#= +The lines plotted above are the **indicator timeseries**. + +### Change metric timeseries + +From here, we process the **indicator timeseries** to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the **change metric timeseries**. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a [`RidgeRegressionSlope`](@ref): +=# + +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + +#= +### Timeseries surrogates + +As expected from [Critical Slowing Down](@ref approaches), an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance. + +In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the [TimeseriesSurrogates.jl](https://github.com/JuliaDynamics/TimeseriesSurrogates.jl) Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that `TimeseriesSurrogates` is re-exported by `TransitionsInTimeseries`, so that you don't have to `using` both of them. + +To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries. +=# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) + +function gridfig(nrows, ncols) + fig = Figure() + axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false) + for j in 1:ncols, i in 1:nrows] + rowgap!(fig.layout, 10) + return fig, axs +end +fig, axs = gridfig(2, 1) +lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2)) +lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3)) +axs[1].title = "real signal vs. surrogate(s)" + +## compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2)) +lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3)) +axislegend() +axs[2].title = "change metric" + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +### Quantifying significance + +To quantify the significance of the values of the **change metric timeseries** we perform a standard surrogate test by computing the [p-value](https://en.wikipedia.org/wiki/P-value) w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically `p<0.05`) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time: +=# + +n_surrogates = 1_000 +fig, axs = gridfig(2, 2) +axs[1].title = "linear" +axs[2].title = "nonlinear" + +for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + ## Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change) # ; color = Cycled(j) + lines!(axsig, t_change, pval) # ; color = Cycled(j+2) +end + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar. + +Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section. + +## [Tutorial -- TransitionsInTimeseries.jl] (@id example_fastforward) + +TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go. + +The interface is simple, and directly parallelizes the [Workflow](@ref). It is based on the creation of a [`TransitionsSurrogatesConfig`](@ref), which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate. + +The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +## input timeseries and time +input = x_nl_fluct = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(t, input) +ax.title = "input timeseries" +fig + +#= +To perform all of the above analysis we follow a 2-step process. + +Step 1, we decide what indicators and change metrics to use in [`SlidingWindowConfig`](@ref) and apply those via +a sliding window to the input timeseries using [`transition_metrics`](@ref). +=# + +## These indicators are suitable for Critical Slowing Down +indicators = (var, ar1_whitenoise) + +## use the ridge regression slope for both indicators +change_metrics = RidgeRegressionSlope() + +## choices go into a configuration struct +config = SlidingWindowConfig(indicators, change_metrics; + width_ind = 400, width_cha = 30, whichtime = last) + +## choices are processed +results = estimate_indicator_changes(config, input, t) + +#= +From `result` we can plot the change metric timeseries: +=# + +fig, axs = gridfig(3, 1) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, results.x_change[:, 1]; + label = "var slopes", color = Cycled(3)) +scatter!(axs[3], results.t_change, results.x_change[:, 2]; + label = "ar1 slopes", color = Cycled(4)) +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +Step 2 is to estimate significance using [`SurrogatesConfig`](@ref) +and the function [`estimate_significance!`](@ref). +=# + +signif = SurrogatesSignificance(n = 1000, tail = :right) +flags = significant_transitions(results, signif) + +#= +We can now plot the p-values corresponding to each time series of the change metrics. From the `flags` we can additionally obtain the time points where _both_ indicators show significance, via a simple reduction: +=# + +fig, axs = gridfig(2, 1) +lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1)) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 1]; + label = "var p-values", color = Cycled(3)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 2]; + label = "ar1 p-values", color = Cycled(4)) + +flagsboth = vec(reduce(&, flags; dims = 2)) +vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1)) + +[axislegend(ax) for ax in axs] +[xlims!(ax, 0, 50) for ax in axs] +fig \ No newline at end of file diff --git a/previews/PR54/tutorial/index.html b/previews/PR54/tutorial/index.html new file mode 100644 index 00000000..df98ed92 --- /dev/null +++ b/previews/PR54/tutorial/index.html @@ -0,0 +1,160 @@ + +Tutorial · TransitionsInTimeseries.jl
                                  Edit on GitHub

                                  Tutorial

                                  Workflow

                                  Computing transition indicators consists of the following steps:

                                  1. Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                                  2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                                  3. Computing the changes of the indicator by sliding a window over its timeseries.
                                  4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                                  5. Performing step 2 and 3 for the surrogate timeseries.
                                  6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                                  These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                                  Tutorial – Educational

                                  Raw input data

                                  Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                                  \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                                  with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                                  using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig

                                  Preprocessing

                                  Not part of TransitionsInTimeseries.jl

                                  Any timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                                  The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                                  x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                                  At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                                  Detrending in Julia

                                  Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                                  Indicator timeseries

                                  We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                                  indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector,
+# we obtain the last time step of each window.
+# This therefore only uses information from `k-width+1` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                                  The lines plotted above are the indicator timeseries.

                                  Change metric timeseries

                                  From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                                  change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                                  Timeseries surrogates

                                  As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                                  In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                                  To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                                  # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+
+function gridfig(nrows, ncols)
+    fig = Figure()
+    axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)
+        for j in 1:ncols, i in 1:nrows]
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+fig, axs = gridfig(2, 1)
+lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))
+lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))
+axs[1].title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2))
+lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3))
+axislegend()
+axs[2].title = "change metric"
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                  Quantifying significance

                                  To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                                  n_surrogates = 1_000
+fig, axs = gridfig(2, 2)
+axs[1].title = "linear"
+axs[2].title = "nonlinear"
+
+for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change)   # ; color = Cycled(j)
+    lines!(axsig, t_change, pval)       # ; color = Cycled(j+2)
+end
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                  As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                                  Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                                  Tutorial – TransitionsInTimeseries.jl

                                  TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                                  The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

                                  The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

                                  using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig

                                  To perform all of the above analysis we follow a 2-step process.

                                  Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.

                                  # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = RidgeRegressionSlope()
+
+# choices go into a configuration struct
+config = SlidingWindowConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last)
+
+# choices are processed
+results = estimate_indicator_changes(config, input, t)
                                  IndicatorsChangesResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                                  From result we can plot the change metric timeseries:

                                  fig, axs = gridfig(3, 1)
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, results.x_change[:, 1];
+    label = "var slopes", color = Cycled(3))
+scatter!(axs[3], results.t_change, results.x_change[:, 2];
+    label = "ar1 slopes", color = Cycled(4))
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                  Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.

                                  signif = SurrogatesSignificance(n = 1000, tail = :right)
+flags = significant_transitions(results, signif)
                                  2072×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ ⋮  
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0

                                  We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:

                                  fig, axs = gridfig(2, 1)
+lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1))
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 1];
+    label = "var p-values", color = Cycled(3))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 2];
+    label = "ar1 p-values", color = Cycled(4))
+
+flagsboth = vec(reduce(&, flags; dims = 2))
+vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1))
+
+[axislegend(ax) for ax in axs]
+[xlims!(ax, 0, 50) for ax in axs]
+fig
                                  diff --git a/previews/PR55/api/index.html b/previews/PR55/api/index.html new file mode 100644 index 00000000..ca05ab50 --- /dev/null +++ b/previews/PR55/api/index.html @@ -0,0 +1,22 @@ + +API · TransitionsInTimeseries.jl
                                  Edit on GitHub

                                  API

                                  Main analysis functions

                                  TransitionsInTimeseries.SlidingWindowConfig — Type
                                  SlidingWindowConfig <: IndicatorsChangesConfig
+SlidingWindowConfig(indicators, change_metrics; kwargs...)

                                  A configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:

                                  1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                                  2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                                  indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                                  Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.

                                  The results output corresponding to SlidingWindowConfig is SlidingWindowResults.

                                  Keyword arguments

                                  • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.
                                  • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.
                                  • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:
                                    • last: use the last timepoint of each window
                                    • midpoint: use the mid timepoint of each time window
                                    • first: use first timepoint of each window
                                    In fact, the indicators time vector is computed simply via
                                    t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)
                                    so any other function of the time window may be given to extract the time point itself, such as mean or median.
                                  • T = Float64: Element type of input timeseries to initialize some computations.
                                  source
                                  TransitionsInTimeseries.SegmentedWindowConfig — Type
                                  SegmentedWindowConfig <: IndicatorsChangeConfig
+SegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)

                                  A configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:

                                  1. For each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).
                                  2. For each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d

                                  tseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.

                                  The results output corresponding to SlidingWindowConfig is SegmentedWindowResults.

                                  Keyword arguments

                                  • width_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.
                                  • min_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.
                                  source
                                  TransitionsInTimeseries.estimate_indicator_changes — Function
                                  estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → result

                                  Estimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).

                                  Return the output as subtype of IndicatorsChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                                  source
                                  TransitionsInTimeseries.SlidingWindowResults — Type
                                  SlidingWindowResults <: IndicatorsChangesResults

                                  A struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                                  It has the following fields that the user may access

                                  • x: the input timeseries.

                                  • t: the time vector of the input timeseries.

                                  • x_indicator, the indicator timeseries (matrix with each column one indicator).

                                  • t_indicator, the time vector of the indicator timeseries.

                                  • x_change, the change metric timeseries (matrix with each column one change metric).

                                  • t_change, the time vector of the change metric timeseries.

                                  • config::SlidingWindowConfig, what was used for the analysis.

                                  source
                                  TransitionsInTimeseries.SegmentedWindowResults — Type
                                  SegmentedWindowResults <: IndicatorsChangesResults

                                  A struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                                  It has the following fields that the user may access

                                  • x: the input timeseries.

                                  • t: the time vector of the input timeseries.

                                  • x_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.

                                  • t_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.

                                  • x_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.

                                  • t_change, the time vector of the change metric.

                                  • config::SegmentedWindowConfig, what was used for the analysis.

                                  source

                                  Significance testing

                                  TransitionsInTimeseries.significant_transitions — Function
                                  significant_transitions(res::IndicatorsChangesResults, signif::TransitionsSignificance)

                                  Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.

                                  source
                                  TransitionsInTimeseries.SurrogatesSignificance — Type
                                  SurrogatesSignificance <: TransitionsSignificance
+SurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)

                                  A configuration struct for significance testing significant_transitions using timeseries surrogates.

                                  Keyword arguments

                                  • surromethod = RandomFourier(): method to generate surrogates
                                  • n = 1000: how many surrogates to generate
                                  • rng = Random.default_rng(): random number generator for the surrogates
                                  • p = 0.05: threshold for significance of the p-value
                                  • tail = :both: tail type used, see below

                                  Description

                                  When used with IndicatorsChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

                                  The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in IndicatorsChangesResults.

                                  Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

                                  source
                                  TransitionsInTimeseries.QuantileSignificance — Type
                                  QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance

                                  A configuration struct for significance testing significant_transitions. When used with IndicatorsChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                                  QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

                                  source

                                  Indicators

                                  Value distribution

                                  Statistics.mean — Method
                                  mean(itr)

                                  Compute the mean of all elements in a collection.

                                  Note

                                  If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

                                  Examples

                                  julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
                                  StatsBase.skewness — Function
                                  skewness(v, [wv::AbstractWeights], m=mean(v))

                                  Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                                  StatsBase.kurtosis — Function
                                  kurtosis(v, [wv::AbstractWeights], m=mean(v))

                                  Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                                  Critical Slowing Down

                                  Statistics.var — Method
                                  var(itr; corrected::Bool=true, mean=nothing[, dims])

                                  Compute the sample variance of collection itr.

                                  The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

                                  If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

                                  A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

                                  Note

                                  If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

                                  TransitionsInTimeseries.ar1_whitenoise — Function
                                  ar1_whitenoise(x::AbstractVector)

                                  Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

                                  \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                                  source

                                  Spectrum

                                  TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                                  LowfreqPowerSpectrum(; q_lofreq = 0.1)

                                  Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                                  lfps = precompute( LowfreqPowerSpectrum() )

                                  Keyword arguments:

                                  • q_lofreq: a number between 0 and 1 that characterises which portion of the

                                  frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                                  source

                                  Nonlinear dynamics

                                  Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.

                                  For example, using the permutation entropy as an indicator is as simple as doing

                                  using ComplexityMeasures
+est = OrdinalPatterns(; m = 3) # order 3
+# create a function that given timeseries returns permutation entropy
+indicator = x -> entropy_normalized(est, x)

                                  and giving the created indicator to e.g., SlidingWindowConfig.

                                  Change metrics

                                  Slope

                                  TransitionsInTimeseries.kendalltau — Function
                                  kendalltau(x::AbstractVector)

                                  Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                                  source
                                  TransitionsInTimeseries.spearman — Function
                                  spearman(x::AbstractVector)

                                  Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                                  source

                                  Value distribution differences

                                  TransitionsInTimeseries.difference_of_means — Function
                                  difference_of_means(x::AbstractArray)

                                  Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                                  # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                                  difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                                  source

                                  Make your own indicator/metric!

                                  The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                                  There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:

                                  Missing docstring.

                                  Missing docstring for precompute. Check Documenter's build log for details.

                                  Surrogates

                                  For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                                  Sliding windows

                                  TransitionsInTimeseries.WindowViewer — Type
                                  WindowViewer(x; width, stride)

                                  Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                                  If not given, the keywords width, stride are taken as default_window_width(x) and 1.

                                  source
                                  TransitionsInTimeseries.windowmap — Function
                                  windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                                  A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                                  source

                                  Load data

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+ } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR55/assets/search.js b/previews/PR55/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/previews/PR55/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
                                • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR55/assets/themes/documenter-dark.css 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rgba(255,255,255,0.25)}html.theme--documenter-dark .button.is-white:active,html.theme--documenter-dark .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white{background-color:#fff;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark 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.button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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rgba(245,245,245,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#f5f5f5;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:#292929}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#2f2f2f;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,54,54,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#292929;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#e8e8e8}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#4eb5de;border-color:#4eb5de;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #4eb5de #4eb5de !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#4eb5de;box-shadow:none;color:#4eb5de}html.theme--documenter-dark 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They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found [here](https://www.iceandclimate.nbi.ku.dk/data/) in its raw format. This analysis has already been done in [boers-early-warning-2018](@cite) and we here try to reproduce Figure 2.d-f. + +## Preprocessing NGRIP + +Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps: +1. Load the data, reverse and offset it to have time vector = time before 2000 AD. +2. Filter non-unique points in time and sort the data. +3. Regrid the data from uneven to even sampling. + +The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing. + +### Step 1: +=# + +using DelimitedFiles, Downloads + +function load_ngrip() + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP.csv") + data, labels = readdlm(tmp, header = true) + return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors +end + +t1, x1 = load_ngrip() + +#= +### Step 2 +=# + +uniqueidx(v) = unique(i -> v[i], eachindex(v)) +function keep_unique(t, x) + unique_idx = uniqueidx(t) + return t[unique_idx], x[unique_idx] +end + +function sort_timeseries!(t, x) + p = sortperm(t) + permute!(t, p) + permute!(x, p) + return nothing +end + +t2, x2 = keep_unique(t1, x1) +sort_timeseries!(t2, x2) + +#= +### Step 3 +=# + +using BSplineKit + +function regrid2evensampling(t, x, dt) + itp = BSplineKit.interpolate(t, x, BSplineOrder(4)) + tspan = (ceil(minimum(t)), floor(maximum(t))) + t_even = collect(tspan[1]:dt:tspan[2]) + x_even = itp.(t_even) + return t_even, x_even +end + +dt = 5.0 # dt = 5 yr as in (Boers 2018) +t3, x3 = regrid2evensampling(t2, x2, dt) + +#= +### Step 4 + +For the final step we drop the indices: +=# + +using DSP + +function chebyshev_filter(t, x, fcutoff) + ii = 10 # Chebyshev filtering requires to prune first points of timeseries. + responsetype = Highpass(fcutoff, fs = 1/dt) + designmethod = Chebyshev1(8, 0.05) + r = filt(digitalfilter(responsetype, designmethod), x) + xtrend = x - r + return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end] +end + +fcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018) +t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff) + +#= +Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from [rasmussen-stratigraphic-2014](@cite) (which will soon be available as downloadable): +=# + +using CairoMakie, Loess + +function loess_filter(t, x; span = 0.005) + loessmodel = loess(t, x, span = span) + xtrend = Loess.predict(loessmodel, t) + r = x - xtrend + return t, x, xtrend, r +end + +function kyr_xticks(tticks_yr) + tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)] + return (tticks_yr, tticks_kyr) +end + +function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks) + fig = Figure(resolution = (1600, 1200), fontsize = 24) + + ## Original timeseries with transition marked by vertical lines + ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)", + xaxisposition = :top, xticks = xticks) + lines!(ax1, traw, xraw, color = (:gray70, 0.5)) + lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3) + vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3) + + ## Residual timeseries + ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + lines!(ax2, t, r, color = :gray50, linewidth = 1) + + ## Axes for variance and AC1 timeseries + ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$", + xticks = xticks) + + axs = [ax1, ax2, ax3, ax4] + [xlims!(ax, xlims) for ax in axs] + ylims!(axs[1], (-48, -34)) + rowgap!(fig.layout, 10) + return fig, axs +end + +xlims = (-60e3, -10e3) +xticks = kyr_xticks(-60e3:5e3:5e3) +t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160, + 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703] +tloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +fig + +#= +## Hindcast on NGRIP data + +As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including [boers-early-warning-2018](@cite), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using `SegmentedWindowConfig`, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here: +=# + +using TransitionsInTimeseries, StatsBase +using Random: Xoshiro + +ac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase +indicators = (var, ac1) +change_metrics = RidgeRegressionSlope() +tseg_start = t_rasmussen[1:end-1] .+ 200 +tseg_end = t_rasmussen[2:end] .- 200 +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) # require >=100 data points to estimate change metric +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) + +#= +That's it! We can now visulaise our results with a generic function that we will re-use later: +=# + +function plot_segment_analysis!(axs, results, signif) + (; t_indicator, x_indicator) = results + for k in eachindex(t_indicator) # loop over the segments + for i in axes(signif.pvalues, 2) # loop over the indicators + if !isinf(signif.pvalues[k, i]) # plot if segment long enough + ## Plot indicator timeseries and its linear regression + ti, xi = t_indicator[k], x_indicator[k][:, i] + lines!(axs[i+2], ti, xi, color = Cycled(1)) + m, p = ridgematrix(ti, 0.0) * xi + if signif.pvalues[k, i] < 0.05 + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3) + else + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3) + end + end + end + end +end +plot_segment_analysis!(axs, results, signif) +fig + +#= +In [boers-early-warning-2018](@cite), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in [boers-early-warning-2018](@cite), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of [boers-early-warning-2018](@cite). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media. + +## CSD: only a necessary condition, only in some cases + +For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a **necessary condition** for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is **not a sufficient condition** for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition: +=# + +tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +plot_segment_analysis!(axs, results, signif) +fig + +#= +For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD. + +We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC). + +!!! warning "Degrees of freedom" + These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice. + +!!! info "Future improvement" + Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias. + +## Hindcasting simulated DO-events + +In CLIMBER-X, the EMIC described in [willeit-earth-2022](@cite), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs: +=# + +t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050], + [1, 3500, 4370, 5790, 7200, 8140]] +t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]] +tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]] +tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50] + +figvec = Figure[] + +for j in 1:2 + ## Download the data and perform loess filtering on it + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" * + "master/timeseries/climberx-do$(j)-omaxa.csv") + data = readdlm(tmp) + tcx, xcx = data[1, 1000:end], data[2, 1000:end] + t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02) + + ## Initialize figure + xlims = (0, last(tcx)) + xticks = kyr_xticks(xlims[1]:1e3:xlims[2]) + fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks) + ylims!(axs[1], (5, 40)) + axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$" + + ## Run sliding analysis and update figure with results + dt = mean(diff(tcx)) + config = SegmentedWindowConfig( + indicators, change_metrics, tseg_start[j], tseg_end[j], + whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100) + results = estimate_indicator_changes(config, r, t) + signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995)) + flags = significant_transitions(results, signif) + + plot_segment_analysis!(axs, results, signif) + vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3) + push!(figvec, fig) +end +figvec[1] + +#= +It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case: +=# + +figvec[2] + +#= +Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience. +=# \ No newline at end of file diff --git a/previews/PR55/examples/do-events/index.html b/previews/PR55/examples/do-events/index.html new file mode 100644 index 00000000..5f61c606 --- /dev/null +++ b/previews/PR55/examples/do-events/index.html @@ -0,0 +1,191 @@ + +Dansgaard-Oescher events and Critical Slowing Down · TransitionsInTimeseries.jl
                                  Edit on GitHub

                                  Dansgaard-Oescher events and Critical Slowing Down

                                  The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.

                                  Preprocessing NGRIP

                                  Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:

                                  1. Load the data, reverse and offset it to have time vector = time before 2000 AD.
                                  2. Filter non-unique points in time and sort the data.
                                  3. Regrid the data from uneven to even sampling.

                                  The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.

                                  Step 1:

                                  using DelimitedFiles, Downloads
+
+function load_ngrip()
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+        "master/timeseries/NGRIP.csv")
+    data, labels = readdlm(tmp, header = true)
+    return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors
+end
+
+t1, x1 = load_ngrip()
                                  ([-59944.5, -59939.6, -59935.9, -59930.5, -59925.0, -59919.0, -59914.3, -59909.4, -59904.5, -59899.7  …  -27.40000000000009, -27.40000000000009, -27.299999999999955, -27.299999999999955, -27.200000000000045, -27.09999999999991, -27.09999999999991, -27.0, -26.90000000000009, -26.799999999999955], [-43.52, -42.94, -42.13, -40.04, -41.09, -43.57, -42.28, -41.2, -44.07, -44.53  …  -35.29, -35.18, -35.51, -36.03, -36.52, -37.12, -37.41, -37.21, -36.62, -35.52])

                                  Step 2

                                  uniqueidx(v) = unique(i -> v[i], eachindex(v))
+function keep_unique(t, x)
+    unique_idx = uniqueidx(t)
+    return t[unique_idx], x[unique_idx]
+end
+
+function sort_timeseries!(t, x)
+    p = sortperm(t)
+    permute!(t, p)
+    permute!(x, p)
+    return nothing
+end
+
+t2, x2 = keep_unique(t1, x1)
+sort_timeseries!(t2, x2)

                                  Step 3

                                  using BSplineKit
+
+function regrid2evensampling(t, x, dt)
+    itp = BSplineKit.interpolate(t, x, BSplineOrder(4))
+    tspan = (ceil(minimum(t)), floor(maximum(t)))
+    t_even = collect(tspan[1]:dt:tspan[2])
+    x_even = itp.(t_even)
+    return t_even, x_even
+end
+
+dt = 5.0        # dt = 5 yr as in (Boers 2018)
+t3, x3 = regrid2evensampling(t2, x2, dt)
                                  ([-59944.0, -59939.0, -59934.0, -59929.0, -59924.0, -59919.0, -59914.0, -59909.0, -59904.0, -59899.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-43.445268010797946, -42.85408835164853, -41.357360665158936, -39.9365468206892, -41.60554051352076, -43.57000000000001, -42.145558689100454, -41.33160823883399, -44.273597725729985, -44.4622612304012  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46])

                                  Step 4

                                  For the final step we drop the indices:

                                  using DSP
+
+function chebyshev_filter(t, x, fcutoff)
+    ii = 10             # Chebyshev filtering requires to prune first points of timeseries.
+    responsetype = Highpass(fcutoff, fs = 1/dt)
+    designmethod = Chebyshev1(8, 0.05)
+    r = filt(digitalfilter(responsetype, designmethod), x)
+    xtrend = x - r
+    return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]
+end
+
+fcutoff = 0.95 * 0.01   # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)
+t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)
                                  ([-59899.0, -59894.0, -59889.0, -59884.0, -59879.0, -59874.0, -59869.0, -59864.0, -59859.0, -59854.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-44.4622612304012, -44.264401428210874, -44.02956767939856, -42.29334237357212, -42.594341674200344, -41.09704877854712, -40.39837540966913, -44.369155046413255, -42.74492506508012, -43.737014520530145  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46], [-43.89287787976461, -48.663435112414156, -51.31169981050155, -51.269094666491796, -49.90310432724566, -47.721430022512344, -44.36050569418247, -43.87556827410048, -43.57802291229893, -41.36870967826094  …  -34.81349114528442, -36.01634453179986, -36.150446802907226, -36.37595639697143, -35.96843653265903, -33.899634243732976, -32.49784036951535, -33.06575312724142, -34.07956188682297, -34.4079080530096], [-0.5693833506365866, 4.399033684203284, 7.282132131102991, 8.975752292919669, 7.308762653045311, 6.624381243965224, 3.9621302845133433, -0.493586772312777, 0.8330978472188112, -2.368304842269206  …  -0.30650885471557926, -0.17365546820014846, 1.0104468029072273, -0.684043603028572, 1.0384365326590237, -0.3303657562670192, -1.0321596304846505, -2.0242468727585807, 0.07956188682296689, -0.05209194699039831])

                                  Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):

                                  using CairoMakie, Loess
+
+function loess_filter(t, x; span = 0.005)
+    loessmodel = loess(t, x, span = span)
+    xtrend = Loess.predict(loessmodel, t)
+    r = x - xtrend
+    return t, x, xtrend, r
+end
+
+function kyr_xticks(tticks_yr)
+    tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)]
+    return (tticks_yr, tticks_kyr)
+end
+
+function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)
+    fig = Figure(resolution = (1600, 1200), fontsize = 24)
+
+    # Original timeseries with transition marked by vertical lines
+    ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)",
+        xaxisposition = :top, xticks = xticks)
+    lines!(ax1, traw, xraw, color = (:gray70, 0.5))
+    lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)
+    vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)
+
+    # Residual timeseries
+    ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    lines!(ax2, t, r, color = :gray50, linewidth = 1)
+
+    # Axes for variance and AC1 timeseries
+    ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$",
+        xticks = xticks)
+
+    axs = [ax1, ax2, ax3, ax4]
+    [xlims!(ax, xlims) for ax in axs]
+    ylims!(axs[1], (-48, -34))
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+
+xlims = (-60e3, -10e3)
+xticks = kyr_xticks(-60e3:5e3:5e3)
+t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,
+                38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]
+tloess, _, xloess, rloess = loess_filter(t3, x3)    # loess-filtered signal for visualization
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+fig

                                  Hindcast on NGRIP data

                                  As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:

                                  using TransitionsInTimeseries, StatsBase
+using Random: Xoshiro
+
+ac1(x) = sum(autocor(x, [1]))   # AC1 from StatsBase
+indicators = (var, ac1)
+change_metrics = RidgeRegressionSlope()
+tseg_start = t_rasmussen[1:end-1] .+ 200
+tseg_end = t_rasmussen[2:end] .- 200
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)        # require >=100 data points to estimate change metric
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
                                  18×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 1  0
+ 1  1
+ 1  1
+ 1  1
+ 0  0
+ 1  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 1  0

                                  That's it! We can now visulaise our results with a generic function that we will re-use later:

                                  function plot_segment_analysis!(axs, results, signif)
+    (; t_indicator, x_indicator) = results
+    for k in eachindex(t_indicator)             # loop over the segments
+        for i in axes(signif.pvalues, 2)        # loop over the indicators
+            if !isinf(signif.pvalues[k, i])     # plot if segment long enough
+                # Plot indicator timeseries and its linear regression
+                ti, xi = t_indicator[k], x_indicator[k][:, i]
+                lines!(axs[i+2], ti, xi, color = Cycled(1))
+                m, p = ridgematrix(ti, 0.0) * xi
+                if signif.pvalues[k, i] < 0.05
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)
+                else
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)
+                end
+            end
+        end
+    end
+end
+plot_segment_analysis!(axs, results, signif)
+fig

                                  In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.

                                  CSD: only a necessary condition, only in some cases

                                  For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:

                                  tseg_end = t_rasmussen[2:end] .- 700    # stop analysis 500 years earlier than before
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+plot_segment_analysis!(axs, results, signif)
+fig

                                  For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD.

                                  We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).

                                  Degrees of freedom

                                  These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.

                                  Future improvement

                                  Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.

                                  Hindcasting simulated DO-events

                                  In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:

                                  t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],
+                 [1, 3500, 4370, 5790, 7200, 8140]]
+t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]
+tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]
+tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]
+
+figvec = Figure[]
+
+for j in 1:2
+    # Download the data and perform loess filtering on it
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" *
+        "master/timeseries/climberx-do$(j)-omaxa.csv")
+    data = readdlm(tmp)
+    tcx, xcx = data[1, 1000:end], data[2, 1000:end]
+    t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)
+
+    # Initialize figure
+    xlims = (0, last(tcx))
+    xticks = kyr_xticks(xlims[1]:1e3:xlims[2])
+    fig, axs = plot_do(tcx, xcx,  t, xtrend, t, r, t_transitions[j], extrema(t), xticks)
+    ylims!(axs[1], (5, 40))
+    axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$"
+
+    # Run sliding analysis and update figure with results
+    dt = mean(diff(tcx))
+    config = SegmentedWindowConfig(
+        indicators, change_metrics, tseg_start[j], tseg_end[j],
+        whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)
+    results = estimate_indicator_changes(config, r, t)
+    signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))
+    flags = significant_transitions(results, signif)
+
+    plot_segment_analysis!(axs, results, signif)
+    vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)
+    push!(figvec, fig)
+end
+figvec[1]

                                  It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:

                                  figvec[2]

                                  Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.

                                  diff --git a/previews/PR55/examples/logistic.jl b/previews/PR55/examples/logistic.jl new file mode 100644 index 00000000..a2894fbd --- /dev/null +++ b/previews/PR55/examples/logistic.jl @@ -0,0 +1,203 @@ +# # Permutation entropy for dynamic regime changes + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ## Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +## time-dependent logistic map, so that the `r` parameter increases with time +r1 = 3.83 +r2 = 3.86 +N = 2000 +rs = range(r1, r2; length = N) + +function logistic_drifting_rule(u, rs, n) + r = rs[n+1] # time is `n`, starting from 0 + return SVector(r*u[1]*(1 - u[1])) +end + +ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs) +x = trajectory(ds, N-1)[1][:, 1] + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ## Using a simpler change metric + +# Now, let's compute and various indicators and their changes, +# focusing on the permutation entropy as an indicator. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries, ComplexityMeasures + +function permutation_entropy(m) + est = SymbolicPermutation(; m) # order 3 + indicator = x -> entropy_normalized(est, x) + return indicator +end + +indicators = (var, ar1_whitenoise, permutation_entropy(4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as stride half the window width +metric = difference_of_means + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = SlidingWindowConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = estimate_indicator_changes(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + if i < 3 + hidexdecorations!(ax; grid = false) + else + ax.xlabel = "r (time)" + end + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ## Significance via random Fourier surrogates + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +using Random: Xoshiro +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42), + ) + flags = significant_transitions(results, signif) + + ## and also plot the flags with same color + for (i, indicator) in enumerate(indicators) + ## To make things visually clear, we will also plot some example surrogate + ## timeseries for each indicator and change metric pair + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surromethod) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric, p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1) + end + ## Plot the flags as vertical dashed lines + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = color, linestyle = :dash, linewidth = 3 + ) + end + ## add a title to the figure with how we estimate significance + content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod))) +end + +surromethod = RandomFourier() +overplot_surrogate_significance!(fig, surromethod) + +fig + +# ## Different surrogates +# %% #src +# Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# highlighting the _local_ dynamics or information that preserves the local +# changes of dynamical behavior. + +# A surrogate type that does a better job in preserving local sharp +# changes in the timeseries (and hence provides **stricter** +# surrogate-based significance) is for example `RelativePartialRandomization`. + +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = RelativePartialRandomization(0.25) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "gray") +fig + +# Our results have improved. In the permutation entropy, we see only two +# transitions detected as significant, which is correct: only two +# real dynamical transitions exist in the data. +# In the other two indicators we also see fewer transitions, but as we +# have already discussed, no results with the other indicators should +# be taken into meaningful consideration, as these indicators +# are simply inappropriate for what we are looking for here. + +# ## Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be less strict and more simple with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`SigmaSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation. + +fig = plot_change_metrics() +flags = significant_transitions(results, SigmaSignificance(factor = 5.0)) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = Cycled(3), linestyle = :dash, linewidth = 3 + ) +end +content(fig[1, 1]).title = "significance from std" +fig diff --git a/previews/PR55/examples/logistic/index.html b/previews/PR55/examples/logistic/index.html new file mode 100644 index 00000000..7427887f --- /dev/null +++ b/previews/PR55/examples/logistic/index.html @@ -0,0 +1,128 @@ + +Permutation entropy for dynamic regime changes · TransitionsInTimeseries.jl
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                                  Permutation entropy for dynamic regime changes

                                  Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.

                                  This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.

                                  Logistic map timeseries

                                  A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map

                                  using DynamicalSystemsBase
+using CairoMakie
+
+# time-dependent logistic map, so that the `r` parameter increases with time
+r1 = 3.83
+r2 = 3.86
+N = 2000
+rs = range(r1, r2; length = N)
+
+function logistic_drifting_rule(u, rs, n)
+    r = rs[n+1] # time is `n`, starting from 0
+    return SVector(r*u[1]*(1 - u[1]))
+end
+
+ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)
+x = trajectory(ds, N-1)[1][:, 1]
                                  2000-element Vector{Float64}:
+ 0.5
+ 0.9575
+ 0.15585767321160574
+ 0.5039019545917718
+ 0.9574529422362281
+ 0.15602441103002537
+ 0.5043473227583317
+ 0.9574501255597653
+ 0.1560361152301728
+ 0.5043840906474082
+ ⋮
+ 0.4253904015445437
+ 0.9434836074964187
+ 0.20581843730311683
+ 0.6309301050251992
+ 0.8988117342940414
+ 0.3510584545931264
+ 0.8793611090928393
+ 0.40948549063776396
+ 0.9333718681550522

                                  Plot it, using as time the parameter value (they coincide)

                                  fig, ax = lines(rs, x; linewidth = 0.5)
+ax.xlabel = "r (time)"
+ax.ylabel = "x"
+fig

                                  In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.

                                  Using a simpler change metric

                                  Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.

                                  using TransitionsInTimeseries, ComplexityMeasures
+
+function permutation_entropy(m)
+    est = SymbolicPermutation(; m) # order 3
+    indicator = x -> entropy_normalized(est, x)
+    return indicator
+end
+
+indicators = (var, ar1_whitenoise, permutation_entropy(4))
+indistrings = ("var", "ar1", "pe")
                                  ("var", "ar1", "pe")

                                  In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width

                                  metric = difference_of_means
+
+width_ind = N÷100
+width_cha = 20
+stride_cha = 10
+
+config = SlidingWindowConfig(indicators, metric;
+    width_ind, width_cha, stride_cha,
+)
+
+results = estimate_indicator_changes(config, x, rs)
                                  IndicatorsChangesResults
+ input timeseries:              2000-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise, Symbol("#1")]
+ indicator (window, stride):    (20, 1)
+ change metrics:                [:difference_of_means]
+ change metric (window, stride): (20, 10)
+

                                  Let's now plot the change metrics of the indicators

                                  function plot_change_metrics()
+    fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),))
+    hidexdecorations!(ax; grid = false)
+    # plot all change metrics
+    for (i, c) in enumerate(eachcol(results.x_change))
+        ax, = scatterlines(fig[i+1, 1], results.t_change, c;
+            axis = (ylabel = indistrings[i],), label = "input"
+        )
+        if i < 3
+            hidexdecorations!(ax; grid = false)
+        else
+            ax.xlabel = "r (time)"
+        end
+    end
+    return fig
+end
+
+fig = plot_change_metrics()

                                  We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)

                                  Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.

                                  Significance via random Fourier surrogates

                                  One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.

                                  Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!

                                  surromethod = RandomFourier()
+
+# Define a function because we will re-use later
+using Random: Xoshiro
+function overplot_surrogate_significance!(fig, surromethod, color = "black")
+
+    signif = SurrogatesSignificance(;
+        n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),
+    )
+    flags = significant_transitions(results, signif)
+
+    # and also plot the flags with same color
+    for (i, indicator) in enumerate(indicators)
+        # To make things visually clear, we will also plot some example surrogate
+        # timeseries for each indicator and change metric pair
+        for _ in 1:10
+            s = TimeseriesSurrogates.surrogate(x, surromethod)
+            p = windowmap(indicator, s; width = width_ind)
+            q = windowmap(metric, p; width = width_cha, stride = stride_cha)
+            lines!(fig[i+1, 1], results.t_change, q;  color = (color, 0.2), linewidth = 1)
+        end
+        # Plot the flags as vertical dashed lines
+        vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+            color = color, linestyle = :dash, linewidth = 3
+        )
+    end
+    # add a title to the figure with how we estimate significance
+    content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod)))
+end
+
+surromethod = RandomFourier()
+overplot_surrogate_significance!(fig, surromethod)
+
+fig

                                  Different surrogates

                                  Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

                                  A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

                                  A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

                                  surromethod = RelativePartialRandomization(0.25)
+fig = plot_change_metrics()
+overplot_surrogate_significance!(fig, surromethod, "gray")
+fig

                                  Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

                                  Simpler Significance

                                  Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

                                  fig = plot_change_metrics()
+flags = significant_transitions(results, SigmaSignificance(factor = 5.0))
+
+# Plot the flags
+for (i, indicator) in enumerate(indicators)
+    vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+        color = Cycled(3), linestyle = :dash, linewidth = 3
+    )
+end
+content(fig[1, 1]).title = "significance from std"
+fig
                                  diff --git a/previews/PR55/index.html b/previews/PR55/index.html new file mode 100644 index 00000000..864f0a61 --- /dev/null +++ b/previews/PR55/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
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                                  TransitionsInTimeseries.jl

                                  TransitionsInTimeseries.jl

                                  TransitionsInTimeseries — Module

                                  TransitionsInTimeseries.jl

                                  CI codecov Package Downloads

                                  A Julia package for estimating transitions (from one dynamic regime or stable state to another) in timeseries and testing the statistical significance of found transitions. It integrates with the entire Julia ecosystem of timeseries analysis, and hence offers thousands of metrics that can indicate transitions right out of the box. It also offers a variety of analysis pipelines for identifying transitions and a variety of statistical pipelines for testing for significance.

                                  In contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:

                                  1. Add new indicators that work with the existing analysis pipelines for finding transitions
                                  2. Add new analysis pipelines for finding transitions
                                  3. Add new ways for testing whether already found transitions are significant

                                  This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

                                  add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

                                  All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                                  Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                                  source
                                  Star us on GitHub!

