From 944358bb4bd3d0355c02c8d09694bbf8d7b1da5a Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Thu, 31 Oct 2024 08:35:25 +0000 Subject: [PATCH] build based on 346834e --- DifferentiationInterface/stable | 2 +- DifferentiationInterface/v0.6 | 2 +- .../v0.6.18/.documenter-siteinfo.json | 1 + .../v0.6.18/api/index.html | 97 ++ .../v0.6.18/assets/documenter.js | 1064 +++++++++++++++++ .../v0.6.18/assets/favicon.ico | Bin 0 -> 121769 bytes .../v0.6.18/assets/logo.jl | 674 +++++++++++ .../v0.6.18/assets/logo.svg | 20 + .../assets/themes/catppuccin-frappe.css | 1 + .../assets/themes/catppuccin-latte.css | 1 + .../assets/themes/catppuccin-macchiato.css | 1 + .../assets/themes/catppuccin-mocha.css | 1 + .../v0.6.18/assets/themes/documenter-dark.css | 7 + .../assets/themes/documenter-light.css | 9 + .../v0.6.18/assets/themeswap.js | 84 ++ .../v0.6.18/assets/warner.js | 52 + .../v0.6.18/dev_guide/index.html | 7 + .../v0.6.18/explanation/advanced/index.html | 8 + .../v0.6.18/explanation/backends/index.html | 7 + .../v0.6.18/explanation/operators/index.html | 8 + DifferentiationInterface/v0.6.18/index.html | 23 + DifferentiationInterface/v0.6.18/objects.inv | Bin 0 -> 1949 bytes .../v0.6.18/search_index.js | 3 + DifferentiationInterface/v0.6.18/siteinfo.js | 1 + .../v0.6.18/tutorials/advanced/index.html | 146 +++ .../v0.6.18/tutorials/basic/index.html | 80 ++ DifferentiationInterface/versions.js | 2 +- 27 files changed, 2298 insertions(+), 3 deletions(-) create mode 100644 DifferentiationInterface/v0.6.18/.documenter-siteinfo.json create mode 100644 DifferentiationInterface/v0.6.18/api/index.html create mode 100644 DifferentiationInterface/v0.6.18/assets/documenter.js create mode 100644 DifferentiationInterface/v0.6.18/assets/favicon.ico create mode 100644 DifferentiationInterface/v0.6.18/assets/logo.jl create mode 100644 DifferentiationInterface/v0.6.18/assets/logo.svg create mode 100644 DifferentiationInterface/v0.6.18/assets/themes/catppuccin-frappe.css create mode 100644 DifferentiationInterface/v0.6.18/assets/themes/catppuccin-latte.css create mode 100644 DifferentiationInterface/v0.6.18/assets/themes/catppuccin-macchiato.css create mode 100644 DifferentiationInterface/v0.6.18/assets/themes/catppuccin-mocha.css create mode 100644 DifferentiationInterface/v0.6.18/assets/themes/documenter-dark.css create mode 100644 DifferentiationInterface/v0.6.18/assets/themes/documenter-light.css create mode 100644 DifferentiationInterface/v0.6.18/assets/themeswap.js create mode 100644 DifferentiationInterface/v0.6.18/assets/warner.js create mode 100644 DifferentiationInterface/v0.6.18/dev_guide/index.html create mode 100644 DifferentiationInterface/v0.6.18/explanation/advanced/index.html create mode 100644 DifferentiationInterface/v0.6.18/explanation/backends/index.html create mode 100644 DifferentiationInterface/v0.6.18/explanation/operators/index.html create mode 100644 DifferentiationInterface/v0.6.18/index.html create mode 100644 DifferentiationInterface/v0.6.18/objects.inv create mode 100644 DifferentiationInterface/v0.6.18/search_index.js create mode 100644 DifferentiationInterface/v0.6.18/siteinfo.js create mode 100644 DifferentiationInterface/v0.6.18/tutorials/advanced/index.html create mode 100644 DifferentiationInterface/v0.6.18/tutorials/basic/index.html diff --git a/DifferentiationInterface/stable b/DifferentiationInterface/stable index 7f4db7fbb..5c06962d5 120000 --- a/DifferentiationInterface/stable +++ b/DifferentiationInterface/stable @@ -1 +1 @@ -v0.6.17 \ No newline at end of file +v0.6.18 \ No newline at end of file diff --git a/DifferentiationInterface/v0.6 b/DifferentiationInterface/v0.6 index 7f4db7fbb..5c06962d5 120000 --- a/DifferentiationInterface/v0.6 +++ b/DifferentiationInterface/v0.6 @@ -1 +1 @@ -v0.6.17 \ No newline at end of file +v0.6.18 \ No newline at end of file diff --git a/DifferentiationInterface/v0.6.18/.documenter-siteinfo.json b/DifferentiationInterface/v0.6.18/.documenter-siteinfo.json new file mode 100644 index 000000000..f9c7eb625 --- /dev/null +++ b/DifferentiationInterface/v0.6.18/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-10-31T08:35:18","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/DifferentiationInterface/v0.6.18/api/index.html b/DifferentiationInterface/v0.6.18/api/index.html new file mode 100644 index 000000000..884e90fe5 --- /dev/null +++ b/DifferentiationInterface/v0.6.18/api/index.html @@ -0,0 +1,97 @@ + +API · DifferentiationInterface.jl
GitHub

API

Argument wrappers

DifferentiationInterface.Constant — Type
Constant

Concrete type of Context argument which is kept constant during differentiation.

Note that an operator can be prepared with an arbitrary value of the constant. However, same-point preparation must occur with the exact value that will be reused later.

Example

julia> using DifferentiationInterface
+
+julia> import ForwardDiff
+
+julia> f(x, c) = c * sum(abs2, x);
+
+julia> gradient(f, AutoForwardDiff(), [1.0, 2.0], Constant(10))
+2-element Vector{Float64}:
+ 20.0
+ 40.0
+
+julia> gradient(f, AutoForwardDiff(), [1.0, 2.0], Constant(100))
+2-element Vector{Float64}:
+ 200.0
+ 400.0
source

First order

Pushforward

DifferentiationInterface.prepare_pushforward — Function
prepare_pushforward(f,     backend, x, tx, [contexts...]) -> prep
+prepare_pushforward(f!, y, backend, x, tx, [contexts...]) -> prep

Create a prep object that can be given to pushforward and its variants.

Warning

If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.

source
DifferentiationInterface.prepare_pushforward_same_point — Function
prepare_pushforward_same_point(f,     backend, x, tx, [contexts...]) -> prep_same
+prepare_pushforward_same_point(f!, y, backend, x, tx, [contexts...]) -> prep_same

Create an prep_same object that can be given to pushforward and its variants if they are applied at the same point x and with the same contexts.