                                  If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                                  Content

                                  Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                                  • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                                  • Makes the surrogate analysis to test for significance under the hub.
                                  • Can be easily extended by any user without touching the source code.
                                  • Reduces the programming overhead for any researcher willing to benchmark new methods.
                                  • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                                  • Increases trustworthiness thanks to a large test suite.
                                  Similar projects

                                  An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                                  Approaches

                                  Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                                  diff --git a/previews/PR55/refs.bib b/previews/PR55/refs.bib new file mode 100644 index 00000000..8010a9d3 --- /dev/null +++ b/previews/PR55/refs.bib @@ -0,0 +1,54 @@ + +@article{willeit-earth-2022, + title = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1: {Climate} model description and validation​​​​​​​​​​​​​​}, + volume = {15}, + issn = {1991-9603}, + shorttitle = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1}, + url = {https://gmd.copernicus.org/articles/15/5905/2022/}, + doi = {10.5194/gmd-15-5905-2022}, + abstract = {The newly developed fast Earth system model CLIMBER-X is presented. The climate component of CLIMBER-X consists of a 2.5-D semi-empirical statistical–dynamical atmosphere model, a 3-D frictional–geostrophic ocean model, a dynamic–thermodynamic sea ice model and a land surface model. All the model components are discretized on a regular lat–long grid with a horizontal resolution of 5 ◦ × 5 ◦. The model has a throughput of ∼ 10 000 simulation years per day on a single node with 16 CPUs on a high-performance computer and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to {\textgreater} 100 000 years. A comprehensive evaluation of the model performance for the present day and the historical period shows that CLIMBER-X is capable of realistically reproducing many observed climate characteristics, with results that generally lie within the range of state-of-theart general circulation models. The analysis of model performance is complemented by a thorough assessment of climate feedbacks and model sensitivities to changes in external forcings and boundary conditions. Limitations and applicability of the model are critically discussed. CLIMBER-X also includes a detailed representation of the global carbon cycle and is coupled to an ice sheet model, which will be described in separate papers. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.}, + language = {en}, + number = {14}, + urldate = {2022-08-11}, + journal = {Geoscientific Model Development}, + author = {Willeit, Matteo and Ganopolski, Andrey and Robinson, Alexander and Edwards, Neil R.}, + month = jul, + year = {2022}, + pages = {5905--5948}, + file = {Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:/home/jan/Zotero/storage/75NKS975/Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:application/pdf}, +} + +@article{boers-early-warning-2018, + title = {Early-warning signals for {Dansgaard}-{Oeschger} events in a high-resolution ice core record}, + volume = {9}, + issn = {2041-1723}, + url = {http://www.nature.com/articles/s41467-018-04881-7}, + doi = {10.1038/s41467-018-04881-7}, + language = {en}, + number = {1}, + urldate = {2022-10-28}, + journal = {Nature Communications}, + author = {Boers, Niklas}, + month = dec, + year = {2018}, + pages = {2556}, + file = {Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:/home/jan/Zotero/storage/DS97Z9UC/Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:application/pdf}, +} + +@article{rasmussen-stratigraphic-2014, + title = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records: refining and extending the {INTIMATE} event stratigraphy}, + volume = {106}, + issn = {02773791}, + shorttitle = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0277379114003485}, + doi = {10.1016/j.quascirev.2014.09.007}, + abstract = {Due to their outstanding resolution and well-constrained chronologies, Greenland ice-core records provide a master record of past climatic changes throughout the Last InterglacialeGlacial cycle in the North Atlantic region. As part of the INTIMATE (INTegration of Ice-core, MArine and TErrestrial records) project, protocols have been proposed to ensure consistent and robust correlation between different records of past climate. A key element of these protocols has been the formal definition and ordinal numbering of the sequence of Greenland Stadials (GS) and Greenland Interstadials (GI) within the most recent glacial period. The GS and GI periods are the Greenland expressions of the characteristic DansgaardeOeschger events that represent cold and warm phases of the North Atlantic region, respectively. We present here a more detailed and extended GS/GI template for the whole of the Last Glacial period. It is based on a synchronization of the NGRIP, GRIP, and GISP2 ice-core records that allows the parallel analysis of all three records on a common time scale. The boundaries of the GS and GI periods are defined based on a combination of stable-oxygen isotope ratios of the ice (d18O, reflecting mainly local temperature) and calcium ion concentrations (reflecting mainly atmospheric dust loading) measured in the ice. The data not only resolve the well-known sequence of DansgaardeOeschger events that were first defined and numbered in the ice-core records more than two decades ago, but also better resolve a number of short-lived climatic oscillations, some defined here for the first time. Using this revised scheme, we propose a consistent approach for discriminating and naming all the significant abrupt climatic events of the Last Glacial period that are represented in the Greenland ice records. The final product constitutes an extended and better resolved Greenland stratotype sequence, against which other proxy records can be compared and correlated. It also provides a more secure basis for investigating the dynamics and fundamental causes of these climatic perturbations.}, + language = {en}, + urldate = {2023-10-04}, + journal = {Quaternary Science Reviews}, + author = {Rasmussen, Sune O. and Bigler, Matthias and Blockley, Simon P. and Blunier, Thomas and Buchardt, Susanne L. and Clausen, Henrik B. and Cvijanovic, Ivana and Dahl-Jensen, Dorthe and Johnsen, Sigfus J. and Fischer, Hubertus and Gkinis, Vasileios and Guillevic, Myriam and Hoek, Wim Z. and Lowe, J. John and Pedro, Joel B. and Popp, Trevor and Seierstad, Inger K. and Steffensen, Jørgen Peder and Svensson, Anders M. and Vallelonga, Paul and Vinther, Bo M. and Walker, Mike J.C. and Wheatley, Joe J. and Winstrup, Mai}, + month = dec, + year = {2014}, + pages = {14--28}, + file = {Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:/home/jan/Zotero/storage/VSUTVWPN/Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:application/pdf}, +} diff --git a/previews/PR55/refs/index.html b/previews/PR55/refs/index.html new file mode 100644 index 00000000..8d79a0c8 --- /dev/null +++ b/previews/PR55/refs/index.html @@ -0,0 +1,9 @@ + +References · TransitionsInTimeseries.jl
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                                  References

                                  diff --git a/previews/PR55/search/index.html b/previews/PR55/search/index.html new file mode 100644 index 00000000..8e24e881 --- /dev/null +++ b/previews/PR55/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

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                                    diff --git a/previews/PR55/search_index.js b/previews/PR55/search_index.js new file mode 100644 index 00000000..0396ea47 --- /dev/null +++ b/previews/PR55/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"IndicatorsChangesConfig\nSlidingWindowConfig\nSegmentedWindowConfig\nestimate_indicator_changes\nIndicatorsChangesResults\nSlidingWindowResults\nSegmentedWindowResults","category":"page"},{"location":"api/#TransitionsInTimeseries.IndicatorsChangesConfig","page":"API","title":"TransitionsInTimeseries.IndicatorsChangesConfig","text":"IndicatorsChangesConfig\n\nSupertype used to define how indicators and their changes are estimated in estimate_indicator_changes. Valid subtypes are:\n\nSlidingWindowConfig.\nSegmentedWindowConfig.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowConfig","page":"API","title":"TransitionsInTimeseries.SlidingWindowConfig","text":"SlidingWindowConfig <: IndicatorsChangesConfig\nSlidingWindowConfig(indicators, change_metrics; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.\n\nThe results output corresponding to SlidingWindowConfig is SlidingWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowConfig","page":"API","title":"TransitionsInTimeseries.SegmentedWindowConfig","text":"SegmentedWindowConfig <: IndicatorsChangeConfig\nSegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:\n\nFor each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).\nFor each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d\n\ntseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.\n\nThe results output corresponding to SlidingWindowConfig is SegmentedWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.\nmin_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.estimate_indicator_changes","page":"API","title":"TransitionsInTimeseries.estimate_indicator_changes","text":"estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → result\n\nEstimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).\n\nReturn the output as subtype of IndicatorsChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.IndicatorsChangesResults","page":"API","title":"TransitionsInTimeseries.IndicatorsChangesResults","text":"IndicatorsChangesResults\n\nSupertype used to gather results of estimate_indicator_changes. The concrete subtype instances are described in the docstrings of configuration types.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowResults","page":"API","title":"TransitionsInTimeseries.SlidingWindowResults","text":"SlidingWindowResults <: IndicatorsChangesResults\n\nA struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nconfig::SlidingWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowResults","page":"API","title":"TransitionsInTimeseries.SegmentedWindowResults","text":"SegmentedWindowResults <: IndicatorsChangesResults\n\nA struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.\nt_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.\nx_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.\nt_change, the time vector of the change metric.\nconfig::SegmentedWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"significant_transitions\nTransitionsSignificance\nSurrogatesSignificance\nQuantileSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::IndicatorsChangesResults, signif::TransitionsSignificance)\n\nEstimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.TransitionsSignificance","page":"API","title":"TransitionsInTimeseries.TransitionsSignificance","text":"TransitionsSignificance\n\nSupertype used to test for significance in significant_transitions. Valid subtypes are:\n\nSurrogatesSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: TransitionsSignificance\nSurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)\n\nA configuration struct for significance testing significant_transitions using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\n\nDescription\n\nWhen used with IndicatorsChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in IndicatorsChangesResults.\n\nNote that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance\n\nA configuration struct for significance testing significant_transitions. When used with IndicatorsChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\nQuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.","category":"page"},{"location":"api/","page":"API","title":"API","text":"For example, using the permutation entropy as an indicator is as simple as doing","category":"page"},{"location":"api/","page":"API","title":"API","text":"using ComplexityMeasures\nest = OrdinalPatterns(; m = 3) # order 3\n# create a function that given timeseries returns permutation entropy\nindicator = x -> entropy_normalized(est, x)","category":"page"},{"location":"api/","page":"API","title":"API","text":"and giving the created indicator to e.g., SlidingWindowConfig.","category":"page"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"EditURL = \"do-events.jl\"","category":"page"},{"location":"examples/do-events/#Dansgaard-Oescher-events-and-Critical-Slowing-Down","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The delta^18O timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.","category":"page"},{"location":"examples/do-events/#Preprocessing-NGRIP","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Preprocessing NGRIP","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Load the data, reverse and offset it to have time vector = time before 2000 AD.\nFilter non-unique points in time and sort the data.\nRegrid the data from uneven to even sampling.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The time and delta^18O vectors resulting from the i-th preprocessing step are respectively called t_i and x_i. The final step consists in obtaining a residual r, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.","category":"page"},{"location":"examples/do-events/#Step-1:","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 1:","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DelimitedFiles, Downloads\n\nfunction load_ngrip()\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP.csv\")\n data, labels = readdlm(tmp, header = true)\n return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors\nend\n\nt1, x1 = load_ngrip()","category":"page"},{"location":"examples/do-events/#Step-2","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 2","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"uniqueidx(v) = unique(i -> v[i], eachindex(v))\nfunction keep_unique(t, x)\n unique_idx = uniqueidx(t)\n return t[unique_idx], x[unique_idx]\nend\n\nfunction sort_timeseries!(t, x)\n p = sortperm(t)\n permute!(t, p)\n permute!(x, p)\n return nothing\nend\n\nt2, x2 = keep_unique(t1, x1)\nsort_timeseries!(t2, x2)","category":"page"},{"location":"examples/do-events/#Step-3","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 3","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using BSplineKit\n\nfunction regrid2evensampling(t, x, dt)\n itp = BSplineKit.interpolate(t, x, BSplineOrder(4))\n tspan = (ceil(minimum(t)), floor(maximum(t)))\n t_even = collect(tspan[1]:dt:tspan[2])\n x_even = itp.(t_even)\n return t_even, x_even\nend\n\ndt = 5.0 # dt = 5 yr as in (Boers 2018)\nt3, x3 = regrid2evensampling(t2, x2, dt)","category":"page"},{"location":"examples/do-events/#Step-4","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 4","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the final step we drop the indices:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DSP\n\nfunction chebyshev_filter(t, x, fcutoff)\n ii = 10 # Chebyshev filtering requires to prune first points of timeseries.\n responsetype = Highpass(fcutoff, fs = 1/dt)\n designmethod = Chebyshev1(8, 0.05)\n r = filt(digitalfilter(responsetype, designmethod), x)\n xtrend = x - r\n return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]\nend\n\nfcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)\nt, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using CairoMakie, Loess\n\nfunction loess_filter(t, x; span = 0.005)\n loessmodel = loess(t, x, span = span)\n xtrend = Loess.predict(loessmodel, t)\n r = x - xtrend\n return t, x, xtrend, r\nend\n\nfunction kyr_xticks(tticks_yr)\n tticks_kyr = [\"$t\" for t in Int.(tticks_yr ./ 1e3)]\n return (tticks_yr, tticks_kyr)\nend\n\nfunction plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)\n fig = Figure(resolution = (1600, 1200), fontsize = 24)\n\n # Original timeseries with transition marked by vertical lines\n ax1 = Axis(fig[1, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"$\\delta^{18}$O (permil)\",\n xaxisposition = :top, xticks = xticks)\n lines!(ax1, traw, xraw, color = (:gray70, 0.5))\n lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)\n vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)\n\n # Residual timeseries\n ax2 = Axis(fig[2, 1], ylabel = L\"Residual $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n lines!(ax2, t, r, color = :gray50, linewidth = 1)\n\n # Axes for variance and AC1 timeseries\n ax3 = Axis(fig[3, 1], ylabel = L\"Variance $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n ax4 = Axis(fig[4, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"Lag-1 autocor. $\\,$\",\n xticks = xticks)\n\n axs = [ax1, ax2, ax3, ax4]\n [xlims!(ax, xlims) for ax in axs]\n ylims!(axs[1], (-48, -34))\n rowgap!(fig.layout, 10)\n return fig, axs\nend\n\nxlims = (-60e3, -10e3)\nxticks = kyr_xticks(-60e3:5e3:5e3)\nt_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,\n 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]\ntloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nfig","category":"page"},{"location":"examples/do-events/#Hindcast-on-NGRIP-data","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcast on NGRIP data","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using TransitionsInTimeseries, StatsBase\nusing Random: Xoshiro\n\nac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase\nindicators = (var, ac1)\nchange_metrics = RidgeRegressionSlope()\ntseg_start = t_rasmussen[1:end-1] .+ 200\ntseg_end = t_rasmussen[2:end] .- 200\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100) # require >=100 data points to estimate change metric\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"That's it! We can now visulaise our results with a generic function that we will re-use later:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"function plot_segment_analysis!(axs, results, signif)\n (; t_indicator, x_indicator) = results\n for k in eachindex(t_indicator) # loop over the segments\n for i in axes(signif.pvalues, 2) # loop over the indicators\n if !isinf(signif.pvalues[k, i]) # plot if segment long enough\n # Plot indicator timeseries and its linear regression\n ti, xi = t_indicator[k], x_indicator[k][:, i]\n lines!(axs[i+2], ti, xi, color = Cycled(1))\n m, p = ridgematrix(ti, 0.0) * xi\n if signif.pvalues[k, i] < 0.05\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)\n else\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)\n end\n end\n end\n end\nend\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.","category":"page"},{"location":"examples/do-events/#CSD:-only-a-necessary-condition,-only-in-some-cases","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"CSD: only a necessary condition, only in some cases","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential U, which defines the deterministic term f = -U of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100)\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that \"resilience-loss indicators\" is a more accurate name than \"early-warning signals\" when using CSD.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"We draw attention upon the fact that the delta^18O timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"warning: Degrees of freedom\nThese sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"info: Future improvement\nSupporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.","category":"page"},{"location":"examples/do-events/#Hindcasting-simulated-DO-events","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcasting simulated DO-events","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],\n [1, 3500, 4370, 5790, 7200, 8140]]\nt_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]\ntseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]\ntseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]\n\nfigvec = Figure[]\n\nfor j in 1:2\n # Download the data and perform loess filtering on it\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\" *\n \"master/timeseries/climberx-do$(j)-omaxa.csv\")\n data = readdlm(tmp)\n tcx, xcx = data[1, 1000:end], data[2, 1000:end]\n t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)\n\n # Initialize figure\n xlims = (0, last(tcx))\n xticks = kyr_xticks(xlims[1]:1e3:xlims[2])\n fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks)\n ylims!(axs[1], (5, 40))\n axs[1].ylabel = L\"Max. Atlantic overturning (Sv) $\\,$\"\n\n # Run sliding analysis and update figure with results\n dt = mean(diff(tcx))\n config = SegmentedWindowConfig(\n indicators, change_metrics, tseg_start[j], tseg_end[j],\n whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)\n results = estimate_indicator_changes(config, r, t)\n signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))\n flags = significant_transitions(results, signif)\n\n plot_segment_analysis!(axs, results, signif)\n vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)\n push!(figvec, fig)\nend\nfigvec[1]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"figvec[2]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"EditURL = \"logistic.jl\"","category":"page"},{"location":"examples/logistic/#Permutation-entropy-for-dynamic-regime-changes","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.","category":"page"},{"location":"examples/logistic/#Logistic-map-timeseries","page":"Permutation entropy for dynamic regime changes","title":"Logistic map timeseries","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using DynamicalSystemsBase\nusing CairoMakie\n\n# time-dependent logistic map, so that the `r` parameter increases with time\nr1 = 3.83\nr2 = 3.86\nN = 2000\nrs = range(r1, r2; length = N)\n\nfunction logistic_drifting_rule(u, rs, n)\n r = rs[n+1] # time is `n`, starting from 0\n return SVector(r*u[1]*(1 - u[1]))\nend\n\nds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)\nx = trajectory(ds, N-1)[1][:, 1]","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Plot it, using as time the parameter value (they coincide)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig, ax = lines(rs, x; linewidth = 0.5)\nax.xlabel = \"r (time)\"\nax.ylabel = \"x\"\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.","category":"page"},{"location":"examples/logistic/#Using-a-simpler-change-metric","page":"Permutation entropy for dynamic regime changes","title":"Using a simpler change metric","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using TransitionsInTimeseries, ComplexityMeasures\n\nfunction permutation_entropy(m)\n est = SymbolicPermutation(; m) # order 3\n indicator = x -> entropy_normalized(est, x)\n return indicator\nend\n\nindicators = (var, ar1_whitenoise, permutation_entropy(4))\nindistrings = (\"var\", \"ar1\", \"pe\")","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"metric = difference_of_means\n\nwidth_ind = N÷100\nwidth_cha = 20\nstride_cha = 10\n\nconfig = SlidingWindowConfig(indicators, metric;\n width_ind, width_cha, stride_cha,\n)\n\nresults = estimate_indicator_changes(config, x, rs)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's now plot the change metrics of the indicators","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"function plot_change_metrics()\n fig, ax = lines(rs, x; axis = (ylabel = \"input\",), figure = (resolution = (600, 600),))\n hidexdecorations!(ax; grid = false)\n # plot all change metrics\n for (i, c) in enumerate(eachcol(results.x_change))\n ax, = scatterlines(fig[i+1, 1], results.t_change, c;\n axis = (ylabel = indistrings[i],), label = \"input\"\n )\n if i < 3\n hidexdecorations!(ax; grid = false)\n else\n ax.xlabel = \"r (time)\"\n end\n end\n return fig\nend\n\nfig = plot_change_metrics()","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.","category":"page"},{"location":"examples/logistic/#Significance-via-random-Fourier-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Significance via random Fourier surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RandomFourier()\n\n# Define a function because we will re-use later\nusing Random: Xoshiro\nfunction overplot_surrogate_significance!(fig, surromethod, color = \"black\")\n\n signif = SurrogatesSignificance(;\n n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),\n )\n flags = significant_transitions(results, signif)\n\n # and also plot the flags with same color\n for (i, indicator) in enumerate(indicators)\n # To make things visually clear, we will also plot some example surrogate\n # timeseries for each indicator and change metric pair\n for _ in 1:10\n s = TimeseriesSurrogates.surrogate(x, surromethod)\n p = windowmap(indicator, s; width = width_ind)\n q = windowmap(metric, p; width = width_cha, stride = stride_cha)\n lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1)\n end\n # Plot the flags as vertical dashed lines\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = color, linestyle = :dash, linewidth = 3\n )\n end\n # add a title to the figure with how we estimate significance\n content(fig[1, 1]).title = \"surrogates: \"*string(nameof(typeof(surromethod)))\nend\n\nsurromethod = RandomFourier()\noverplot_surrogate_significance!(fig, surromethod)\n\nfig","category":"page"},{"location":"examples/logistic/#Different-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Different surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RelativePartialRandomization(0.25)\nfig = plot_change_metrics()\noverplot_surrogate_significance!(fig, surromethod, \"gray\")\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.","category":"page"},{"location":"examples/logistic/#Simpler-Significance","page":"Permutation entropy for dynamic regime changes","title":"Simpler Significance","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig = plot_change_metrics()\nflags = significant_transitions(results, SigmaSignificance(factor = 5.0))\n\n# Plot the flags\nfor (i, indicator) in enumerate(indicators)\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = Cycled(3), linestyle = :dash, linewidth = 3\n )\nend\ncontent(fig[1, 1]).title = \"significance from std\"\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package for estimating transitions (from one dynamic regime or stable state to another) in timeseries and testing the statistical significance of found transitions. It integrates with the entire Julia ecosystem of timeseries analysis, and hence offers thousands of metrics that can indicate transitions right out of the box. It also offers a variety of analysis pipelines for identifying transitions and a variety of statistical pipelines for testing for significance.\n\nIn contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:\n\nAdd new indicators that work with the existing analysis pipelines for finding transitions\nAdd new analysis pipelines for finding transitions\nAdd new ways for testing whether already found transitions are significant\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\nAlternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"refs/#References","page":"References","title":"References","text":"","category":"section"},{"location":"refs/","page":"References","title":"References","text":"","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"EditURL = \"tutorial.jl\"","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector,\n# we obtain the last time step of each window.\n# This therefore only uses information from `k-width+1` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\n\nfunction gridfig(nrows, ncols)\n fig = Figure()\n axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)\n for j in 1:ncols, i in 1:nrows]\n rowgap!(fig.layout, 10)\n return fig, axs\nend\nfig, axs = gridfig(2, 1)\nlines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))\nlines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))\naxs[1].title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nlines!(axs[2], t_change, change_nl, label = \"nonlin\", color = Cycled(2))\nlines!(axs[2], t_change, change_s, label = \"surrogate\", color = Cycled(3))\naxislegend()\naxs[2].title = \"change metric\"\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig, axs = gridfig(2, 2)\naxs[1].title = \"linear\"\naxs[2].title = \"nonlinear\"\n\nfor (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change) # ; color = Cycled(j)\n lines!(axsig, t_change, pval) # ; color = Cycled(j+2)\nend\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = RidgeRegressionSlope()\n\n# choices go into a configuration struct\nconfig = SlidingWindowConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last)\n\n# choices are processed\nresults = estimate_indicator_changes(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From result we can plot the change metric timeseries:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(3, 1)\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, results.x_change[:, 1];\n label = \"var slopes\", color = Cycled(3))\nscatter!(axs[3], results.t_change, results.x_change[:, 2];\n label = \"ar1 slopes\", color = Cycled(4))\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = :right)\nflags = significant_transitions(results, signif)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(2, 1)\nlines!(axs[1], vcat(0.0, t), x_nlinear; label = \"raw\", color = Cycled(1))\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 1];\n label = \"var p-values\", color = Cycled(3))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 2];\n label = \"ar1 p-values\", color = Cycled(4))\n\nflagsboth = vec(reduce(&, flags; dims = 2))\nvlines!(axs[1], results.t_change[flagsboth]; label = \"flags\", color = (\"black\", 0.1))\n\n[axislegend(ax) for ax in axs]\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"}] +} diff --git a/previews/PR55/siteinfo.js b/previews/PR55/siteinfo.js new file mode 100644 index 00000000..b15de5be --- /dev/null +++ b/previews/PR55/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR55"; diff --git a/previews/PR55/tutorial.jl b/previews/PR55/tutorial.jl new file mode 100644 index 00000000..3f135673 --- /dev/null +++ b/previews/PR55/tutorial.jl @@ -0,0 +1,263 @@ +#= + +# Tutorial + +## [Workflow] (@id workflow) + +Computing transition indicators consists of the following steps: + +1. Doing any preprocessing of raw data first, such as detrending (_not part of TransitionsInTimeseries.jl_). This yields the **input timeseries**. +2. Estimating the timeseries of an indicator by sliding a window over the input timeseries. +3. Computing the changes of the indicator by sliding a window over its timeseries. +4. Generating many surrogates that preserve important statistical properties of the original timeseries. +5. Performing step 2 and 3 for the surrogate timeseries. +6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data. + +These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports. + +## [Tutorial -- Educational] (@id example_stepbystep) + +### Raw input data + +Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by: + +```math +\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t) +``` + +with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with [Makie](https://docs.makie.org/stable/)) such prototypical data to test some indicators can be done by simply running: +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_linear) +lines!(ax, t, x_nlinear) +ax.title = "raw data" +fig + +#= +### Preprocessing + +!!! note "Not part of TransitionsInTimeseries.jl" + Any timeseries preprocessing, such as the de-trending step we do here, + is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher. + + +The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1. +=# + +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +#= +At this point, `x_l_fluct` and `x_nl_fluct` are considered the **input timeseries**. + +!!! info "Detrending in Julia" + Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as [Loess.jl](https://github.com/JuliaStats/Loess.jl) or [DSP.jl](https://docs.juliadsp.org/latest/contents/). There the detrending step consists of subtracting the smoothed signal from the original one. + +### Indicator timeseries + +We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the **input timeseries**, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as [`ar1_whitenoise`](@ref): +=# + +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +## By mapping `last::Function` over a windowviewer of the time vector, +## we obtain the last time step of each window. +## This therefore only uses information from `k-width+1` to `k` at time step `k`. +## Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +#= +The lines plotted above are the **indicator timeseries**. + +### Change metric timeseries + +From here, we process the **indicator timeseries** to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the **change metric timeseries**. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a [`RidgeRegressionSlope`](@ref): +=# + +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + +#= +### Timeseries surrogates + +As expected from [Critical Slowing Down](@ref approaches), an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance. + +In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the [TimeseriesSurrogates.jl](https://github.com/JuliaDynamics/TimeseriesSurrogates.jl) Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that `TimeseriesSurrogates` is re-exported by `TransitionsInTimeseries`, so that you don't have to `using` both of them. + +To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries. +=# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) + +function gridfig(nrows, ncols) + fig = Figure() + axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false) + for j in 1:ncols, i in 1:nrows] + rowgap!(fig.layout, 10) + return fig, axs +end +fig, axs = gridfig(2, 1) +lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2)) +lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3)) +axs[1].title = "real signal vs. surrogate(s)" + +## compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2)) +lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3)) +axislegend() +axs[2].title = "change metric" + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +### Quantifying significance + +To quantify the significance of the values of the **change metric timeseries** we perform a standard surrogate test by computing the [p-value](https://en.wikipedia.org/wiki/P-value) w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically `p<0.05`) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time: +=# + +n_surrogates = 1_000 +fig, axs = gridfig(2, 2) +axs[1].title = "linear" +axs[2].title = "nonlinear" + +for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + ## Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change) # ; color = Cycled(j) + lines!(axsig, t_change, pval) # ; color = Cycled(j+2) +end + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar. + +Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section. + +## [Tutorial -- TransitionsInTimeseries.jl] (@id example_fastforward) + +TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go. + +The interface is simple, and directly parallelizes the [Workflow](@ref). It is based on the creation of a [`TransitionsSurrogatesConfig`](@ref), which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate. + +The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +## input timeseries and time +input = x_nl_fluct = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(t, input) +ax.title = "input timeseries" +fig + +#= +To perform all of the above analysis we follow a 2-step process. + +Step 1, we decide what indicators and change metrics to use in [`SlidingWindowConfig`](@ref) and apply those via +a sliding window to the input timeseries using [`transition_metrics`](@ref). +=# + +## These indicators are suitable for Critical Slowing Down +indicators = (var, ar1_whitenoise) + +## use the ridge regression slope for both indicators +change_metrics = RidgeRegressionSlope() + +## choices go into a configuration struct +config = SlidingWindowConfig(indicators, change_metrics; + width_ind = 400, width_cha = 30, whichtime = last) + +## choices are processed +results = estimate_indicator_changes(config, input, t) + +#= +From `result` we can plot the change metric timeseries: +=# + +fig, axs = gridfig(3, 1) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, results.x_change[:, 1]; + label = "var slopes", color = Cycled(3)) +scatter!(axs[3], results.t_change, results.x_change[:, 2]; + label = "ar1 slopes", color = Cycled(4)) +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +Step 2 is to estimate significance using [`SurrogatesConfig`](@ref) +and the function [`estimate_significance!`](@ref). +=# + +signif = SurrogatesSignificance(n = 1000, tail = :right) +flags = significant_transitions(results, signif) + +#= +We can now plot the p-values corresponding to each time series of the change metrics. From the `flags` we can additionally obtain the time points where _both_ indicators show significance, via a simple reduction: +=# + +fig, axs = gridfig(2, 1) +lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1)) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 1]; + label = "var p-values", color = Cycled(3)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 2]; + label = "ar1 p-values", color = Cycled(4)) + +flagsboth = vec(reduce(&, flags; dims = 2)) +vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1)) + +[axislegend(ax) for ax in axs] +[xlims!(ax, 0, 50) for ax in axs] +fig \ No newline at end of file diff --git a/previews/PR55/tutorial/index.html b/previews/PR55/tutorial/index.html new file mode 100644 index 00000000..c563994b --- /dev/null +++ b/previews/PR55/tutorial/index.html @@ -0,0 +1,160 @@ + +Tutorial · TransitionsInTimeseries.jl
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                                    Tutorial

                                    Workflow

                                    Computing transition indicators consists of the following steps:

                                    1. Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                                    2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                                    3. Computing the changes of the indicator by sliding a window over its timeseries.
                                    4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                                    5. Performing step 2 and 3 for the surrogate timeseries.
                                    6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                                    These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                                    Tutorial – Educational

                                    Raw input data

                                    Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                                    \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                                    with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                                    using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig

                                    Preprocessing

                                    Not part of TransitionsInTimeseries.jl

                                    Any timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                                    The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                                    x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                                    At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                                    Detrending in Julia

                                    Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                                    Indicator timeseries

                                    We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                                    indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector,
+# we obtain the last time step of each window.
+# This therefore only uses information from `k-width+1` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                                    The lines plotted above are the indicator timeseries.

                                    Change metric timeseries

                                    From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                                    change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                                    Timeseries surrogates

                                    As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                                    In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                                    To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                                    # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+
+function gridfig(nrows, ncols)
+    fig = Figure()
+    axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)
+        for j in 1:ncols, i in 1:nrows]
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+fig, axs = gridfig(2, 1)
+lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))
+lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))
+axs[1].title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2))
+lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3))
+axislegend()
+axs[2].title = "change metric"
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                    Quantifying significance

                                    To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                                    n_surrogates = 1_000
+fig, axs = gridfig(2, 2)
+axs[1].title = "linear"
+axs[2].title = "nonlinear"
+
+for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change)   # ; color = Cycled(j)
+    lines!(axsig, t_change, pval)       # ; color = Cycled(j+2)
+end
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                    As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                                    Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                                    Tutorial – TransitionsInTimeseries.jl

                                    TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                                    The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

                                    The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

                                    using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig

                                    To perform all of the above analysis we follow a 2-step process.

                                    Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.

                                    # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = RidgeRegressionSlope()
+
+# choices go into a configuration struct
+config = SlidingWindowConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last)
+
+# choices are processed
+results = estimate_indicator_changes(config, input, t)
                                    IndicatorsChangesResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                                    From result we can plot the change metric timeseries:

                                    fig, axs = gridfig(3, 1)
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, results.x_change[:, 1];
+    label = "var slopes", color = Cycled(3))
+scatter!(axs[3], results.t_change, results.x_change[:, 2];
+    label = "ar1 slopes", color = Cycled(4))
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                    Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.

                                    signif = SurrogatesSignificance(n = 1000, tail = :right)
+flags = significant_transitions(results, signif)
                                    2072×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ ⋮  
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0

                                    We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:

                                    fig, axs = gridfig(2, 1)
+lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1))
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 1];
+    label = "var p-values", color = Cycled(3))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 2];
+    label = "ar1 p-values", color = Cycled(4))
+
+flagsboth = vec(reduce(&, flags; dims = 2))
+vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1))
+
+[axislegend(ax) for ax in axs]
+[xlims!(ax, 0, 50) for ax in axs]
+fig
                                    diff --git a/stable b/stable new file mode 120000 index 00000000..a1c2c6a9 --- /dev/null +++ b/stable @@ -0,0 +1 @@ +v0.1.1 \ No newline at end of file diff --git a/v0.1 b/v0.1 new file mode 120000 index 00000000..a1c2c6a9 --- /dev/null +++ b/v0.1 @@ -0,0 +1 @@ +v0.1.1 \ No newline at end of file diff --git a/v0.1.0/api/index.html b/v0.1.0/api/index.html new file mode 100644 index 00000000..a004da20 --- /dev/null +++ b/v0.1.0/api/index.html @@ -0,0 +1,22 @@ + +API · TransitionsInTimeseries.jl
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                                    API

                                    Main analysis functions

                                    TransitionsInTimeseries.SlidingWindowConfig — Type
                                    SlidingWindowConfig <: IndicatorsChangesConfig
+SlidingWindowConfig(indicators, change_metrics; kwargs...)

                                    A configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:

                                    1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                                    2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                                    indicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                                    Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.

                                    The results output corresponding to SlidingWindowConfig is SlidingWindowResults.

                                    Keyword arguments

                                    • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.
                                    • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.
                                    • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:
                                      • last: use the last timepoint of each window
                                      • midpoint: use the mid timepoint of each time window
                                      • first: use first timepoint of each window
                                      In fact, the indicators time vector is computed simply via
                                      t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)
                                      so any other function of the time window may be given to extract the time point itself, such as mean or median.
                                    • T = Float64: Element type of input timeseries to initialize some computations.
                                    source
                                    TransitionsInTimeseries.SegmentedWindowConfig — Type
                                    SegmentedWindowConfig <: IndicatorsChangeConfig
+SegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)

                                    A configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:

                                    1. For each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).
                                    2. For each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d

                                    tseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.

                                    The results output corresponding to SlidingWindowConfig is SegmentedWindowResults.

                                    Keyword arguments

                                    • width_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.
                                    • min_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.
                                    source
                                    TransitionsInTimeseries.estimate_indicator_changes — Function
                                    estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → result

                                    Estimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).

                                    Return the output as subtype of IndicatorsChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                                    source
                                    TransitionsInTimeseries.SlidingWindowResults — Type
                                    SlidingWindowResults <: IndicatorsChangesResults

                                    A struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                                    It has the following fields that the user may access

                                    • x: the input timeseries.

                                    • t: the time vector of the input timeseries.

                                    • x_indicator, the indicator timeseries (matrix with each column one indicator).

                                    • t_indicator, the time vector of the indicator timeseries.

                                    • x_change, the change metric timeseries (matrix with each column one change metric).

                                    • t_change, the time vector of the change metric timeseries.

                                    • config::SlidingWindowConfig, what was used for the analysis.

                                    source
                                    TransitionsInTimeseries.SegmentedWindowResults — Type
                                    SegmentedWindowResults <: IndicatorsChangesResults

                                    A struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                                    It has the following fields that the user may access

                                    • x: the input timeseries.

                                    • t: the time vector of the input timeseries.

                                    • x_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.

                                    • t_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.

                                    • x_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.

                                    • t_change, the time vector of the change metric.

                                    • config::SegmentedWindowConfig, what was used for the analysis.

                                    source

                                    Significance testing

                                    TransitionsInTimeseries.significant_transitions — Function
                                    significant_transitions(res::IndicatorsChangesResults, signif::TransitionsSignificance)

                                    Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.

                                    source
                                    TransitionsInTimeseries.SurrogatesSignificance — Type
                                    SurrogatesSignificance <: TransitionsSignificance
+SurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)

                                    A configuration struct for significance testing significant_transitions using timeseries surrogates.

                                    Keyword arguments

                                    • surromethod = RandomFourier(): method to generate surrogates
                                    • n = 1000: how many surrogates to generate
                                    • rng = Random.default_rng(): random number generator for the surrogates
                                    • p = 0.05: threshold for significance of the p-value
                                    • tail = :both: tail type used, see below

                                    Description

                                    When used with IndicatorsChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

                                    The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in IndicatorsChangesResults.

                                    Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

                                    source
                                    TransitionsInTimeseries.QuantileSignificance — Type
                                    QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance

                                    A configuration struct for significance testing significant_transitions. When used with IndicatorsChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                                    QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

                                    source

                                    Indicators

                                    Value distribution

                                    Statistics.mean — Method
                                    mean(itr)

                                    Compute the mean of all elements in a collection.

                                    Note

                                    If itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.

                                    Examples

                                    julia> using Statistics
+
+julia> mean(1:20)
+10.5
+
+julia> mean([1, missing, 3])
+missing
+
+julia> mean(skipmissing([1, missing, 3]))
+2.0
                                    StatsBase.skewness — Function
                                    skewness(v, [wv::AbstractWeights], m=mean(v))

                                    Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                                    StatsBase.kurtosis — Function
                                    kurtosis(v, [wv::AbstractWeights], m=mean(v))

                                    Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                                    Critical Slowing Down

                                    Statistics.var — Method
                                    var(itr; corrected::Bool=true, mean=nothing[, dims])

                                    Compute the sample variance of collection itr.

                                    The algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.

                                    If itr is an AbstractArray, dims can be provided to compute the variance over dimensions.

                                    A pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).

                                    Note

                                    If array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.

                                    TransitionsInTimeseries.ar1_whitenoise — Function
                                    ar1_whitenoise(x::AbstractVector)

                                    Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

                                    \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                                    source

                                    Spectrum

                                    TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                                    LowfreqPowerSpectrum(; q_lofreq = 0.1)

                                    Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                                    lfps = precompute( LowfreqPowerSpectrum() )

                                    Keyword arguments:

                                    • q_lofreq: a number between 0 and 1 that characterises which portion of the

                                    frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                                    source

                                    Nonlinear dynamics

                                    Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.

                                    For example, using the permutation entropy as an indicator is as simple as doing

                                    using ComplexityMeasures
+est = OrdinalPatterns(; m = 3) # order 3
+# create a function that given timeseries returns permutation entropy
+indicator = x -> entropy_normalized(est, x)

                                    and giving the created indicator to e.g., SlidingWindowConfig.