Warning

If the function or the point changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.

source
DifferentiationInterface.pushforward — Function
pushforward(f,     [prep,] backend, x, tx, [contexts...]) -> ty
+pushforward(f!, y, [prep,] backend, x, tx, [contexts...]) -> ty

Compute the pushforward of the function f at point x with a tuple of tangents tx.

To improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.

Tip

Pushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named jvp.

source
DifferentiationInterface.pushforward! — Function
pushforward!(f,     dy, [prep,] backend, x, tx, [contexts...]) -> ty
+pushforward!(f!, y, dy, [prep,] backend, x, tx, [contexts...]) -> ty

Compute the pushforward of the function f at point x with a tuple of tangents tx, overwriting ty.

To improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.

Tip

Pushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named jvp!.

source
DifferentiationInterface.value_and_pushforward — Function
value_and_pushforward(f,     [prep,] backend, x, tx, [contexts...]) -> (y, ty)
+value_and_pushforward(f!, y, [prep,] backend, x, tx, [contexts...]) -> (y, ty)

Compute the value and the pushforward of the function f at point x with a tuple of tangents tx.

To improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.

Tip

Pushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named value_and_jvp.

Info

Required primitive for forward mode backends.

source
DifferentiationInterface.value_and_pushforward! — Function
value_and_pushforward!(f,     dy, [prep,] backend, x, tx, [contexts...]) -> (y, ty)
+value_and_pushforward!(f!, y, dy, [prep,] backend, x, tx, [contexts...]) -> (y, ty)

Compute the value and the pushforward of the function f at point x with a tuple of tangents tx, overwriting ty.

To improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.

Tip

Pushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named value_and_jvp!.

source

Pullback

DifferentiationInterface.prepare_pullback — Function
prepare_pullback(f,     backend, x, ty, [contexts...]) -> prep
+prepare_pullback(f!, y, backend, x, ty, [contexts...]) -> prep

Create a prep object that can be given to pullback and its variants.

Warning

If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.

source
DifferentiationInterface.prepare_pullback_same_point — Function
prepare_pullback_same_point(f,     backend, x, ty, [contexts...]) -> prep_same
+prepare_pullback_same_point(f!, y, backend, x, ty, [contexts...]) -> prep_same

Create an prep_same object that can be given to pullback and its variants if they are applied at the same point x and with the same contexts.

Warning

If the function or the point changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.

source
DifferentiationInterface.pullback — Function
pullback(f,     [prep,] backend, x, ty, [contexts...]) -> tx
+pullback(f!, y, [prep,] backend, x, ty, [contexts...]) -> tx

Compute the pullback of the function f at point x with a tuple of tangents ty.

To improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.

Tip

Pullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named vjp.

source
DifferentiationInterface.pullback! — Function
pullback!(f,     dx, [prep,] backend, x, ty, [contexts...]) -> tx
+pullback!(f!, y, dx, [prep,] backend, x, ty, [contexts...]) -> tx

Compute the pullback of the function f at point x with a tuple of tangents ty, overwriting dx.

To improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.

Tip

Pullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named vjp!.

source
DifferentiationInterface.value_and_pullback — Function
value_and_pullback(f,     [prep,] backend, x, ty, [contexts...]) -> (y, tx)
+value_and_pullback(f!, y, [prep,] backend, x, ty, [contexts...]) -> (y, tx)

Compute the value and the pullback of the function f at point x with a tuple of tangents ty.

To improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.

Tip

Pullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named value_and_vjp.

Info

Required primitive for reverse mode backends.

source
DifferentiationInterface.value_and_pullback! — Function
value_and_pullback!(f,     dx, [prep,] backend, x, ty, [contexts...]) -> (y, tx)
+value_and_pullback!(f!, y, dx, [prep,] backend, x, ty, [contexts...]) -> (y, tx)

Compute the value and the pullback of the function f at point x with a tuple of tangents ty, overwriting dx.

To improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.

Tip

Pullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named value_and_vjp!.

source

Derivative

DifferentiationInterface.prepare_derivative — Function
prepare_derivative(f,     backend, x, [contexts...]) -> prep
+prepare_derivative(f!, y, backend, x, [contexts...]) -> prep

Create a prep object that can be given to derivative and its variants.

Warning

If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.

source
DifferentiationInterface.derivative — Function
derivative(f,     [prep,] backend, x, [contexts...]) -> der
+derivative(f!, y, [prep,] backend, x, [contexts...]) -> der

Compute the derivative of the function f at point x.

To improve performance via operator preparation, refer to prepare_derivative.

source
DifferentiationInterface.derivative! — Function
derivative!(f,     der, [prep,] backend, x, [contexts...]) -> der
+derivative!(f!, y, der, [prep,] backend, x, [contexts...]) -> der

Compute the derivative of the function f at point x, overwriting der.

To improve performance via operator preparation, refer to prepare_derivative.

source
DifferentiationInterface.value_and_derivative — Function
value_and_derivative(f,     [prep,] backend, x, [contexts...]) -> (y, der)
+value_and_derivative(f!, y, [prep,] backend, x, [contexts...]) -> (y, der)

Compute the value and the derivative of the function f at point x.

To improve performance via operator preparation, refer to prepare_derivative.

source
DifferentiationInterface.value_and_derivative! — Function
value_and_derivative!(f,     der, [prep,] backend, x, [contexts...]) -> (y, der)
+value_and_derivative!(f!, y, der, [prep,] backend, x, [contexts...]) -> (y, der)

Compute the value and the derivative of the function f at point x, overwriting der.

To improve performance via operator preparation, refer to prepare_derivative.

source

Gradient

DifferentiationInterface.prepare_gradient — Function
prepare_gradient(f, backend, x, [contexts...]) -> prep

Create a prep object that can be given to gradient and its variants.

Warning

If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again.

source

Jacobian

DifferentiationInterface.prepare_jacobian — Function
prepare_jacobian(f,     backend, x, [contexts...]) -> prep
+prepare_jacobian(f!, y, backend, x, [contexts...]) -> prep

Create a prep object that can be given to jacobian and its variants.

Warning

If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.

source
DifferentiationInterface.jacobian — Function
jacobian(f,     [prep,] backend, x, [contexts...]) -> jac
+jacobian(f!, y, [prep,] backend, x, [contexts...]) -> jac

Compute the Jacobian matrix of the function f at point x.

To improve performance via operator preparation, refer to prepare_jacobian.

source
DifferentiationInterface.jacobian! — Function
jacobian!(f,     jac, [prep,] backend, x, [contexts...]) -> jac
+jacobian!(f!, y, jac, [prep,] backend, x, [contexts...]) -> jac

Compute the Jacobian matrix of the function f at point x, overwriting jac.

To improve performance via operator preparation, refer to prepare_jacobian.

source
DifferentiationInterface.value_and_jacobian — Function
value_and_jacobian(f,     [prep,] backend, x, [contexts...]) -> (y, jac)
+value_and_jacobian(f!, y, [prep,] backend, x, [contexts...]) -> (y, jac)

Compute the value and the Jacobian matrix of the function f at point x.

To improve performance via operator preparation, refer to prepare_jacobian.

source
DifferentiationInterface.value_and_jacobian! — Function
value_and_jacobian!(f,     jac, [prep,] backend, x, [contexts...]) -> (y, jac)
+value_and_jacobian!(f!, y, jac, [prep,] backend, x, [contexts...]) -> (y, jac)

Compute the value and the Jacobian matrix of the function f at point x, overwriting jac.

To improve performance via operator preparation, refer to prepare_jacobian.

source

Second order

DifferentiationInterface.SecondOrder — Type
SecondOrder

Combination of two backends for second-order differentiation.

Danger

SecondOrder backends do not support first-order operators.

Constructor

SecondOrder(outer_backend, inner_backend)

Fields

  • outer::AbstractADType: backend for the outer differentiation
  • inner::AbstractADType: backend for the inner differentiation
source

Second derivative

Hessian-vector product

DifferentiationInterface.prepare_hvp — Function
prepare_hvp(f, backend, x, tx, [contexts...]) -> prep

Create a prep object that can be given to hvp and its variants.

Warning

If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again.

source
DifferentiationInterface.prepare_hvp_same_point — Function
prepare_hvp_same_point(f, backend, x, tx, [contexts...]) -> prep_same

Create an prep_same object that can be given to hvp and its variants if they are applied at the same point x and with the same contexts.

Warning

If the function or the point changes in any way, the result of preparation will be invalidated, and you will need to run it again.

source

Hessian

DifferentiationInterface.prepare_hessian — Function
prepare_hessian(f, backend, x, [contexts...]) -> prep

Create a prep object that can be given to hessian and its variants.

Warning

If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again.

source

Utilities

Backend queries

DifferentiationInterface.outer — Function
outer(backend::SecondOrder)
+outer(backend::AbstractADType)

Return the outer backend of a SecondOrder object, tasked with differentiation at the second order.

For any other backend type, this function acts like the identity.

source
DifferentiationInterface.inner — Function
inner(backend::SecondOrder)
+inner(backend::AbstractADType)

Return the inner backend of a SecondOrder object, tasked with differentiation at the first order.

For any other backend type, this function acts like the identity.

source

Backend switch

DifferentiationInterface.DifferentiateWith — Type
DifferentiateWith

Function wrapper that enforces differentiation with a "substitute" AD backend, possible different from the "true" AD backend that is called.

For instance, suppose a function f is not differentiable with Zygote because it involves mutation, but you know that it is differentiable with Enzyme. Then f2 = DifferentiateWith(f, AutoEnzyme()) is a new function that behaves like f, except that f2 is differentiable with Zygote (thanks to a chain rule which calls Enzyme under the hood). Moreover, any larger algorithm alg that calls f2 instead of f will also be differentiable with Zygote (as long as f was the only Zygote blocker).

Tip

This is mainly relevant for package developers who want to produce differentiable code at low cost, without writing the differentiation rules themselves. If you sprinkle a few DifferentiateWith in places where some AD backends may struggle, end users can pick from a wider variety of packages to differentiate your algorithms.

Warning

DifferentiateWith only supports out-of-place functions y = f(x) without additional context arguments. It only makes these functions differentiable if the true backend is either ForwardDiff or compatible with ChainRules. For any other true backend, the differentiation behavior is not altered by DifferentiateWith (it becomes a transparent wrapper).

Fields

  • f: the function in question, with signature f(x)
  • backend::AbstractADType: the substitute backend to use for differentiation
Note

For the substitute AD backend to be called under the hood, its package needs to be loaded in addition to the package of the true AD backend.

Constructor

DifferentiateWith(f, backend)

Example

julia> using DifferentiationInterface
+
+julia> import FiniteDiff, ForwardDiff, Zygote
+
+julia> function f(x::Vector{Float64})
+           a = Vector{Float64}(undef, 1)  # type constraint breaks ForwardDiff
+           a[1] = sum(abs2, x)  # mutation breaks Zygote
+           return a[1]
+       end;
+
+julia> f2 = DifferentiateWith(f, AutoFiniteDiff());
+
+julia> f([3.0, 5.0]) == f2([3.0, 5.0])
+true
+
+julia> alg(x) = 7 * f2(x);
+
+julia> ForwardDiff.gradient(alg, [3.0, 5.0])
+2-element Vector{Float64}:
+ 42.0
+ 70.0
+
+julia> Zygote.gradient(alg, [3.0, 5.0])[1]
+2-element Vector{Float64}:
+ 42.0
+ 70.0
source

Sparsity detection

DifferentiationInterface.DenseSparsityDetector — Type
DenseSparsityDetector

Sparsity pattern detector satisfying the detection API of ADTypes.jl.

The nonzeros in a Jacobian or Hessian are detected by computing the relevant matrix with dense AD, and thresholding the entries with a given tolerance (which can be numerically inaccurate). This process can be very slow, and should only be used if its output can be exploited multiple times to compute many sparse matrices.

Danger

In general, the sparsity pattern you obtain can depend on the provided input x. If you want to reuse the pattern, make sure that it is input-agnostic.

Warning

DenseSparsityDetector functionality is now located in a package extension, please load the SparseArrays.jl standard library before you use it.

Fields

  • backend::AbstractADType is the dense AD backend used under the hood
  • atol::Float64 is the minimum magnitude of a matrix entry to be considered nonzero

Constructor

DenseSparsityDetector(backend; atol, method=:iterative)

The keyword argument method::Symbol can be either:

  • :iterative: compute the matrix in a sequence of matrix-vector products (memory-efficient)
  • :direct: compute the matrix all at once (memory-hungry but sometimes faster).

Note that the constructor is type-unstable because method ends up being a type parameter of the DenseSparsityDetector object (this is not part of the API and might change).

Examples

using ADTypes, DifferentiationInterface, SparseArrays
+import ForwardDiff
+
+detector = DenseSparsityDetector(AutoForwardDiff(); atol=1e-5, method=:direct)
+
+ADTypes.jacobian_sparsity(diff, rand(5), detector)
+
+# output
+
+4×5 SparseMatrixCSC{Bool, Int64} with 8 stored entries:
+ 1  1  ⋅  ⋅  ⋅
+ ⋅  1  1  ⋅  ⋅
+ ⋅  ⋅  1  1  ⋅
+ ⋅  ⋅  ⋅  1  1

Sometimes the sparsity pattern is input-dependent:

ADTypes.jacobian_sparsity(x -> [prod(x)], rand(2), detector)
+
+# output
+
+1×2 SparseMatrixCSC{Bool, Int64} with 2 stored entries:
+ 1  1
ADTypes.jacobian_sparsity(x -> [prod(x)], [0, 1], detector)
+
+# output
+
+1×2 SparseMatrixCSC{Bool, Int64} with 1 stored entry:
+ 1  ⋅
source

Internals

The following is not part of the public API.