                                    Change metrics

                                    Slope

                                    TransitionsInTimeseries.kendalltau — Function
                                    kendalltau(x::AbstractVector)

                                    Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                                    source
                                    TransitionsInTimeseries.spearman — Function
                                    spearman(x::AbstractVector)

                                    Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                                    source

                                    Value distribution differences

                                    TransitionsInTimeseries.difference_of_means — Function
                                    difference_of_means(x::AbstractArray)

                                    Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                                    # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                                    difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                                    source

                                    Make your own indicator/metric!

                                    The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                                    There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:

                                    Missing docstring.

                                    Missing docstring for precompute. Check Documenter's build log for details.

                                    Surrogates

                                    For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                                    Sliding windows

                                    TransitionsInTimeseries.WindowViewer — Type
                                    WindowViewer(x; width, stride)

                                    Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                                    If not given, the keywords width, stride are taken as default_window_width(x) and 1.

                                    source
                                    TransitionsInTimeseries.windowmap — Function
                                    windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                                    A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                                    source

                                    Load data

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+ } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/v0.1.0/assets/search.js b/v0.1.0/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/v0.1.0/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
                                  • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/v0.1.0/assets/themes/documenter-dark.css 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rgba(255,255,255,0.25)}html.theme--documenter-dark .button.is-white:active,html.theme--documenter-dark .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white{background-color:#fff;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark 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.button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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rgba(245,245,245,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#f5f5f5;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:#292929}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#2f2f2f;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,54,54,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#292929;border-color:transparent;color:#f5f5f5}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#e8e8e8}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#f5f5f5;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#f5f5f5;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#4eb5de;border-color:#4eb5de;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #4eb5de #4eb5de !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#4eb5de;box-shadow:none;color:#4eb5de}html.theme--documenter-dark 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They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found [here](https://www.iceandclimate.nbi.ku.dk/data/) in its raw format. This analysis has already been done in [boers-early-warning-2018](@cite) and we here try to reproduce Figure 2.d-f. + +## Preprocessing NGRIP + +Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps: +1. Load the data, reverse and offset it to have time vector = time before 2000 AD. +2. Filter non-unique points in time and sort the data. +3. Regrid the data from uneven to even sampling. + +The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing. + +### Step 1: +=# + +using DelimitedFiles, Downloads + +function load_ngrip() + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP.csv") + data, labels = readdlm(tmp, header = true) + return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors +end + +t1, x1 = load_ngrip() + +#= +### Step 2 +=# + +uniqueidx(v) = unique(i -> v[i], eachindex(v)) +function keep_unique(t, x) + unique_idx = uniqueidx(t) + return t[unique_idx], x[unique_idx] +end + +function sort_timeseries!(t, x) + p = sortperm(t) + permute!(t, p) + permute!(x, p) + return nothing +end + +t2, x2 = keep_unique(t1, x1) +sort_timeseries!(t2, x2) + +#= +### Step 3 +=# + +using BSplineKit + +function regrid2evensampling(t, x, dt) + itp = BSplineKit.interpolate(t, x, BSplineOrder(4)) + tspan = (ceil(minimum(t)), floor(maximum(t))) + t_even = collect(tspan[1]:dt:tspan[2]) + x_even = itp.(t_even) + return t_even, x_even +end + +dt = 5.0 # dt = 5 yr as in (Boers 2018) +t3, x3 = regrid2evensampling(t2, x2, dt) + +#= +### Step 4 + +For the final step we drop the indices: +=# + +using DSP + +function chebyshev_filter(t, x, fcutoff) + ii = 10 # Chebyshev filtering requires to prune first points of timeseries. + responsetype = Highpass(fcutoff, fs = 1/dt) + designmethod = Chebyshev1(8, 0.05) + r = filt(digitalfilter(responsetype, designmethod), x) + xtrend = x - r + return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end] +end + +fcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018) +t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff) + +#= +Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from [rasmussen-stratigraphic-2014](@cite) (which will soon be available as downloadable): +=# + +using CairoMakie, Loess + +function loess_filter(t, x; span = 0.005) + loessmodel = loess(t, x, span = span) + xtrend = Loess.predict(loessmodel, t) + r = x - xtrend + return t, x, xtrend, r +end + +function kyr_xticks(tticks_yr) + tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)] + return (tticks_yr, tticks_kyr) +end + +function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks) + fig = Figure(resolution = (1600, 1200), fontsize = 24) + + ## Original timeseries with transition marked by vertical lines + ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)", + xaxisposition = :top, xticks = xticks) + lines!(ax1, traw, xraw, color = (:gray70, 0.5)) + lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3) + vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3) + + ## Residual timeseries + ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + lines!(ax2, t, r, color = :gray50, linewidth = 1) + + ## Axes for variance and AC1 timeseries + ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$", + xticks = xticks) + + axs = [ax1, ax2, ax3, ax4] + [xlims!(ax, xlims) for ax in axs] + ylims!(axs[1], (-48, -34)) + rowgap!(fig.layout, 10) + return fig, axs +end + +xlims = (-60e3, -10e3) +xticks = kyr_xticks(-60e3:5e3:5e3) +t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160, + 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703] +tloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +fig + +#= +## Hindcast on NGRIP data + +As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including [boers-early-warning-2018](@cite), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using `SegmentedWindowConfig`, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here: +=# + +using TransitionsInTimeseries, StatsBase +using Random: Xoshiro + +ac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase +indicators = (var, ac1) +change_metrics = RidgeRegressionSlope() +tseg_start = t_rasmussen[1:end-1] .+ 200 +tseg_end = t_rasmussen[2:end] .- 200 +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) # require >=100 data points to estimate change metric +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) + +#= +That's it! We can now visulaise our results with a generic function that we will re-use later: +=# + +function plot_segment_analysis!(axs, results, signif) + (; t_indicator, x_indicator) = results + for k in eachindex(t_indicator) # loop over the segments + for i in axes(signif.pvalues, 2) # loop over the indicators + if !isinf(signif.pvalues[k, i]) # plot if segment long enough + ## Plot indicator timeseries and its linear regression + ti, xi = t_indicator[k], x_indicator[k][:, i] + lines!(axs[i+2], ti, xi, color = Cycled(1)) + m, p = ridgematrix(ti, 0.0) * xi + if signif.pvalues[k, i] < 0.05 + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3) + else + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3) + end + end + end + end +end +plot_segment_analysis!(axs, results, signif) +fig + +#= +In [boers-early-warning-2018](@cite), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in [boers-early-warning-2018](@cite), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of [boers-early-warning-2018](@cite). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media. + +## CSD: only a necessary condition, only in some cases + +For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a **necessary condition** for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is **not a sufficient condition** for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition: +=# + +tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) +results = estimate_indicator_changes(config, r, t) +signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +plot_segment_analysis!(axs, results, signif) +fig + +#= +For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD. + +We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC). + +!!! warning "Degrees of freedom" + These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice. + +!!! info "Future improvement" + Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias. + +## Hindcasting simulated DO-events + +In CLIMBER-X, the EMIC described in [willeit-earth-2022](@cite), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs: +=# + +t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050], + [1, 3500, 4370, 5790, 7200, 8140]] +t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]] +tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]] +tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50] + +figvec = Figure[] + +for j in 1:2 + ## Download the data and perform loess filtering on it + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" * + "master/timeseries/climberx-do$(j)-omaxa.csv") + data = readdlm(tmp) + tcx, xcx = data[1, 1000:end], data[2, 1000:end] + t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02) + + ## Initialize figure + xlims = (0, last(tcx)) + xticks = kyr_xticks(xlims[1]:1e3:xlims[2]) + fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks) + ylims!(axs[1], (5, 40)) + axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$" + + ## Run sliding analysis and update figure with results + dt = mean(diff(tcx)) + config = SegmentedWindowConfig( + indicators, change_metrics, tseg_start[j], tseg_end[j], + whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100) + results = estimate_indicator_changes(config, r, t) + signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995)) + flags = significant_transitions(results, signif) + + plot_segment_analysis!(axs, results, signif) + vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3) + push!(figvec, fig) +end +figvec[1] + +#= +It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case: +=# + +figvec[2] + +#= +Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience. +=# \ No newline at end of file diff --git a/v0.1.0/examples/do-events/index.html b/v0.1.0/examples/do-events/index.html new file mode 100644 index 00000000..231de161 --- /dev/null +++ b/v0.1.0/examples/do-events/index.html @@ -0,0 +1,191 @@ + +Dansgaard-Oescher events and Critical Slowing Down · TransitionsInTimeseries.jl
                                    Edit on GitHub

                                    Dansgaard-Oescher events and Critical Slowing Down

                                    The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.

                                    Preprocessing NGRIP

                                    Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:

                                    1. Load the data, reverse and offset it to have time vector = time before 2000 AD.
                                    2. Filter non-unique points in time and sort the data.
                                    3. Regrid the data from uneven to even sampling.

                                    The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.

                                    Step 1:

                                    using DelimitedFiles, Downloads
+
+function load_ngrip()
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+        "master/timeseries/NGRIP.csv")
+    data, labels = readdlm(tmp, header = true)
+    return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors
+end
+
+t1, x1 = load_ngrip()
                                    ([-59944.5, -59939.6, -59935.9, -59930.5, -59925.0, -59919.0, -59914.3, -59909.4, -59904.5, -59899.7  …  -27.40000000000009, -27.40000000000009, -27.299999999999955, -27.299999999999955, -27.200000000000045, -27.09999999999991, -27.09999999999991, -27.0, -26.90000000000009, -26.799999999999955], [-43.52, -42.94, -42.13, -40.04, -41.09, -43.57, -42.28, -41.2, -44.07, -44.53  …  -35.29, -35.18, -35.51, -36.03, -36.52, -37.12, -37.41, -37.21, -36.62, -35.52])

                                    Step 2

                                    uniqueidx(v) = unique(i -> v[i], eachindex(v))
+function keep_unique(t, x)
+    unique_idx = uniqueidx(t)
+    return t[unique_idx], x[unique_idx]
+end
+
+function sort_timeseries!(t, x)
+    p = sortperm(t)
+    permute!(t, p)
+    permute!(x, p)
+    return nothing
+end
+
+t2, x2 = keep_unique(t1, x1)
+sort_timeseries!(t2, x2)

                                    Step 3

                                    using BSplineKit
+
+function regrid2evensampling(t, x, dt)
+    itp = BSplineKit.interpolate(t, x, BSplineOrder(4))
+    tspan = (ceil(minimum(t)), floor(maximum(t)))
+    t_even = collect(tspan[1]:dt:tspan[2])
+    x_even = itp.(t_even)
+    return t_even, x_even
+end
+
+dt = 5.0        # dt = 5 yr as in (Boers 2018)
+t3, x3 = regrid2evensampling(t2, x2, dt)
                                    ([-59944.0, -59939.0, -59934.0, -59929.0, -59924.0, -59919.0, -59914.0, -59909.0, -59904.0, -59899.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-43.445268010797946, -42.85408835164853, -41.357360665158936, -39.9365468206892, -41.60554051352076, -43.57000000000001, -42.145558689100454, -41.33160823883399, -44.273597725729985, -44.4622612304012  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46])

                                    Step 4

                                    For the final step we drop the indices:

                                    using DSP
+
+function chebyshev_filter(t, x, fcutoff)
+    ii = 10             # Chebyshev filtering requires to prune first points of timeseries.
+    responsetype = Highpass(fcutoff, fs = 1/dt)
+    designmethod = Chebyshev1(8, 0.05)
+    r = filt(digitalfilter(responsetype, designmethod), x)
+    xtrend = x - r
+    return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]
+end
+
+fcutoff = 0.95 * 0.01   # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)
+t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)
                                    ([-59899.0, -59894.0, -59889.0, -59884.0, -59879.0, -59874.0, -59869.0, -59864.0, -59859.0, -59854.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-44.4622612304012, -44.264401428210874, -44.02956767939856, -42.29334237357212, -42.594341674200344, -41.09704877854712, -40.39837540966913, -44.369155046413255, -42.74492506508012, -43.737014520530145  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46], [-43.89287787976461, -48.663435112414156, -51.31169981050155, -51.269094666491796, -49.90310432724566, -47.721430022512344, -44.36050569418247, -43.87556827410048, -43.57802291229893, -41.36870967826094  …  -34.81349114528442, -36.01634453179986, -36.150446802907226, -36.37595639697143, -35.96843653265903, -33.899634243732976, -32.49784036951535, -33.06575312724142, -34.07956188682297, -34.4079080530096], [-0.5693833506365866, 4.399033684203284, 7.282132131102991, 8.975752292919669, 7.308762653045311, 6.624381243965224, 3.9621302845133433, -0.493586772312777, 0.8330978472188112, -2.368304842269206  …  -0.30650885471557926, -0.17365546820014846, 1.0104468029072273, -0.684043603028572, 1.0384365326590237, -0.3303657562670192, -1.0321596304846505, -2.0242468727585807, 0.07956188682296689, -0.05209194699039831])

                                    Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):

                                    using CairoMakie, Loess
+
+function loess_filter(t, x; span = 0.005)
+    loessmodel = loess(t, x, span = span)
+    xtrend = Loess.predict(loessmodel, t)
+    r = x - xtrend
+    return t, x, xtrend, r
+end
+
+function kyr_xticks(tticks_yr)
+    tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)]
+    return (tticks_yr, tticks_kyr)
+end
+
+function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)
+    fig = Figure(resolution = (1600, 1200), fontsize = 24)
+
+    # Original timeseries with transition marked by vertical lines
+    ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)",
+        xaxisposition = :top, xticks = xticks)
+    lines!(ax1, traw, xraw, color = (:gray70, 0.5))
+    lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)
+    vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)
+
+    # Residual timeseries
+    ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    lines!(ax2, t, r, color = :gray50, linewidth = 1)
+
+    # Axes for variance and AC1 timeseries
+    ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$",
+        xticks = xticks)
+
+    axs = [ax1, ax2, ax3, ax4]
+    [xlims!(ax, xlims) for ax in axs]
+    ylims!(axs[1], (-48, -34))
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+
+xlims = (-60e3, -10e3)
+xticks = kyr_xticks(-60e3:5e3:5e3)
+t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,
+                38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]
+tloess, _, xloess, rloess = loess_filter(t3, x3)    # loess-filtered signal for visualization
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+fig

                                    Hindcast on NGRIP data

                                    As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:

                                    using TransitionsInTimeseries, StatsBase
+using Random: Xoshiro
+
+ac1(x) = sum(autocor(x, [1]))   # AC1 from StatsBase
+indicators = (var, ac1)
+change_metrics = RidgeRegressionSlope()
+tseg_start = t_rasmussen[1:end-1] .+ 200
+tseg_end = t_rasmussen[2:end] .- 200
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)        # require >=100 data points to estimate change metric
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
                                    18×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 1  0
+ 1  1
+ 1  1
+ 1  1
+ 0  0
+ 1  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 1  0

                                    That's it! We can now visulaise our results with a generic function that we will re-use later:

                                    function plot_segment_analysis!(axs, results, signif)
+    (; t_indicator, x_indicator) = results
+    for k in eachindex(t_indicator)             # loop over the segments
+        for i in axes(signif.pvalues, 2)        # loop over the indicators
+            if !isinf(signif.pvalues[k, i])     # plot if segment long enough
+                # Plot indicator timeseries and its linear regression
+                ti, xi = t_indicator[k], x_indicator[k][:, i]
+                lines!(axs[i+2], ti, xi, color = Cycled(1))
+                m, p = ridgematrix(ti, 0.0) * xi
+                if signif.pvalues[k, i] < 0.05
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)
+                else
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)
+                end
+            end
+        end
+    end
+end
+plot_segment_analysis!(axs, results, signif)
+fig

                                    In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.

                                    CSD: only a necessary condition, only in some cases

                                    For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:

                                    tseg_end = t_rasmussen[2:end] .- 700    # stop analysis 500 years earlier than before
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)
+results = estimate_indicator_changes(config, r, t)
+signif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+plot_segment_analysis!(axs, results, signif)
+fig

                                    For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD.

                                    We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).

                                    Degrees of freedom

                                    These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.

                                    Future improvement

                                    Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.

                                    Hindcasting simulated DO-events

                                    In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:

                                    t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],
+                 [1, 3500, 4370, 5790, 7200, 8140]]
+t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]
+tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]
+tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]
+
+figvec = Figure[]
+
+for j in 1:2
+    # Download the data and perform loess filtering on it
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" *
+        "master/timeseries/climberx-do$(j)-omaxa.csv")
+    data = readdlm(tmp)
+    tcx, xcx = data[1, 1000:end], data[2, 1000:end]
+    t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)
+
+    # Initialize figure
+    xlims = (0, last(tcx))
+    xticks = kyr_xticks(xlims[1]:1e3:xlims[2])
+    fig, axs = plot_do(tcx, xcx,  t, xtrend, t, r, t_transitions[j], extrema(t), xticks)
+    ylims!(axs[1], (5, 40))
+    axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$"
+
+    # Run sliding analysis and update figure with results
+    dt = mean(diff(tcx))
+    config = SegmentedWindowConfig(
+        indicators, change_metrics, tseg_start[j], tseg_end[j],
+        whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)
+    results = estimate_indicator_changes(config, r, t)
+    signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))
+    flags = significant_transitions(results, signif)
+
+    plot_segment_analysis!(axs, results, signif)
+    vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)
+    push!(figvec, fig)
+end
+figvec[1]

                                    It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:

                                    figvec[2]

                                    Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.

                                    diff --git a/v0.1.0/examples/logistic.jl b/v0.1.0/examples/logistic.jl new file mode 100644 index 00000000..a2894fbd --- /dev/null +++ b/v0.1.0/examples/logistic.jl @@ -0,0 +1,203 @@ +# # Permutation entropy for dynamic regime changes + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ## Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +## time-dependent logistic map, so that the `r` parameter increases with time +r1 = 3.83 +r2 = 3.86 +N = 2000 +rs = range(r1, r2; length = N) + +function logistic_drifting_rule(u, rs, n) + r = rs[n+1] # time is `n`, starting from 0 + return SVector(r*u[1]*(1 - u[1])) +end + +ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs) +x = trajectory(ds, N-1)[1][:, 1] + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ## Using a simpler change metric + +# Now, let's compute and various indicators and their changes, +# focusing on the permutation entropy as an indicator. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries, ComplexityMeasures + +function permutation_entropy(m) + est = SymbolicPermutation(; m) # order 3 + indicator = x -> entropy_normalized(est, x) + return indicator +end + +indicators = (var, ar1_whitenoise, permutation_entropy(4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as stride half the window width +metric = difference_of_means + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = SlidingWindowConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = estimate_indicator_changes(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + if i < 3 + hidexdecorations!(ax; grid = false) + else + ax.xlabel = "r (time)" + end + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ## Significance via random Fourier surrogates + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +using Random: Xoshiro +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42), + ) + flags = significant_transitions(results, signif) + + ## and also plot the flags with same color + for (i, indicator) in enumerate(indicators) + ## To make things visually clear, we will also plot some example surrogate + ## timeseries for each indicator and change metric pair + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surromethod) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric, p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1) + end + ## Plot the flags as vertical dashed lines + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = color, linestyle = :dash, linewidth = 3 + ) + end + ## add a title to the figure with how we estimate significance + content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod))) +end + +surromethod = RandomFourier() +overplot_surrogate_significance!(fig, surromethod) + +fig + +# ## Different surrogates +# %% #src +# Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# highlighting the _local_ dynamics or information that preserves the local +# changes of dynamical behavior. + +# A surrogate type that does a better job in preserving local sharp +# changes in the timeseries (and hence provides **stricter** +# surrogate-based significance) is for example `RelativePartialRandomization`. + +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = RelativePartialRandomization(0.25) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "gray") +fig + +# Our results have improved. In the permutation entropy, we see only two +# transitions detected as significant, which is correct: only two +# real dynamical transitions exist in the data. +# In the other two indicators we also see fewer transitions, but as we +# have already discussed, no results with the other indicators should +# be taken into meaningful consideration, as these indicators +# are simply inappropriate for what we are looking for here. + +# ## Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be less strict and more simple with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`SigmaSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation. + +fig = plot_change_metrics() +flags = significant_transitions(results, SigmaSignificance(factor = 5.0)) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = Cycled(3), linestyle = :dash, linewidth = 3 + ) +end +content(fig[1, 1]).title = "significance from std" +fig diff --git a/v0.1.0/examples/logistic/index.html b/v0.1.0/examples/logistic/index.html new file mode 100644 index 00000000..7b38625b --- /dev/null +++ b/v0.1.0/examples/logistic/index.html @@ -0,0 +1,128 @@ + +Permutation entropy for dynamic regime changes · TransitionsInTimeseries.jl
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                                    Permutation entropy for dynamic regime changes

                                    Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.

                                    This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.

                                    Logistic map timeseries

                                    A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map

                                    using DynamicalSystemsBase
+using CairoMakie
+
+# time-dependent logistic map, so that the `r` parameter increases with time
+r1 = 3.83
+r2 = 3.86
+N = 2000
+rs = range(r1, r2; length = N)
+
+function logistic_drifting_rule(u, rs, n)
+    r = rs[n+1] # time is `n`, starting from 0
+    return SVector(r*u[1]*(1 - u[1]))
+end
+
+ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)
+x = trajectory(ds, N-1)[1][:, 1]
                                    2000-element Vector{Float64}:
+ 0.5
+ 0.9575
+ 0.15585767321160574
+ 0.5039019545917718
+ 0.9574529422362281
+ 0.15602441103002537
+ 0.5043473227583317
+ 0.9574501255597653
+ 0.1560361152301728
+ 0.5043840906474082
+ ⋮
+ 0.4253904015445437
+ 0.9434836074964187
+ 0.20581843730311683
+ 0.6309301050251992
+ 0.8988117342940414
+ 0.3510584545931264
+ 0.8793611090928393
+ 0.40948549063776396
+ 0.9333718681550522

                                    Plot it, using as time the parameter value (they coincide)

                                    fig, ax = lines(rs, x; linewidth = 0.5)
+ax.xlabel = "r (time)"
+ax.ylabel = "x"
+fig

                                    In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.

                                    Using a simpler change metric

                                    Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.

                                    using TransitionsInTimeseries, ComplexityMeasures
+
+function permutation_entropy(m)
+    est = SymbolicPermutation(; m) # order 3
+    indicator = x -> entropy_normalized(est, x)
+    return indicator
+end
+
+indicators = (var, ar1_whitenoise, permutation_entropy(4))
+indistrings = ("var", "ar1", "pe")
                                    ("var", "ar1", "pe")

                                    In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width

                                    metric = difference_of_means
+
+width_ind = N÷100
+width_cha = 20
+stride_cha = 10
+
+config = SlidingWindowConfig(indicators, metric;
+    width_ind, width_cha, stride_cha,
+)
+
+results = estimate_indicator_changes(config, x, rs)
                                    IndicatorsChangesResults
+ input timeseries:              2000-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise, Symbol("#1")]
+ indicator (window, stride):    (20, 1)
+ change metrics:                [:difference_of_means]
+ change metric (window, stride): (20, 10)
+

                                    Let's now plot the change metrics of the indicators

                                    function plot_change_metrics()
+    fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (resolution = (600, 600),))
+    hidexdecorations!(ax; grid = false)
+    # plot all change metrics
+    for (i, c) in enumerate(eachcol(results.x_change))
+        ax, = scatterlines(fig[i+1, 1], results.t_change, c;
+            axis = (ylabel = indistrings[i],), label = "input"
+        )
+        if i < 3
+            hidexdecorations!(ax; grid = false)
+        else
+            ax.xlabel = "r (time)"
+        end
+    end
+    return fig
+end
+
+fig = plot_change_metrics()

                                    We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)

                                    Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.

                                    Significance via random Fourier surrogates

                                    One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.

                                    Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!

                                    surromethod = RandomFourier()
+
+# Define a function because we will re-use later
+using Random: Xoshiro
+function overplot_surrogate_significance!(fig, surromethod, color = "black")
+
+    signif = SurrogatesSignificance(;
+        n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),
+    )
+    flags = significant_transitions(results, signif)
+
+    # and also plot the flags with same color
+    for (i, indicator) in enumerate(indicators)
+        # To make things visually clear, we will also plot some example surrogate
+        # timeseries for each indicator and change metric pair
+        for _ in 1:10
+            s = TimeseriesSurrogates.surrogate(x, surromethod)
+            p = windowmap(indicator, s; width = width_ind)
+            q = windowmap(metric, p; width = width_cha, stride = stride_cha)
+            lines!(fig[i+1, 1], results.t_change, q;  color = (color, 0.2), linewidth = 1)
+        end
+        # Plot the flags as vertical dashed lines
+        vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+            color = color, linestyle = :dash, linewidth = 3
+        )
+    end
+    # add a title to the figure with how we estimate significance
+    content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod)))
+end
+
+surromethod = RandomFourier()
+overplot_surrogate_significance!(fig, surromethod)
+
+fig

                                    Different surrogates

                                    Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

                                    A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

                                    A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

                                    surromethod = RelativePartialRandomization(0.25)
+fig = plot_change_metrics()
+overplot_surrogate_significance!(fig, surromethod, "gray")
+fig

                                    Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

                                    Simpler Significance

                                    Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

                                    fig = plot_change_metrics()
+flags = significant_transitions(results, SigmaSignificance(factor = 5.0))
+
+# Plot the flags
+for (i, indicator) in enumerate(indicators)
+    vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+        color = Cycled(3), linestyle = :dash, linewidth = 3
+    )
+end
+content(fig[1, 1]).title = "significance from std"
+fig
                                    diff --git a/v0.1.0/index.html b/v0.1.0/index.html new file mode 100644 index 00000000..6e20367c --- /dev/null +++ b/v0.1.0/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
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                                    TransitionsInTimeseries.jl

                                    TransitionsInTimeseries.jl

                                    TransitionsInTimeseries — Module

                                    TransitionsInTimeseries.jl

                                    CI codecov Package Downloads

                                    A Julia package for estimating transitions (from one dynamic regime or stable state to another) in timeseries and testing the statistical significance of found transitions. It integrates with the entire Julia ecosystem of timeseries analysis, and hence offers thousands of metrics that can indicate transitions right out of the box. It also offers a variety of analysis pipelines for identifying transitions and a variety of statistical pipelines for testing for significance.

                                    In contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:

                                    1. Add new indicators that work with the existing analysis pipelines for finding transitions
                                    2. Add new analysis pipelines for finding transitions
                                    3. Add new ways for testing whether already found transitions are significant

                                    This package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run

                                    add https://github.com/JuliaDynamics/TransitionsInTimeseries.jl

                                    All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                                    Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                                    source
                                    Star us on GitHub!

                                    If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                                    Content

                                    Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                                    • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                                    • Makes the surrogate analysis to test for significance under the hub.
                                    • Can be easily extended by any user without touching the source code.
                                    • Reduces the programming overhead for any researcher willing to benchmark new methods.
                                    • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                                    • Increases trustworthiness thanks to a large test suite.
                                    Similar projects

                                    An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                                    Approaches

                                    Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                                    diff --git a/v0.1.0/refs.bib b/v0.1.0/refs.bib new file mode 100644 index 00000000..8010a9d3 --- /dev/null +++ b/v0.1.0/refs.bib @@ -0,0 +1,54 @@ + +@article{willeit-earth-2022, + title = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1: {Climate} model description and validation​​​​​​​​​​​​​​}, + volume = {15}, + issn = {1991-9603}, + shorttitle = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1}, + url = {https://gmd.copernicus.org/articles/15/5905/2022/}, + doi = {10.5194/gmd-15-5905-2022}, + abstract = {The newly developed fast Earth system model CLIMBER-X is presented. The climate component of CLIMBER-X consists of a 2.5-D semi-empirical statistical–dynamical atmosphere model, a 3-D frictional–geostrophic ocean model, a dynamic–thermodynamic sea ice model and a land surface model. All the model components are discretized on a regular lat–long grid with a horizontal resolution of 5 ◦ × 5 ◦. The model has a throughput of ∼ 10 000 simulation years per day on a single node with 16 CPUs on a high-performance computer and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to {\textgreater} 100 000 years. A comprehensive evaluation of the model performance for the present day and the historical period shows that CLIMBER-X is capable of realistically reproducing many observed climate characteristics, with results that generally lie within the range of state-of-theart general circulation models. The analysis of model performance is complemented by a thorough assessment of climate feedbacks and model sensitivities to changes in external forcings and boundary conditions. Limitations and applicability of the model are critically discussed. CLIMBER-X also includes a detailed representation of the global carbon cycle and is coupled to an ice sheet model, which will be described in separate papers. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.}, + language = {en}, + number = {14}, + urldate = {2022-08-11}, + journal = {Geoscientific Model Development}, + author = {Willeit, Matteo and Ganopolski, Andrey and Robinson, Alexander and Edwards, Neil R.}, + month = jul, + year = {2022}, + pages = {5905--5948}, + file = {Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:/home/jan/Zotero/storage/75NKS975/Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:application/pdf}, +} + +@article{boers-early-warning-2018, + title = {Early-warning signals for {Dansgaard}-{Oeschger} events in a high-resolution ice core record}, + volume = {9}, + issn = {2041-1723}, + url = {http://www.nature.com/articles/s41467-018-04881-7}, + doi = {10.1038/s41467-018-04881-7}, + language = {en}, + number = {1}, + urldate = {2022-10-28}, + journal = {Nature Communications}, + author = {Boers, Niklas}, + month = dec, + year = {2018}, + pages = {2556}, + file = {Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:/home/jan/Zotero/storage/DS97Z9UC/Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:application/pdf}, +} + +@article{rasmussen-stratigraphic-2014, + title = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records: refining and extending the {INTIMATE} event stratigraphy}, + volume = {106}, + issn = {02773791}, + shorttitle = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0277379114003485}, + doi = {10.1016/j.quascirev.2014.09.007}, + abstract = {Due to their outstanding resolution and well-constrained chronologies, Greenland ice-core records provide a master record of past climatic changes throughout the Last InterglacialeGlacial cycle in the North Atlantic region. As part of the INTIMATE (INTegration of Ice-core, MArine and TErrestrial records) project, protocols have been proposed to ensure consistent and robust correlation between different records of past climate. A key element of these protocols has been the formal definition and ordinal numbering of the sequence of Greenland Stadials (GS) and Greenland Interstadials (GI) within the most recent glacial period. The GS and GI periods are the Greenland expressions of the characteristic DansgaardeOeschger events that represent cold and warm phases of the North Atlantic region, respectively. We present here a more detailed and extended GS/GI template for the whole of the Last Glacial period. It is based on a synchronization of the NGRIP, GRIP, and GISP2 ice-core records that allows the parallel analysis of all three records on a common time scale. The boundaries of the GS and GI periods are defined based on a combination of stable-oxygen isotope ratios of the ice (d18O, reflecting mainly local temperature) and calcium ion concentrations (reflecting mainly atmospheric dust loading) measured in the ice. The data not only resolve the well-known sequence of DansgaardeOeschger events that were first defined and numbered in the ice-core records more than two decades ago, but also better resolve a number of short-lived climatic oscillations, some defined here for the first time. Using this revised scheme, we propose a consistent approach for discriminating and naming all the significant abrupt climatic events of the Last Glacial period that are represented in the Greenland ice records. The final product constitutes an extended and better resolved Greenland stratotype sequence, against which other proxy records can be compared and correlated. It also provides a more secure basis for investigating the dynamics and fundamental causes of these climatic perturbations.}, + language = {en}, + urldate = {2023-10-04}, + journal = {Quaternary Science Reviews}, + author = {Rasmussen, Sune O. and Bigler, Matthias and Blockley, Simon P. and Blunier, Thomas and Buchardt, Susanne L. and Clausen, Henrik B. and Cvijanovic, Ivana and Dahl-Jensen, Dorthe and Johnsen, Sigfus J. and Fischer, Hubertus and Gkinis, Vasileios and Guillevic, Myriam and Hoek, Wim Z. and Lowe, J. John and Pedro, Joel B. and Popp, Trevor and Seierstad, Inger K. and Steffensen, Jørgen Peder and Svensson, Anders M. and Vallelonga, Paul and Vinther, Bo M. and Walker, Mike J.C. and Wheatley, Joe J. and Winstrup, Mai}, + month = dec, + year = {2014}, + pages = {14--28}, + file = {Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:/home/jan/Zotero/storage/VSUTVWPN/Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:application/pdf}, +} diff --git a/v0.1.0/refs/index.html b/v0.1.0/refs/index.html new file mode 100644 index 00000000..88d946bc --- /dev/null +++ b/v0.1.0/refs/index.html @@ -0,0 +1,9 @@ + +References · TransitionsInTimeseries.jl
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                                    References

                                    diff --git a/v0.1.0/search/index.html b/v0.1.0/search/index.html new file mode 100644 index 00000000..1307658b --- /dev/null +++ b/v0.1.0/search/index.html @@ -0,0 +1,2 @@ + +Search · TransitionsInTimeseries.jl

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                                      diff --git a/v0.1.0/search_index.js b/v0.1.0/search_index.js new file mode 100644 index 00000000..0396ea47 --- /dev/null +++ b/v0.1.0/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"IndicatorsChangesConfig\nSlidingWindowConfig\nSegmentedWindowConfig\nestimate_indicator_changes\nIndicatorsChangesResults\nSlidingWindowResults\nSegmentedWindowResults","category":"page"},{"location":"api/#TransitionsInTimeseries.IndicatorsChangesConfig","page":"API","title":"TransitionsInTimeseries.IndicatorsChangesConfig","text":"IndicatorsChangesConfig\n\nSupertype used to define how indicators and their changes are estimated in estimate_indicator_changes. Valid subtypes are:\n\nSlidingWindowConfig.\nSegmentedWindowConfig.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowConfig","page":"API","title":"TransitionsInTimeseries.SlidingWindowConfig","text":"SlidingWindowConfig <: IndicatorsChangesConfig\nSlidingWindowConfig(indicators, change_metrics; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by a sliding window approach:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nindicators is a tuple of indicators (or a single indicator). change_metrics is also a tuple or a single function. If a single function, the same change metric is used for all provided indicators. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.\n\nThe results output corresponding to SlidingWindowConfig is SlidingWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_indicator_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowConfig","page":"API","title":"TransitionsInTimeseries.SegmentedWindowConfig","text":"SegmentedWindowConfig <: IndicatorsChangeConfig\nSegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)\n\nA configuration that can be given to estimate_indicator_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:\n\nFor each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).\nFor each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d\n\ntseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.\n\nThe results output corresponding to SlidingWindowConfig is SegmentedWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.\nmin_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.estimate_indicator_changes","page":"API","title":"TransitionsInTimeseries.estimate_indicator_changes","text":"estimate_indicator_changes(config::IndicatorsChangesConfig, x [,t]) → result\n\nEstimate possible transitions for input timeseries x using the approach specified in the configuration type config, see IndicatorsChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).\n\nReturn the output as subtype of IndicatorsChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.IndicatorsChangesResults","page":"API","title":"TransitionsInTimeseries.IndicatorsChangesResults","text":"IndicatorsChangesResults\n\nSupertype used to gather results of estimate_indicator_changes. The concrete subtype instances are described in the docstrings of configuration types.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowResults","page":"API","title":"TransitionsInTimeseries.SlidingWindowResults","text":"SlidingWindowResults <: IndicatorsChangesResults\n\nA struct containing the output of estimate_indicator_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nconfig::SlidingWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowResults","page":"API","title":"TransitionsInTimeseries.SegmentedWindowResults","text":"SegmentedWindowResults <: IndicatorsChangesResults\n\nA struct containing the output of estimate_indicator_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.\nt_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.\nx_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.\nt_change, the time vector of the change metric.\nconfig::SegmentedWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"significant_transitions\nTransitionsSignificance\nSurrogatesSignificance\nQuantileSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::IndicatorsChangesResults, signif::TransitionsSignificance)\n\nEstimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as res.x_change. It contains trues wherever a change metric of res is deemed significant.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.TransitionsSignificance","page":"API","title":"TransitionsInTimeseries.TransitionsSignificance","text":"TransitionsSignificance\n\nSupertype used to test for significance in significant_transitions. Valid subtypes are:\n\nSurrogatesSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: TransitionsSignificance\nSurrogatesSignificance(; surrogate = RandomFourier(), n = 10_000, tail = :both, rng)\n\nA configuration struct for significance testing significant_transitions using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\n\nDescription\n\nWhen used with IndicatorsChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric, discriminatory statistic values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in IndicatorsChangesResults.\n\nNote that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :both) <: TransitionsSignificance\n\nA configuration struct for significance testing significant_transitions. When used with IndicatorsChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\nQuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.mean(::Any)\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean-Tuple{Any}","page":"API","title":"Statistics.mean","text":"mean(itr)\n\nCompute the mean of all elements in a collection.\n\nnote: Note\nIf itr contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the mean of non-missing values.\n\nExamples\n\njulia> using Statistics\n\njulia> mean(1:20)\n10.5\n\njulia> mean([1, missing, 3])\nmissing\n\njulia> mean(skipmissing([1, missing, 3]))\n2.0\n\n\n\n\n\n","category":"method"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Statistics.var(::AbstractArray)\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var-Tuple{AbstractArray}","page":"API","title":"Statistics.var","text":"var(itr; corrected::Bool=true, mean=nothing[, dims])\n\nCompute the sample variance of collection itr.\n\nThe algorithm returns an estimator of the generative distribution's variance under the assumption that each entry of itr is a sample drawn from the same unknown distribution, with the samples uncorrelated. For arrays, this computation is equivalent to calculating sum((itr .- mean(itr)).^2) / (length(itr) - 1). If corrected is true, then the sum is scaled with n-1, whereas the sum is scaled with n if corrected is false where n is the number of elements in itr.\n\nIf itr is an AbstractArray, dims can be provided to compute the variance over dimensions.\n\nA pre-computed mean may be provided. When dims is specified, mean must be an array with the same shape as mean(itr, dims=dims) (additional trailing singleton dimensions are allowed).\n\nnote: Note\nIf array contains NaN or missing values, the result is also NaN or missing (missing takes precedence if array contains both). Use the skipmissing function to omit missing entries and compute the variance of non-missing values.\n\n\n\n\n\n","category":"method"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.","category":"page"},{"location":"api/","page":"API","title":"API","text":"For example, using the permutation entropy as an indicator is as simple as doing","category":"page"},{"location":"api/","page":"API","title":"API","text":"using ComplexityMeasures\nest = OrdinalPatterns(; m = 3) # order 3\n# create a function that given timeseries returns permutation entropy\nindicator = x -> entropy_normalized(est, x)","category":"page"},{"location":"api/","page":"API","title":"API","text":"and giving the created indicator to e.g., SlidingWindowConfig.","category":"page"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"EditURL = \"do-events.jl\"","category":"page"},{"location":"examples/do-events/#Dansgaard-Oescher-events-and-Critical-Slowing-Down","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The delta^18O timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.","category":"page"},{"location":"examples/do-events/#Preprocessing-NGRIP","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Preprocessing NGRIP","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Load the data, reverse and offset it to have time vector = time before 2000 AD.\nFilter non-unique points in time and sort the data.\nRegrid the data from uneven to even sampling.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The time and delta^18O vectors resulting from the i-th preprocessing step are respectively called t_i and x_i. The final step consists in obtaining a residual r, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.","category":"page"},{"location":"examples/do-events/#Step-1:","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 1:","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DelimitedFiles, Downloads\n\nfunction load_ngrip()\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP.csv\")\n data, labels = readdlm(tmp, header = true)\n return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors\nend\n\nt1, x1 = load_ngrip()","category":"page"},{"location":"examples/do-events/#Step-2","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 2","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"uniqueidx(v) = unique(i -> v[i], eachindex(v))\nfunction keep_unique(t, x)\n unique_idx = uniqueidx(t)\n return t[unique_idx], x[unique_idx]\nend\n\nfunction sort_timeseries!(t, x)\n p = sortperm(t)\n permute!(t, p)\n permute!(x, p)\n return nothing\nend\n\nt2, x2 = keep_unique(t1, x1)\nsort_timeseries!(t2, x2)","category":"page"},{"location":"examples/do-events/#Step-3","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 3","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using BSplineKit\n\nfunction regrid2evensampling(t, x, dt)\n itp = BSplineKit.interpolate(t, x, BSplineOrder(4))\n tspan = (ceil(minimum(t)), floor(maximum(t)))\n t_even = collect(tspan[1]:dt:tspan[2])\n x_even = itp.(t_even)\n return t_even, x_even\nend\n\ndt = 5.0 # dt = 5 yr as in (Boers 2018)\nt3, x3 = regrid2evensampling(t2, x2, dt)","category":"page"},{"location":"examples/do-events/#Step-4","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 4","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the final step we drop the indices:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DSP\n\nfunction chebyshev_filter(t, x, fcutoff)\n ii = 10 # Chebyshev filtering requires to prune first points of timeseries.\n responsetype = Highpass(fcutoff, fs = 1/dt)\n designmethod = Chebyshev1(8, 0.05)\n r = filt(digitalfilter(responsetype, designmethod), x)\n xtrend = x - r\n return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]\nend\n\nfcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)\nt, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using CairoMakie, Loess\n\nfunction loess_filter(t, x; span = 0.005)\n loessmodel = loess(t, x, span = span)\n xtrend = Loess.predict(loessmodel, t)\n r = x - xtrend\n return t, x, xtrend, r\nend\n\nfunction kyr_xticks(tticks_yr)\n tticks_kyr = [\"$t\" for t in Int.(tticks_yr ./ 1e3)]\n return (tticks_yr, tticks_kyr)\nend\n\nfunction plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)\n fig = Figure(resolution = (1600, 1200), fontsize = 24)\n\n # Original timeseries with transition marked by vertical lines\n ax1 = Axis(fig[1, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"$\\delta^{18}$O (permil)\",\n xaxisposition = :top, xticks = xticks)\n lines!(ax1, traw, xraw, color = (:gray70, 0.5))\n lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)\n vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)\n\n # Residual timeseries\n ax2 = Axis(fig[2, 1], ylabel = L\"Residual $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n lines!(ax2, t, r, color = :gray50, linewidth = 1)\n\n # Axes for variance and AC1 timeseries\n ax3 = Axis(fig[3, 1], ylabel = L\"Variance $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n ax4 = Axis(fig[4, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"Lag-1 autocor. $\\,$\",\n xticks = xticks)\n\n axs = [ax1, ax2, ax3, ax4]\n [xlims!(ax, xlims) for ax in axs]\n ylims!(axs[1], (-48, -34))\n rowgap!(fig.layout, 10)\n return fig, axs\nend\n\nxlims = (-60e3, -10e3)\nxticks = kyr_xticks(-60e3:5e3:5e3)\nt_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,\n 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]\ntloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nfig","category":"page"},{"location":"examples/do-events/#Hindcast-on-NGRIP-data","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcast on NGRIP data","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using TransitionsInTimeseries, StatsBase\nusing Random: Xoshiro\n\nac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase\nindicators = (var, ac1)\nchange_metrics = RidgeRegressionSlope()\ntseg_start = t_rasmussen[1:end-1] .+ 200\ntseg_end = t_rasmussen[2:end] .- 200\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100) # require >=100 data points to estimate change metric\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"That's it! We can now visulaise our results with a generic function that we will re-use later:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"function plot_segment_analysis!(axs, results, signif)\n (; t_indicator, x_indicator) = results\n for k in eachindex(t_indicator) # loop over the segments\n for i in axes(signif.pvalues, 2) # loop over the indicators\n if !isinf(signif.pvalues[k, i]) # plot if segment long enough\n # Plot indicator timeseries and its linear regression\n ti, xi = t_indicator[k], x_indicator[k][:, i]\n lines!(axs[i+2], ti, xi, color = Cycled(1))\n m, p = ridgematrix(ti, 0.0) * xi\n if signif.pvalues[k, i] < 0.05\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)\n else\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)\n end\n end\n end\n end\nend\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.","category":"page"},{"location":"examples/do-events/#CSD:-only-a-necessary-condition,-only-in-some-cases","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"CSD: only a necessary condition, only in some cases","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential U, which defines the deterministic term f = -U of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100)\nresults = estimate_indicator_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 10_000, tail = :right, rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that \"resilience-loss indicators\" is a more accurate name than \"early-warning signals\" when using CSD.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"We draw attention upon the fact that the delta^18O timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"warning: Degrees of freedom\nThese sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"info: Future improvement\nSupporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.","category":"page"},{"location":"examples/do-events/#Hindcasting-simulated-DO-events","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcasting simulated DO-events","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],\n [1, 3500, 4370, 5790, 7200, 8140]]\nt_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]\ntseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]\ntseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]\n\nfigvec = Figure[]\n\nfor j in 1:2\n # Download the data and perform loess filtering on it\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\" *\n \"master/timeseries/climberx-do$(j)-omaxa.csv\")\n data = readdlm(tmp)\n tcx, xcx = data[1, 1000:end], data[2, 1000:end]\n t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)\n\n # Initialize figure\n xlims = (0, last(tcx))\n xticks = kyr_xticks(xlims[1]:1e3:xlims[2])\n fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks)\n ylims!(axs[1], (5, 40))\n axs[1].ylabel = L\"Max. Atlantic overturning (Sv) $\\,$\"\n\n # Run sliding analysis and update figure with results\n dt = mean(diff(tcx))\n config = SegmentedWindowConfig(\n indicators, change_metrics, tseg_start[j], tseg_end[j],\n whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)\n results = estimate_indicator_changes(config, r, t)\n signif = SurrogatesSignificance(n = 1_000, tail = :right, rng = Xoshiro(1995))\n flags = significant_transitions(results, signif)\n\n plot_segment_analysis!(axs, results, signif)\n vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)\n push!(figvec, fig)\nend\nfigvec[1]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"figvec[2]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"EditURL = \"logistic.jl\"","category":"page"},{"location":"examples/logistic/#Permutation-entropy-for-dynamic-regime-changes","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.","category":"page"},{"location":"examples/logistic/#Logistic-map-timeseries","page":"Permutation entropy for dynamic regime changes","title":"Logistic map timeseries","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using DynamicalSystemsBase\nusing CairoMakie\n\n# time-dependent logistic map, so that the `r` parameter increases with time\nr1 = 3.83\nr2 = 3.86\nN = 2000\nrs = range(r1, r2; length = N)\n\nfunction logistic_drifting_rule(u, rs, n)\n r = rs[n+1] # time is `n`, starting from 0\n return SVector(r*u[1]*(1 - u[1]))\nend\n\nds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)\nx = trajectory(ds, N-1)[1][:, 1]","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Plot it, using as time the parameter value (they coincide)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig, ax = lines(rs, x; linewidth = 0.5)\nax.xlabel = \"r (time)\"\nax.ylabel = \"x\"\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.","category":"page"},{"location":"examples/logistic/#Using-a-simpler-change-metric","page":"Permutation entropy for dynamic regime changes","title":"Using a simpler change metric","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using TransitionsInTimeseries, ComplexityMeasures\n\nfunction permutation_entropy(m)\n est = SymbolicPermutation(; m) # order 3\n indicator = x -> entropy_normalized(est, x)\n return indicator\nend\n\nindicators = (var, ar1_whitenoise, permutation_entropy(4))\nindistrings = (\"var\", \"ar1\", \"pe\")","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"metric = difference_of_means\n\nwidth_ind = N÷100\nwidth_cha = 20\nstride_cha = 10\n\nconfig = SlidingWindowConfig(indicators, metric;\n width_ind, width_cha, stride_cha,\n)\n\nresults = estimate_indicator_changes(config, x, rs)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's now plot the change metrics of the indicators","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"function plot_change_metrics()\n fig, ax = lines(rs, x; axis = (ylabel = \"input\",), figure = (resolution = (600, 600),))\n hidexdecorations!(ax; grid = false)\n # plot all change metrics\n for (i, c) in enumerate(eachcol(results.x_change))\n ax, = scatterlines(fig[i+1, 1], results.t_change, c;\n axis = (ylabel = indistrings[i],), label = \"input\"\n )\n if i < 3\n hidexdecorations!(ax; grid = false)\n else\n ax.xlabel = \"r (time)\"\n end\n end\n return fig\nend\n\nfig = plot_change_metrics()","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.","category":"page"},{"location":"examples/logistic/#Significance-via-random-Fourier-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Significance via random Fourier surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RandomFourier()\n\n# Define a function because we will re-use later\nusing Random: Xoshiro\nfunction overplot_surrogate_significance!(fig, surromethod, color = \"black\")\n\n signif = SurrogatesSignificance(;\n n = 2000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),\n )\n flags = significant_transitions(results, signif)\n\n # and also plot the flags with same color\n for (i, indicator) in enumerate(indicators)\n # To make things visually clear, we will also plot some example surrogate\n # timeseries for each indicator and change metric pair\n for _ in 1:10\n s = TimeseriesSurrogates.surrogate(x, surromethod)\n p = windowmap(indicator, s; width = width_ind)\n q = windowmap(metric, p; width = width_cha, stride = stride_cha)\n lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1)\n end\n # Plot the flags as vertical dashed lines\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = color, linestyle = :dash, linewidth = 3\n )\n end\n # add a title to the figure with how we estimate significance\n content(fig[1, 1]).title = \"surrogates: \"*string(nameof(typeof(surromethod)))\nend\n\nsurromethod = RandomFourier()\noverplot_surrogate_significance!(fig, surromethod)\n\nfig","category":"page"},{"location":"examples/logistic/#Different-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Different surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RelativePartialRandomization(0.25)\nfig = plot_change_metrics()\noverplot_surrogate_significance!(fig, surromethod, \"gray\")\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.","category":"page"},{"location":"examples/logistic/#Simpler-Significance","page":"Permutation entropy for dynamic regime changes","title":"Simpler Significance","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig = plot_change_metrics()\nflags = significant_transitions(results, SigmaSignificance(factor = 5.0))\n\n# Plot the flags\nfor (i, indicator) in enumerate(indicators)\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = Cycled(3), linestyle = :dash, linewidth = 3\n )\nend\ncontent(fig[1, 1]).title = \"significance from std\"\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nA Julia package for estimating transitions (from one dynamic regime or stable state to another) in timeseries and testing the statistical significance of found transitions. It integrates with the entire Julia ecosystem of timeseries analysis, and hence offers thousands of metrics that can indicate transitions right out of the box. It also offers a variety of analysis pipelines for identifying transitions and a variety of statistical pipelines for testing for significance.\n\nIn contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:\n\nAdd new indicators that work with the existing analysis pipelines for finding transitions\nAdd new analysis pipelines for finding transitions\nAdd new ways for testing whether already found transitions are significant\n\nThis package is currently under active development and not yet registered in the Julia general registry. To install it, first go into package-manager mode in the Julia REPL (press ]) and then run\n\nadd https://github.com/JuliaDynamics/TransitionsInTimeseries.jl\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\nAlternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"refs/#References","page":"References","title":"References","text":"","category":"section"},{"location":"refs/","page":"References","title":"References","text":"","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"EditURL = \"tutorial.jl\"","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector,\n# we obtain the last time step of each window.\n# This therefore only uses information from `k-width+1` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\n\nfunction gridfig(nrows, ncols)\n fig = Figure()\n axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)\n for j in 1:ncols, i in 1:nrows]\n rowgap!(fig.layout, 10)\n return fig, axs\nend\nfig, axs = gridfig(2, 1)\nlines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))\nlines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))\naxs[1].title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nlines!(axs[2], t_change, change_nl, label = \"nonlin\", color = Cycled(2))\nlines!(axs[2], t_change, change_s, label = \"surrogate\", color = Cycled(3))\naxislegend()\naxs[2].title = \"change metric\"\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig, axs = gridfig(2, 2)\naxs[1].title = \"linear\"\naxs[2].title = \"nonlinear\"\n\nfor (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change) # ; color = Cycled(j)\n lines!(axsig, t_change, pval) # ; color = Cycled(j+2)\nend\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = RidgeRegressionSlope()\n\n# choices go into a configuration struct\nconfig = SlidingWindowConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last)\n\n# choices are processed\nresults = estimate_indicator_changes(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From result we can plot the change metric timeseries:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(3, 1)\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, results.x_change[:, 1];\n label = \"var slopes\", color = Cycled(3))\nscatter!(axs[3], results.t_change, results.x_change[:, 2];\n label = \"ar1 slopes\", color = Cycled(4))\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = :right)\nflags = significant_transitions(results, signif)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig, axs = gridfig(2, 1)\nlines!(axs[1], vcat(0.0, t), x_nlinear; label = \"raw\", color = Cycled(1))\nlines!(axs[1], t, input; label = \"input\", color = Cycled(2))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 1];\n label = \"var p-values\", color = Cycled(3))\nscatter!(axs[2], results.t_change, signif.pvalues[:, 2];\n label = \"ar1 p-values\", color = Cycled(4))\n\nflagsboth = vec(reduce(&, flags; dims = 2))\nvlines!(axs[1], results.t_change[flagsboth]; label = \"flags\", color = (\"black\", 0.1))\n\n[axislegend(ax) for ax in axs]\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"}] +} diff --git a/v0.1.0/siteinfo.js b/v0.1.0/siteinfo.js new file mode 100644 index 00000000..a7a85ce6 --- /dev/null +++ b/v0.1.0/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.1.0"; diff --git a/v0.1.0/tutorial.jl b/v0.1.0/tutorial.jl new file mode 100644 index 00000000..3f135673 --- /dev/null +++ b/v0.1.0/tutorial.jl @@ -0,0 +1,263 @@ +#= + +# Tutorial + +## [Workflow] (@id workflow) + +Computing transition indicators consists of the following steps: + +1. Doing any preprocessing of raw data first, such as detrending (_not part of TransitionsInTimeseries.jl_). This yields the **input timeseries**. +2. Estimating the timeseries of an indicator by sliding a window over the input timeseries. +3. Computing the changes of the indicator by sliding a window over its timeseries. +4. Generating many surrogates that preserve important statistical properties of the original timeseries. +5. Performing step 2 and 3 for the surrogate timeseries. +6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data. + +These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports. + +## [Tutorial -- Educational] (@id example_stepbystep) + +### Raw input data + +Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by: + +```math +\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t) +``` + +with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with [Makie](https://docs.makie.org/stable/)) such prototypical data to test some indicators can be done by simply running: +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_linear) +lines!(ax, t, x_nlinear) +ax.title = "raw data" +fig + +#= +### Preprocessing + +!!! note "Not part of TransitionsInTimeseries.jl" + Any timeseries preprocessing, such as the de-trending step we do here, + is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher. + + +The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1. +=# + +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +#= +At this point, `x_l_fluct` and `x_nl_fluct` are considered the **input timeseries**. + +!!! info "Detrending in Julia" + Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as [Loess.jl](https://github.com/JuliaStats/Loess.jl) or [DSP.jl](https://docs.juliadsp.org/latest/contents/). There the detrending step consists of subtracting the smoothed signal from the original one. + +### Indicator timeseries + +We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the **input timeseries**, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as [`ar1_whitenoise`](@ref): +=# + +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +## By mapping `last::Function` over a windowviewer of the time vector, +## we obtain the last time step of each window. +## This therefore only uses information from `k-width+1` to `k` at time step `k`. +## Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +#= +The lines plotted above are the **indicator timeseries**. + +### Change metric timeseries + +From here, we process the **indicator timeseries** to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the **change metric timeseries**. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a [`RidgeRegressionSlope`](@ref): +=# + +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + +#= +### Timeseries surrogates + +As expected from [Critical Slowing Down](@ref approaches), an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance. + +In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the [TimeseriesSurrogates.jl](https://github.com/JuliaDynamics/TimeseriesSurrogates.jl) Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that `TimeseriesSurrogates` is re-exported by `TransitionsInTimeseries`, so that you don't have to `using` both of them. + +To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries. +=# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) + +function gridfig(nrows, ncols) + fig = Figure() + axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false) + for j in 1:ncols, i in 1:nrows] + rowgap!(fig.layout, 10) + return fig, axs +end +fig, axs = gridfig(2, 1) +lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2)) +lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3)) +axs[1].title = "real signal vs. surrogate(s)" + +## compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2)) +lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3)) +axislegend() +axs[2].title = "change metric" + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +### Quantifying significance + +To quantify the significance of the values of the **change metric timeseries** we perform a standard surrogate test by computing the [p-value](https://en.wikipedia.org/wiki/P-value) w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically `p<0.05`) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time: +=# + +n_surrogates = 1_000 +fig, axs = gridfig(2, 2) +axs[1].title = "linear" +axs[2].title = "nonlinear" + +for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + ## Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change) # ; color = Cycled(j) + lines!(axsig, t_change, pval) # ; color = Cycled(j+2) +end + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar. + +Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section. + +## [Tutorial -- TransitionsInTimeseries.jl] (@id example_fastforward) + +TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go. + +The interface is simple, and directly parallelizes the [Workflow](@ref). It is based on the creation of a [`TransitionsSurrogatesConfig`](@ref), which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate. + +The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +## input timeseries and time +input = x_nl_fluct = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(t, input) +ax.title = "input timeseries" +fig + +#= +To perform all of the above analysis we follow a 2-step process. + +Step 1, we decide what indicators and change metrics to use in [`SlidingWindowConfig`](@ref) and apply those via +a sliding window to the input timeseries using [`transition_metrics`](@ref). +=# + +## These indicators are suitable for Critical Slowing Down +indicators = (var, ar1_whitenoise) + +## use the ridge regression slope for both indicators +change_metrics = RidgeRegressionSlope() + +## choices go into a configuration struct +config = SlidingWindowConfig(indicators, change_metrics; + width_ind = 400, width_cha = 30, whichtime = last) + +## choices are processed +results = estimate_indicator_changes(config, input, t) + +#= +From `result` we can plot the change metric timeseries: +=# + +fig, axs = gridfig(3, 1) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, results.x_change[:, 1]; + label = "var slopes", color = Cycled(3)) +scatter!(axs[3], results.t_change, results.x_change[:, 2]; + label = "ar1 slopes", color = Cycled(4)) +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +Step 2 is to estimate significance using [`SurrogatesConfig`](@ref) +and the function [`estimate_significance!`](@ref). +=# + +signif = SurrogatesSignificance(n = 1000, tail = :right) +flags = significant_transitions(results, signif) + +#= +We can now plot the p-values corresponding to each time series of the change metrics. From the `flags` we can additionally obtain the time points where _both_ indicators show significance, via a simple reduction: +=# + +fig, axs = gridfig(2, 1) +lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1)) +lines!(axs[1], t, input; label = "input", color = Cycled(2)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 1]; + label = "var p-values", color = Cycled(3)) +scatter!(axs[2], results.t_change, signif.pvalues[:, 2]; + label = "ar1 p-values", color = Cycled(4)) + +flagsboth = vec(reduce(&, flags; dims = 2)) +vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1)) + +[axislegend(ax) for ax in axs] +[xlims!(ax, 0, 50) for ax in axs] +fig \ No newline at end of file diff --git a/v0.1.0/tutorial/index.html b/v0.1.0/tutorial/index.html new file mode 100644 index 00000000..4354e30b --- /dev/null +++ b/v0.1.0/tutorial/index.html @@ -0,0 +1,160 @@ + +Tutorial · TransitionsInTimeseries.jl
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                                      Tutorial

                                      Workflow

                                      Computing transition indicators consists of the following steps:

                                      1. Doing any preprocessing of raw data first, such as detrending (not part of TransitionsInTimeseries.jl). This yields the input timeseries.
                                      2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                                      3. Computing the changes of the indicator by sliding a window over its timeseries.
                                      4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                                      5. Performing step 2 and 3 for the surrogate timeseries.
                                      6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                                      These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                                      Tutorial – Educational

                                      Raw input data

                                      Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                                      \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                                      with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                                      using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig

                                      Preprocessing

                                      Not part of TransitionsInTimeseries.jl

                                      Any timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                                      The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                                      x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig

                                      At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                                      Detrending in Julia

                                      Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                                      Indicator timeseries

                                      We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                                      indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector,
+# we obtain the last time step of each window.
+# This therefore only uses information from `k-width+1` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig

                                      The lines plotted above are the indicator timeseries.

                                      Change metric timeseries

                                      From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                                      change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig

                                      Timeseries surrogates

                                      As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                                      In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                                      To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                                      # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+
+function gridfig(nrows, ncols)
+    fig = Figure()
+    axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)
+        for j in 1:ncols, i in 1:nrows]
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+fig, axs = gridfig(2, 1)
+lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))
+lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))
+axs[1].title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2))
+lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3))
+axislegend()
+axs[2].title = "change metric"
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                      Quantifying significance

                                      To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                                      n_surrogates = 1_000
+fig, axs = gridfig(2, 2)
+axs[1].title = "linear"
+axs[2].title = "nonlinear"
+
+for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change)   # ; color = Cycled(j)
+    lines!(axsig, t_change, pval)       # ; color = Cycled(j+2)
+end
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                      As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                                      Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                                      Tutorial – TransitionsInTimeseries.jl

                                      TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                                      The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a TransitionsSurrogatesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

                                      The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

                                      using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig

                                      To perform all of the above analysis we follow a 2-step process.

                                      Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using transition_metrics.

                                      # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = RidgeRegressionSlope()
+
+# choices go into a configuration struct
+config = SlidingWindowConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last)
+
+# choices are processed
+results = estimate_indicator_changes(config, input, t)
                                      IndicatorsChangesResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                                      From result we can plot the change metric timeseries:

                                      fig, axs = gridfig(3, 1)
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, results.x_change[:, 1];
+    label = "var slopes", color = Cycled(3))
+scatter!(axs[3], results.t_change, results.x_change[:, 2];
+    label = "ar1 slopes", color = Cycled(4))
+[xlims!(ax, 0, 50) for ax in axs]
+fig

                                      Step 2 is to estimate significance using SurrogatesConfig and the function estimate_significance!.

                                      signif = SurrogatesSignificance(n = 1000, tail = :right)
+flags = significant_transitions(results, signif)
                                      2072×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ ⋮  
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 0  0

                                      We can now plot the p-values corresponding to each time series of the change metrics. From the flags we can additionally obtain the time points where both indicators show significance, via a simple reduction:

                                      fig, axs = gridfig(2, 1)
+lines!(axs[1], vcat(0.0, t), x_nlinear; label = "raw", color = Cycled(1))
+lines!(axs[1], t, input; label = "input", color = Cycled(2))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 1];
+    label = "var p-values", color = Cycled(3))
+scatter!(axs[2], results.t_change, signif.pvalues[:, 2];
+    label = "ar1 p-values", color = Cycled(4))
+
+flagsboth = vec(reduce(&, flags; dims = 2))
+vlines!(axs[1], results.t_change[flagsboth]; label = "flags", color = ("black", 0.1))
+
+[axislegend(ax) for ax in axs]
+[xlims!(ax, 0, 50) for ax in axs]
+fig
                                      diff --git a/v0.1.1/.documenter-siteinfo.json b/v0.1.1/.documenter-siteinfo.json new file mode 100644 index 00000000..30690a9f --- /dev/null +++ b/v0.1.1/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-03-13T15:45:46","documenter_version":"1.3.0"}} \ No newline at end of file diff --git a/v0.1.1/api/index.html b/v0.1.1/api/index.html new file mode 100644 index 00000000..6668e42f --- /dev/null +++ b/v0.1.1/api/index.html @@ -0,0 +1,18 @@ + +API · TransitionsInTimeseries.jl
                                      GitHub

                                      API

                                      Main analysis functions

                                      TransitionsInTimeseries.estimate_changes — Function
                                      estimate_changes(config::ChangesConfig, x [,t]) → result

                                      Estimate possible transitions for input timeseries x using the approach specified in the configuration type config, see ChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).

                                      Return the output as subtype of ChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

                                      source

                                      Sliding window

                                      TransitionsInTimeseries.SlidingWindowConfig — Type
                                      SlidingWindowConfig <: ChangesConfig
+SlidingWindowConfig(indicators, change_metrics; kwargs...)

                                      A configuration that can be given to estimate_changes. It estimates transitions by a sliding window approach:

                                      1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
                                      2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

                                      Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.

                                      indicators can be a single function or a tuple of indicators. Similarly, change_metrics can be a tuple or a single function. If tuples, the length of indicators and change_metrics must match. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

                                      The results output corresponding to SlidingWindowConfig is SlidingWindowResults.

                                      Step 1. is skipped if nothing is provided as indicators, in which case the change metrics are estimated directly from input data.

                                      Keyword arguments

                                      • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.
                                      • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.
                                      • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_changes using the keyword whichtime. Options include:
                                        • last: use the last timepoint of each window
                                        • midpoint: use the mid timepoint of each time window
                                        • first: use first timepoint of each window
                                        In fact, the indicators time vector is computed simply via
                                        t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)
                                        so any other function of the time window may be given to extract the time point itself, such as mean or median.
                                      • T = Float64: Element type of input timeseries to initialize some computations.
                                      source
                                      TransitionsInTimeseries.SlidingWindowResults — Type
                                      SlidingWindowResults <: ChangesResults

                                      A struct containing the output of estimate_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                                      It has the following fields that the user may access

                                      • x: the input timeseries.

                                      • t: the time vector of the input timeseries.

                                      • x_indicator, the indicator timeseries (matrix with each column one indicator).

                                      • t_indicator, the time vector of the indicator timeseries.

                                      • x_change, the change metric timeseries (matrix with each column one change metric).

                                      • t_change, the time vector of the change metric timeseries.

                                      • config::SlidingWindowConfig, what was used for the analysis.

                                      source

                                      Segmented window

                                      TransitionsInTimeseries.SegmentedWindowConfig — Type
                                      SegmentedWindowConfig <: IndicatorsChangeConfig
+SegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)

                                      A configuration that can be given to estimate_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:

                                      1. For each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).
                                      2. For each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d

                                      tseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.

                                      The results output corresponding to SlidingWindowConfig is SegmentedWindowResults.

                                      Keyword arguments

                                      • width_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.
                                      • min_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.
                                      source
                                      TransitionsInTimeseries.SegmentedWindowResults — Type
                                      SegmentedWindowResults <: ChangesResults

                                      A struct containing the output of estimate_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

                                      It has the following fields that the user may access

                                      • x: the input timeseries.

                                      • t: the time vector of the input timeseries.

                                      • x_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.

                                      • t_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.

                                      • x_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.

                                      • t_change, the time vector of the change metric.

                                      • config::SegmentedWindowConfig, what was used for the analysis.

                                      • i1::Vector{Int} indices corresponding to start time of each segment.

                                      • i2::Vector{Int} indices corresponding to end time of each segment.

                                      • precomp_change_metrics vector containing the precomputed change metrics of each segment.

                                      source

                                      Slope change

                                      TransitionsInTimeseries.SlopeChangeConfig — Type
                                      SlopeChangeConfig <: ChangesConfig
+SlopeChangeConfig(; indicator = nothing, kw...)

                                      A configuration that can be given to estimate_changes. It estimates a change of slope in the timeseries by fitting two connected linear segments to the timeseries, returning the results (i.e., the two-linear fits) as SlopeChangeResults.

                                      Keyword arguments

                                      • indicator = nothing: if not nothing. Otherwise it should be a function f(x) -> Real. The slope fitting is then done over an indicator of the timeseries, which itself is estimated via a sliding window exactly as in SlidingWindowConfig.
                                      • width_ind, stride_ind, whichtime: exactly as in SlidingWindowConfig if indicator is not nothing.
                                      source
                                      TransitionsInTimeseries.SlopeChangeResults — Type
                                      SlopeChangeResults <: ChangesResults

                                      A struct containing the output of estimate_changes used with SlopeChangeConfig. It can be used for further analysis, visualization, or given to significant_transitions. The only significance type that you can use this with significant_transitions is SlopeChangeSignificance.

                                      It has the following fields that the user may access:

                                      • x: the input timeseries.
                                      • t: the time vector of the input timeseries.
                                      • x_indicator, the indicator timeseries.
                                      • t_indicator, the time vector of the indicator timeseries.
                                      • t_change, the time the slope changes.
                                      • fitparams = a, b, c, d, the fitted linear coefficients, a + b*t before. t_change and c + d*t after t_change.
                                      source

                                      Significance testing

                                      TransitionsInTimeseries.significant_transitions — Function
                                      significant_transitions(res::ChangesResults, signif::Significance)

                                      Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as the changes stored in res (which typically is stored in the field res.x_change). flags is true wherever a change metric of res is deemed significant.

                                      source
                                      TransitionsInTimeseries.SurrogatesSignificance — Type
                                      SurrogatesSignificance <: Significance
+SurrogatesSignificance(; kwargs...)

                                      A configuration struct for significance testing significant_transitions using timeseries surrogates.

                                      Keyword arguments

                                      • surromethod = RandomFourier(): method to generate surrogates
                                      • n = 1000: how many surrogates to generate
                                      • rng = Random.default_rng(): random number generator for the surrogates
                                      • p = 0.05: threshold for significance of the p-value
                                      • tail = :both: tail type used, see below

                                      Description

                                      When used with ChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

                                      The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in ChangesResults.

                                      Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

                                      source
                                      TransitionsInTimeseries.ThresholdSignificance — Type
                                      ThresholdSignificance(threshold::Real; tail = :right) <: Significance

                                      A configuration struct for significance testing in significant_transitions. Significance is estimated by comparing the value of each change metric with the given threshold. Values that exceed the threshold (if tail = :right) or subseed the threshold (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                                      source
                                      TransitionsInTimeseries.SigmaSignificance — Type
                                      SigmaSignificance(; factor = 3.0, tail = :both) <: Significance

                                      A configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing how many standard deviations (σ) the value exceeds the mean value (μ). Values that exceed (if tail = :right) μ + factor*σ, or subseed (if tail = :left) μ - factor*σ are deemed significant. If tail = :both then either condition is checked.

                                      factor can also be a vector of values, in which case a different value is used for each change metric.

                                      See also QuantileSignificance.

                                      source
                                      TransitionsInTimeseries.QuantileSignificance — Type
                                      QuantileSignificance(; p = 0.95, tail = :both) <: Significance

                                      A configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

                                      QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

                                      source
                                      TransitionsInTimeseries.SlopeChangeSignificance — Type
                                      SlopeChangeSignificance(; moe_slope, moe_offset, slope_diff = moe_slope, pvalue = 0.05)

                                      Test whether the result of SlopeChangeResults is statistically significant.

                                      Two tests are done:

                                      1. Check whether the margin of error of the fitted parameters a, b, c, d of the two linear segments a + b*t, c + d*t is less than the specified margins of error, for a chosen pvalue.
                                      2. Test that the two slopes b, d have difference greater than slope_diff.

                                      The Boolean & of the above two is the final test.

                                      The margin of error is simply half the size of the confidence interval, also known as radius of the confidence interval.

                                      source

                                      Indicators

                                      Note that any Julia function can be an indicator or change metric, so the list here is only just a couple of indicators directly implemented in this package.

                                      Value distribution

                                      Statistics.mean — Function
                                      mean(A::AbstractArray, w::AbstractWeights[, dims::Int])

                                      Compute the weighted mean of array A with weight vector w (of type AbstractWeights). If dim is provided, compute the weighted mean along dimension dims.

                                      Examples

                                      n = 20
+x = rand(n)
+w = rand(n)
+mean(x, weights(w))
                                      source
                                      StatsBase.skewness — Function
                                      skewness(v, [wv::AbstractWeights], m=mean(v))

                                      Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                                      source
                                      StatsBase.kurtosis — Function
                                      kurtosis(v, [wv::AbstractWeights], m=mean(v))

                                      Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

                                      source

                                      Critical Slowing Down

                                      Statistics.var — Function
                                      var(x::AbstractArray, w::AbstractWeights, [dim]; mean=nothing, corrected=false)

                                      Compute the variance of a real-valued array x, optionally over a dimension dim. Observations in x are weighted using weight vector w. The uncorrected (when corrected=false) sample variance is defined as:

                                      \[\frac{1}{\sum{w}} \sum_{i=1}^n {w_i\left({x_i - μ}\right)^2 }\]

                                      where $n$ is the length of the input and $μ$ is the mean. The unbiased estimate (when corrected=true) of the population variance is computed by replacing $\frac{1}{\sum{w}}$ with a factor dependent on the type of weights used:

                                      • AnalyticWeights: $\frac{1}{\sum w - \sum {w^2} / \sum w}$
                                      • FrequencyWeights: $\frac{1}{\sum{w} - 1}$
                                      • ProbabilityWeights: $\frac{n}{(n - 1) \sum w}$ where $n$ equals count(!iszero, w)
                                      • Weights: ArgumentError (bias correction not supported)
                                      source
                                      var(ce::CovarianceEstimator, x::AbstractVector; mean=nothing)

                                      Compute the variance of the vector x using the estimator ce.

                                      source
                                      TransitionsInTimeseries.ar1_whitenoise — Function
                                      ar1_whitenoise(x::AbstractVector)

                                      Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

                                      \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

                                      source

                                      Spectrum

                                      TransitionsInTimeseries.LowfreqPowerSpectrum — Type
                                      LowfreqPowerSpectrum(; q_lofreq = 0.1)

                                      Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

                                      lfps = precompute( LowfreqPowerSpectrum() )

                                      Keyword arguments:

                                      • q_lofreq: a number between 0 and 1 that characterises which portion of the

                                      frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

                                      source
                                      TransitionsInTimeseries.PrecomputedLowfreqPowerSpectrum — Type
                                      PrecomputedLowfreqPowerSpectrum

                                      A struct containing all the precomputed fields to efficiently perform repetitive computation of the low-frequency power spectrum (LFPS), a number between 0 and 1 that characterizes the amount of power contained in the low frequencies of the power density spectrum of x. Once lfps::PrecomputedLowfreqPowerSpectrum is initialized, it can be used as a function to obtain the LFPS of x::AbstractVector by:

                                      lfps(x)
                                      source

                                      Nonlinear dynamics

                                      Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.

                                      For example, using the permutation entropy as an indicator is as simple as doing

                                      using ComplexityMeasures
+est = OrdinalPatterns(; m = 3) # order 3
+# create a function that given timeseries returns permutation entropy
+indicator = x -> entropy_normalized(est, x)

                                      and giving the created indicator to e.g., SlidingWindowConfig.

                                      Change metrics

                                      Slope

                                      TransitionsInTimeseries.kendalltau — Function
                                      kendalltau(x::AbstractVector)

                                      Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

                                      source
                                      TransitionsInTimeseries.spearman — Function
                                      spearman(x::AbstractVector)

                                      Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

                                      source

                                      Value distribution differences

                                      TransitionsInTimeseries.difference_of_means — Function
                                      difference_of_means(x::AbstractArray)

                                      Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

                                      # assumes 1-based indexing
+n = length(x)
+x1 = view(x, 1:n÷2)
+x2 = view(x, (n÷2 + 1):n)
+return abs(mean(x1) - mean(x2))

                                      difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

                                      source

                                      Make your own indicator/metric!

                                      The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

                                      There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:

                                      Surrogates

                                      For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

                                      Sliding windows

                                      TransitionsInTimeseries.WindowViewer — Type
                                      WindowViewer(x; width, stride)

                                      Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

                                      If not given, the keywords width, stride are respectively taken as default_window_width(x) and 1.

                                      source
                                      TransitionsInTimeseries.windowmap — Function
                                      windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

                                      A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

                                      source

                                      Load data

                                      Visualization

                                      TransitionsInTimeseries.plot_indicator_changes — Function
                                      plot_indicator_changes(res) → (fig, axs)

                                      Return fig::Figure and axs::Matrix{Axis}, on which res::ChangesResults has been visualised.

                                      Keyword arguments:

                                      • colors = default_colors sets the colors of the line plots that are to

                                      be cycled through. The default correspond to the color scheme of Julia Dynamics.

                                      • `indicatornames = defaultindicatorlabel(res), chametricnames =

                                      defaultchametriclabel(res)sets the labels for the indicators and the change metrics, with the default inferring them from the names ofres.config.indicatorsandres.config.change_metrics`.

                                      • accent_linewidth = 3 sets the line width for the original signals (the

                                      surrogates have linewidth = 1)

                                      source
                                      TransitionsInTimeseries.plot_significance! — Function
                                      plot_significance!(axs, res, signif)

                                      Update the axs::Matrix{Axis} of a figure obtained with plot_indicator_changes(res) with the signif::SurrogatesSignificance.

                                      Keyword arguments:

                                      • flags = nothing provides the significance flags, for instance obtained by

                                      thresholding the pvalues.