DifferentiationInterface.BatchSizeSettings — Type
BatchSizeSettings{B,singlebatch,aligned}

Configuration for the batch size deduced from a backend and a sample array of length N.

Type parameters

  • B::Int: batch size
  • singlebatch::Bool: whether B > N
  • aligned::Bool: whether N % B == 0

Fields

  • N::Int: array length
  • A::Int: number of batches A = div(N, B, RoundUp)
  • B_last::Int: size of the last batch (if aligned is false)
source
ADTypes.mode — Method
mode(backend::SecondOrder)

Return the outer mode of the second-order backend.

source
DifferentiationInterface.basis — Method
basis(backend, a::AbstractArray, i)

Construct the i-th standard basis array in the vector space of a with element type eltype(a).

Note

If an AD backend benefits from a more specialized basis array implementation, this function can be extended on the backend type.

source
DifferentiationInterface.multibasis — Method
multibasis(backend, a::AbstractArray, inds::AbstractVector)

Construct the sum of the i-th standard basis arrays in the vector space of a with element type eltype(a), for all i ∈ inds.

Note

If an AD backend benefits from a more specialized basis array implementation, this function can be extended on the backend type.

source
DifferentiationInterface.prepare!_derivative — Function
prepare!_derivative(f,     prep, backend, x, [contexts...]) -> new_prep
+prepare!_derivative(f!, y, prep, backend, x, [contexts...]) -> new_prep

Same behavior as prepare_derivative but can modify an existing prep object to avoid some allocations.

There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.

Danger

For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.

source
DifferentiationInterface.prepare!_gradient — Function
prepare!_gradient(f, prep, backend, x, [contexts...]) -> new_prep

Same behavior as prepare_gradient but can modify an existing prep object to avoid some allocations.

There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.

Danger

For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.

source
DifferentiationInterface.prepare!_hessian — Function
prepare!_hessian(f, backend, x, [contexts...]) -> new_prep

Same behavior as prepare_hessian but can modify an existing prep object to avoid some allocations.

There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.

Danger

For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.

source
DifferentiationInterface.prepare!_hvp — Function
prepare!_hvp(f, backend, x, tx, [contexts...]) -> new_prep

Same behavior as prepare_hvp but can modify an existing prep object to avoid some allocations.

There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.

Danger

For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.

source
DifferentiationInterface.prepare!_jacobian — Function
prepare!_jacobian(f,     prep, backend, x, [contexts...]) -> new_prep
+prepare!_jacobian(f!, y, prep, backend, x, [contexts...]) -> new_prep

Same behavior as prepare_jacobian but can modify an existing prep object to avoid some allocations.

There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.

Danger

For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.

source
DifferentiationInterface.prepare!_pullback — Function
prepare!_pullback(f,     prep, backend, x, ty, [contexts...]) -> new_prep
+prepare!_pullback(f!, y, prep, backend, x, ty, [contexts...]) -> new_prep

Same behavior as prepare_pullback but can modify an existing prep object to avoid some allocations.

There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.

Danger

For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.

source
DifferentiationInterface.prepare!_pushforward — Function
prepare!_pushforward(f,     prep, backend, x, tx, [contexts...]) -> new_prep
+prepare!_pushforward(f!, y, prep, backend, x, tx, [contexts...]) -> new_prep

Same behavior as prepare_pushforward but can modify an existing prep object to avoid some allocations.

There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.

Danger

For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.