                                      • nsurro = 20 sets the number of surrogates to plot.
                                      source

                                      Utils

                                      default_window_width
                                      diff --git a/v0.1.1/assets/documenter.js b/v0.1.1/assets/documenter.js new file mode 100644 index 00000000..c6562b55 --- /dev/null +++ b/v0.1.1/assets/documenter.js @@ -0,0 +1,1050 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
                                      `; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`${querystring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(querystring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
                                      +
                                      ${escape(result.title)}
                                      +
                                      ${result.category}
                                      +
                                      +

                                      + ${display_result} +

                                      +
                                      + ${display_link} +
                                      +                                       + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
                                      `; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
                                      ${count_str}
                                      `; + + search_result_container = ` +
                                      + ${modal_filters} + ${search_divider} + ${result_count} +
                                      + ${search_results} +
                                      +
                                      + `; + } else { + search_result_container = ` +
                                      + ${modal_filters} + ${search_divider} +
                                      0 result(s)
                                      +
                                      +
                                      No result found!
                                      + `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
                                      Type something to get started!
                                      + `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
                                      + Filters: + ${str} +
                                      `; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
                                      +
                                      +

                                      + + + + +

                                      +
                                      +
                                      + +
                                      +
                                      + `; + + let initial_search_body = ` +
                                      Type something to get started!
                                      + `; + + let search_modal_footer = ` +
                                      + + Ctrl + + / to search + + esc to close +
                                      + `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
                                      Type something to get started!
                                      + `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v0.1.1/assets/themes/documenter-dark.css b/v0.1.1/assets/themes/documenter-dark.css new file mode 100644 index 00000000..7c679a76 --- /dev/null +++ b/v0.1.1/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ +html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:4px;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--documenter-dark .is-focused.button,html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active,html.theme--documenter-dark .pagination-ellipsis:active,html.theme--documenter-dark .file-cta:active,html.theme--documenter-dark .file-name:active,html.theme--documenter-dark .select select:active,html.theme--documenter-dark .textarea:active,html.theme--documenter-dark .input:active,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:active,html.theme--documenter-dark .button:active,html.theme--documenter-dark .is-active.pagination-previous,html.theme--documenter-dark .is-active.pagination-next,html.theme--documenter-dark .is-active.pagination-link,html.theme--documenter-dark .is-active.pagination-ellipsis,html.theme--documenter-dark .is-active.file-cta,html.theme--documenter-dark .is-active.file-name,html.theme--documenter-dark .select select.is-active,html.theme--documenter-dark .is-active.textarea,html.theme--documenter-dark .is-active.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-active,html.theme--documenter-dark .is-active.button{outline:none}html.theme--documenter-dark .pagination-previous[disabled],html.theme--documenter-dark .pagination-next[disabled],html.theme--documenter-dark .pagination-link[disabled],html.theme--documenter-dark .pagination-ellipsis[disabled],html.theme--documenter-dark .file-cta[disabled],html.theme--documenter-dark .file-name[disabled],html.theme--documenter-dark .select select[disabled],html.theme--documenter-dark .textarea[disabled],html.theme--documenter-dark .input[disabled],html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input[disabled],html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark fieldset[disabled] .pagination-previous,fieldset[disabled] html.theme--documenter-dark .pagination-next,html.theme--documenter-dark fieldset[disabled] .pagination-next,fieldset[disabled] html.theme--documenter-dark .pagination-link,html.theme--documenter-dark fieldset[disabled] .pagination-link,fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis,fieldset[disabled] html.theme--documenter-dark .file-cta,html.theme--documenter-dark fieldset[disabled] .file-cta,fieldset[disabled] html.theme--documenter-dark .file-name,html.theme--documenter-dark fieldset[disabled] .file-name,fieldset[disabled] html.theme--documenter-dark .select select,fieldset[disabled] html.theme--documenter-dark .textarea,fieldset[disabled] html.theme--documenter-dark .input,fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar 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html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark 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html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark 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.button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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kbd.button{background-color:#363636;border-color:#363636;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark 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.button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#f4c72f;box-shadow:none;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fefaec;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fdf7e0;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fdf3d3;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#c13930;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(203,60,51,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#b7362e;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:#cb3c33;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-outlined.is-focused{background-color:#cb3c33;border-color:#cb3c33;color:#fff}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:2px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#fff;border-color:#dbdbdb;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#f5f5f5;border-color:#dbdbdb;color:#7a7a7a;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:2px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#cdc3e3;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#f5f5f5;border-left:5px solid #dbdbdb;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #dbdbdb;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#cdc3e3}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#cdc3e3}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#cdc3e3}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 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                                      GitHub

                                      Developer's documentation

                                      This documentation addresses users that would like to contribute to the software by either solving bugs, improving documentation, or adding new methods. All contributions come in the form of Pull Requests, for which we strongly advise to follow good practices in scientific code, which means that they properly formatted, documented, tested, etc.

                                      New indicators or change metrics

                                      As explained already in e.g., SlidingWindowConfig, new indicators or change metrics are standard Julia functions, so you only need to define such a function (and document it, test it, etc.).

                                      New pipeline for estimating changes

                                      This means to contribute a fundamentally new "pipeline" for estimating/detecting transitions in timeseries. This new pipeline defines what a "transition" means. To add a new pipeline follow these steps:

                                      1. Define a new subtype of ChangesConfig
                                      2. Define a new subtype of ChangesResults
                                      3. Add a method for estimate_changes which accepts the new ChangesConfig subtype you defined and returns the ChangesResults subtype you defined.

                                      And that's it!

                                      Optionally you can further extend:

                                      • TransitionsInTimeseries.plot_indicator_changes with the new ChangesResults type you defined. Note the plotting functions are in the ext folder of the repository.
                                      • significant_transitions(res::ChangesResults, signif::Significance) with your new ChangesResults type and as many Significance subtypes you have the capacity to extend for.

                                      New pipeline for estimating significance

                                      Statistically significant changes are "transitions". However, what "significant" means is not universal. There are different ways to test for significance and TransitionsInTimeseries.jl allows various methods.

                                      To add a new pipeline for estimating significance follow these steps:

                                      1. Define a new subtype of Significance
                                      2. Extend significant_transitions(res::ChangesResults, signif::Significance) with your new type and as many ChangesResults subtypes as you have capacity for.

                                      And that's it! Unfortunately so far we have found no way to make the significant_transitions code agnostic of the changes result, so you would need to add a method manually for every ChangesResults.

                                      Optionally you can further extend TransitionsInTimeseries.plot_significance! (which you can find in the ext folder) for visualizing the significance results.

                                      diff --git a/v0.1.1/examples/do-events.jl b/v0.1.1/examples/do-events.jl new file mode 100644 index 00000000..9e93f1f4 --- /dev/null +++ b/v0.1.1/examples/do-events.jl @@ -0,0 +1,318 @@ +#= +# Dansgaard-Oescher events and Critical Slowing Down + +The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project +([NGRIP](https://en.wikipedia.org/wiki/North_Greenland_Ice_Core_Project)) are, +to this date, the best proxy record for the Dansgaard-Oeschger events +([DO-events](https://en.wikipedia.org/wiki/Dansgaard%E2%80%93Oeschger_event)). +DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees +of regional warming within 100 years. They happened quasi-periodically over the +last glacial cycle due to transitions between strong and weak states of the Atlantic +Meridional Overturning Circulation and might be therefore be the most prominent +examples of abrupt transitions in the field of climate science. We here propose +to hindcast these events by applying the theory of Critical Slowing Down (CSD) +on the NGRIP data, which can be found [here](https://www.iceandclimate.nbi.ku.dk/data/) +in its raw format. This analysis has already been done in [boers-early-warning-2018](@cite) +and we here try to reproduce Figure 2.d-f. + +## Preprocessing NGRIP + +Data pre-processing is not part of TransitionsInTimeseries.jl, +but a step the user has to do before using the package. +To present an example with a complete scientific workflow, +we will showcase typical data pre-processing here, that consist of the following steps: +1. Load the data, reverse and offset it to have time vector = time before 2000 AD. +2. Filter non-unique points in time and sort the data. +3. Regrid the data from uneven to even sampling. + +The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are +respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual +$r$, i.e. the fluctuations of the system around the attractor, which, within the CSD +theory, is assumed to be tracked. Over this example, it will appear that the +convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written +for plotting and preprocessing. + +### Step 1: +=# + +using DelimitedFiles, Downloads + +function load_ngrip() + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP.csv") + data, labels = readdlm(tmp, header = true) + return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors +end + +t1, x1 = load_ngrip() + +#= +### Step 2 +=# + +uniqueidx(v) = unique(i -> v[i], eachindex(v)) +function keep_unique(t, x) + unique_idx = uniqueidx(t) + return t[unique_idx], x[unique_idx] +end + +function sort_timeseries!(t, x) + p = sortperm(t) + permute!(t, p) + permute!(x, p) + return nothing +end + +t2, x2 = keep_unique(t1, x1) +sort_timeseries!(t2, x2) + +#= +### Step 3 +=# + +using BSplineKit + +function regrid2evensampling(t, x, dt) + itp = BSplineKit.interpolate(t, x, BSplineOrder(4)) + tspan = (ceil(minimum(t)), floor(maximum(t))) + t_even = collect(tspan[1]:dt:tspan[2]) + x_even = itp.(t_even) + return t_even, x_even +end + +dt = 5.0 # dt = 5 yr as in (Boers 2018) +t3, x3 = regrid2evensampling(t2, x2, dt) + +#= +### Step 4 + +For the final step we drop the indices: +=# + +using DSP + +function chebyshev_filter(t, x, fcutoff) + ii = 10 # Chebyshev filtering requires to prune first points of timeseries. + responsetype = Highpass(fcutoff, fs = 1/dt) + designmethod = Chebyshev1(8, 0.05) + r = filt(digitalfilter(responsetype, designmethod), x) + xtrend = x - r + return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end] +end + +fcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018) +t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff) + +#= +Let's now visualize our data in what will become our main figure. +For the segmentation of the DO-events, we rely on the tabulated +data from [rasmussen-stratigraphic-2014](@cite) (which will soon be available as downloadable): +=# + +using CairoMakie, Loess + +function loess_filter(t, x; span = 0.005) + loessmodel = loess(t, x, span = span) + xtrend = Loess.predict(loessmodel, t) + r = x - xtrend + return t, x, xtrend, r +end + +function kyr_xticks(tticks_yr) + tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)] + return (tticks_yr, tticks_kyr) +end + +function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks) + fig = Figure(size = (1600, 1200), fontsize = 24) + + ## Original timeseries with transition marked by vertical lines + ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)", + xaxisposition = :top, xticks = xticks) + lines!(ax1, traw, xraw, color = (:gray70, 0.5)) + lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3) + vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3) + + ## Residual timeseries + ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + lines!(ax2, t, r, color = :gray50, linewidth = 1) + + ## Axes for variance and AC1 timeseries + ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks, + xticksvisible = false, xticklabelsvisible = false) + ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$", + xticks = xticks) + + axs = [ax1, ax2, ax3, ax4] + [xlims!(ax, xlims) for ax in axs] + ylims!(axs[1], (-48, -34)) + rowgap!(fig.layout, 10) + return fig, axs +end + +xlims = (-60e3, -10e3) +xticks = kyr_xticks(-60e3:5e3:5e3) +t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160, + 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703] +tloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +fig + +#= +## Hindcast on NGRIP data + +As one can see... there is not much to see so far. +Residuals are impossible to simply eye-ball and we therefore use +TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression +slope of the residual's variance and lag-1 autocorrelation (AC1) over time. +In many examples of the literature, including [boers-early-warning-2018](@cite), +the CSD analysis is performed over segments (sometimes only one) of the timeseries, +such that a significance value is obtained for each segment. By using +`SegmentedWindowConfig`, dealing with segments can be easily done in +TransitionsInTimeseries.jl and is demonstrated here: +=# + +using TransitionsInTimeseries, StatsBase +using Random: Xoshiro + +ac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase +indicators = (var, ac1) +change_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope()) +tseg_start = t_rasmussen[1:end-1] .+ 200 +tseg_end = t_rasmussen[2:end] .- 200 +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) # require >=100 data points to estimate change metric +results = estimate_changes(config, r, t) +signif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) + +#= +That's it! We can now visulaise our results with a generic function that we will re-use later: +=# + +function plot_segment_analysis!(axs, results, signif) + (; t_indicator, x_indicator) = results + for k in eachindex(t_indicator) # loop over the segments + for i in axes(signif.pvalues, 2) # loop over the indicators + if !isnan(signif.pvalues[k, i]) # plot if segment long enough + ## Plot indicator timeseries and its linear regression + ti, xi = t_indicator[k], x_indicator[k][:, i] + lines!(axs[i+2], ti, xi, color = Cycled(1)) + m, p = ridgematrix(ti, 0.0) * xi + if signif.pvalues[k, i] < 0.05 + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3) + else + lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3) + end + end + end + end +end +plot_segment_analysis!(axs, results, signif) +fig + +#= +In [boers-early-warning-2018](@cite), 13/16 and 7/16 true positives are respectively +found for the variance and AC1, with 16 referring to the total number of transitions. +The timeseries actually includes 18 transition but, in +[boers-early-warning-2018](@cite), some segments are considered too small to be analysed. +In contrast, we here respectively find 9/16 true positives +for the variance and 3/16 for AC1. We can track down the discrepancies to be in the +surrogate testing, since the indicator timeseries computed here are almost exactly +similar to those of [boers-early-warning-2018](@cite). This mismatch points +out that packages like TransitionsInTimeseries.jl are wishful for research to be +reproducible, especially since CSD is gaining attention - not only within the +scientific community but also in popular media. + +## CSD: only a necessary condition, only in some cases + +For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies +a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the +SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore +a **necessary condition** for crossing one of these bifurcations - although it is not +always assessable by analysing the timeseries due to practical limitations (e.g. sparse +data subject to large measurement noise). It is nonetheless not given that DO-events, +as many other real-life applications, can be seen as a codimension-1 fold, Hopf or +transcritical bifurcations. Besides this, we emphasise that CSD is **not a sufficient +condition** for assessing a transition being ahead in near future, since a resilience +loss can happen without actually crossing any bifurcation. This can be illustrated on +the present example by performing the same analysis only until few hundred years before +the transition: +=# + +tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before +config = SegmentedWindowConfig(indicators, change_metrics, + tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt), + min_width_cha = 100) +results = estimate_changes(config, r, t) +signif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995)) +flags = significant_transitions(results, signif) +fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks) +plot_segment_analysis!(axs, results, signif) +fig + +#= +For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD. + +We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC). + +!!! warning "Degrees of freedom" + These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice. + +!!! info "Future improvement" + Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias. + +## Hindcasting simulated DO-events + +In CLIMBER-X, the EMIC described in [willeit-earth-2022](@cite), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs: +=# + +t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050], + [1, 3500, 4370, 5790, 7200, 8140]] +t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]] +tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]] +tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50] + +figvec = Figure[] + +for j in 1:2 + ## Download the data and perform loess filtering on it + tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" * + "master/timeseries/climberx-do$(j)-omaxa.csv") + data = readdlm(tmp) + tcx, xcx = data[1, 1000:end], data[2, 1000:end] + t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02) + + ## Initialize figure + xlims = (0, last(tcx)) + xticks = kyr_xticks(xlims[1]:1e3:xlims[2]) + fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks) + ylims!(axs[1], (5, 40)) + axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$" + + ## Run sliding analysis and update figure with results + dt = mean(diff(tcx)) + config = SegmentedWindowConfig( + indicators, change_metrics, tseg_start[j], tseg_end[j], + whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100) + results = estimate_changes(config, r, t) + signif = SurrogatesSignificance(n = 1_000, tail = [:right, :right], rng = Xoshiro(1995)) + flags = significant_transitions(results, signif) + + plot_segment_analysis!(axs, results, signif) + vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3) + push!(figvec, fig) +end +figvec[1] + +#= +It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case: +=# + +figvec[2] + +#= +Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience. +=# \ No newline at end of file diff --git a/v0.1.1/examples/do-events/04e32464.png b/v0.1.1/examples/do-events/04e32464.png new file mode 100644 index 00000000..7bfca68e Binary files /dev/null and b/v0.1.1/examples/do-events/04e32464.png differ diff --git a/v0.1.1/examples/do-events/119c6a22.png b/v0.1.1/examples/do-events/119c6a22.png new file mode 100644 index 00000000..c389928b Binary files /dev/null and b/v0.1.1/examples/do-events/119c6a22.png differ diff --git a/v0.1.1/examples/do-events/1a3693f0.png b/v0.1.1/examples/do-events/1a3693f0.png new file mode 100644 index 00000000..5924cba8 Binary files /dev/null and b/v0.1.1/examples/do-events/1a3693f0.png differ diff --git a/v0.1.1/examples/do-events/809214dc.png b/v0.1.1/examples/do-events/809214dc.png new file mode 100644 index 00000000..e77d6d06 Binary files /dev/null and b/v0.1.1/examples/do-events/809214dc.png differ diff --git a/v0.1.1/examples/do-events/a53dd564.png b/v0.1.1/examples/do-events/a53dd564.png new file mode 100644 index 00000000..80ab24b4 Binary files /dev/null and b/v0.1.1/examples/do-events/a53dd564.png differ diff --git a/v0.1.1/examples/do-events/index.html b/v0.1.1/examples/do-events/index.html new file mode 100644 index 00000000..20055820 --- /dev/null +++ b/v0.1.1/examples/do-events/index.html @@ -0,0 +1,191 @@ + +Dansgaard-Oescher events and Critical Slowing Down · TransitionsInTimeseries.jl
                                      GitHub

                                      Dansgaard-Oescher events and Critical Slowing Down

                                      The $\delta^{18}O$ timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.

                                      Preprocessing NGRIP

                                      Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:

                                      1. Load the data, reverse and offset it to have time vector = time before 2000 AD.
                                      2. Filter non-unique points in time and sort the data.
                                      3. Regrid the data from uneven to even sampling.

                                      The time and $\delta^{18}O$ vectors resulting from the $i$-th preprocessing step are respectively called $t_i$ and $x_i$. The final step consists in obtaining a residual $r$, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.

                                      Step 1:

                                      using DelimitedFiles, Downloads
+
+function load_ngrip()
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+        "master/timeseries/NGRIP.csv")
+    data, labels = readdlm(tmp, header = true)
+    return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors
+end
+
+t1, x1 = load_ngrip()
                                      ([-59944.5, -59939.6, -59935.9, -59930.5, -59925.0, -59919.0, -59914.3, -59909.4, -59904.5, -59899.7  …  -27.40000000000009, -27.40000000000009, -27.299999999999955, -27.299999999999955, -27.200000000000045, -27.09999999999991, -27.09999999999991, -27.0, -26.90000000000009, -26.799999999999955], [-43.52, -42.94, -42.13, -40.04, -41.09, -43.57, -42.28, -41.2, -44.07, -44.53  …  -35.29, -35.18, -35.51, -36.03, -36.52, -37.12, -37.41, -37.21, -36.62, -35.52])

                                      Step 2

                                      uniqueidx(v) = unique(i -> v[i], eachindex(v))
+function keep_unique(t, x)
+    unique_idx = uniqueidx(t)
+    return t[unique_idx], x[unique_idx]
+end
+
+function sort_timeseries!(t, x)
+    p = sortperm(t)
+    permute!(t, p)
+    permute!(x, p)
+    return nothing
+end
+
+t2, x2 = keep_unique(t1, x1)
+sort_timeseries!(t2, x2)

                                      Step 3

                                      using BSplineKit
+
+function regrid2evensampling(t, x, dt)
+    itp = BSplineKit.interpolate(t, x, BSplineOrder(4))
+    tspan = (ceil(minimum(t)), floor(maximum(t)))
+    t_even = collect(tspan[1]:dt:tspan[2])
+    x_even = itp.(t_even)
+    return t_even, x_even
+end
+
+dt = 5.0        # dt = 5 yr as in (Boers 2018)
+t3, x3 = regrid2evensampling(t2, x2, dt)
                                      ([-59944.0, -59939.0, -59934.0, -59929.0, -59924.0, -59919.0, -59914.0, -59909.0, -59904.0, -59899.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-43.445268010797946, -42.85408835164853, -41.357360665158936, -39.9365468206892, -41.60554051352076, -43.57000000000001, -42.145558689100454, -41.33160823883399, -44.273597725729985, -44.4622612304012  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46])

                                      Step 4

                                      For the final step we drop the indices:

                                      using DSP
+
+function chebyshev_filter(t, x, fcutoff)
+    ii = 10             # Chebyshev filtering requires to prune first points of timeseries.
+    responsetype = Highpass(fcutoff, fs = 1/dt)
+    designmethod = Chebyshev1(8, 0.05)
+    r = filt(digitalfilter(responsetype, designmethod), x)
+    xtrend = x - r
+    return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]
+end
+
+fcutoff = 0.95 * 0.01   # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)
+t, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)
                                      ([-59899.0, -59894.0, -59889.0, -59884.0, -59879.0, -59874.0, -59869.0, -59864.0, -59859.0, -59854.0  …  -74.0, -69.0, -64.0, -59.0, -54.0, -49.0, -44.0, -39.0, -34.0, -29.0], [-44.4622612304012, -44.264401428210874, -44.02956767939856, -42.29334237357212, -42.594341674200344, -41.09704877854712, -40.39837540966913, -44.369155046413255, -42.74492506508012, -43.737014520530145  …  -35.12, -36.190000000000005, -35.14, -37.06, -34.93, -34.23, -33.53, -35.09, -34.00000000000001, -34.46], [-43.89287787976461, -48.663435112414156, -51.31169981050155, -51.269094666491796, -49.90310432724566, -47.721430022512344, -44.36050569418247, -43.87556827410048, -43.57802291229893, -41.36870967826094  …  -34.81349114528442, -36.01634453179986, -36.150446802907226, -36.37595639697143, -35.96843653265903, -33.899634243732976, -32.49784036951535, -33.06575312724142, -34.07956188682297, -34.4079080530096], [-0.5693833506365866, 4.399033684203284, 7.282132131102991, 8.975752292919669, 7.308762653045311, 6.624381243965224, 3.9621302845133433, -0.493586772312777, 0.8330978472188112, -2.368304842269206  …  -0.30650885471557926, -0.17365546820014846, 1.0104468029072273, -0.684043603028572, 1.0384365326590237, -0.3303657562670192, -1.0321596304846505, -2.0242468727585807, 0.07956188682296689, -0.05209194699039831])

                                      Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):

                                      using CairoMakie, Loess
+
+function loess_filter(t, x; span = 0.005)
+    loessmodel = loess(t, x, span = span)
+    xtrend = Loess.predict(loessmodel, t)
+    r = x - xtrend
+    return t, x, xtrend, r
+end
+
+function kyr_xticks(tticks_yr)
+    tticks_kyr = ["$t" for t in Int.(tticks_yr ./ 1e3)]
+    return (tticks_yr, tticks_kyr)
+end
+
+function plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)
+    fig = Figure(size = (1600, 1200), fontsize = 24)
+
+    # Original timeseries with transition marked by vertical lines
+    ax1 = Axis(fig[1, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"$\delta^{18}$O (permil)",
+        xaxisposition = :top, xticks = xticks)
+    lines!(ax1, traw, xraw, color = (:gray70, 0.5))
+    lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)
+    vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)
+
+    # Residual timeseries
+    ax2 = Axis(fig[2, 1], ylabel = L"Residual $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    lines!(ax2, t, r, color = :gray50, linewidth = 1)
+
+    # Axes for variance and AC1 timeseries
+    ax3 = Axis(fig[3, 1], ylabel = L"Variance $\,$", xticks = xticks,
+        xticksvisible = false, xticklabelsvisible = false)
+    ax4 = Axis(fig[4, 1], xlabel = L"Time (kyr) $\,$", ylabel = L"Lag-1 autocor. $\,$",
+        xticks = xticks)
+
+    axs = [ax1, ax2, ax3, ax4]
+    [xlims!(ax, xlims) for ax in axs]
+    ylims!(axs[1], (-48, -34))
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+
+xlims = (-60e3, -10e3)
+xticks = kyr_xticks(-60e3:5e3:5e3)
+t_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,
+                38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]
+tloess, _, xloess, rloess = loess_filter(t3, x3)    # loess-filtered signal for visualization
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+fig
                                      Example block output

                                      Hindcast on NGRIP data

                                      As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:

                                      using TransitionsInTimeseries, StatsBase
+using Random: Xoshiro
+
+ac1(x) = sum(autocor(x, [1]))   # AC1 from StatsBase
+indicators = (var, ac1)
+change_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope())
+tseg_start = t_rasmussen[1:end-1] .+ 200
+tseg_end = t_rasmussen[2:end] .- 200
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)        # require >=100 data points to estimate change metric
+results = estimate_changes(config, r, t)
+signif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
                                      18×2 BitMatrix:
+ 0  0
+ 0  0
+ 0  0
+ 0  0
+ 1  0
+ 1  1
+ 1  1
+ 1  1
+ 0  0
+ 1  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 0  0
+ 0  0
+ 1  0
+ 1  0

                                      That's it! We can now visulaise our results with a generic function that we will re-use later:

                                      function plot_segment_analysis!(axs, results, signif)
+    (; t_indicator, x_indicator) = results
+    for k in eachindex(t_indicator)             # loop over the segments
+        for i in axes(signif.pvalues, 2)        # loop over the indicators
+            if !isnan(signif.pvalues[k, i])     # plot if segment long enough
+                # Plot indicator timeseries and its linear regression
+                ti, xi = t_indicator[k], x_indicator[k][:, i]
+                lines!(axs[i+2], ti, xi, color = Cycled(1))
+                m, p = ridgematrix(ti, 0.0) * xi
+                if signif.pvalues[k, i] < 0.05
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)
+                else
+                    lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)
+                end
+            end
+        end
+    end
+end
+plot_segment_analysis!(axs, results, signif)
+fig
                                      Example block output

                                      In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.

                                      CSD: only a necessary condition, only in some cases

                                      For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential $U$, which defines the deterministic term $f = -∇U$ of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:

                                      tseg_end = t_rasmussen[2:end] .- 700    # stop analysis 500 years earlier than before
+config = SegmentedWindowConfig(indicators, change_metrics,
+    tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),
+    min_width_cha = 100)
+results = estimate_changes(config, r, t)
+signif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995))
+flags = significant_transitions(results, signif)
+fig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)
+plot_segment_analysis!(axs, results, signif)
+fig
                                      Example block output

                                      For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that "resilience-loss indicators" is a more accurate name than "early-warning signals" when using CSD.

                                      We draw attention upon the fact that the $\delta^{18}O$ timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).

                                      Degrees of freedom

                                      These sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.

                                      Future improvement

                                      Supporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.

                                      Hindcasting simulated DO-events

                                      In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:

                                      t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],
+                 [1, 3500, 4370, 5790, 7200, 8140]]
+t_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]
+tseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]
+tseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]
+
+figvec = Figure[]
+
+for j in 1:2
+    # Download the data and perform loess filtering on it
+    tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/" *
+        "master/timeseries/climberx-do$(j)-omaxa.csv")
+    data = readdlm(tmp)
+    tcx, xcx = data[1, 1000:end], data[2, 1000:end]
+    t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)
+
+    # Initialize figure
+    xlims = (0, last(tcx))
+    xticks = kyr_xticks(xlims[1]:1e3:xlims[2])
+    fig, axs = plot_do(tcx, xcx,  t, xtrend, t, r, t_transitions[j], extrema(t), xticks)
+    ylims!(axs[1], (5, 40))
+    axs[1].ylabel = L"Max. Atlantic overturning (Sv) $\,$"
+
+    # Run sliding analysis and update figure with results
+    dt = mean(diff(tcx))
+    config = SegmentedWindowConfig(
+        indicators, change_metrics, tseg_start[j], tseg_end[j],
+        whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)
+    results = estimate_changes(config, r, t)
+    signif = SurrogatesSignificance(n = 1_000, tail = [:right, :right], rng = Xoshiro(1995))
+    flags = significant_transitions(results, signif)
+
+    plot_segment_analysis!(axs, results, signif)
+    vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)
+    push!(figvec, fig)
+end
+figvec[1]
                                      Example block output

                                      It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:

                                      figvec[2]
                                      Example block output

                                      Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.

                                      diff --git a/v0.1.1/examples/ks_paleojump.jl b/v0.1.1/examples/ks_paleojump.jl new file mode 100644 index 00000000..012e0254 --- /dev/null +++ b/v0.1.1/examples/ks_paleojump.jl @@ -0,0 +1,168 @@ +# # Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries + +# The goal of this example is to show how simple it is to re-create an analysis _similar_ +# to what was done in the paper +# "Automatic detection of abrupt transitions in paleoclimate records", +# [Bagniewski2021](@cite). The same analysis was then used to create a database +# of transitions in paleoclimate records in [Bagniewski2023](@cite) +# Using TransitionsInTimeseries.jl and HypothesisTests.jl, +# the analysis becomes a 10-lines-of-code script (for a given timeseries). + +# ## Scientific background + +# The approach of [Bagniewski2021](@cite) is based on the [two-sample +# Kolmogorov Smirnov test](https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test#Two-sample_Kolmogorov%E2%80%93Smirnov_test). +# It tests whether the samples from two datasets or timeseries +# are distributed according to the same cumulative density function or not. +# This can be estimated by comparing the value of the _KS-statistic_ +# versus some threshold that depends on the required confidence. + +# The application of this test for identifying transitions in timeseries is simple: + +# 1. A sliding window analysis is performed in the timesries +# 1. In each window, the KS statistic is estimated between the first half and the second +# half of the timeseries within this window. +# 1. Transitions are defined by when the KS statistic exceeds a particular value +# based on some confidence. The transition occurs in the middle of the window. + +# We should point out that in [Bagniewski2021](@cite) the authors did a +# more detailed analysis: analyzed many different window widths, added a +# conditional clause to exclude transitions that do not exceed a predefined minimum +# "jump" in the data, and also added another conditional clause that +# filtered out transitions that are grouped in time (which is a natural consequence +# of using the Kolmogorov-Smirov test for detecting transitions). +# +# Here we won't do that post processing, mainly because it is rather simple +# to include these additional conditional clauses to filter transitions after they are found. + +# ## Steps for TransitionsInTimeseries.jl + +# Doing this kind of work with TransitionsInTimeseries.jl is so easy you won't even trip! +# This analysis follows the same sliding window approach showcased in our [Tutorial](@ref), +# and it even excludes the "indicator" aspect: the change metric is estimated directly +# from the input data! + +# As such, we really only need to define/do these things before we have finished the analysis: + +# 1. Load the input data (we will use the same example as the NGRIP data of +# [Dansgaard-Oescher events and Critical Slowing Down](@ref) example) +# and set the appropriate time window. +# 3. Define the function that estimates the change metric (i.e., the KS-statistic) +# 3. Perform the sliding window analysis as in the [Tutorial](@ref) with [`estimate_changes`](@ref) +# 4. Estimate the "confident" transitions in the data by comparing the estimated +# KS-statistic with a predefined threshold. + +# ## Load timeseries and window length +# Following the Dansgaard-Oescher events example, we load +# the data after all the processing steps done in that example: + +using DelimitedFiles, CairoMakie + +tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"* + "master/timeseries/NGRIP_processed.csv") +data = readdlm(tmp) +t, xtrend, xresid, xloess = collect.(eachcol(data)) + +fig, ax = lines(t, xtrend; axis = (ylabel = "NGRIP (processed)", xlabel = "time")) +lines!(ax, t, xloess; linewidth = 2) +fig + +# For the window, since we are using a sliding window here, we will be using a +# window of length 500 (which is approximately 1/2 to 1/4 the span between typical +# transitions found by [rasmussen-stratigraphic-2014](@cite)). + +window = 500 + +# ## Defining the change metric function + +# HypothesisTest.jl implements the Kolmogorov-Smirnov test, however here we are interested +# in the value of the test iself (the so-called KS-statistic), rather than a p-value. +# To this end, we define the following function to compute the statistic, +# which also normalizes it as in [Bagniewski2021](@cite). + +using HypothesisTests + +function normalized_KS_statistic(timeseries) + N = length(timeseries) + i = N÷2 + x = view(timeseries, 1:i) + y = view(timeseries, (i+1):N) + kstest = ApproximateTwoSampleKSTest(x, y) + nx = ny = i # length of each timeseries half of total + n = nx*ny/(nx + ny) # written fully for concreteness + D_KS = kstest.δ # can be compared directly with sqrt(-log(α/2)/2) + ## Rescale according to eq. (5) of the paper + rescaled = 1 - ((1 - D_KS)/(1 - sqrt(1/n))) + return rescaled +end + +N = 1000 # the statistic is independent of `N` for large enough `N`! +x = randn(N) +y = 1.8randn(N) .+ 1.0 +z = randn(N) +w = 0.6randn(N) .- 2.0 + +fig, ax = density(x; color = ("black", 0.5), strokewidth = 4.0, label = "reference distribution") +ax.title = "showcase of normalized KS-statistic" +for q in (y, z, w) + D_KS = normalized_KS_statistic(vcat(x, q)) + density!(ax, q; label = "D_KS = $(D_KS)") +end +axislegend(ax) +fig + +# ## Perform the sliding window analysis + +# This is just a straightforward call to [`estimate_changes`](@ref). +# In fact, it is even simpler than the tutorial. Here we skip completely +# the "indicator" estimation step, and we evaluate the change metric directly +# on input data. We do this by simply passing `nothing` as the indicators. + +using TransitionsInTimeseries + +config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 500) + +results = estimate_changes(config, xtrend, t) + +# Which we can visualize +function visualize_results(results) + fig, ax1 = lines(t, xtrend; axis = (ylabel = "NGRIP (processed)",)) + ax2, = lines(fig[2, 1], results.t_change, vec(results.x_change), axis = (ylabel = "D_KS (normalized)", xlabel = "time")) + linkxaxes!(ax1, ax2) + hidexdecorations!(ax1; grid = false) + xloess_normed = (xloess .- minimum(xloess))./(maximum(xloess) - minimum(xloess)) + lines!(ax2, t, xloess_normed; color = ("gray", 0.5)) + fig +end + +visualize_results(results) + +# By overplotting the (smoothened) NGRIP timeseries and the +# normalized KS-statistic, it already becomes pretty clear +# that the statistic peaks when transitions occur. + +# The same thing happens if we alter the window duration + +config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 200) +results = estimate_changes(config, xtrend, t) +visualize_results(results) + +# So one can easily obtain extra confidence by varying window +# size as in [Bagniewski2021](@cite). + +# ## Identifying "confident" transitions + +# As this identification here is done via a simple threshold, +# identifying the transitions is a nearly trivial call +# to [`significant_transitions`](@ref) with [`ThresholdSignificance`](@ref) + +signif = ThresholdSignificance(0.5) # or any other threshold +flags = significant_transitions(results, signif) + +fig = visualize_results(results) +axDKS = content(fig[2,1]) +vlines!(axDKS, results.t_change[vec(flags)], color = ("red", 0.25)) +fig + +# We could proceed with a lot of preprocessing as in [Bagniewski2021](@cite) +# but we skip this here for the sake of simplicity. \ No newline at end of file diff --git a/v0.1.1/examples/ks_paleojump/3befc971.png b/v0.1.1/examples/ks_paleojump/3befc971.png new file mode 100644 index 00000000..a89a9f76 Binary files /dev/null and b/v0.1.1/examples/ks_paleojump/3befc971.png differ diff --git a/v0.1.1/examples/ks_paleojump/49311be6.png b/v0.1.1/examples/ks_paleojump/49311be6.png new file mode 100644 index 00000000..4fe44522 Binary files /dev/null and b/v0.1.1/examples/ks_paleojump/49311be6.png differ diff --git a/v0.1.1/examples/ks_paleojump/5801bd1a.png b/v0.1.1/examples/ks_paleojump/5801bd1a.png new file mode 100644 index 00000000..e3ed5b93 Binary files /dev/null and b/v0.1.1/examples/ks_paleojump/5801bd1a.png differ diff --git a/v0.1.1/examples/ks_paleojump/a2ae2b48.png b/v0.1.1/examples/ks_paleojump/a2ae2b48.png new file mode 100644 index 00000000..db20d767 Binary files /dev/null and b/v0.1.1/examples/ks_paleojump/a2ae2b48.png differ diff --git a/v0.1.1/examples/ks_paleojump/b6611089.png b/v0.1.1/examples/ks_paleojump/b6611089.png new file mode 100644 index 00000000..d2ed69e0 Binary files /dev/null and b/v0.1.1/examples/ks_paleojump/b6611089.png differ diff --git a/v0.1.1/examples/ks_paleojump/index.html b/v0.1.1/examples/ks_paleojump/index.html new file mode 100644 index 00000000..f3469fb6 --- /dev/null +++ b/v0.1.1/examples/ks_paleojump/index.html @@ -0,0 +1,68 @@ + +Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries · TransitionsInTimeseries.jl
                                      GitHub

                                      Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries

                                      The goal of this example is to show how simple it is to re-create an analysis similar to what was done in the paper "Automatic detection of abrupt transitions in paleoclimate records", (Bagniewski et al., 2021). The same analysis was then used to create a database of transitions in paleoclimate records in (Bagniewski et al., 2023) Using TransitionsInTimeseries.jl and HypothesisTests.jl, the analysis becomes a 10-lines-of-code script (for a given timeseries).

                                      Scientific background

                                      The approach of (Bagniewski et al., 2021) is based on the two-sample Kolmogorov Smirnov test. It tests whether the samples from two datasets or timeseries are distributed according to the same cumulative density function or not. This can be estimated by comparing the value of the KS-statistic versus some threshold that depends on the required confidence.

                                      The application of this test for identifying transitions in timeseries is simple:

                                      1. A sliding window analysis is performed in the timesries
                                      2. In each window, the KS statistic is estimated between the first half and the second half of the timeseries within this window.
                                      3. Transitions are defined by when the KS statistic exceeds a particular value based on some confidence. The transition occurs in the middle of the window.

                                      We should point out that in (Bagniewski et al., 2021) the authors did a more detailed analysis: analyzed many different window widths, added a conditional clause to exclude transitions that do not exceed a predefined minimum "jump" in the data, and also added another conditional clause that filtered out transitions that are grouped in time (which is a natural consequence of using the Kolmogorov-Smirov test for detecting transitions).

                                      Here we won't do that post processing, mainly because it is rather simple to include these additional conditional clauses to filter transitions after they are found.

                                      Steps for TransitionsInTimeseries.jl

                                      Doing this kind of work with TransitionsInTimeseries.jl is so easy you won't even trip! This analysis follows the same sliding window approach showcased in our Tutorial, and it even excludes the "indicator" aspect: the change metric is estimated directly from the input data!

                                      As such, we really only need to define/do these things before we have finished the analysis:

                                      1. Load the input data (we will use the same example as the NGRIP data of Dansgaard-Oescher events and Critical Slowing Down example) and set the appropriate time window.
                                      2. Define the function that estimates the change metric (i.e., the KS-statistic)
                                      3. Perform the sliding window analysis as in the Tutorial with estimate_changes
                                      4. Estimate the "confident" transitions in the data by comparing the estimated KS-statistic with a predefined threshold.

                                      Load timeseries and window length

                                      Following the Dansgaard-Oescher events example, we load the data after all the processing steps done in that example:

                                      using DelimitedFiles, CairoMakie
+
+tmp = Base.download("https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/"*
+    "master/timeseries/NGRIP_processed.csv")
+data = readdlm(tmp)
+t, xtrend, xresid, xloess = collect.(eachcol(data))
+
+fig, ax = lines(t, xtrend; axis = (ylabel = "NGRIP (processed)", xlabel = "time"))
+lines!(ax, t, xloess; linewidth = 2)
+fig
                                      Example block output

                                      For the window, since we are using a sliding window here, we will be using a window of length 500 (which is approximately 1/2 to 1/4 the span between typical transitions found by (Rasmussen et al., 2014)).

                                      window = 500
                                      500

                                      Defining the change metric function

                                      HypothesisTest.jl implements the Kolmogorov-Smirnov test, however here we are interested in the value of the test iself (the so-called KS-statistic), rather than a p-value. To this end, we define the following function to compute the statistic, which also normalizes it as in (Bagniewski et al., 2021).

                                      using HypothesisTests
+
+function normalized_KS_statistic(timeseries)
+    N = length(timeseries)
+    i = N÷2
+    x = view(timeseries, 1:i)
+    y = view(timeseries, (i+1):N)
+    kstest = ApproximateTwoSampleKSTest(x, y)
+    nx = ny = i # length of each timeseries half of total
+    n = nx*ny/(nx + ny) # written fully for concreteness
+    D_KS = kstest.δ # can be compared directly with sqrt(-log(α/2)/2)
+    # Rescale according to eq. (5) of the paper
+    rescaled = 1 - ((1 - D_KS)/(1 - sqrt(1/n)))
+    return rescaled
+end
+
+N = 1000 # the statistic is independent of `N` for large enough `N`!
+x = randn(N)
+y = 1.8randn(N) .+ 1.0
+z = randn(N)
+w = 0.6randn(N) .- 2.0
+
+fig, ax = density(x; color = ("black", 0.5), strokewidth = 4.0, label = "reference distribution")
+ax.title = "showcase of normalized KS-statistic"
+for q in (y, z, w)
+    D_KS = normalized_KS_statistic(vcat(x, q))
+    density!(ax, q; label = "D_KS = $(D_KS)")
+end
+axislegend(ax)
+fig
                                      Example block output

                                      Perform the sliding window analysis

                                      This is just a straightforward call to estimate_changes. In fact, it is even simpler than the tutorial. Here we skip completely the "indicator" estimation step, and we evaluate the change metric directly on input data. We do this by simply passing nothing as the indicators.

                                      using TransitionsInTimeseries
+
+config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 500)
+
+results = estimate_changes(config, xtrend, t)
                                      SlidingWindowResults
+ input timeseries:              6975-element Vector{Float64}
+ indicators:                    nothing
+ indicator (window, stride):    (100, 1)
+ change metrics:                [:normalized_KS_statistic]
+ change metric (window, stride): (500, 1)
+

                                      Which we can visualize

                                      function visualize_results(results)
+    fig, ax1 = lines(t, xtrend; axis = (ylabel = "NGRIP (processed)",))
+    ax2, = lines(fig[2, 1], results.t_change, vec(results.x_change), axis = (ylabel = "D_KS (normalized)", xlabel = "time"))
+    linkxaxes!(ax1, ax2)
+    hidexdecorations!(ax1; grid = false)
+    xloess_normed = (xloess .- minimum(xloess))./(maximum(xloess) - minimum(xloess))
+    lines!(ax2, t, xloess_normed; color = ("gray", 0.5))
+    fig
+end
+
+visualize_results(results)
                                      Example block output

                                      By overplotting the (smoothened) NGRIP timeseries and the normalized KS-statistic, it already becomes pretty clear that the statistic peaks when transitions occur.

                                      The same thing happens if we alter the window duration

                                      config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 200)
+results = estimate_changes(config, xtrend, t)
+visualize_results(results)
                                      Example block output

                                      So one can easily obtain extra confidence by varying window size as in (Bagniewski et al., 2021).

                                      Identifying "confident" transitions

                                      As this identification here is done via a simple threshold, identifying the transitions is a nearly trivial call to significant_transitions with ThresholdSignificance

                                      signif = ThresholdSignificance(0.5) # or any other threshold
+flags = significant_transitions(results, signif)
+
+fig = visualize_results(results)
+axDKS = content(fig[2,1])
+vlines!(axDKS, results.t_change[vec(flags)], color = ("red", 0.25))
+fig
                                      Example block output

                                      We could proceed with a lot of preprocessing as in (Bagniewski et al., 2021) but we skip this here for the sake of simplicity.

                                      diff --git a/v0.1.1/examples/logistic.jl b/v0.1.1/examples/logistic.jl new file mode 100644 index 00000000..19eaae31 --- /dev/null +++ b/v0.1.1/examples/logistic.jl @@ -0,0 +1,203 @@ +# # Permutation entropy for dynamic regime changes + +# Permutation entropy is used frequently to detect a transition between +# one dynamic regime to another. It is useful when the mean and std. of the +# timeseries values are very similar between the two regimes, which would mean that +# common distribution-based indicators, or common critical-slowing-down based indicators, +# would fail. + +# This example will also explore different ways to test for significance that +# are arguably better suitable in such an application than the [Tutorial](@ref)'s default +# of significance via random Fourier surrogates. + +# ## Logistic map timeseries + +# A simple example of this is transitions from periodic to weakly chaotic to chaotic +# motion in the logistic map. First, let's generate a timeseries of the logistic map + +using DynamicalSystemsBase +using CairoMakie + +## time-dependent logistic map, so that the `r` parameter increases with time +r1 = 3.83 +r2 = 3.86 +N = 2000 +rs = range(r1, r2; length = N) + +function logistic_drifting_rule(u, rs, n) + r = rs[n+1] # time is `n`, starting from 0 + return SVector(r*u[1]*(1 - u[1])) +end + +ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs) +x = trajectory(ds, N-1)[1][:, 1] + +# Plot it, using as time the parameter value (they coincide) +fig, ax = lines(rs, x; linewidth = 0.5) +ax.xlabel = "r (time)" +ax.ylabel = "x" +fig + +# In this example there is a rather obvious transition to strongly +# chaotic motion at r ≈ 3.855. However, there is also a subtle transition +# to weak chaos at r ≈ 3.847. This transition is barely visible in the +# timeseries, and in fact many of the timeseries statistical properties remain identical. + +# ## Using a simpler change metric + +# Now, let's compute and various indicators and their changes, +# focusing on the permutation entropy as an indicator. We use +# order 4 here, because we know that to detect changes in a period `m` we would need +# an order ≥ `m+1` permutation entropy. + +using TransitionsInTimeseries, ComplexityMeasures + +function permutation_entropy(m) + est = SymbolicPermutation(; m) # order 3 + indicator = x -> entropy_normalized(est, x) + return indicator +end + +indicators = (var, ar1_whitenoise, permutation_entropy(4)) +indistrings = ("var", "ar1", "pe") + +# In this example there is no critical slowing down; +# instead, there is a sharp transition between periodic and chaotic motion. +# Hence, we shouldn't be using any trend-based change metrics. +# Instead, we will use the most basic change metric, [`difference_of_means`](@ref). +# With this metric it also makes most sense to use as stride half the window width +metric = (difference_of_means, difference_of_means, difference_of_means) + +width_ind = N÷100 +width_cha = 20 +stride_cha = 10 + +config = SlidingWindowConfig(indicators, metric; + width_ind, width_cha, stride_cha, +) + +results = estimate_changes(config, x, rs) + +# Let's now plot the change metrics of the indicators + +function plot_change_metrics() + fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (size = (600, 600),)) + hidexdecorations!(ax; grid = false) + ## plot all change metrics + for (i, c) in enumerate(eachcol(results.x_change)) + ax, = scatterlines(fig[i+1, 1], results.t_change, c; + axis = (ylabel = indistrings[i],), label = "input" + ) + if i < 3 + hidexdecorations!(ax; grid = false) + else + ax.xlabel = "r (time)" + end + end + return fig +end + +fig = plot_change_metrics() + +# We already see the interesting results we expect: the permutation entropy shows a +# striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. +# (Remember: the plotted quantity is how much the indicator changes within a time window. +# High values mean large changes.) + +# Due to its construction, permutation entropy will have a spike for periodic data at the +# start of the timeseries, so we can safely ignore the spike at r ≈ 3.83. + +# ## Significance via random Fourier surrogates + +# One way to test for significance would be via the standard way as in the [Tutorial](@ref), +# utilizing surrogate timeseries and [`SurrogatesSignificance`](@ref). + +# Let's do it here for an example, but, we have to be **careful**. +# It is crucial that for permutation entropy we use `:right` as the `tail`, +# because it is expected that the surrogates will have higher +# differences in the permutation entropy timeseries (because, if there is no +# dynamical change, the permutation entropy will stay the same, while in the surrogates +# there are always random fluctuations! + +surromethod = RandomFourier() + +## Define a function because we will re-use later +using Random: Xoshiro +function overplot_surrogate_significance!(fig, surromethod, color = "black") + + signif = SurrogatesSignificance(; + n = 1000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42), + ) + flags = significant_transitions(results, signif) + + ## and also plot the flags with same color + for (i, indicator) in enumerate(indicators) + ## To make things visually clear, we will also plot some example surrogate + ## timeseries for each indicator and change metric pair + for _ in 1:10 + s = TimeseriesSurrogates.surrogate(x, surromethod) + p = windowmap(indicator, s; width = width_ind) + q = windowmap(metric[i], p; width = width_cha, stride = stride_cha) + lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1) + end + ## Plot the flags as vertical dashed lines + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = color, linestyle = :dash, linewidth = 3 + ) + end + ## add a title to the figure with how we estimate significance + content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod))) +end + +surromethod = RandomFourier() +overplot_surrogate_significance!(fig, surromethod) + +fig + +# ## Different surrogates +# %% #src +# Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum +# is a property integrated over the whole timeseries. It doesn't contain any information +# highlighting the _local_ dynamics or information that preserves the local +# changes of dynamical behavior. + +# A surrogate type that does a better job in preserving local sharp +# changes in the timeseries (and hence provides **stricter** +# surrogate-based significance) is for example `RelativePartialRandomization`. + +# A much better alternative is to use block-shuffled surrogates, which +# preserve the short term local temporal correlation in the timeseries and hence +# also preserve local short term sharp changes in the dynamic behavior. + +surromethod = RelativePartialRandomization(0.25) +fig = plot_change_metrics() +overplot_surrogate_significance!(fig, surromethod, "gray") +fig + +# Our results have improved. In the permutation entropy, we see only two +# transitions detected as significant, which is correct: only two +# real dynamical transitions exist in the data. +# In the other two indicators we also see fewer transitions, but as we +# have already discussed, no results with the other indicators should +# be taken into meaningful consideration, as these indicators +# are simply inappropriate for what we are looking for here. + +# ## Simpler Significance +# %% #src +# Arguably, exactly because we are using the [`difference_of_means`](@ref) as a +# change metric, we may want to be less strict and more simple with our tests for significance. +# Instead of using [`SurrogatesSignificance`](@ref) we may use the simpler and much faster +# [`SigmaSignificance`](@ref), which simply claims significant time points +# whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation. + +fig = plot_change_metrics() +flags = significant_transitions(results, SigmaSignificance(factor = 5.0)) + +## Plot the flags +for (i, indicator) in enumerate(indicators) + vlines!(fig[i+1, 1], results.t_change[flags[:, i]]; + color = Cycled(3), linestyle = :dash, linewidth = 3 + ) +end +content(fig[1, 1]).title = "significance from std" +fig diff --git a/v0.1.1/examples/logistic/056afaf1.png b/v0.1.1/examples/logistic/056afaf1.png new file mode 100644 index 00000000..b31fbc9a Binary files /dev/null and b/v0.1.1/examples/logistic/056afaf1.png differ diff --git a/v0.1.1/examples/logistic/6562bd0b.png b/v0.1.1/examples/logistic/6562bd0b.png new file mode 100644 index 00000000..6faac237 Binary files /dev/null and b/v0.1.1/examples/logistic/6562bd0b.png differ diff --git a/v0.1.1/examples/logistic/92ea13f0.png b/v0.1.1/examples/logistic/92ea13f0.png new file mode 100644 index 00000000..3af35185 Binary files /dev/null and b/v0.1.1/examples/logistic/92ea13f0.png differ diff --git a/v0.1.1/examples/logistic/c46d303b.png b/v0.1.1/examples/logistic/c46d303b.png new file mode 100644 index 00000000..cadee697 Binary files /dev/null and b/v0.1.1/examples/logistic/c46d303b.png differ diff --git a/v0.1.1/examples/logistic/e67ee1a9.png b/v0.1.1/examples/logistic/e67ee1a9.png new file mode 100644 index 00000000..5ad93df2 Binary files /dev/null and b/v0.1.1/examples/logistic/e67ee1a9.png differ diff --git a/v0.1.1/examples/logistic/index.html b/v0.1.1/examples/logistic/index.html new file mode 100644 index 00000000..387e2067 --- /dev/null +++ b/v0.1.1/examples/logistic/index.html @@ -0,0 +1,128 @@ + +Permutation entropy for dynamic regime changes · TransitionsInTimeseries.jl
                                      GitHub

                                      Permutation entropy for dynamic regime changes

                                      Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.

                                      This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.

                                      Logistic map timeseries

                                      A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map

                                      using DynamicalSystemsBase
+using CairoMakie
+
+# time-dependent logistic map, so that the `r` parameter increases with time
+r1 = 3.83
+r2 = 3.86
+N = 2000
+rs = range(r1, r2; length = N)
+
+function logistic_drifting_rule(u, rs, n)
+    r = rs[n+1] # time is `n`, starting from 0
+    return SVector(r*u[1]*(1 - u[1]))
+end
+
+ds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)
+x = trajectory(ds, N-1)[1][:, 1]
                                      2000-element Vector{Float64}:
+ 0.5
+ 0.9575
+ 0.15585767321160574
+ 0.5039019545917718
+ 0.9574529422362281
+ 0.15602441103002537
+ 0.5043473227583317
+ 0.9574501255597653
+ 0.1560361152301728
+ 0.5043840906474082
+ ⋮
+ 0.4253904015445437
+ 0.9434836074964187
+ 0.20581843730311683
+ 0.6309301050251992
+ 0.8988117342940414
+ 0.3510584545931264
+ 0.8793611090928393
+ 0.40948549063776396
+ 0.9333718681550522

                                      Plot it, using as time the parameter value (they coincide)

                                      fig, ax = lines(rs, x; linewidth = 0.5)
+ax.xlabel = "r (time)"
+ax.ylabel = "x"
+fig
                                      Example block output

                                      In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.

                                      Using a simpler change metric

                                      Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.

                                      using TransitionsInTimeseries, ComplexityMeasures
+
+function permutation_entropy(m)
+    est = SymbolicPermutation(; m) # order 3
+    indicator = x -> entropy_normalized(est, x)
+    return indicator
+end
+
+indicators = (var, ar1_whitenoise, permutation_entropy(4))
+indistrings = ("var", "ar1", "pe")
                                      ("var", "ar1", "pe")

                                      In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width

                                      metric = (difference_of_means, difference_of_means, difference_of_means)
+
+width_ind = N÷100
+width_cha = 20
+stride_cha = 10
+
+config = SlidingWindowConfig(indicators, metric;
+    width_ind, width_cha, stride_cha,
+)
+
+results = estimate_changes(config, x, rs)
                                      SlidingWindowResults
+ input timeseries:              2000-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise, Symbol("#1")]
+ indicator (window, stride):    (20, 1)
+ change metrics:                [:difference_of_means, :difference_of_means, :difference_of_means]
+ change metric (window, stride): (20, 10)
+

                                      Let's now plot the change metrics of the indicators

                                      function plot_change_metrics()
+    fig, ax = lines(rs, x; axis = (ylabel = "input",), figure = (size = (600, 600),))
+    hidexdecorations!(ax; grid = false)
+    # plot all change metrics
+    for (i, c) in enumerate(eachcol(results.x_change))
+        ax, = scatterlines(fig[i+1, 1], results.t_change, c;
+            axis = (ylabel = indistrings[i],), label = "input"
+        )
+        if i < 3
+            hidexdecorations!(ax; grid = false)
+        else
+            ax.xlabel = "r (time)"
+        end
+    end
+    return fig
+end
+
+fig = plot_change_metrics()
                                      Example block output

                                      We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)

                                      Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.

                                      Significance via random Fourier surrogates

                                      One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.

                                      Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!

                                      surromethod = RandomFourier()
+
+# Define a function because we will re-use later
+using Random: Xoshiro
+function overplot_surrogate_significance!(fig, surromethod, color = "black")
+
+    signif = SurrogatesSignificance(;
+        n = 1000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),
+    )
+    flags = significant_transitions(results, signif)
+
+    # and also plot the flags with same color
+    for (i, indicator) in enumerate(indicators)
+        # To make things visually clear, we will also plot some example surrogate
+        # timeseries for each indicator and change metric pair
+        for _ in 1:10
+            s = TimeseriesSurrogates.surrogate(x, surromethod)
+            p = windowmap(indicator, s; width = width_ind)
+            q = windowmap(metric[i], p; width = width_cha, stride = stride_cha)
+            lines!(fig[i+1, 1], results.t_change, q;  color = (color, 0.2), linewidth = 1)
+        end
+        # Plot the flags as vertical dashed lines
+        vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+            color = color, linestyle = :dash, linewidth = 3
+        )
+    end
+    # add a title to the figure with how we estimate significance
+    content(fig[1, 1]).title = "surrogates: "*string(nameof(typeof(surromethod)))
+end
+
+surromethod = RandomFourier()
+overplot_surrogate_significance!(fig, surromethod)
+
+fig
                                      Example block output

                                      Different surrogates

                                      Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

                                      A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

                                      A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

                                      surromethod = RelativePartialRandomization(0.25)
+fig = plot_change_metrics()
+overplot_surrogate_significance!(fig, surromethod, "gray")
+fig
                                      Example block output

                                      Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

                                      Simpler Significance

                                      Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

                                      fig = plot_change_metrics()
+flags = significant_transitions(results, SigmaSignificance(factor = 5.0))
+
+# Plot the flags
+for (i, indicator) in enumerate(indicators)
+    vlines!(fig[i+1, 1], results.t_change[flags[:, i]];
+        color = Cycled(3), linestyle = :dash, linewidth = 3
+    )
+end
+content(fig[1, 1]).title = "significance from std"
+fig
                                      Example block output
                                      diff --git a/v0.1.1/index.html b/v0.1.1/index.html new file mode 100644 index 00000000..821feda9 --- /dev/null +++ b/v0.1.1/index.html @@ -0,0 +1,2 @@ + +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl
                                      GitHub

                                      TransitionsInTimeseries.jl

                                      TransitionsInTimeseries.jl

                                      TransitionsInTimeseries — Module

                                      TransitionsInTimeseries.jl

                                      CI codecov Package Downloads

                                      TransitionsInTimeseries.jl is a free and open-source software to easily analyse transitions within timeseries in a reproducible, performant, extensible and reliable way. In contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:

                                      1. Provide the analysis pipelines with new indicators, which can be either self-written or imported from other packages. In particular, the latter offers thousands of metrics that can indicate transitions right out of the box.
                                      2. Add new analysis pipelines for finding transitions.
                                      3. Add new ways for significance testing.

                                      TransitionsInTimeseries is a registered Julia package and can be installed by running:

                                      ] add TransitionsInTimeseries

                                      All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

                                      Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

                                      source
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                                      If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

                                      Content

                                      Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

                                      • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
                                      • Makes the surrogate analysis to test for significance under the hub.
                                      • Can be easily extended by any user without touching the source code.
                                      • Reduces the programming overhead for any researcher willing to benchmark new methods.
                                      • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
                                      • Increases trustworthiness thanks to a large test suite.
                                      Similar projects

                                      An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

                                      Approaches

                                      Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

                                      diff --git a/v0.1.1/objects.inv b/v0.1.1/objects.inv new file mode 100644 index 00000000..cb12258f Binary files /dev/null and b/v0.1.1/objects.inv differ diff --git a/v0.1.1/refs.bib b/v0.1.1/refs.bib new file mode 100644 index 00000000..8cc9690b --- /dev/null +++ b/v0.1.1/refs.bib @@ -0,0 +1,87 @@ + +@article{willeit-earth-2022, + title = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1: {Climate} model description and validation​​​​​​​​​​​​​​}, + volume = {15}, + issn = {1991-9603}, + shorttitle = {The {Earth} system model {CLIMBER}-{X} v1.0 – {Part} 1}, + url = {https://gmd.copernicus.org/articles/15/5905/2022/}, + doi = {10.5194/gmd-15-5905-2022}, + abstract = {The newly developed fast Earth system model CLIMBER-X is presented. The climate component of CLIMBER-X consists of a 2.5-D semi-empirical statistical–dynamical atmosphere model, a 3-D frictional–geostrophic ocean model, a dynamic–thermodynamic sea ice model and a land surface model. All the model components are discretized on a regular lat–long grid with a horizontal resolution of 5 ◦ × 5 ◦. The model has a throughput of ∼ 10 000 simulation years per day on a single node with 16 CPUs on a high-performance computer and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to {\textgreater} 100 000 years. A comprehensive evaluation of the model performance for the present day and the historical period shows that CLIMBER-X is capable of realistically reproducing many observed climate characteristics, with results that generally lie within the range of state-of-theart general circulation models. The analysis of model performance is complemented by a thorough assessment of climate feedbacks and model sensitivities to changes in external forcings and boundary conditions. Limitations and applicability of the model are critically discussed. CLIMBER-X also includes a detailed representation of the global carbon cycle and is coupled to an ice sheet model, which will be described in separate papers. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.}, + language = {en}, + number = {14}, + urldate = {2022-08-11}, + journal = {Geoscientific Model Development}, + author = {Willeit, Matteo and Ganopolski, Andrey and Robinson, Alexander and Edwards, Neil R.}, + month = jul, + year = {2022}, + pages = {5905--5948}, + file = {Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:/home/jan/Zotero/storage/75NKS975/Willeit et al. - 2022 - The Earth system model CLIMBER-X v1.0 – Part 1 Cl.pdf:application/pdf}, +} + +@article{boers-early-warning-2018, + title = {Early-warning signals for {Dansgaard}-{Oeschger} events in a high-resolution ice core record}, + volume = {9}, + issn = {2041-1723}, + url = {http://www.nature.com/articles/s41467-018-04881-7}, + doi = {10.1038/s41467-018-04881-7}, + language = {en}, + number = {1}, + urldate = {2022-10-28}, + journal = {Nature Communications}, + author = {Boers, Niklas}, + month = dec, + year = {2018}, + pages = {2556}, + file = {Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:/home/jan/Zotero/storage/DS97Z9UC/Boers - 2018 - Early-warning signals for Dansgaard-Oeschger event.pdf:application/pdf}, +} + +@article{rasmussen-stratigraphic-2014, + title = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records: refining and extending the {INTIMATE} event stratigraphy}, + volume = {106}, + issn = {02773791}, + shorttitle = {A stratigraphic framework for abrupt climatic changes during the {Last} {Glacial} period based on three synchronized {Greenland} ice-core records}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0277379114003485}, + doi = {10.1016/j.quascirev.2014.09.007}, + abstract = {Due to their outstanding resolution and well-constrained chronologies, Greenland ice-core records provide a master record of past climatic changes throughout the Last InterglacialeGlacial cycle in the North Atlantic region. As part of the INTIMATE (INTegration of Ice-core, MArine and TErrestrial records) project, protocols have been proposed to ensure consistent and robust correlation between different records of past climate. A key element of these protocols has been the formal definition and ordinal numbering of the sequence of Greenland Stadials (GS) and Greenland Interstadials (GI) within the most recent glacial period. The GS and GI periods are the Greenland expressions of the characteristic DansgaardeOeschger events that represent cold and warm phases of the North Atlantic region, respectively. We present here a more detailed and extended GS/GI template for the whole of the Last Glacial period. It is based on a synchronization of the NGRIP, GRIP, and GISP2 ice-core records that allows the parallel analysis of all three records on a common time scale. The boundaries of the GS and GI periods are defined based on a combination of stable-oxygen isotope ratios of the ice (d18O, reflecting mainly local temperature) and calcium ion concentrations (reflecting mainly atmospheric dust loading) measured in the ice. The data not only resolve the well-known sequence of DansgaardeOeschger events that were first defined and numbered in the ice-core records more than two decades ago, but also better resolve a number of short-lived climatic oscillations, some defined here for the first time. Using this revised scheme, we propose a consistent approach for discriminating and naming all the significant abrupt climatic events of the Last Glacial period that are represented in the Greenland ice records. The final product constitutes an extended and better resolved Greenland stratotype sequence, against which other proxy records can be compared and correlated. It also provides a more secure basis for investigating the dynamics and fundamental causes of these climatic perturbations.}, + language = {en}, + urldate = {2023-10-04}, + journal = {Quaternary Science Reviews}, + author = {Rasmussen, Sune O. and Bigler, Matthias and Blockley, Simon P. and Blunier, Thomas and Buchardt, Susanne L. and Clausen, Henrik B. and Cvijanovic, Ivana and Dahl-Jensen, Dorthe and Johnsen, Sigfus J. and Fischer, Hubertus and Gkinis, Vasileios and Guillevic, Myriam and Hoek, Wim Z. and Lowe, J. John and Pedro, Joel B. and Popp, Trevor and Seierstad, Inger K. and Steffensen, Jørgen Peder and Svensson, Anders M. and Vallelonga, Paul and Vinther, Bo M. and Walker, Mike J.C. and Wheatley, Joe J. and Winstrup, Mai}, + month = dec, + year = {2014}, + pages = {14--28}, + file = {Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:/home/jan/Zotero/storage/VSUTVWPN/Rasmussen et al. - 2014 - A stratigraphic framework for abrupt climatic chan.pdf:application/pdf}, +} + +@article{Bagniewski2023, +abstract = {Tipping points (TPs) in Earth's climate system have been the subject of increasing interest and concern in recent years, given the risk that anthropogenic forcing could cause abrupt, potentially irreversible, climate transitions. Paleoclimate records are essential for identifying past TPs and for gaining a thorough understanding of the underlying nonlinearities and bifurcation mechanisms. However, the quality, resolution, and reliability of these records can vary, making it important to carefully select the ones that provide the most accurate representation of past climates. Moreover, as paleoclimate time series vary in their origin, time spans, and periodicities, an objective, automated methodology is crucial for identifying and comparing TPs. To address these challenges, we introduce the open-source PaleoJump database, which contains a collection of carefully selected, high-resolution records originating in ice cores, marine sediments, speleothems, terrestrial records, and lake sediments. These records describe climate variability on centennial, millennial and longer time scales and cover all the continents and ocean basins. We provide an overview of their spatial distribution and discuss the gaps in coverage. Our statistical methodology includes an augmented Kolmogorov–Smirnov test and Recurrence Quantification Analysis; it is applied here, for illustration purposes, to selected records in which abrupt transitions are automatically detected and the presence of potential tipping elements is investigated. These transitions are shown in the PaleoJump database along with other essential information about the records, including location, temporal scale and resolution, as well as temporal plots. This open-source database represents, therefore, a valuable resource for researchers investigating TPs in past climates.}, +archivePrefix = {arXiv}, +arxivId = {2206.06832}, +author = {Bagniewski, Witold and Rousseau, Denis Didier and Ghil, Michael}, +doi = {10.1038/s41598-023-30592-1}, +eprint = {2206.06832}, +isbn = {0123456789}, +issn = {20452322}, +journal = {Scientific Reports}, +number = {1}, +pages = {1--18}, +pmid = {36934110}, +publisher = {Nature Publishing Group UK}, +title = {{The PaleoJump database for abrupt transitions in past climates}}, +url = {https://doi.org/10.1038/s41598-023-30592-1}, +volume = {13}, +year = {2023} +} +@article{Bagniewski2021, +abstract = {Bifurcations and tipping points (TPs) are an important part of the Earth system's behavior. These critical points represent thresholds at which small changes in the system's parameters or in the forcing abruptly switch it from one state or type of behavior to another. Current concern with TPs is largely due to the potential of slow anthropogenic forcing to bring about abrupt, and possibly irreversible, change to the physical climate system and impacted ecosystems. Paleoclimate proxy records have been shown to contain abrupt transitions, or "jumps,"which may represent former instances of such dramatic climate change events. These transitions can provide valuable information for identifying critical TPs in current and future climate evolution. Here, we present a robust methodology for detecting abrupt transitions in proxy records that is applied to ice core and speleothem records of the last climate cycle. This methodology is based on the nonparametric Kolmogorov-Smirnov (KS) test for the equality, or not, of the probability distributions associated with two samples drawn from a time series, before and after any potential jump. To improve the detection of abrupt transitions in proxy records, the KS test is augmented by several other criteria and it is compared with recurrence analysis. The augmented KS test results show substantial skill when compared with more subjective criteria for jump detection. This test can also usefully complement recurrence analysis and improve upon certain aspects of its results.}, +author = {Bagniewski, W. and Ghil, M. and Rousseau, D. D.}, +doi = {10.1063/5.0062543}, +issn = {10897682}, +journal = {Chaos}, +number = {11}, +pmid = {34881579}, +publisher = {AIP Publishing LLC}, +title = {{Automatic detection of abrupt transitions in paleoclimate records}}, +volume = {31}, +year = {2021} +} diff --git a/v0.1.1/refs/index.html b/v0.1.1/refs/index.html new file mode 100644 index 00000000..8fc2b667 --- /dev/null +++ b/v0.1.1/refs/index.html @@ -0,0 +1,2 @@ + +References · TransitionsInTimeseries.jl
                                      GitHub