source
diff --git a/DifferentiationInterface/v0.6.18/assets/documenter.js b/DifferentiationInterface/v0.6.18/assets/documenter.js new file mode 100644 index 000000000..82252a11d --- /dev/null +++ b/DifferentiationInterface/v0.6.18/assets/documenter.js @@ -0,0 +1,1064 @@ +// 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 .docstring-article-toggle-button", + function () { + let articleToggleTitle = "Expand docstring"; + const parent = $(this).parent(); + + debounce(() => { + if (parent.siblings("section").is(":visible")) { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + parent + .children(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + parent.siblings("section").slideToggle(); + }); + } +); + +$(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"); + $("a.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"); + $("a.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@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "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; + }, + combineWith: "AND", + }); + + // 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/DifferentiationInterface/v0.6.18/assets/favicon.ico b/DifferentiationInterface/v0.6.18/assets/favicon.ico new file mode 100644 index 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.button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-outlined:hover,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-white.is-outlined:focus,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black:hover,html.theme--catppuccin-frappe .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black:focus,html.theme--catppuccin-frappe .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black:focus:not(:active),html.theme--catppuccin-frappe .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-frappe .button.is-black:active,html.theme--catppuccin-frappe .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-frappe .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted:hover,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-outlined:hover,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-black.is-outlined:focus,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:hover,html.theme--catppuccin-frappe .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:focus,html.theme--catppuccin-frappe .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:focus:not(:active),html.theme--catppuccin-frappe .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-frappe .button.is-light:active,html.theme--catppuccin-frappe .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-frappe .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted:hover,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-outlined:hover,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-light.is-outlined:focus,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-light.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--catppuccin-frappe .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-frappe .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--catppuccin-frappe .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light.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--catppuccin-frappe .button.is-dark,html.theme--catppuccin-frappe .content kbd.button{background-color:#414559;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark:hover,html.theme--catppuccin-frappe .content kbd.button:hover,html.theme--catppuccin-frappe .button.is-dark.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-hovered{background-color:#3c3f52;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark:focus,html.theme--catppuccin-frappe .content kbd.button:focus,html.theme--catppuccin-frappe .button.is-dark.is-focused,html.theme--catppuccin-frappe .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark:focus:not(:active),html.theme--catppuccin-frappe .content kbd.button:focus:not(:active),html.theme--catppuccin-frappe .button.is-dark.is-focused:not(:active),html.theme--catppuccin-frappe .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(65,69,89,0.25)}html.theme--catppuccin-frappe .button.is-dark:active,html.theme--catppuccin-frappe .content kbd.button:active,html.theme--catppuccin-frappe .button.is-dark.is-active,html.theme--catppuccin-frappe .content kbd.button.is-active{background-color:#363a4a;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark[disabled],html.theme--catppuccin-frappe .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button{background-color:#414559;border-color:#414559;box-shadow:none}html.theme--catppuccin-frappe .button.is-dark.is-inverted,html.theme--catppuccin-frappe .content kbd.button.is-inverted{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-dark.is-inverted[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-loading::after,html.theme--catppuccin-frappe .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-dark.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-focused{background-color:#414559;border-color:#414559;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #414559 #414559 !important}html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-dark.is-outlined[disabled],html.theme--catppuccin-frappe .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #414559 #414559 !important}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-primary,html.theme--catppuccin-frappe .docstring>section>a.button.docs-sourcelink{background-color:#8caaee;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-primary:hover,html.theme--catppuccin-frappe .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-frappe .button.is-primary.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#81a2ec;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-primary:focus,html.theme--catppuccin-frappe .docstring>section>a.button.docs-sourcelink:focus,html.theme--catppuccin-frappe .button.is-primary.is-focused,html.theme--catppuccin-frappe .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-primary:focus:not(:active),html.theme--catppuccin-frappe .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--catppuccin-frappe .button.is-primary.is-focused:not(:active),html.theme--catppuccin-frappe .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(140,170,238,0.25)}html.theme--catppuccin-frappe .button.is-primary:active,html.theme--catppuccin-frappe .docstring>section>a.button.docs-sourcelink:active,html.theme--catppuccin-frappe .button.is-primary.is-active,html.theme--catppuccin-frappe .docstring>section>a.button.is-active.docs-sourcelink{background-color:#769aeb;border-color:transparent;color:#fff}html.theme--catppuccin-frappe 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.button.is-primary.is-outlined.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-frappe .button.is-primary.is-outlined:focus,html.theme--catppuccin-frappe .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--catppuccin-frappe .button.is-primary.is-outlined.is-focused,html.theme--catppuccin-frappe .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#8caaee;border-color:#8caaee;color:#fff}html.theme--catppuccin-frappe .button.is-primary.is-outlined.is-loading::after,html.theme--catppuccin-frappe .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-primary.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--catppuccin-frappe .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--catppuccin-frappe .button.is-primary.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-frappe .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-primary.is-outlined[disabled],html.theme--catppuccin-frappe .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-primary.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#8caaee;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined,html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:hover,html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:focus,html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.is-focused.docs-sourcelink{background-color:#fff;color:#8caaee}html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined[disabled],html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-primary.is-light,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.docs-sourcelink{background-color:#edf2fc;color:#153a8e}html.theme--catppuccin-frappe .button.is-primary.is-light:hover,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--catppuccin-frappe .button.is-primary.is-light.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-primary.is-light:active,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-frappe .button.is-primary.is-light.is-active,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link{background-color:#8caaee;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link:hover,html.theme--catppuccin-frappe .button.is-link.is-hovered{background-color:#81a2ec;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link:focus,html.theme--catppuccin-frappe .button.is-link.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link:focus:not(:active),html.theme--catppuccin-frappe .button.is-link.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(140,170,238,0.25)}html.theme--catppuccin-frappe .button.is-link:active,html.theme--catppuccin-frappe .button.is-link.is-active{background-color:#769aeb;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link{background-color:#8caaee;border-color:#8caaee;box-shadow:none}html.theme--catppuccin-frappe .button.is-link.is-inverted{background-color:#fff;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-inverted:hover,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-link.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-outlined:focus,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-focused{background-color:#8caaee;border-color:#8caaee;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe 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.button.is-link.is-light.is-hovered{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:active,html.theme--catppuccin-frappe .button.is-link.is-light.is-active{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:hover,html.theme--catppuccin-frappe .button.is-info.is-hovered{background-color:#78c4b9;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus,html.theme--catppuccin-frappe .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus:not(:active),html.theme--catppuccin-frappe .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(129,200,190,0.25)}html.theme--catppuccin-frappe .button.is-info:active,html.theme--catppuccin-frappe .button.is-info.is-active{background-color:#6fc0b5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:#81c8be;box-shadow:none}html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) 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.button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.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--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:hover,html.theme--catppuccin-frappe .button.is-success.is-hovered{background-color:#9fcd80;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus,html.theme--catppuccin-frappe .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus:not(:active),html.theme--catppuccin-frappe .