                                      References

                                      diff --git a/v0.1.1/search_index.js b/v0.1.1/search_index.js new file mode 100644 index 00000000..aa3b317c --- /dev/null +++ b/v0.1.1/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"EditURL = \"tutorial.jl\"","category":"page"},{"location":"tutorial/#Tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"tutorial/#workflow","page":"Tutorial","title":"Workflow","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Computing transition indicators consists of the following steps:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Doing any preprocessing of raw data first, such as detrending. This not part of TransitionsInTimeseries.jl and yields the input timeseries.\nEstimating the timeseries of an indicator by sliding a window over the input timeseries.\nComputing the changes of the indicator by sliding a window over its timeseries. Alternatively, the change metric can be estimated over the whole segment, as examplified in the section Segmented windows.\nGenerating many surrogates that preserve important statistical properties of the original timeseries.\nPerforming step 2 and 3 for the surrogate timeseries.\nChecking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.","category":"page"},{"location":"tutorial/#example_stepbystep","page":"Tutorial","title":"Tutorial – Educational","text":"","category":"section"},{"location":"tutorial/#Raw-input-data","page":"Tutorial","title":"Raw input data","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dfracmathrmdx_lmathrmdt = - x_l - 1 + f(t) + n(t) \ndfracmathrmdx_nlmathrmdt = - x_nl^3 + x_nl + f(t) + n(t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"with x_l the state of the linear model, x_nl the state of the bistable model, f the forcing and n the noise. For f=0 they both display an equilibrium point at x=-1. However, the bistable model also displays a further equilibrium point at x=1. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\nfig, ax = lines(t, x_linear)\nlines!(ax, t, x_nlinear)\nax.title = \"raw data\"\nfig","category":"page"},{"location":"tutorial/#Preprocessing","page":"Tutorial","title":"Preprocessing","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"note: Not part of TransitionsInTimeseries.jl\nAny timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"x_l_fluct = diff(x_linear)\nx_nl_fluct = diff(x_nlinear)\ntfluct = t[2:end]\n\nfig, ax = lines(tfluct, x_l_fluct)\nlines!(ax, tfluct, x_nl_fluct .+ 0.05)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"info: Detrending in Julia\nDetrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.","category":"page"},{"location":"tutorial/#Indicator-timeseries","page":"Tutorial","title":"Indicator timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can then compute the values of some \"indicator\" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"indicator = ar1_whitenoise\nindicator_window = (width = 400, stride = 1)\n\n# By mapping `last::Function` over a windowviewer of the time vector,\n# we obtain the last time step of each window.\n# This therefore only uses information from `k-width+1` to `k` at time step `k`.\n# Alternatives: `first::Function`, `midpoint:::Function`.\nt_indicator = windowmap(last, tfluct; indicator_window...)\nindicator_l = windowmap(indicator, x_l_fluct; indicator_window...)\nindicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)\n\nfig, ax = lines(t_indicator, indicator_l)\nlines!(ax, t_indicator, indicator_nl)\nax.title = \"indicator timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The lines plotted above are the indicator timeseries.","category":"page"},{"location":"tutorial/#Change-metric-timeseries","page":"Tutorial","title":"Change metric timeseries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"change_window = (width = 30, stride = 1)\nridgereg = RidgeRegressionSlope(lambda = 0.0)\nprecompridgereg = precompute(ridgereg, t[1:change_window.width])\n\nt_change = windowmap(last, t_indicator; change_window...)\nchange_l = windowmap(precompridgereg, indicator_l; change_window...)\nchange_nl = windowmap(precompridgereg, indicator_nl; change_window...)\n\nfig, ax = lines(t_change, change_l)\nlines!(ax, t_change, change_nl)\nax.title = \"change metric timeseries\"\nfig","category":"page"},{"location":"tutorial/#Timeseries-surrogates","page":"Tutorial","title":"Timeseries surrogates","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# Generate Fourier random-phase surrogates\nusing Random: Xoshiro\ns = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))\n\nfunction gridfig(nrows, ncols)\n fig = Figure()\n axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)\n for j in 1:ncols, i in 1:nrows]\n rowgap!(fig.layout, 10)\n return fig, axs\nend\nfig, axs = gridfig(2, 1)\nlines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))\nlines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))\naxs[1].title = \"real signal vs. surrogate(s)\"\n\n# compute and plot indicator and change metric\nindicator_s = windowmap(indicator, s; indicator_window...)\nchange_s = windowmap(precompridgereg, indicator_s; change_window...)\n\nlines!(axs[2], t_change, change_nl, label = \"nonlin\", color = Cycled(2))\nlines!(axs[2], t_change, change_s, label = \"surrogate\", color = Cycled(3))\naxislegend()\naxs[2].title = \"change metric\"\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/#Quantifying-significance","page":"Tutorial","title":"Quantifying significance","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"n_surrogates = 1_000\nfig, axs = gridfig(2, 2)\naxs[1].title = \"linear\"\naxs[2].title = \"nonlinear\"\n\nfor (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))\n\n orig_change = j == 1 ? change_l : change_nl\n sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))\n pval = zeros(length(change_s))\n\n # Collect all surrogate change metrics\n for i in 1:n_surrogates\n s = sgen()\n indicator_s = windowmap(indicator, s; indicator_window...)\n change_s = windowmap(precompridgereg, indicator_s; change_window...)\n pval += orig_change .< change_s\n end\n\n pval ./= n_surrogates\n lines!(ax, t_change, orig_change) # ; color = Cycled(j)\n lines!(axsig, t_change, pval) # ; color = Cycled(j+2)\nend\n\n[xlims!(ax, 0, 50) for ax in axs]\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.","category":"page"},{"location":"tutorial/#example_fastforward","page":"Tutorial","title":"Tutorial – TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a ChangesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.","category":"page"},{"location":"tutorial/#Sliding-windows","page":"Tutorial","title":"Sliding windows","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using TransitionsInTimeseries, CairoMakie\n\nt, x_linear, x_nlinear = load_linear_vs_doublewell()\n\n# input timeseries and time\ninput = x_nl_fluct = diff(x_nlinear)\nt = t[2:end]\n\nfig, ax = lines(t, input)\nax.title = \"input timeseries\"\nfig","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To perform all of the above analysis we follow a 2-step process.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using estimate_changes.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"# These indicators are suitable for Critical Slowing Down\nindicators = (var, ar1_whitenoise)\n\n# use the ridge regression slope for both indicators\nchange_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope())\n\n# choices go into a configuration struct\nconfig = SlidingWindowConfig(indicators, change_metrics;\n width_ind = 400, width_cha = 30, whichtime = last)\n\n# choices are processed\nresults = estimate_changes(config, input, t)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can conveniently plot the information contained in results by using plot_indicator_changes:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"fig = plot_indicator_changes(results)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Step 2 is to estimate significance using SurrogatesSignificance and the function significant_transitions. Finally, we can conveniently plot the results obtained by updating the figure obtained above with plot_significance!:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"signif = SurrogatesSignificance(n = 1000, tail = [:right, :right])\nflags = significant_transitions(results, signif)\nplot_significance!(fig, results, signif, flags = flags)\nfig","category":"page"},{"location":"tutorial/#segmented_windows","page":"Tutorial","title":"Segmented windows","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The analysis shown so far relies on sliding windows of the change metric. This is particularly convenient for transition detection tasks. Segmented windows for the change metric computation are however preferable when it comes to prediction tasks. By only slightly modifying the syntax used so far, one can perform the same computations on segmented windows, as well as visualise the results conveniently:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"config = SegmentedWindowConfig(indicators, change_metrics,\n t[1:1], t[1200:1200]; whichtime = last, width_ind = 200,\n min_width_cha = 100)\nresults = estimate_changes(config, input, t)\nsignif = SurrogatesSignificance(n = 1000, tail = [:right, :right])\nflags = significant_transitions(results, signif)\nfig = plot_changes_significance(results, signif)","category":"page"},{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/#Main-analysis-functions","page":"API","title":"Main analysis functions","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"estimate_changes\nChangesConfig\nChangesResults","category":"page"},{"location":"api/#TransitionsInTimeseries.estimate_changes","page":"API","title":"TransitionsInTimeseries.estimate_changes","text":"estimate_changes(config::ChangesConfig, x [,t]) → result\n\nEstimate possible transitions for input timeseries x using the approach specified in the configuration type config, see ChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).\n\nReturn the output as subtype of ChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.ChangesConfig","page":"API","title":"TransitionsInTimeseries.ChangesConfig","text":"ChangesConfig\n\nSupertype for how \"changes\" in a timeseries are estimated in estimate_changes. \"Changes\" deemed statistically significant in significant_transitions are \"transitions\" in the timeseries.\n\nExisting subtypes of ChangesConfig are:\n\nSlidingWindowConfig.\nSegmentedWindowConfig.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.ChangesResults","page":"API","title":"TransitionsInTimeseries.ChangesResults","text":"ChangesResults\n\nSupertype used to gather results of estimate_changes. The concrete subtype instances are described in the docstrings of configuration types.\n\n\n\n\n\n","category":"type"},{"location":"api/#Sliding-window","page":"API","title":"Sliding window","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"SlidingWindowConfig\nSlidingWindowResults","category":"page"},{"location":"api/#TransitionsInTimeseries.SlidingWindowConfig","page":"API","title":"TransitionsInTimeseries.SlidingWindowConfig","text":"SlidingWindowConfig <: ChangesConfig\nSlidingWindowConfig(indicators, change_metrics; kwargs...)\n\nA configuration that can be given to estimate_changes. It estimates transitions by a sliding window approach:\n\nEstimate the timeseries of an indicator by sliding a window over the input timeseries.\nEstimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.\n\nBoth indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.\n\nindicators can be a single function or a tuple of indicators. Similarly, change_metrics can be a tuple or a single function. If tuples, the length of indicators and change_metrics must match. This way the analysis can be efficiently repeated for many indicators and/or change metrics.\n\nThe results output corresponding to SlidingWindowConfig is SlidingWindowResults.\n\nStep 1. is skipped if nothing is provided as indicators, in which case the change metrics are estimated directly from input data.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.\nwidth_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.\nwhichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_changes using the keyword whichtime. Options include:\nlast: use the last timepoint of each window\nmidpoint: use the mid timepoint of each time window\nfirst: use first timepoint of each window\nIn fact, the indicators time vector is computed simply via\nt_indicator = windowmap(whichtime, t; width_ind, stride_ind)\nt_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)\nso any other function of the time window may be given to extract the time point itself, such as mean or median.\nT = Float64: Element type of input timeseries to initialize some computations.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlidingWindowResults","page":"API","title":"TransitionsInTimeseries.SlidingWindowResults","text":"SlidingWindowResults <: ChangesResults\n\nA struct containing the output of estimate_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries (matrix with each column one indicator).\nt_indicator, the time vector of the indicator timeseries.\nx_change, the change metric timeseries (matrix with each column one change metric).\nt_change, the time vector of the change metric timeseries.\nconfig::SlidingWindowConfig, what was used for the analysis.\n\n\n\n\n\n","category":"type"},{"location":"api/#Segmented-window","page":"API","title":"Segmented window","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"SegmentedWindowConfig\nSegmentedWindowResults","category":"page"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowConfig","page":"API","title":"TransitionsInTimeseries.SegmentedWindowConfig","text":"SegmentedWindowConfig <: IndicatorsChangeConfig\nSegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)\n\nA configuration that can be given to estimate_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:\n\nFor each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).\nFor each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d\n\ntseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.\n\nThe results output corresponding to SlidingWindowConfig is SegmentedWindowResults.\n\nKeyword arguments\n\nwidth_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.\nmin_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SegmentedWindowResults","page":"API","title":"TransitionsInTimeseries.SegmentedWindowResults","text":"SegmentedWindowResults <: ChangesResults\n\nA struct containing the output of estimate_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.\n\nIt has the following fields that the user may access\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.\nt_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.\nx_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.\nt_change, the time vector of the change metric.\nconfig::SegmentedWindowConfig, what was used for the analysis.\ni1::Vector{Int} indices corresponding to start time of each segment.\ni2::Vector{Int} indices corresponding to end time of each segment.\nprecomp_change_metrics vector containing the precomputed change metrics of each segment.\n\n\n\n\n\n","category":"type"},{"location":"api/#Slope-change","page":"API","title":"Slope change","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"SlopeChangeConfig\nSlopeChangeResults","category":"page"},{"location":"api/#TransitionsInTimeseries.SlopeChangeConfig","page":"API","title":"TransitionsInTimeseries.SlopeChangeConfig","text":"SlopeChangeConfig <: ChangesConfig\nSlopeChangeConfig(; indicator = nothing, kw...)\n\nA configuration that can be given to estimate_changes. It estimates a change of slope in the timeseries by fitting two connected linear segments to the timeseries, returning the results (i.e., the two-linear fits) as SlopeChangeResults.\n\nKeyword arguments\n\nindicator = nothing: if not nothing. Otherwise it should be a function f(x) -> Real. The slope fitting is then done over an indicator of the timeseries, which itself is estimated via a sliding window exactly as in SlidingWindowConfig.\nwidth_ind, stride_ind, whichtime: exactly as in SlidingWindowConfig if indicator is not nothing.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlopeChangeResults","page":"API","title":"TransitionsInTimeseries.SlopeChangeResults","text":"SlopeChangeResults <: ChangesResults\n\nA struct containing the output of estimate_changes used with SlopeChangeConfig. It can be used for further analysis, visualization, or given to significant_transitions. The only significance type that you can use this with significant_transitions is SlopeChangeSignificance.\n\nIt has the following fields that the user may access:\n\nx: the input timeseries.\nt: the time vector of the input timeseries.\nx_indicator, the indicator timeseries.\nt_indicator, the time vector of the indicator timeseries.\nt_change, the time the slope changes.\nfitparams = a, b, c, d, the fitted linear coefficients, a + b*t before. t_change and c + d*t after t_change.\n\n\n\n\n\n","category":"type"},{"location":"api/#Significance-testing","page":"API","title":"Significance testing","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"significant_transitions\nSignificance\nSurrogatesSignificance\nThresholdSignificance\nSigmaSignificance\nQuantileSignificance\nSlopeChangeSignificance","category":"page"},{"location":"api/#TransitionsInTimeseries.significant_transitions","page":"API","title":"TransitionsInTimeseries.significant_transitions","text":"significant_transitions(res::ChangesResults, signif::Significance)\n\nEstimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as the changes stored in res (which typically is stored in the field res.x_change). flags is true wherever a change metric of res is deemed significant.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.Significance","page":"API","title":"TransitionsInTimeseries.Significance","text":"Significance\n\nSupertype used to test for significance in significant_transitions. Changes that are statistically significant are \"transitions\".\n\nValid subtypes are:\n\nSurrogatesSignificance.\nSigmaSignificance.\nQuantileSignificance.\nThresholdSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SurrogatesSignificance","page":"API","title":"TransitionsInTimeseries.SurrogatesSignificance","text":"SurrogatesSignificance <: Significance\nSurrogatesSignificance(; kwargs...)\n\nA configuration struct for significance testing significant_transitions using timeseries surrogates.\n\nKeyword arguments\n\nsurromethod = RandomFourier(): method to generate surrogates\nn = 1000: how many surrogates to generate\nrng = Random.default_rng(): random number generator for the surrogates\np = 0.05: threshold for significance of the p-value\ntail = :both: tail type used, see below\n\nDescription\n\nWhen used with ChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).\n\nThe p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in ChangesResults.\n\nNote that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.ThresholdSignificance","page":"API","title":"TransitionsInTimeseries.ThresholdSignificance","text":"ThresholdSignificance(threshold::Real; tail = :right) <: Significance\n\nA configuration struct for significance testing in significant_transitions. Significance is estimated by comparing the value of each change metric with the given threshold. Values that exceed the threshold (if tail = :right) or subseed the threshold (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SigmaSignificance","page":"API","title":"TransitionsInTimeseries.SigmaSignificance","text":"SigmaSignificance(; factor = 3.0, tail = :both) <: Significance\n\nA configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing how many standard deviations (σ) the value exceeds the mean value (μ). Values that exceed (if tail = :right) μ + factor*σ, or subseed (if tail = :left) μ - factor*σ are deemed significant. If tail = :both then either condition is checked.\n\nfactor can also be a vector of values, in which case a different value is used for each change metric.\n\nSee also QuantileSignificance.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.QuantileSignificance","page":"API","title":"TransitionsInTimeseries.QuantileSignificance","text":"QuantileSignificance(; p = 0.95, tail = :both) <: Significance\n\nA configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.\n\nQuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.SlopeChangeSignificance","page":"API","title":"TransitionsInTimeseries.SlopeChangeSignificance","text":"SlopeChangeSignificance(; moe_slope, moe_offset, slope_diff = moe_slope, pvalue = 0.05)\n\nTest whether the result of SlopeChangeResults is statistically significant.\n\nTwo tests are done:\n\nCheck whether the margin of error of the fitted parameters a, b, c, d of the two linear segments a + b*t, c + d*t is less than the specified margins of error, for a chosen pvalue.\nTest that the two slopes b, d have difference greater than slope_diff.\n\nThe Boolean & of the above two is the final test.\n\nThe margin of error is simply half the size of the confidence interval, also known as radius of the confidence interval.\n\n\n\n\n\n","category":"type"},{"location":"api/#indicators","page":"API","title":"Indicators","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Note that any Julia function can be an indicator or change metric, so the list here is only just a couple of indicators directly implemented in this package.","category":"page"},{"location":"api/#Value-distribution","page":"API","title":"Value distribution","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"StatsBase.mean\nStatsBase.skewness\nStatsBase.kurtosis","category":"page"},{"location":"api/#Statistics.mean","page":"API","title":"Statistics.mean","text":"mean(A::AbstractArray, w::AbstractWeights[, dims::Int])\n\nCompute the weighted mean of array A with weight vector w (of type AbstractWeights). If dim is provided, compute the weighted mean along dimension dims.\n\nExamples\n\nn = 20\nx = rand(n)\nw = rand(n)\nmean(x, weights(w))\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.skewness","page":"API","title":"StatsBase.skewness","text":"skewness(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#StatsBase.kurtosis","page":"API","title":"StatsBase.kurtosis","text":"kurtosis(v, [wv::AbstractWeights], m=mean(v))\n\nCompute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.\n\n\n\n\n\n","category":"function"},{"location":"api/#Critical-Slowing-Down","page":"API","title":"Critical Slowing Down","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"StatsBase.var\nar1_whitenoise","category":"page"},{"location":"api/#Statistics.var","page":"API","title":"Statistics.var","text":"var(x::AbstractArray, w::AbstractWeights, [dim]; mean=nothing, corrected=false)\n\nCompute the variance of a real-valued array x, optionally over a dimension dim. Observations in x are weighted using weight vector w. The uncorrected (when corrected=false) sample variance is defined as:\n\nfrac1sumw sum_i=1^n w_ileft(x_i - μright)^2 \n\nwhere n is the length of the input and μ is the mean. The unbiased estimate (when corrected=true) of the population variance is computed by replacing frac1sumw with a factor dependent on the type of weights used:\n\nAnalyticWeights: frac1sum w - sum w^2 sum w\nFrequencyWeights: frac1sumw - 1\nProbabilityWeights: fracn(n - 1) sum w where n equals count(!iszero, w)\nWeights: ArgumentError (bias correction not supported)\n\n\n\n\n\nvar(ce::CovarianceEstimator, x::AbstractVector; mean=nothing)\n\nCompute the variance of the vector x using the estimator ce.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.ar1_whitenoise","page":"API","title":"TransitionsInTimeseries.ar1_whitenoise","text":"ar1_whitenoise(x::AbstractVector)\n\nReturn the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:\n\ntheta = sum_i=2^n x_i x_i-1 sum_i=2^n x_i-1^2\n\n\n\n\n\n","category":"function"},{"location":"api/#Spectrum","page":"API","title":"Spectrum","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"LowfreqPowerSpectrum\nPrecomputedLowfreqPowerSpectrum","category":"page"},{"location":"api/#TransitionsInTimeseries.LowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.LowfreqPowerSpectrum","text":"LowfreqPowerSpectrum(; q_lofreq = 0.1)\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:\n\nlfps = precompute( LowfreqPowerSpectrum() )\n\nKeyword arguments:\n\nq_lofreq: a number between 0 and 1 that characterises which portion of the\n\nfrequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.PrecomputedLowfreqPowerSpectrum","page":"API","title":"TransitionsInTimeseries.PrecomputedLowfreqPowerSpectrum","text":"PrecomputedLowfreqPowerSpectrum\n\nA struct containing all the precomputed fields to efficiently perform repetitive computation of the low-frequency power spectrum (LFPS), a number between 0 and 1 that characterizes the amount of power contained in the low frequencies of the power density spectrum of x. Once lfps::PrecomputedLowfreqPowerSpectrum is initialized, it can be used as a function to obtain the LFPS of x::AbstractVector by:\n\nlfps(x)\n\n\n\n\n\n","category":"type"},{"location":"api/#Nonlinear-dynamics","page":"API","title":"Nonlinear dynamics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.","category":"page"},{"location":"api/","page":"API","title":"API","text":"For example, using the permutation entropy as an indicator is as simple as doing","category":"page"},{"location":"api/","page":"API","title":"API","text":"using ComplexityMeasures\nest = OrdinalPatterns(; m = 3) # order 3\n# create a function that given timeseries returns permutation entropy\nindicator = x -> entropy_normalized(est, x)","category":"page"},{"location":"api/","page":"API","title":"API","text":"and giving the created indicator to e.g., SlidingWindowConfig.","category":"page"},{"location":"api/#change_metrics","page":"API","title":"Change metrics","text":"","category":"section"},{"location":"api/#Slope","page":"API","title":"Slope","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"kendalltau\nspearman\nRidgeRegressionSlope\nPrecomputedRidgeRegressionSlope","category":"page"},{"location":"api/#TransitionsInTimeseries.kendalltau","page":"API","title":"TransitionsInTimeseries.kendalltau","text":"kendalltau(x::AbstractVector)\n\nCompute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.spearman","page":"API","title":"TransitionsInTimeseries.spearman","text":"spearman(x::AbstractVector)\n\nCompute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.RidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.RidgeRegressionSlope","text":"RidgeRegressionSlope(; lambda = 0.0) → rr\n\nReturn a PrecomputableFunction containing all the necessary fields to generate a PrecomputedRidgeRegressionSlope. rr can be used as a change metric focused on trend.\n\nlambda is a regularization constant, usually between 0 and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.PrecomputedRidgeRegressionSlope","page":"API","title":"TransitionsInTimeseries.PrecomputedRidgeRegressionSlope","text":"PrecomputedRidgeRegressionSlope\n\nA struct containing the precomputed ridge regression matrix. Once rrslope::PrecomputedRidgeRegressionSlope is initialized, it can be used as a function to obtain the ridge regression slope of x::AbstractVector by applying:\n\nrrslope(x)\n\n\n\n\n\n","category":"type"},{"location":"api/#Value-distribution-differences","page":"API","title":"Value distribution differences","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"difference_of_means","category":"page"},{"location":"api/#TransitionsInTimeseries.difference_of_means","page":"API","title":"TransitionsInTimeseries.difference_of_means","text":"difference_of_means(x::AbstractArray)\n\nReturn the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:\n\n# assumes 1-based indexing\nn = length(x)\nx1 = view(x, 1:n÷2)\nx2 = view(x, (n÷2 + 1):n)\nreturn abs(mean(x1) - mean(x2))\n\ndifference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.\n\n\n\n\n\n","category":"function"},{"location":"api/#own_indicator","page":"API","title":"Make your own indicator/metric!","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The only difference between what is an \"indicator\" and what is a \"change metric\" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.","category":"page"},{"location":"api/","page":"API","title":"API","text":"There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:","category":"page"},{"location":"api/","page":"API","title":"API","text":"PrecomputableFunction\nprecompute","category":"page"},{"location":"api/#TransitionsInTimeseries.PrecomputableFunction","page":"API","title":"TransitionsInTimeseries.PrecomputableFunction","text":"PrecomputableFunction\n\nSupertype of structs containing the necessary field to precompute a ::Function by:\n\nprecompute(f::PrecomputableFunction, t)\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.precompute","page":"API","title":"TransitionsInTimeseries.precompute","text":"precompute(f, t)\n\nPrecompute the function f given a time vector t.\n\n\n\n\n\n","category":"function"},{"location":"api/#Surrogates","page":"API","title":"Surrogates","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.","category":"page"},{"location":"api/#Sliding-windows","page":"API","title":"Sliding windows","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"WindowViewer\nwindowmap\nwindowmap!","category":"page"},{"location":"api/#TransitionsInTimeseries.WindowViewer","page":"API","title":"TransitionsInTimeseries.WindowViewer","text":"WindowViewer(x; width, stride)\n\nInitialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.\n\nIf not given, the keywords width, stride are respectively taken as default_window_width(x) and 1.\n\n\n\n\n\n","category":"type"},{"location":"api/#TransitionsInTimeseries.windowmap","page":"API","title":"TransitionsInTimeseries.windowmap","text":"windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f\n\nA shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.windowmap!","page":"API","title":"TransitionsInTimeseries.windowmap!","text":"windowmap!(f::Function, out, x::AbstractVector; kwargs...)\n\nSame as windowmap, but writes the output in-place in out.\n\n\n\n\n\n","category":"function"},{"location":"api/#Load-data","page":"API","title":"Load data","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"load_linear_vs_doublewell()","category":"page"},{"location":"api/#TransitionsInTimeseries.load_linear_vs_doublewell-Tuple{}","page":"API","title":"TransitionsInTimeseries.load_linear_vs_doublewell","text":"load_linear_vs_doublewell()\n\nLoad prototypical data from a linear and a double-well model to test some indicators.\n\n\n\n\n\n","category":"method"},{"location":"api/#Visualization","page":"API","title":"Visualization","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"plot_indicator_changes\nplot_significance!\nplot_changes_significance","category":"page"},{"location":"api/#TransitionsInTimeseries.plot_indicator_changes","page":"API","title":"TransitionsInTimeseries.plot_indicator_changes","text":"plot_indicator_changes(res) → (fig, axs)\n\nReturn fig::Figure and axs::Matrix{Axis}, on which res::ChangesResults has been visualised.\n\nKeyword arguments:\n\ncolors = default_colors sets the colors of the line plots that are to\n\nbe cycled through. The default correspond to the color scheme of Julia Dynamics.\n\n`indicatornames = defaultindicatorlabel(res), chametricnames =\n\ndefaultchametriclabel(res)sets the labels for the indicators and the change metrics, with the default inferring them from the names ofres.config.indicatorsandres.config.change_metrics`.\n\naccent_linewidth = 3 sets the line width for the original signals (the\n\nsurrogates have linewidth = 1)\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.plot_significance!","page":"API","title":"TransitionsInTimeseries.plot_significance!","text":"plot_significance!(axs, res, signif)\n\nUpdate the axs::Matrix{Axis} of a figure obtained with plot_indicator_changes(res) with the signif::SurrogatesSignificance.\n\nKeyword arguments:\n\nflags = nothing provides the significance flags, for instance obtained by\n\nthresholding the pvalues.\n\nnsurro = 20 sets the number of surrogates to plot.\n\n\n\n\n\n","category":"function"},{"location":"api/#TransitionsInTimeseries.plot_changes_significance","page":"API","title":"TransitionsInTimeseries.plot_changes_significance","text":"plot_changes_significance(res, signif) → (fig, axs)\n\nReturn fig::Figure and axs::Matrix{Axis}, on which res::ChangesResults and signif::SurrogatesSignificance have been visualised. The source code is as simple as:\n\nfig, axs = plot_indicator_changes(res; kwargs...)\nplot_significance!(axs, res, signif; kwargs...)\n\nFor more information, refer to plot_indicator_changes and plot_significance!.\n\n\n\n\n\n","category":"function"},{"location":"api/#Utils","page":"API","title":"Utils","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"default_window_width","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"EditURL = \"do-events.jl\"","category":"page"},{"location":"examples/do-events/#Dansgaard-Oescher-events-and-Critical-Slowing-Down","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The delta^18O timeseries of the North Greenland Ice Core Project (NGRIP) are, to this date, the best proxy record for the Dansgaard-Oeschger events (DO-events). DO-events are sudden warming episodes of the North Atlantic, reaching 10 degrees of regional warming within 100 years. They happened quasi-periodically over the last glacial cycle due to transitions between strong and weak states of the Atlantic Meridional Overturning Circulation and might be therefore be the most prominent examples of abrupt transitions in the field of climate science. We here propose to hindcast these events by applying the theory of Critical Slowing Down (CSD) on the NGRIP data, which can be found here in its raw format. This analysis has already been done in (Boers, 2018) and we here try to reproduce Figure 2.d-f.","category":"page"},{"location":"examples/do-events/#Preprocessing-NGRIP","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Preprocessing NGRIP","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Data pre-processing is not part of TransitionsInTimeseries.jl, but a step the user has to do before using the package. To present an example with a complete scientific workflow, we will showcase typical data pre-processing here, that consist of the following steps:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Load the data, reverse and offset it to have time vector = time before 2000 AD.\nFilter non-unique points in time and sort the data.\nRegrid the data from uneven to even sampling.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"The time and delta^18O vectors resulting from the i-th preprocessing step are respectively called t_i and x_i. The final step consists in obtaining a residual r, i.e. the fluctuations of the system around the attractor, which, within the CSD theory, is assumed to be tracked. Over this example, it will appear that the convenience of TransitionsInTimeseries.jl leads the bulk of the code to be written for plotting and preprocessing.","category":"page"},{"location":"examples/do-events/#Step-1:","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 1:","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DelimitedFiles, Downloads\n\nfunction load_ngrip()\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP.csv\")\n data, labels = readdlm(tmp, header = true)\n return reverse(data[:, 1]) .- 2000, reverse(data[:, 2]) # (time, delta-18-0) vectors\nend\n\nt1, x1 = load_ngrip()","category":"page"},{"location":"examples/do-events/#Step-2","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 2","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"uniqueidx(v) = unique(i -> v[i], eachindex(v))\nfunction keep_unique(t, x)\n unique_idx = uniqueidx(t)\n return t[unique_idx], x[unique_idx]\nend\n\nfunction sort_timeseries!(t, x)\n p = sortperm(t)\n permute!(t, p)\n permute!(x, p)\n return nothing\nend\n\nt2, x2 = keep_unique(t1, x1)\nsort_timeseries!(t2, x2)","category":"page"},{"location":"examples/do-events/#Step-3","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 3","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using BSplineKit\n\nfunction regrid2evensampling(t, x, dt)\n itp = BSplineKit.interpolate(t, x, BSplineOrder(4))\n tspan = (ceil(minimum(t)), floor(maximum(t)))\n t_even = collect(tspan[1]:dt:tspan[2])\n x_even = itp.(t_even)\n return t_even, x_even\nend\n\ndt = 5.0 # dt = 5 yr as in (Boers 2018)\nt3, x3 = regrid2evensampling(t2, x2, dt)","category":"page"},{"location":"examples/do-events/#Step-4","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Step 4","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the final step we drop the indices:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using DSP\n\nfunction chebyshev_filter(t, x, fcutoff)\n ii = 10 # Chebyshev filtering requires to prune first points of timeseries.\n responsetype = Highpass(fcutoff, fs = 1/dt)\n designmethod = Chebyshev1(8, 0.05)\n r = filt(digitalfilter(responsetype, designmethod), x)\n xtrend = x - r\n return t[ii:end], x[ii:end], xtrend[ii:end], r[ii:end]\nend\n\nfcutoff = 0.95 * 0.01 # cutoff ≃ 0.01 yr^-1 as in (Boers 2018)\nt, x, xtrend, r = chebyshev_filter(t3, x3, fcutoff)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Let's now visualize our data in what will become our main figure. For the segmentation of the DO-events, we rely on the tabulated data from (Rasmussen et al., 2014) (which will soon be available as downloadable):","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using CairoMakie, Loess\n\nfunction loess_filter(t, x; span = 0.005)\n loessmodel = loess(t, x, span = span)\n xtrend = Loess.predict(loessmodel, t)\n r = x - xtrend\n return t, x, xtrend, r\nend\n\nfunction kyr_xticks(tticks_yr)\n tticks_kyr = [\"$t\" for t in Int.(tticks_yr ./ 1e3)]\n return (tticks_yr, tticks_kyr)\nend\n\nfunction plot_do(traw, xraw, tfilt, xfilt, t, r, t_transitions, xlims, xticks)\n fig = Figure(size = (1600, 1200), fontsize = 24)\n\n # Original timeseries with transition marked by vertical lines\n ax1 = Axis(fig[1, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"$\\delta^{18}$O (permil)\",\n xaxisposition = :top, xticks = xticks)\n lines!(ax1, traw, xraw, color = (:gray70, 0.5))\n lines!(ax1, tfilt, xfilt, color = :gray10, linewidth = 3)\n vlines!(ax1, t_transitions, color = Cycled(1), linewidth = 3)\n\n # Residual timeseries\n ax2 = Axis(fig[2, 1], ylabel = L\"Residual $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n lines!(ax2, t, r, color = :gray50, linewidth = 1)\n\n # Axes for variance and AC1 timeseries\n ax3 = Axis(fig[3, 1], ylabel = L\"Variance $\\,$\", xticks = xticks,\n xticksvisible = false, xticklabelsvisible = false)\n ax4 = Axis(fig[4, 1], xlabel = L\"Time (kyr) $\\,$\", ylabel = L\"Lag-1 autocor. $\\,$\",\n xticks = xticks)\n\n axs = [ax1, ax2, ax3, ax4]\n [xlims!(ax, xlims) for ax in axs]\n ylims!(axs[1], (-48, -34))\n rowgap!(fig.layout, 10)\n return fig, axs\nend\n\nxlims = (-60e3, -10e3)\nxticks = kyr_xticks(-60e3:5e3:5e3)\nt_rasmussen = -[-60000, 59440, 58280, 55800, 54220, 49280, 46860, 43340, 41460, 40160,\n 38220, 35480, 33740, 32500, 28900, 27780, 23340, 14692, 11703]\ntloess, _, xloess, rloess = loess_filter(t3, x3) # loess-filtered signal for visualization\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nfig","category":"page"},{"location":"examples/do-events/#Hindcast-on-NGRIP-data","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcast on NGRIP data","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"As one can see... there is not much to see so far. Residuals are impossible to simply eye-ball and we therefore use TransitionsInTimeseries.jl to study the evolution, measured by the ridge-regression slope of the residual's variance and lag-1 autocorrelation (AC1) over time. In many examples of the literature, including (Boers, 2018), the CSD analysis is performed over segments (sometimes only one) of the timeseries, such that a significance value is obtained for each segment. By using SegmentedWindowConfig, dealing with segments can be easily done in TransitionsInTimeseries.jl and is demonstrated here:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"using TransitionsInTimeseries, StatsBase\nusing Random: Xoshiro\n\nac1(x) = sum(autocor(x, [1])) # AC1 from StatsBase\nindicators = (var, ac1)\nchange_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope())\ntseg_start = t_rasmussen[1:end-1] .+ 200\ntseg_end = t_rasmussen[2:end] .- 200\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end; whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100) # require >=100 data points to estimate change metric\nresults = estimate_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"That's it! We can now visulaise our results with a generic function that we will re-use later:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"function plot_segment_analysis!(axs, results, signif)\n (; t_indicator, x_indicator) = results\n for k in eachindex(t_indicator) # loop over the segments\n for i in axes(signif.pvalues, 2) # loop over the indicators\n if !isnan(signif.pvalues[k, i]) # plot if segment long enough\n # Plot indicator timeseries and its linear regression\n ti, xi = t_indicator[k], x_indicator[k][:, i]\n lines!(axs[i+2], ti, xi, color = Cycled(1))\n m, p = ridgematrix(ti, 0.0) * xi\n if signif.pvalues[k, i] < 0.05\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray5, linewidth = 3)\n else\n lines!(axs[i+2], ti, m .* ti .+ p, color = :gray60, linewidth = 3)\n end\n end\n end\n end\nend\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In (Boers, 2018), 13/16 and 7/16 true positives are respectively found for the variance and AC1, with 16 referring to the total number of transitions. The timeseries actually includes 18 transition but, in (Boers, 2018), some segments are considered too small to be analysed. In contrast, we here respectively find 9/16 true positives for the variance and 3/16 for AC1. We can track down the discrepancies to be in the surrogate testing, since the indicator timeseries computed here are almost exactly similar to those of (Boers, 2018). This mismatch points out that packages like TransitionsInTimeseries.jl are wishful for research to be reproducible, especially since CSD is gaining attention - not only within the scientific community but also in popular media.","category":"page"},{"location":"examples/do-events/#CSD:-only-a-necessary-condition,-only-in-some-cases","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"CSD: only a necessary condition, only in some cases","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For codimension-1 systems, approaching a fold, Hopf or transcritical bifurcation implies a widening of the potential U, which defines the deterministic term f = -U of the SDE's right-hand-side. In the presence of noise, this leads to CSD, which is therefore a necessary condition for crossing one of these bifurcations - although it is not always assessable by analysing the timeseries due to practical limitations (e.g. sparse data subject to large measurement noise). It is nonetheless not given that DO-events, as many other real-life applications, can be seen as a codimension-1 fold, Hopf or transcritical bifurcations. Besides this, we emphasise that CSD is not a sufficient condition for assessing a transition being ahead in near future, since a resilience loss can happen without actually crossing any bifurcation. This can be illustrated on the present example by performing the same analysis only until few hundred years before the transition:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"tseg_end = t_rasmussen[2:end] .- 700 # stop analysis 500 years earlier than before\nconfig = SegmentedWindowConfig(indicators, change_metrics,\n tseg_start, tseg_end, whichtime = last, width_ind = Int(200÷dt),\n min_width_cha = 100)\nresults = estimate_changes(config, r, t)\nsignif = SurrogatesSignificance(n = 1000, tail = [:right, :right], rng = Xoshiro(1995))\nflags = significant_transitions(results, signif)\nfig, axs = plot_do(t3, x3, tloess, xloess, t, r, t_rasmussen, xlims, xticks)\nplot_segment_analysis!(axs, results, signif)\nfig","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"For the variance and AC1, we here respectively find 6 and 3 positives, although the transitions are still far ahead. This shows that what CSD captures is a potential widening induced by a shift of the forcing parameter rather than the actual transition. We therefore believe, as already suggested in some studies, that \"resilience-loss indicators\" is a more accurate name than \"early-warning signals\" when using CSD.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"We draw attention upon the fact that the delta^18O timeseries is noisy and sparsely re-sampled. Furthermore, interpolating over time introduces a potential bias in the statistics, even if performed on a coarse grid. The NGRIP data therefore represents an example that should be handled with care - as many others where CSD analysis has been applied on transitions in the field of geoscience. To contrast with this, we propose to perform the same analysis on synthethic DO data, obtained from an Earth Model of Intermediate Complexity (EMIC).","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"warning: Degrees of freedom\nThese sources of error come along the usual problem of arbitrarily choosing (1) a filtering method, (2) windowing parameters and (3) appropriate metrics (for instance when the forcing noise is suspected to be correlated). This leads to a large number of degrees of freedom (DoF). Although sensible guesses are possible here, checking that results are robust w.r.t. the DoF should be a standard practice.","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"info: Future improvement\nSupporting the computations for uneven timeseries is a planned improvement of TransitionsInTimeseries.jl. This will avoid the need of regridding data on coarse grids and will prevent from introducing any bias.","category":"page"},{"location":"examples/do-events/#Hindcasting-simulated-DO-events","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Hindcasting simulated DO-events","text":"","category":"section"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"In CLIMBER-X, the EMIC described in (Willeit et al., 2022), DO-like events can be triggered by forcing the North Atlantic with a (white noise) freshwater input. Simulated DO-like events present the big advantage of being evenly sampled in time and free of measurement noise. We run this analysis over two exemplary simulation outputs:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"t_transitions = [[1, 1850, 2970, 3970, 5070, 5810, 7050, 8050],\n [1, 3500, 4370, 5790, 7200, 8140]]\nt_lb = [[300, 500, 300, 600, 300, 500, 500], [1800, 500, 1000, 900, 500]]\ntseg_start = [t_transitions[1][1:end-1] + t_lb[1], t_transitions[2][1:end-1] + t_lb[2]]\ntseg_end = [t_transitions[1][2:end] .- 50, t_transitions[2][2:end] .- 50]\n\nfigvec = Figure[]\n\nfor j in 1:2\n # Download the data and perform loess filtering on it\n tmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\" *\n \"master/timeseries/climberx-do$(j)-omaxa.csv\")\n data = readdlm(tmp)\n tcx, xcx = data[1, 1000:end], data[2, 1000:end]\n t, x, xtrend, r = loess_filter(tcx, xcx, span = 0.02)\n\n # Initialize figure\n xlims = (0, last(tcx))\n xticks = kyr_xticks(xlims[1]:1e3:xlims[2])\n fig, axs = plot_do(tcx, xcx, t, xtrend, t, r, t_transitions[j], extrema(t), xticks)\n ylims!(axs[1], (5, 40))\n axs[1].ylabel = L\"Max. Atlantic overturning (Sv) $\\,$\"\n\n # Run sliding analysis and update figure with results\n dt = mean(diff(tcx))\n config = SegmentedWindowConfig(\n indicators, change_metrics, tseg_start[j], tseg_end[j],\n whichtime = last, width_ind = Int(200÷dt), min_width_cha = 100)\n results = estimate_changes(config, r, t)\n signif = SurrogatesSignificance(n = 1_000, tail = [:right, :right], rng = Xoshiro(1995))\n flags = significant_transitions(results, signif)\n\n plot_segment_analysis!(axs, results, signif)\n vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)\n push!(figvec, fig)\nend\nfigvec[1]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"figvec[2]","category":"page"},{"location":"examples/do-events/","page":"Dansgaard-Oescher events and Critical Slowing Down","title":"Dansgaard-Oescher events and Critical Slowing Down","text":"Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"EditURL = \"ks_paleojump.jl\"","category":"page"},{"location":"examples/ks_paleojump/#Kolmogorov-Smirnov-test-for-detecting-transitions-in-paleoclimate-timeseries","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"The goal of this example is to show how simple it is to re-create an analysis similar to what was done in the paper \"Automatic detection of abrupt transitions in paleoclimate records\", (Bagniewski et al., 2021). The same analysis was then used to create a database of transitions in paleoclimate records in (Bagniewski et al., 2023) Using TransitionsInTimeseries.jl and HypothesisTests.jl, the analysis becomes a 10-lines-of-code script (for a given timeseries).","category":"page"},{"location":"examples/ks_paleojump/#Scientific-background","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Scientific background","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"The approach of (Bagniewski et al., 2021) is based on the two-sample Kolmogorov Smirnov test. It tests whether the samples from two datasets or timeseries are distributed according to the same cumulative density function or not. This can be estimated by comparing the value of the KS-statistic versus some threshold that depends on the required confidence.","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"The application of this test for identifying transitions in timeseries is simple:","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"A sliding window analysis is performed in the timesries\nIn each window, the KS statistic is estimated between the first half and the second half of the timeseries within this window.\nTransitions are defined by when the KS statistic exceeds a particular value based on some confidence. The transition occurs in the middle of the window.","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"We should point out that in (Bagniewski et al., 2021) the authors did a more detailed analysis: analyzed many different window widths, added a conditional clause to exclude transitions that do not exceed a predefined minimum \"jump\" in the data, and also added another conditional clause that filtered out transitions that are grouped in time (which is a natural consequence of using the Kolmogorov-Smirov test for detecting transitions).","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"Here we won't do that post processing, mainly because it is rather simple to include these additional conditional clauses to filter transitions after they are found.","category":"page"},{"location":"examples/ks_paleojump/#Steps-for-TransitionsInTimeseries.jl","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Steps for TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"Doing this kind of work with TransitionsInTimeseries.jl is so easy you won't even trip! This analysis follows the same sliding window approach showcased in our Tutorial, and it even excludes the \"indicator\" aspect: the change metric is estimated directly from the input data!","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"As such, we really only need to define/do these things before we have finished the analysis:","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"Load the input data (we will use the same example as the NGRIP data of Dansgaard-Oescher events and Critical Slowing Down example) and set the appropriate time window.\nDefine the function that estimates the change metric (i.e., the KS-statistic)\nPerform the sliding window analysis as in the Tutorial with estimate_changes\nEstimate the \"confident\" transitions in the data by comparing the estimated KS-statistic with a predefined threshold.","category":"page"},{"location":"examples/ks_paleojump/#Load-timeseries-and-window-length","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Load timeseries and window length","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"Following the Dansgaard-Oescher events example, we load the data after all the processing steps done in that example:","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"using DelimitedFiles, CairoMakie\n\ntmp = Base.download(\"https://raw.githubusercontent.com/JuliaDynamics/JuliaDynamics/\"*\n \"master/timeseries/NGRIP_processed.csv\")\ndata = readdlm(tmp)\nt, xtrend, xresid, xloess = collect.(eachcol(data))\n\nfig, ax = lines(t, xtrend; axis = (ylabel = \"NGRIP (processed)\", xlabel = \"time\"))\nlines!(ax, t, xloess; linewidth = 2)\nfig","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"For the window, since we are using a sliding window here, we will be using a window of length 500 (which is approximately 1/2 to 1/4 the span between typical transitions found by (Rasmussen et al., 2014)).","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"window = 500","category":"page"},{"location":"examples/ks_paleojump/#Defining-the-change-metric-function","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Defining the change metric function","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"HypothesisTest.jl implements the Kolmogorov-Smirnov test, however here we are interested in the value of the test iself (the so-called KS-statistic), rather than a p-value. To this end, we define the following function to compute the statistic, which also normalizes it as in (Bagniewski et al., 2021).","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"using HypothesisTests\n\nfunction normalized_KS_statistic(timeseries)\n N = length(timeseries)\n i = N÷2\n x = view(timeseries, 1:i)\n y = view(timeseries, (i+1):N)\n kstest = ApproximateTwoSampleKSTest(x, y)\n nx = ny = i # length of each timeseries half of total\n n = nx*ny/(nx + ny) # written fully for concreteness\n D_KS = kstest.δ # can be compared directly with sqrt(-log(α/2)/2)\n # Rescale according to eq. (5) of the paper\n rescaled = 1 - ((1 - D_KS)/(1 - sqrt(1/n)))\n return rescaled\nend\n\nN = 1000 # the statistic is independent of `N` for large enough `N`!\nx = randn(N)\ny = 1.8randn(N) .+ 1.0\nz = randn(N)\nw = 0.6randn(N) .- 2.0\n\nfig, ax = density(x; color = (\"black\", 0.5), strokewidth = 4.0, label = \"reference distribution\")\nax.title = \"showcase of normalized KS-statistic\"\nfor q in (y, z, w)\n D_KS = normalized_KS_statistic(vcat(x, q))\n density!(ax, q; label = \"D_KS = $(D_KS)\")\nend\naxislegend(ax)\nfig","category":"page"},{"location":"examples/ks_paleojump/#Perform-the-sliding-window-analysis","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Perform the sliding window analysis","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"This is just a straightforward call to estimate_changes. In fact, it is even simpler than the tutorial. Here we skip completely the \"indicator\" estimation step, and we evaluate the change metric directly on input data. We do this by simply passing nothing as the indicators.","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"using TransitionsInTimeseries\n\nconfig = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 500)\n\nresults = estimate_changes(config, xtrend, t)","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"Which we can visualize","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"function visualize_results(results)\n fig, ax1 = lines(t, xtrend; axis = (ylabel = \"NGRIP (processed)\",))\n ax2, = lines(fig[2, 1], results.t_change, vec(results.x_change), axis = (ylabel = \"D_KS (normalized)\", xlabel = \"time\"))\n linkxaxes!(ax1, ax2)\n hidexdecorations!(ax1; grid = false)\n xloess_normed = (xloess .- minimum(xloess))./(maximum(xloess) - minimum(xloess))\n lines!(ax2, t, xloess_normed; color = (\"gray\", 0.5))\n fig\nend\n\nvisualize_results(results)","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"By overplotting the (smoothened) NGRIP timeseries and the normalized KS-statistic, it already becomes pretty clear that the statistic peaks when transitions occur.","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"The same thing happens if we alter the window duration","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 200)\nresults = estimate_changes(config, xtrend, t)\nvisualize_results(results)","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"So one can easily obtain extra confidence by varying window size as in (Bagniewski et al., 2021).","category":"page"},{"location":"examples/ks_paleojump/#Identifying-\"confident\"-transitions","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Identifying \"confident\" transitions","text":"","category":"section"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"As this identification here is done via a simple threshold, identifying the transitions is a nearly trivial call to significant_transitions with ThresholdSignificance","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"signif = ThresholdSignificance(0.5) # or any other threshold\nflags = significant_transitions(results, signif)\n\nfig = visualize_results(results)\naxDKS = content(fig[2,1])\nvlines!(axDKS, results.t_change[vec(flags)], color = (\"red\", 0.25))\nfig","category":"page"},{"location":"examples/ks_paleojump/","page":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","title":"Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries","text":"We could proceed with a lot of preprocessing as in (Bagniewski et al., 2021) but we skip this here for the sake of simplicity.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"EditURL = \"logistic.jl\"","category":"page"},{"location":"examples/logistic/#Permutation-entropy-for-dynamic-regime-changes","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Permutation entropy is used frequently to detect a transition between one dynamic regime to another. It is useful when the mean and std. of the timeseries values are very similar between the two regimes, which would mean that common distribution-based indicators, or common critical-slowing-down based indicators, would fail.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"This example will also explore different ways to test for significance that are arguably better suitable in such an application than the Tutorial's default of significance via random Fourier surrogates.","category":"page"},{"location":"examples/logistic/#Logistic-map-timeseries","page":"Permutation entropy for dynamic regime changes","title":"Logistic map timeseries","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A simple example of this is transitions from periodic to weakly chaotic to chaotic motion in the logistic map. First, let's generate a timeseries of the logistic map","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using DynamicalSystemsBase\nusing CairoMakie\n\n# time-dependent logistic map, so that the `r` parameter increases with time\nr1 = 3.83\nr2 = 3.86\nN = 2000\nrs = range(r1, r2; length = N)\n\nfunction logistic_drifting_rule(u, rs, n)\n r = rs[n+1] # time is `n`, starting from 0\n return SVector(r*u[1]*(1 - u[1]))\nend\n\nds = DeterministicIteratedMap(logistic_drifting_rule, [0.5], rs)\nx = trajectory(ds, N-1)[1][:, 1]","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Plot it, using as time the parameter value (they coincide)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig, ax = lines(rs, x; linewidth = 0.5)\nax.xlabel = \"r (time)\"\nax.ylabel = \"x\"\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is a rather obvious transition to strongly chaotic motion at r ≈ 3.855. However, there is also a subtle transition to weak chaos at r ≈ 3.847. This transition is barely visible in the timeseries, and in fact many of the timeseries statistical properties remain identical.","category":"page"},{"location":"examples/logistic/#Using-a-simpler-change-metric","page":"Permutation entropy for dynamic regime changes","title":"Using a simpler change metric","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Now, let's compute and various indicators and their changes, focusing on the permutation entropy as an indicator. We use order 4 here, because we know that to detect changes in a period m we would need an order ≥ m+1 permutation entropy.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"using TransitionsInTimeseries, ComplexityMeasures\n\nfunction permutation_entropy(m)\n est = SymbolicPermutation(; m) # order 3\n indicator = x -> entropy_normalized(est, x)\n return indicator\nend\n\nindicators = (var, ar1_whitenoise, permutation_entropy(4))\nindistrings = (\"var\", \"ar1\", \"pe\")","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"In this example there is no critical slowing down; instead, there is a sharp transition between periodic and chaotic motion. Hence, we shouldn't be using any trend-based change metrics. Instead, we will use the most basic change metric, difference_of_means. With this metric it also makes most sense to use as stride half the window width","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"metric = (difference_of_means, difference_of_means, difference_of_means)\n\nwidth_ind = N÷100\nwidth_cha = 20\nstride_cha = 10\n\nconfig = SlidingWindowConfig(indicators, metric;\n width_ind, width_cha, stride_cha,\n)\n\nresults = estimate_changes(config, x, rs)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's now plot the change metrics of the indicators","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"function plot_change_metrics()\n fig, ax = lines(rs, x; axis = (ylabel = \"input\",), figure = (size = (600, 600),))\n hidexdecorations!(ax; grid = false)\n # plot all change metrics\n for (i, c) in enumerate(eachcol(results.x_change))\n ax, = scatterlines(fig[i+1, 1], results.t_change, c;\n axis = (ylabel = indistrings[i],), label = \"input\"\n )\n if i < 3\n hidexdecorations!(ax; grid = false)\n else\n ax.xlabel = \"r (time)\"\n end\n end\n return fig\nend\n\nfig = plot_change_metrics()","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"We already see the interesting results we expect: the permutation entropy shows a striking change as we go from periodic to weakly chaotic motion at r ≈ 3.847. (Remember: the plotted quantity is how much the indicator changes within a time window. High values mean large changes.)","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Due to its construction, permutation entropy will have a spike for periodic data at the start of the timeseries, so we can safely ignore the spike at r ≈ 3.83.","category":"page"},{"location":"examples/logistic/#Significance-via-random-Fourier-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Significance via random Fourier surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"One way to test for significance would be via the standard way as in the Tutorial, utilizing surrogate timeseries and SurrogatesSignificance.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Let's do it here for an example, but, we have to be careful. It is crucial that for permutation entropy we use :right as the tail, because it is expected that the surrogates will have higher differences in the permutation entropy timeseries (because, if there is no dynamical change, the permutation entropy will stay the same, while in the surrogates there are always random fluctuations!","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RandomFourier()\n\n# Define a function because we will re-use later\nusing Random: Xoshiro\nfunction overplot_surrogate_significance!(fig, surromethod, color = \"black\")\n\n signif = SurrogatesSignificance(;\n n = 1000, tail = [:both, :both, :right], surromethod, rng = Xoshiro(42),\n )\n flags = significant_transitions(results, signif)\n\n # and also plot the flags with same color\n for (i, indicator) in enumerate(indicators)\n # To make things visually clear, we will also plot some example surrogate\n # timeseries for each indicator and change metric pair\n for _ in 1:10\n s = TimeseriesSurrogates.surrogate(x, surromethod)\n p = windowmap(indicator, s; width = width_ind)\n q = windowmap(metric[i], p; width = width_cha, stride = stride_cha)\n lines!(fig[i+1, 1], results.t_change, q; color = (color, 0.2), linewidth = 1)\n end\n # Plot the flags as vertical dashed lines\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = color, linestyle = :dash, linewidth = 3\n )\n end\n # add a title to the figure with how we estimate significance\n content(fig[1, 1]).title = \"surrogates: \"*string(nameof(typeof(surromethod)))\nend\n\nsurromethod = RandomFourier()\noverplot_surrogate_significance!(fig, surromethod)\n\nfig","category":"page"},{"location":"examples/logistic/#Different-surrogates","page":"Permutation entropy for dynamic regime changes","title":"Different surrogates","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"surromethod = RelativePartialRandomization(0.25)\nfig = plot_change_metrics()\noverplot_surrogate_significance!(fig, surromethod, \"gray\")\nfig","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.","category":"page"},{"location":"examples/logistic/#Simpler-Significance","page":"Permutation entropy for dynamic regime changes","title":"Simpler Significance","text":"","category":"section"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.","category":"page"},{"location":"examples/logistic/","page":"Permutation entropy for dynamic regime changes","title":"Permutation entropy for dynamic regime changes","text":"fig = plot_change_metrics()\nflags = significant_transitions(results, SigmaSignificance(factor = 5.0))\n\n# Plot the flags\nfor (i, indicator) in enumerate(indicators)\n vlines!(fig[i+1, 1], results.t_change[flags[:, i]];\n color = Cycled(3), linestyle = :dash, linewidth = 3\n )\nend\ncontent(fig[1, 1]).title = \"significance from std\"\nfig","category":"page"},{"location":"#TransitionsInTimeseries.jl","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"(Image: TransitionsInTimeseries.jl)","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"TransitionsInTimeseries","category":"page"},{"location":"#TransitionsInTimeseries","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries","text":"TransitionsInTimeseries.jl\n\n(Image: ) (Image: ) (Image: CI) (Image: codecov) (Image: Package Downloads)\n\nTransitionsInTimeseries.jl is a free and open-source software to easily analyse transitions within timeseries in a reproducible, performant, extensible and reliable way. In contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:\n\nProvide the analysis pipelines with new indicators, which can be either self-written or imported from other packages. In particular, the latter offers thousands of metrics that can indicate transitions right out of the box.\nAdd new analysis pipelines for finding transitions.\nAdd new ways for significance testing.\n\nTransitionsInTimeseries is a registered Julia package and can be installed by running:\n\n] add TransitionsInTimeseries\n\nAll further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.\n\nAlternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!\n\n\n\n\n\n","category":"module"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Star us on GitHub!\nIf you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.","category":"page"},{"location":"#content","page":"TransitionsInTimeseries.jl","title":"Content","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.\nMakes the surrogate analysis to test for significance under the hub.\nCan be easily extended by any user without touching the source code.\nReduces the programming overhead for any researcher willing to benchmark new methods.\nEases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.\nIncreases trustworthiness thanks to a large test suite.","category":"page"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"info: Similar projects\nAn R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.","category":"page"},{"location":"#approaches","page":"TransitionsInTimeseries.jl","title":"Approaches","text":"","category":"section"},{"location":"","page":"TransitionsInTimeseries.jl","title":"TransitionsInTimeseries.jl","text":"Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.","category":"page"},{"location":"devdocs/#Developer's-documentation","page":"Developer's documentation","title":"Developer's documentation","text":"","category":"section"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"This documentation addresses users that would like to contribute to the software by either solving bugs, improving documentation, or adding new methods. All contributions come in the form of Pull Requests, for which we strongly advise to follow good practices in scientific code, which means that they properly formatted, documented, tested, etc.","category":"page"},{"location":"devdocs/#New-indicators-or-change-metrics","page":"Developer's documentation","title":"New indicators or change metrics","text":"","category":"section"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"As explained already in e.g., SlidingWindowConfig, new indicators or change metrics are standard Julia functions, so you only need to define such a function (and document it, test it, etc.).","category":"page"},{"location":"devdocs/#New-pipeline-for-estimating-changes","page":"Developer's documentation","title":"New pipeline for estimating changes","text":"","category":"section"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"This means to contribute a fundamentally new \"pipeline\" for estimating/detecting transitions in timeseries. This new pipeline defines what a \"transition\" means. To add a new pipeline follow these steps:","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"Define a new subtype of ChangesConfig\nDefine a new subtype of ChangesResults\nAdd a method for estimate_changes which accepts the new ChangesConfig subtype you defined and returns the ChangesResults subtype you defined.","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"And that's it!","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"Optionally you can further extend:","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"TransitionsInTimeseries.plot_indicator_changes with the new ChangesResults type you defined. Note the plotting functions are in the ext folder of the repository.\nsignificant_transitions(res::ChangesResults, signif::Significance) with your new ChangesResults type and as many Significance subtypes you have the capacity to extend for.","category":"page"},{"location":"devdocs/#New-pipeline-for-estimating-significance","page":"Developer's documentation","title":"New pipeline for estimating significance","text":"","category":"section"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"Statistically significant changes are \"transitions\". However, what \"significant\" means is not universal. There are different ways to test for significance and TransitionsInTimeseries.jl allows various methods.","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"To add a new pipeline for estimating significance follow these steps:","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"Define a new subtype of Significance\nExtend significant_transitions(res::ChangesResults, signif::Significance) with your new type and as many ChangesResults subtypes as you have capacity for.","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"And that's it! Unfortunately so far we have found no way to make the significant_transitions code agnostic of the changes result, so you would need to add a method manually for every ChangesResults.","category":"page"},{"location":"devdocs/","page":"Developer's documentation","title":"Developer's documentation","text":"Optionally you can further extend TransitionsInTimeseries.plot_significance! (which you can find in the ext folder) for visualizing the significance results.","category":"page"},{"location":"refs/#References","page":"References","title":"References","text":"","category":"section"},{"location":"refs/","page":"References","title":"References","text":"Bagniewski, W.; Ghil, M. and Rousseau, D. D. (2021). Automatic detection of abrupt transitions in paleoclimate records. Chaos 31.\n\n\n\nBagniewski, W.; Rousseau, D. D. and Ghil, M. (2023). The PaleoJump database for abrupt transitions in past climates. Scientific Reports 13, 1–18, arXiv:2206.06832.\n\n\n\nBoers, N. (2018). Early-warning signals for Dansgaard-Oeschger events in a high-resolution ice core record. Nature Communications 9, 2556. Accessed on Oct 28, 2022.\n\n\n\nRasmussen, S. O.; Bigler, M.; Blockley, S. P.; Blunier, T.; Buchardt, S. L.; Clausen, H. B.; Cvijanovic, I.; Dahl-Jensen, D.; Johnsen, S. J.; Fischer, H.; Gkinis, V.; Guillevic, M.; Hoek, W. Z.; Lowe, J. J.; Pedro, J. B.; Popp, T.; Seierstad, I. K.; Steffensen, J. P.; Svensson, A. M.; Vallelonga, P.; Vinther, B. M.; Walker, M. J.; Wheatley, J. J. and Winstrup, M. (2014). A stratigraphic framework for abrupt climatic changes during the Last Glacial period based on three synchronized Greenland ice-core records: refining and extending the INTIMATE event stratigraphy. Quaternary Science Reviews 106, 14–28. Accessed on Oct 4, 2023.\n\n\n\nWilleit, M.; Ganopolski, A.; Robinson, A. and Edwards, N. R. (2022). The Earth system model CLIMBER-X v1.0 – Part 1: Climate model description and validation​​​​​​​​​​​​​​. Geoscientific Model Development 15, 5905–5948. Accessed on Aug 11, 2022.\n\n\n\n","category":"page"}] +} diff --git a/v0.1.1/siteinfo.js b/v0.1.1/siteinfo.js new file mode 100644 index 00000000..20089fd7 --- /dev/null +++ b/v0.1.1/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.1.1"; diff --git a/v0.1.1/tutorial.jl b/v0.1.1/tutorial.jl new file mode 100644 index 00000000..25a60a91 --- /dev/null +++ b/v0.1.1/tutorial.jl @@ -0,0 +1,263 @@ +#= + +# Tutorial + +## [Workflow] (@id workflow) + +Computing transition indicators consists of the following steps: + +1. Doing any preprocessing of raw data first, such as detrending. _This not part of TransitionsInTimeseries.jl_ and yields the **input timeseries**. +2. Estimating the timeseries of an indicator by sliding a window over the input timeseries. +3. Computing the changes of the indicator by sliding a window over its timeseries. Alternatively, the change metric can be estimated over the whole segment, as examplified in the section [Segmented windows](@ref segmented_windows). +4. Generating many surrogates that preserve important statistical properties of the original timeseries. +5. Performing step 2 and 3 for the surrogate timeseries. +6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data. + +These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports. + +## [Tutorial -- Educational] (@id example_stepbystep) + +### Raw input data + +Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by: + +```math +\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t) +``` + +with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with [Makie](https://docs.makie.org/stable/)) such prototypical data to test some indicators can be done by simply running: +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() +fig, ax = lines(t, x_linear) +lines!(ax, t, x_nlinear) +ax.title = "raw data" +fig + +#= +### Preprocessing + +!!! note "Not part of TransitionsInTimeseries.jl" + Any timeseries preprocessing, such as the de-trending step we do here, + is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher. + + +The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1. +=# + +x_l_fluct = diff(x_linear) +x_nl_fluct = diff(x_nlinear) +tfluct = t[2:end] + +fig, ax = lines(tfluct, x_l_fluct) +lines!(ax, tfluct, x_nl_fluct .+ 0.05) +ax.title = "input timeseries" +fig + +#= +At this point, `x_l_fluct` and `x_nl_fluct` are considered the **input timeseries**. + +!!! info "Detrending in Julia" + Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as [Loess.jl](https://github.com/JuliaStats/Loess.jl) or [DSP.jl](https://docs.juliadsp.org/latest/contents/). There the detrending step consists of subtracting the smoothed signal from the original one. + +### Indicator timeseries + +We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the **input timeseries**, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as [`ar1_whitenoise`](@ref): +=# + +indicator = ar1_whitenoise +indicator_window = (width = 400, stride = 1) + +## By mapping `last::Function` over a windowviewer of the time vector, +## we obtain the last time step of each window. +## This therefore only uses information from `k-width+1` to `k` at time step `k`. +## Alternatives: `first::Function`, `midpoint:::Function`. +t_indicator = windowmap(last, tfluct; indicator_window...) +indicator_l = windowmap(indicator, x_l_fluct; indicator_window...) +indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...) + +fig, ax = lines(t_indicator, indicator_l) +lines!(ax, t_indicator, indicator_nl) +ax.title = "indicator timeseries" +fig + +#= +The lines plotted above are the **indicator timeseries**. + +### Change metric timeseries + +From here, we process the **indicator timeseries** to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the **change metric timeseries**. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a [`RidgeRegressionSlope`](@ref): +=# + +change_window = (width = 30, stride = 1) +ridgereg = RidgeRegressionSlope(lambda = 0.0) +precompridgereg = precompute(ridgereg, t[1:change_window.width]) + +t_change = windowmap(last, t_indicator; change_window...) +change_l = windowmap(precompridgereg, indicator_l; change_window...) +change_nl = windowmap(precompridgereg, indicator_nl; change_window...) + +fig, ax = lines(t_change, change_l) +lines!(ax, t_change, change_nl) +ax.title = "change metric timeseries" +fig + +#= +### Timeseries surrogates + +As expected from [Critical Slowing Down](@ref approaches), an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance. + +In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the [TimeseriesSurrogates.jl](https://github.com/JuliaDynamics/TimeseriesSurrogates.jl) Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that `TimeseriesSurrogates` is re-exported by `TransitionsInTimeseries`, so that you don't have to `using` both of them. + +To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries. +=# + +## Generate Fourier random-phase surrogates +using Random: Xoshiro +s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123)) + +function gridfig(nrows, ncols) + fig = Figure() + axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false) + for j in 1:ncols, i in 1:nrows] + rowgap!(fig.layout, 10) + return fig, axs +end +fig, axs = gridfig(2, 1) +lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2)) +lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3)) +axs[1].title = "real signal vs. surrogate(s)" + +## compute and plot indicator and change metric +indicator_s = windowmap(indicator, s; indicator_window...) +change_s = windowmap(precompridgereg, indicator_s; change_window...) + +lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2)) +lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3)) +axislegend() +axs[2].title = "change metric" + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +### Quantifying significance + +To quantify the significance of the values of the **change metric timeseries** we perform a standard surrogate test by computing the [p-value](https://en.wikipedia.org/wiki/P-value) w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically `p<0.05`) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time: +=# + +n_surrogates = 1_000 +fig, axs = gridfig(2, 2) +axs[1].title = "linear" +axs[2].title = "nonlinear" + +for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct)) + + orig_change = j == 1 ? change_l : change_nl + sgen = surrogenerator(x, RandomFourier(), Xoshiro(123)) + pval = zeros(length(change_s)) + + ## Collect all surrogate change metrics + for i in 1:n_surrogates + s = sgen() + indicator_s = windowmap(indicator, s; indicator_window...) + change_s = windowmap(precompridgereg, indicator_s; change_window...) + pval += orig_change .< change_s + end + + pval ./= n_surrogates + lines!(ax, t_change, orig_change) # ; color = Cycled(j) + lines!(axsig, t_change, pval) # ; color = Cycled(j+2) +end + +[xlims!(ax, 0, 50) for ax in axs] +fig + +#= +As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar. + +Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section. + +## [Tutorial -- TransitionsInTimeseries.jl] (@id example_fastforward) + +TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go. + +The interface is simple, and directly parallelizes the [Workflow](@ref workflow). It is based on the creation of a [`ChangesConfig`](@ref), which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate. + +### Sliding windows + +The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl +=# + +using TransitionsInTimeseries, CairoMakie + +t, x_linear, x_nlinear = load_linear_vs_doublewell() + +## input timeseries and time +input = x_nl_fluct = diff(x_nlinear) +t = t[2:end] + +fig, ax = lines(t, input) +ax.title = "input timeseries" +fig + +#= +To perform all of the above analysis we follow a 2-step process. + +Step 1, we decide what indicators and change metrics to use in [`SlidingWindowConfig`](@ref) and apply those via +a sliding window to the input timeseries using [`estimate_changes`](@ref). +=# + +## These indicators are suitable for Critical Slowing Down +indicators = (var, ar1_whitenoise) + +## use the ridge regression slope for both indicators +change_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope()) + +## choices go into a configuration struct +config = SlidingWindowConfig(indicators, change_metrics; + width_ind = 400, width_cha = 30, whichtime = last) + +## choices are processed +results = estimate_changes(config, input, t) + +#= +We can conveniently plot the information contained in `results` by using +`plot_indicator_changes`: +=# + +fig = plot_indicator_changes(results) + +#= +Step 2 is to estimate significance using [`SurrogatesSignificance`](@ref) +and the function [`significant_transitions`](@ref). Finally, we can +conveniently plot the results obtained by updating the figure obtained +above with `plot_significance!`: +=# + +signif = SurrogatesSignificance(n = 1000, tail = [:right, :right]) +flags = significant_transitions(results, signif) +plot_significance!(fig, results, signif, flags = flags) +fig + +#= +### [Segmented windows] (@id segmented_windows) + +The analysis shown so far relies on sliding windows of the change metric. +This is particularly convenient for transition detection tasks. Segmented +windows for the change metric computation are however preferable when it +comes to prediction tasks. By only slightly modifying the syntax used so far, +one can perform the same computations on segmented windows, as well as +visualise the results conveniently: +=# + +config = SegmentedWindowConfig(indicators, change_metrics, + t[1:1], t[1200:1200]; whichtime = last, width_ind = 200, + min_width_cha = 100) +results = estimate_changes(config, input, t) +signif = SurrogatesSignificance(n = 1000, tail = [:right, :right]) +flags = significant_transitions(results, signif) +fig = plot_changes_significance(results, signif) diff --git a/v0.1.1/tutorial/131c9031.png b/v0.1.1/tutorial/131c9031.png new file mode 100644 index 00000000..8c361d61 Binary files /dev/null and b/v0.1.1/tutorial/131c9031.png differ diff --git a/v0.1.1/tutorial/17977f2d.png b/v0.1.1/tutorial/17977f2d.png new file mode 100644 index 00000000..2ff04220 Binary files /dev/null and b/v0.1.1/tutorial/17977f2d.png differ diff --git a/v0.1.1/tutorial/315b650f.png b/v0.1.1/tutorial/315b650f.png new file mode 100644 index 00000000..363a9614 Binary files /dev/null and b/v0.1.1/tutorial/315b650f.png differ diff --git a/v0.1.1/tutorial/38535bda.png b/v0.1.1/tutorial/38535bda.png new file mode 100644 index 00000000..ab1fb667 Binary files /dev/null and b/v0.1.1/tutorial/38535bda.png differ diff --git a/v0.1.1/tutorial/3e233281.png b/v0.1.1/tutorial/3e233281.png new file mode 100644 index 00000000..a200ba21 Binary files /dev/null and b/v0.1.1/tutorial/3e233281.png differ diff --git a/v0.1.1/tutorial/5a8e0316.png b/v0.1.1/tutorial/5a8e0316.png new file mode 100644 index 00000000..ae2561d7 Binary files /dev/null and b/v0.1.1/tutorial/5a8e0316.png differ diff --git a/v0.1.1/tutorial/69fcdca8.png b/v0.1.1/tutorial/69fcdca8.png new file mode 100644 index 00000000..f3497af6 Binary files /dev/null and b/v0.1.1/tutorial/69fcdca8.png differ diff --git a/v0.1.1/tutorial/973fee1f.png b/v0.1.1/tutorial/973fee1f.png new file mode 100644 index 00000000..7755a0b8 Binary files /dev/null and b/v0.1.1/tutorial/973fee1f.png differ diff --git a/v0.1.1/tutorial/a162dbdc.png b/v0.1.1/tutorial/a162dbdc.png new file mode 100644 index 00000000..d7720c96 Binary files /dev/null and b/v0.1.1/tutorial/a162dbdc.png differ diff --git a/v0.1.1/tutorial/f1105200.png b/v0.1.1/tutorial/f1105200.png new file mode 100644 index 00000000..42648e76 Binary files /dev/null and b/v0.1.1/tutorial/f1105200.png differ diff --git a/v0.1.1/tutorial/index.html b/v0.1.1/tutorial/index.html new file mode 100644 index 00000000..f5c57e0d --- /dev/null +++ b/v0.1.1/tutorial/index.html @@ -0,0 +1,128 @@ + +Tutorial · TransitionsInTimeseries.jl
                                      GitHub