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,209,137,0.25)}html.theme--catppuccin-frappe .button.is-success:active,html.theme--catppuccin-frappe .button.is-success.is-active{background-color:#98ca77;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.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--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.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--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .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--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-focused{background-color:#e5c890;border-color:#e5c890;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .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--catppuccin-frappe .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .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--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .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--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #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--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .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--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content 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body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-frappe a.navbar-item.is-active,html.theme--catppuccin-frappe .navbar-link.is-active{color:#8caaee}html.theme--catppuccin-frappe a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-frappe .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-frappe .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-frappe .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-frappe .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-frappe .pagination.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-frappe 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.button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus,html.theme--catppuccin-latte .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus:not(:active),html.theme--catppuccin-latte .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-latte .button.is-black:active,html.theme--catppuccin-latte .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:hover,html.theme--catppuccin-latte .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus,html.theme--catppuccin-latte .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus:not(:active),html.theme--catppuccin-latte .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-latte .button.is-light:active,html.theme--catppuccin-latte .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.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--catppuccin-latte .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte 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.button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.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--catppuccin-latte .button.is-dark,html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:hover,html.theme--catppuccin-latte .content kbd.button:hover,html.theme--catppuccin-latte .button.is-dark.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-hovered{background-color:#c5c9d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus,html.theme--catppuccin-latte .content kbd.button:focus,html.theme--catppuccin-latte .button.is-dark.is-focused,html.theme--catppuccin-latte .content kbd.button.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte 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kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-focused{background-color:#ccd0da;border-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.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--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.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--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:focus,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:focus,html.theme--catppuccin-latte .button.is-primary.is-focused,html.theme--catppuccin-latte .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:focus:not(:active),html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--catppuccin-latte .button.is-primary.is-focused:not(:active),html.theme--catppuccin-latte .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(30,102,245,0.25)}html.theme--catppuccin-latte .button.is-primary:active,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:active,html.theme--catppuccin-latte .button.is-primary.is-active,html.theme--catppuccin-latte 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.button.is-primary.is-outlined:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-latte .button.is-primary.is-outlined:focus,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-focused,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#1e66f5;border-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-primary.is-outlined[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#1e66f5;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-latte 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.docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-light,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-light.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-latte .button.is-primary.is-light.is-active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-info.is-light{background-color:#edfcfc;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:hover,html.theme--catppuccin-latte .button.is-info.is-light.is-hovered{background-color:#e2f9fb;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:active,html.theme--catppuccin-latte .button.is-info.is-light.is-active{background-color:#d7f7f9;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:hover,html.theme--catppuccin-latte .button.is-success.is-hovered{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus,html.theme--catppuccin-latte .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus:not(:active),html.theme--catppuccin-latte .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(64,160,43,0.25)}html.theme--catppuccin-latte .button.is-success:active,html.theme--catppuccin-latte .button.is-success.is-active{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:#40a02b;box-shadow:none}html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-outlined.is-focused{background-color:#40a02b;border-color:#40a02b;color:#fff}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #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--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .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--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte 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.file.is-link.is-active .file-cta{background-color:#0b57ef;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info .file-cta{background-color:#179299;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info:hover .file-cta,html.theme--catppuccin-latte .file.is-info.is-hovered .file-cta{background-color:#15878e;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info:focus .file-cta,html.theme--catppuccin-latte .file.is-info.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(23,146,153,0.25);color:#fff}html.theme--catppuccin-latte .file.is-info:active .file-cta,html.theme--catppuccin-latte .file.is-info.is-active .file-cta{background-color:#147d83;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success .file-cta{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success:hover .file-cta,html.theme--catppuccin-latte .file.is-success.is-hovered .file-cta{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success:focus .file-cta,html.theme--catppuccin-latte .file.is-success.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(64,160,43,0.25);color:#fff}html.theme--catppuccin-latte .file.is-success:active .file-cta,html.theme--catppuccin-latte .file.is-success.is-active .file-cta{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning .file-cta{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning:hover .file-cta,html.theme--catppuccin-latte .file.is-warning.is-hovered .file-cta{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning:focus .file-cta,html.theme--catppuccin-latte .file.is-warning.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(223,142,29,0.25);color:#fff}html.theme--catppuccin-latte .file.is-warning:active .file-cta,html.theme--catppuccin-latte .file.is-warning.is-active .file-cta{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger .file-cta{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger:hover .file-cta,html.theme--catppuccin-latte .file.is-danger.is-hovered .file-cta{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger:focus .file-cta,html.theme--catppuccin-latte .file.is-danger.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(210,15,57,0.25);color:#fff}html.theme--catppuccin-latte .file.is-danger:active .file-cta,html.theme--catppuccin-latte .file.is-danger.is-active .file-cta{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.file{font-size:.75rem}html.theme--catppuccin-latte .file.is-normal{font-size:1rem}html.theme--catppuccin-latte .file.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .file.is-medium .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-large{font-size:1.5rem}html.theme--catppuccin-latte .file.is-large .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.has-name .file-cta{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .file.has-name .file-name{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .file.has-name.is-empty .file-cta{border-radius:.4em}html.theme--catppuccin-latte .file.has-name.is-empty .file-name{display:none}html.theme--catppuccin-latte .file.is-boxed .file-label{flex-direction:column}html.theme--catppuccin-latte .file.is-boxed .file-cta{flex-direction:column;height:auto;padding:1em 3em}html.theme--catppuccin-latte .file.is-boxed .file-name{border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-boxed .file-icon{height:1.5em;width:1.5em}html.theme--catppuccin-latte .file.is-boxed .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-boxed.is-small .file-icon .fa,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-boxed .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .file.is-boxed.is-medium .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.is-boxed.is-large .file-icon .fa{font-size:35px}html.theme--catppuccin-latte .file.is-boxed.has-name .file-cta{border-radius:.4em .4em 0 0}html.theme--catppuccin-latte .file.is-boxed.has-name .file-name{border-radius:0 0 .4em .4em;border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-centered{justify-content:center}html.theme--catppuccin-latte .file.is-fullwidth .file-label{width:100%}html.theme--catppuccin-latte .file.is-fullwidth .file-name{flex-grow:1;max-width:none}html.theme--catppuccin-latte .file.is-right{justify-content:flex-end}html.theme--catppuccin-latte .file.is-right .file-cta{border-radius:0 .4em .4em 0}html.theme--catppuccin-latte .file.is-right .file-name{border-radius:.4em 0 0 .4em;border-width:1px 0 1px 1px;order:-1}html.theme--catppuccin-latte .file-label{align-items:stretch;display:flex;cursor:pointer;justify-content:flex-start;overflow:hidden;position:relative}html.theme--catppuccin-latte .file-label:hover .file-cta{background-color:#c5c9d5;color:#41445a}html.theme--catppuccin-latte .file-label:hover .file-name{border-color:#a5a9b8}html.theme--catppuccin-latte .file-label:active .file-cta{background-color:#bdc2cf;color:#41445a}html.theme--catppuccin-latte .file-label:active .file-name{border-color:#9ea2b3}html.theme--catppuccin-latte .file-input{height:100%;left:0;opacity:0;outline:none;position:absolute;top:0;width:100%}html.theme--catppuccin-latte .file-cta,html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-radius:.4em;font-size:1em;padding-left:1em;padding-right:1em;white-space:nowrap}html.theme--catppuccin-latte .file-cta{background-color:#ccd0da;color:#4c4f69}html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-style:solid;border-width:1px 1px 1px 0;display:block;max-width:16em;overflow:hidden;text-align:inherit;text-overflow:ellipsis}html.theme--catppuccin-latte .file-icon{align-items:center;display:flex;height:1em;justify-content:center;margin-right:.5em;width:1em}html.theme--catppuccin-latte .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .label{color:#41445a;display:block;font-size:1rem;font-weight:700}html.theme--catppuccin-latte .label:not(:last-child){margin-bottom:0.5em}html.theme--catppuccin-latte .label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.label{font-size:.75rem}html.theme--catppuccin-latte .label.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .label.is-large{font-size:1.5rem}html.theme--catppuccin-latte .help{display:block;font-size:.75rem;margin-top:0.25rem}html.theme--catppuccin-latte .help.is-white{color:#fff}html.theme--catppuccin-latte .help.is-black{color:#0a0a0a}html.theme--catppuccin-latte .help.is-light{color:#f5f5f5}html.theme--catppuccin-latte .help.is-dark,html.theme--catppuccin-latte .content kbd.help{color:#ccd0da}html.theme--catppuccin-latte .help.is-primary,html.theme--catppuccin-latte .docstring>section>a.help.docs-sourcelink{color:#1e66f5}html.theme--catppuccin-latte .help.is-link{color:#1e66f5}html.theme--catppuccin-latte .help.is-info{color:#179299}html.theme--catppuccin-latte .help.is-success{color:#40a02b}html.theme--catppuccin-latte .help.is-warning{color:#df8e1d}html.theme--catppuccin-latte .help.is-danger{color:#d20f39}html.theme--catppuccin-latte .field:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.has-addons{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.has-addons .control:not(:last-child){margin-right:-1px}html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .button,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .select select{border-radius:0}html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .select select{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .select select{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-hovered:not([disabled]){z-index:2}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]){z-index:3}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]):hover{z-index:4}html.theme--catppuccin-latte .field.has-addons .control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.has-addons.has-addons-centered{justify-content:center}html.theme--catppuccin-latte .field.has-addons.has-addons-right{justify-content:flex-end}html.theme--catppuccin-latte .field.has-addons.has-addons-fullwidth .control{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.is-grouped>.control{flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped>.control:not(:last-child){margin-bottom:0;margin-right:.75rem}html.theme--catppuccin-latte .field.is-grouped>.control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.is-grouped.is-grouped-centered{justify-content:center}html.theme--catppuccin-latte .field.is-grouped.is-grouped-right{justify-content:flex-end}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline{flex-wrap:wrap}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:last-child,html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline:last-child{margin-bottom:-0.75rem}html.theme--catppuccin-latte 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.icon:only-child,html.theme--catppuccin-latte .navbar-link .icon:only-child{margin-left:-0.25rem;margin-right:-0.25rem}html.theme--catppuccin-latte a.navbar-item,html.theme--catppuccin-latte .navbar-link{cursor:pointer}html.theme--catppuccin-latte a.navbar-item:focus,html.theme--catppuccin-latte a.navbar-item:focus-within,html.theme--catppuccin-latte a.navbar-item:hover,html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link:focus,html.theme--catppuccin-latte .navbar-link:focus-within,html.theme--catppuccin-latte .navbar-link:hover,html.theme--catppuccin-latte .navbar-link.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}html.theme--catppuccin-latte .navbar-item{flex-grow:0;flex-shrink:0}html.theme--catppuccin-latte .navbar-item img{max-height:1.75rem}html.theme--catppuccin-latte .navbar-item.has-dropdown{padding:0}html.theme--catppuccin-latte .navbar-item.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-latte .navbar-item.is-tab:focus,html.theme--catppuccin-latte .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5}html.theme--catppuccin-latte .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5;border-bottom-style:solid;border-bottom-width:3px;color:#1e66f5;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-latte .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-latte .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-latte .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-latte .navbar>.container{display:block}html.theme--catppuccin-latte .navbar-brand .navbar-item,html.theme--catppuccin-latte .navbar-tabs .navbar-item{align-items:center;display:flex}html.theme--catppuccin-latte .navbar-link::after{display:none}html.theme--catppuccin-latte .navbar-menu{background-color:#1e66f5;box-shadow:0 8px 16px rgba(10,10,10,0.1);padding:0.5rem 0}html.theme--catppuccin-latte .navbar-menu.is-active{display:block}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch,html.theme--catppuccin-latte .navbar.is-fixed-top-touch{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte .navbar.is-fixed-top-touch{top:0}html.theme--catppuccin-latte .navbar.is-fixed-top .navbar-menu,html.theme--catppuccin-latte .navbar.is-fixed-top-touch .navbar-menu{-webkit-overflow-scrolling:touch;max-height:calc(100vh - 4rem);overflow:auto}html.theme--catppuccin-latte html.has-navbar-fixed-top-touch,html.theme--catppuccin-latte body.has-navbar-fixed-top-touch{padding-top:4rem}html.theme--catppuccin-latte html.has-navbar-fixed-bottom-touch,html.theme--catppuccin-latte body.has-navbar-fixed-bottom-touch{padding-bottom:4rem}}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .navbar,html.theme--catppuccin-latte .navbar-menu,html.theme--catppuccin-latte .navbar-start,html.theme--catppuccin-latte .navbar-end{align-items:stretch;display:flex}html.theme--catppuccin-latte .navbar{min-height:4rem}html.theme--catppuccin-latte .navbar.is-spaced{padding:1rem 2rem}html.theme--catppuccin-latte .navbar.is-spaced .navbar-start,html.theme--catppuccin-latte .navbar.is-spaced .navbar-end{align-items:center}html.theme--catppuccin-latte .navbar.is-spaced a.navbar-item,html.theme--catppuccin-latte .navbar.is-spaced .navbar-link{border-radius:.4em}html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item:focus,html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item:hover,html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item.is-active,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link:focus,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link:hover,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link.is-active{background-color:transparent !important}html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link,html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link,html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within 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.navbar-dropdown.is-boxed,.navbar.is-spaced html.theme--catppuccin-latte .navbar-item.is-hoverable:hover .navbar-dropdown,html.theme--catppuccin-latte .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed{opacity:1;pointer-events:auto;transform:translateY(0)}html.theme--catppuccin-latte .navbar-menu{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .navbar-start{justify-content:flex-start;margin-right:auto}html.theme--catppuccin-latte .navbar-end{justify-content:flex-end;margin-left:auto}html.theme--catppuccin-latte .navbar-dropdown{background-color:#1e66f5;border-bottom-left-radius:8px;border-bottom-right-radius:8px;border-top:1px solid rgba(0,0,0,0.2);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--catppuccin-latte .navbar-dropdown .navbar-item{padding:0.375rem 1rem;white-space:nowrap}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item{padding-right:3rem}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:focus,html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#8c8fa1}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}.navbar.is-spaced html.theme--catppuccin-latte .navbar-dropdown,html.theme--catppuccin-latte .navbar-dropdown.is-boxed{border-radius:8px;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--catppuccin-latte .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-latte .navbar-divider{display:block}html.theme--catppuccin-latte .navbar>.container .navbar-brand,html.theme--catppuccin-latte .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--catppuccin-latte .navbar>.container .navbar-menu,html.theme--catppuccin-latte .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop,html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{top:0}html.theme--catppuccin-latte html.has-navbar-fixed-top-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-top-desktop{padding-top:4rem}html.theme--catppuccin-latte html.has-navbar-fixed-bottom-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-bottom-desktop{padding-bottom:4rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-top,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-top{padding-top:6rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-bottom,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link.is-active{color:#1e66f5}html.theme--catppuccin-latte a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-latte .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-latte .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-latte .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-latte .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-latte .pagination.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-latte .pagination.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .pagination.is-large{font-size:1.5rem}html.theme--catppuccin-latte .pagination.is-rounded .pagination-previous,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--catppuccin-latte .pagination.is-rounded .pagination-next,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:9999px}html.theme--catppuccin-latte .pagination.is-rounded .pagination-link,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:9999px}html.theme--catppuccin-latte .pagination,html.theme--catppuccin-latte .