                                      Tutorial

                                      Workflow

                                      Computing transition indicators consists of the following steps:

                                      1. Doing any preprocessing of raw data first, such as detrending. This not part of TransitionsInTimeseries.jl and yields the input timeseries.
                                      2. Estimating the timeseries of an indicator by sliding a window over the input timeseries.
                                      3. Computing the changes of the indicator by sliding a window over its timeseries. Alternatively, the change metric can be estimated over the whole segment, as examplified in the section Segmented windows.
                                      4. Generating many surrogates that preserve important statistical properties of the original timeseries.
                                      5. Performing step 2 and 3 for the surrogate timeseries.
                                      6. Checking whether the indicator change timeseries of the real timeseries shows a significant feature (trend, jump or anything else) when compared to the surrogate data.

                                      These steps are illustrated one by one in the tutorial below, and then summarized in the convenient API that TransitionsInTimeseries.jl exports.

                                      Tutorial – Educational

                                      Raw input data

                                      Let us load data from a bistable nonlinear model subject to noise and to a gradual change of the forcing that leads to a transition. Furthermore, we also load data from a linear model, which is by definition monostable and therefore incapable of transitioning. This is done to control the rate of false positives, a common problem that can emerge when looking for transition indicators. The models are governed by:

                                      \[\dfrac{\mathrm{d}x_{l}}{\mathrm{d}t} = - x_{l} - 1 + f(t) + n(t) \\ +\dfrac{\mathrm{d}x_{nl}}{\mathrm{d}t} = - x_{nl}^3 + x_{nl} + f(t) + n(t)\]

                                      with $x_{l}$ the state of the linear model, $x_{nl}$ the state of the bistable model, $f$ the forcing and $n$ the noise. For $f=0$ they both display an equilibrium point at $x=-1$. However, the bistable model also displays a further equilibrium point at $x=1$. Loading (and visualizing with Makie) such prototypical data to test some indicators can be done by simply running:

                                      using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+fig, ax = lines(t, x_linear)
+lines!(ax, t, x_nlinear)
+ax.title = "raw data"
+fig
                                      Example block output

                                      Preprocessing

                                      Not part of TransitionsInTimeseries.jl

                                      Any timeseries preprocessing, such as the de-trending step we do here, is not part of TransitionsInTimeseries.jl and is the responsibility of the researcher.

                                      The nonlinear system clearly displays a transition between two stability regimes. To forecast such transition, we analyze the fluctuations of the timeseries around the attractor, assumed to be tracked. Therefore, a detrending step is needed - here simply obtained by building the difference of the timeseries with lag 1.

                                      x_l_fluct = diff(x_linear)
+x_nl_fluct = diff(x_nlinear)
+tfluct = t[2:end]
+
+fig, ax = lines(tfluct, x_l_fluct)
+lines!(ax, tfluct, x_nl_fluct .+ 0.05)
+ax.title = "input timeseries"
+fig
                                      Example block output

                                      At this point, x_l_fluct and x_nl_fluct are considered the input timeseries.

                                      Detrending in Julia

                                      Detrending can be performed in many ways. A wide range of Julia packages exists to perform smoothing such as Loess.jl or DSP.jl. There the detrending step consists of subtracting the smoothed signal from the original one.

                                      Indicator timeseries

                                      We can then compute the values of some "indicator" (a Julia function that inputs a timeseries and outputs a number). An indicator should be a quantity that is likely to change if a transition occurs, or is about to occur in the timeseries. We compute indicators by applying a sliding window over the input timeseries, determined by the width and the stride with which it is applied. Here we demonstrate this computation with the AR1-regression coefficient (under white-noise assumption), implemented as ar1_whitenoise:

                                      indicator = ar1_whitenoise
+indicator_window = (width = 400, stride = 1)
+
+# By mapping `last::Function` over a windowviewer of the time vector,
+# we obtain the last time step of each window.
+# This therefore only uses information from `k-width+1` to `k` at time step `k`.
+# Alternatives: `first::Function`, `midpoint:::Function`.
+t_indicator = windowmap(last, tfluct; indicator_window...)
+indicator_l = windowmap(indicator, x_l_fluct; indicator_window...)
+indicator_nl = windowmap(indicator, x_nl_fluct; indicator_window...)
+
+fig, ax = lines(t_indicator, indicator_l)
+lines!(ax, t_indicator, indicator_nl)
+ax.title = "indicator timeseries"
+fig
                                      Example block output

                                      The lines plotted above are the indicator timeseries.

                                      Change metric timeseries

                                      From here, we process the indicator timeseries to quantify changes in it. This step is in essence the same as before: we apply some function over a sliding window of the indicator timeseries. We call this new timeseries the change metric timeseries. In the example here, the change metric we will employ will be the slope (over a sliding window), calculated via means of a RidgeRegressionSlope:

                                      change_window = (width = 30, stride = 1)
+ridgereg = RidgeRegressionSlope(lambda = 0.0)
+precompridgereg = precompute(ridgereg, t[1:change_window.width])
+
+t_change = windowmap(last, t_indicator; change_window...)
+change_l = windowmap(precompridgereg, indicator_l; change_window...)
+change_nl = windowmap(precompridgereg, indicator_nl; change_window...)
+
+fig, ax = lines(t_change, change_l)
+lines!(ax, t_change, change_nl)
+ax.title = "change metric timeseries"
+fig
                                      Example block output

                                      Timeseries surrogates

                                      As expected from Critical Slowing Down, an increase of the AR1-regression coefficient can be observed. Although eyeballing the timeseries might already be suggestive, we want a rigorous framework for testing for significance.

                                      In TransitionsIdentifiers.jl we perform significance testing using the method of timeseries surrogates and the TimeseriesSurrogates.jl Julia package. This has the added benefits of reproducibility, automation and flexibility in choosing the surrogate generation method. Note that TimeseriesSurrogates is re-exported by TransitionsInTimeseries, so that you don't have to using both of them.

                                      To illustrate the surrogate, we compare the change metric computed from the bistable timeseries what that computed from a surrogate of the same timeseries.

                                      # Generate Fourier random-phase surrogates
+using Random: Xoshiro
+s = surrogate(x_nl_fluct, RandomFourier(), Xoshiro(123))
+
+function gridfig(nrows, ncols)
+    fig = Figure()
+    axs = [Axis(fig[i, j], xticklabelsvisible = i == nrows ? true : false)
+        for j in 1:ncols, i in 1:nrows]
+    rowgap!(fig.layout, 10)
+    return fig, axs
+end
+fig, axs = gridfig(2, 1)
+lines!(axs[1], tfluct, x_nl_fluct, color = Cycled(2))
+lines!(axs[1], tfluct, s .- 0.05, color = Cycled(3))
+axs[1].title = "real signal vs. surrogate(s)"
+
+# compute and plot indicator and change metric
+indicator_s = windowmap(indicator, s; indicator_window...)
+change_s = windowmap(precompridgereg, indicator_s; change_window...)
+
+lines!(axs[2], t_change, change_nl, label = "nonlin", color = Cycled(2))
+lines!(axs[2], t_change, change_s, label = "surrogate", color = Cycled(3))
+axislegend()
+axs[2].title = "change metric"
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig
                                      Example block output

                                      Quantifying significance

                                      To quantify the significance of the values of the change metric timeseries we perform a standard surrogate test by computing the p-value w.r.t. the change metrics of thousands of surrogates of the input timeseries. A low p-value (typically p<0.05) is commonly considered as significant. To visualize significant trends, we plot the p-value vs. time:

                                      n_surrogates = 1_000
+fig, axs = gridfig(2, 2)
+axs[1].title = "linear"
+axs[2].title = "nonlinear"
+
+for (j, ax, axsig, x) in zip(1:2, axs[1:2], axs[3:4], (x_l_fluct, x_nl_fluct))
+
+    orig_change = j == 1 ? change_l : change_nl
+    sgen = surrogenerator(x, RandomFourier(), Xoshiro(123))
+    pval = zeros(length(change_s))
+
+    # Collect all surrogate change metrics
+    for i in 1:n_surrogates
+        s = sgen()
+        indicator_s = windowmap(indicator, s; indicator_window...)
+        change_s = windowmap(precompridgereg, indicator_s; change_window...)
+        pval += orig_change .< change_s
+    end
+
+    pval ./= n_surrogates
+    lines!(ax, t_change, orig_change)   # ; color = Cycled(j)
+    lines!(axsig, t_change, pval)       # ; color = Cycled(j+2)
+end
+
+[xlims!(ax, 0, 50) for ax in axs]
+fig
                                      Example block output

                                      As expected, the data generated by the nonlinear model displays a significant increase of the AR1-regression coefficient before the transition, which is manifested by a low p-value. In contrast, the data generated by the linear model does not show anything similar.

                                      Performing the step-by-step analysis of transition indicators is possible and might be preferred for users wanting high flexibility. However, this results in a substantial amount of code. We therefore provide convenience functions that wrap this analysis, as shown in the next section.

                                      Tutorial – TransitionsInTimeseries.jl

                                      TransitionsInTimeseries.jl wraps this typical workflow into a simple, extendable, and modular API that researchers can use with little effort. In addition, it allows performing the same analysis for several indicators / change metrics in one go.

                                      The interface is simple, and directly parallelizes the Workflow. It is based on the creation of a ChangesConfig, which contains a list of indicators, and corresponding metrics, to use for doing the above analysis. It also specifies what kind of surrogates to generate.

                                      Sliding windows

                                      The following blocks illustrate how the above extensive example is re-created in TransitionsInTimeseries.jl

                                      using TransitionsInTimeseries, CairoMakie
+
+t, x_linear, x_nlinear = load_linear_vs_doublewell()
+
+# input timeseries and time
+input = x_nl_fluct = diff(x_nlinear)
+t = t[2:end]
+
+fig, ax = lines(t, input)
+ax.title = "input timeseries"
+fig
                                      Example block output

                                      To perform all of the above analysis we follow a 2-step process.

                                      Step 1, we decide what indicators and change metrics to use in SlidingWindowConfig and apply those via a sliding window to the input timeseries using estimate_changes.

                                      # These indicators are suitable for Critical Slowing Down
+indicators = (var, ar1_whitenoise)
+
+# use the ridge regression slope for both indicators
+change_metrics = (RidgeRegressionSlope(), RidgeRegressionSlope())
+
+# choices go into a configuration struct
+config = SlidingWindowConfig(indicators, change_metrics;
+    width_ind = 400, width_cha = 30, whichtime = last)
+
+# choices are processed
+results = estimate_changes(config, input, t)
                                      SlidingWindowResults
+ input timeseries:              2500-element Vector{Float64}
+ indicators:                    [:var, :ar1_whitenoise]
+ indicator (window, stride):    (400, 1)
+ change metrics:                [:PrecomputedRidgeRegressionSlope, :PrecomputedRidgeRegressionSlope]
+ change metric (window, stride): (30, 1)
+

                                      We can conveniently plot the information contained in results by using plot_indicator_changes:

                                      fig = plot_indicator_changes(results)
                                      Example block output

                                      Step 2 is to estimate significance using SurrogatesSignificance and the function significant_transitions. Finally, we can conveniently plot the results obtained by updating the figure obtained above with plot_significance!:

                                      signif = SurrogatesSignificance(n = 1000, tail = [:right, :right])
+flags = significant_transitions(results, signif)
+plot_significance!(fig, results, signif, flags = flags)
+fig
                                      Example block output

                                      Segmented windows

                                      The analysis shown so far relies on sliding windows of the change metric. This is particularly convenient for transition detection tasks. Segmented windows for the change metric computation are however preferable when it comes to prediction tasks. By only slightly modifying the syntax used so far, one can perform the same computations on segmented windows, as well as visualise the results conveniently:

                                      config = SegmentedWindowConfig(indicators, change_metrics,
+    t[1:1], t[1200:1200]; whichtime = last, width_ind = 200,
+    min_width_cha = 100)
+results = estimate_changes(config, input, t)
+signif = SurrogatesSignificance(n = 1000, tail = [:right, :right])
+flags = significant_transitions(results, signif)
+fig = plot_changes_significance(results, signif)
                                      Example block output
                                      diff --git a/versions.js b/versions.js new file mode 100644 index 00000000..7d3080ba --- /dev/null +++ b/versions.js @@ -0,0 +1,7 @@ +var DOC_VERSIONS = [ + "stable", + "v0.1", + "dev", +]; +var DOCUMENTER_NEWEST = "v0.1.1"; +var DOCUMENTER_STABLE = "stable";