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link{border-color:#acb0be;color:#1e66f5;min-width:2.5em}html.theme--catppuccin-latte .pagination-previous:hover,html.theme--catppuccin-latte .pagination-next:hover,html.theme--catppuccin-latte .pagination-link:hover{border-color:#9ca0b0;color:#04a5e5}html.theme--catppuccin-latte .pagination-previous:focus,html.theme--catppuccin-latte .pagination-next:focus,html.theme--catppuccin-latte .pagination-link:focus{border-color:#9ca0b0}html.theme--catppuccin-latte .pagination-previous:active,html.theme--catppuccin-latte .pagination-next:active,html.theme--catppuccin-latte .pagination-link:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2)}html.theme--catppuccin-latte .pagination-previous[disabled],html.theme--catppuccin-latte .pagination-previous.is-disabled,html.theme--catppuccin-latte .pagination-next[disabled],html.theme--catppuccin-latte .pagination-next.is-disabled,html.theme--catppuccin-latte .pagination-link[disabled],html.theme--catppuccin-latte .pagination-link.is-disabled{background-color:#acb0be;border-color:#acb0be;box-shadow:none;color:#616587;opacity:0.5}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next{padding-left:.75em;padding-right:.75em;white-space:nowrap}html.theme--catppuccin-latte .pagination-link.is-current{background-color:#1e66f5;border-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .pagination-ellipsis{color:#9ca0b0;pointer-events:none}html.theme--catppuccin-latte .pagination-list{flex-wrap:wrap}html.theme--catppuccin-latte .pagination-list li{list-style:none}@media screen and (max-width: 768px){html.theme--catppuccin-latte .pagination{flex-wrap:wrap}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .pagination-list li{flex-grow:1;flex-shrink:1}}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .pagination-list{flex-grow:1;flex-shrink:1;justify-content:flex-start;order:1}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{margin-bottom:0;margin-top:0}html.theme--catppuccin-latte .pagination-previous{order:2}html.theme--catppuccin-latte .pagination-next{order:3}html.theme--catppuccin-latte .pagination{justify-content:space-between;margin-bottom:0;margin-top:0}html.theme--catppuccin-latte .pagination.is-centered .pagination-previous{order:1}html.theme--catppuccin-latte .pagination.is-centered .pagination-list{justify-content:center;order:2}html.theme--catppuccin-latte .pagination.is-centered .pagination-next{order:3}html.theme--catppuccin-latte .pagination.is-right .pagination-previous{order:1}html.theme--catppuccin-latte .pagination.is-right .pagination-next{order:2}html.theme--catppuccin-latte .pagination.is-right .pagination-list{justify-content:flex-end;order:3}}html.theme--catppuccin-latte .panel{border-radius:8px;box-shadow:#171717;font-size:1rem}html.theme--catppuccin-latte .panel:not(:last-child){margin-bottom:1.5rem}html.theme--catppuccin-latte .panel.is-white .panel-heading{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .panel.is-white .panel-tabs a.is-active{border-bottom-color:#fff}html.theme--catppuccin-latte .panel.is-white .panel-block.is-active .panel-icon{color:#fff}html.theme--catppuccin-latte .panel.is-black .panel-heading{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .panel.is-black .panel-tabs a.is-active{border-bottom-color:#0a0a0a}html.theme--catppuccin-latte .panel.is-black .panel-block.is-active .panel-icon{color:#0a0a0a}html.theme--catppuccin-latte .panel.is-light .panel-heading{background-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .panel.is-light .panel-tabs a.is-active{border-bottom-color:#f5f5f5}html.theme--catppuccin-latte .panel.is-light .panel-block.is-active .panel-icon{color:#f5f5f5}html.theme--catppuccin-latte .panel.is-dark .panel-heading,html.theme--catppuccin-latte .content kbd.panel .panel-heading{background-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .panel.is-dark .panel-tabs a.is-active,html.theme--catppuccin-latte .content kbd.panel .panel-tabs a.is-active{border-bottom-color:#ccd0da}html.theme--catppuccin-latte .panel.is-dark .panel-block.is-active .panel-icon,html.theme--catppuccin-latte .content kbd.panel .panel-block.is-active .panel-icon{color:#ccd0da}html.theme--catppuccin-latte .panel.is-primary .panel-heading,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-heading{background-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .panel.is-primary .panel-tabs a.is-active,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-tabs a.is-active{border-bottom-color:#1e66f5}html.theme--catppuccin-latte .panel.is-primary .panel-block.is-active .panel-icon,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-block.is-active .panel-icon{color:#1e66f5}html.theme--catppuccin-latte .panel.is-link .panel-heading{background-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .panel.is-link .panel-tabs a.is-active{border-bottom-color:#1e66f5}html.theme--catppuccin-latte .panel.is-link .panel-block.is-active .panel-icon{color:#1e66f5}html.theme--catppuccin-latte .panel.is-info 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kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363a4f #363a4f !important}html.theme--catppuccin-macchiato 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.button.is-link.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-link.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-focused{background-color:#8aadf4;border-color:#8aadf4;color:#fff}html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #8aadf4 #8aadf4 !important}html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-link.is-outlined{background-color:transparent;border-color:#8aadf4;box-shadow:none;color:#8aadf4}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#8aadf4}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8aadf4 #8aadf4 !important}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-link.is-light{background-color:#ecf2fd;color:#0e3b95}html.theme--catppuccin-macchiato .button.is-link.is-light:hover,html.theme--catppuccin-macchiato .button.is-link.is-light.is-hovered{background-color:#e1eafc;border-color:transparent;color:#0e3b95}html.theme--catppuccin-macchiato .button.is-link.is-light:active,html.theme--catppuccin-macchiato .button.is-link.is-light.is-active{background-color:#d5e2fb;border-color:transparent;color:#0e3b95}html.theme--catppuccin-macchiato 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.button.is-info{background-color:#8bd5ca;border-color:#8bd5ca;box-shadow:none}html.theme--catppuccin-macchiato .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.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--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.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--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.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--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.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--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .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--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .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--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .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--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .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--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato 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.button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #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--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-macchiato .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-macchiato .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused,html.theme--catppuccin-macchiato .buttons.has-addons .button:active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button:active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-macchiato .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-macchiato .buttons.is-centered{justify-content:center}html.theme--catppuccin-macchiato .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-macchiato .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-macchiato .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--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-macchiato .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-macchiato .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-macchiato .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-macchiato .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-macchiato .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-macchiato .content li+li{margin-top:0.25em}html.theme--catppuccin-macchiato .content p:not(:last-child),html.theme--catppuccin-macchiato .content dl:not(:last-child),html.theme--catppuccin-macchiato .content ol:not(:last-child),html.theme--catppuccin-macchiato .content ul:not(:last-child),html.theme--catppuccin-macchiato .content blockquote:not(:last-child),html.theme--catppuccin-macchiato .content pre:not(:last-child),html.theme--catppuccin-macchiato .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-macchiato .content h1,html.theme--catppuccin-macchiato .content h2,html.theme--catppuccin-macchiato .content h3,html.theme--catppuccin-macchiato .content h4,html.theme--catppuccin-macchiato .content h5,html.theme--catppuccin-macchiato .content h6{color:#cad3f5;font-weight:600;line-height:1.125}html.theme--catppuccin-macchiato .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-macchiato .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-macchiato .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-macchiato .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-macchiato .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-macchiato .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-macchiato .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-macchiato .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-macchiato .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-macchiato .content blockquote{background-color:#1e2030;border-left:5px solid #5b6078;padding:1.25em 1.5em}html.theme--catppuccin-macchiato .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-macchiato .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-macchiato .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-macchiato .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-macchiato .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-macchiato .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-macchiato .content ul ul ul{list-style-type:square}html.theme--catppuccin-macchiato .content dd{margin-left:2em}html.theme--catppuccin-macchiato .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-macchiato .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-macchiato .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-macchiato .content figure img{display:inline-block}html.theme--catppuccin-macchiato .content figure figcaption{font-style:italic}html.theme--catppuccin-macchiato .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-macchiato .content sup,html.theme--catppuccin-macchiato .content sub{font-size:75%}html.theme--catppuccin-macchiato .content table{width:100%}html.theme--catppuccin-macchiato .content table td,html.theme--catppuccin-macchiato .content table th{border:1px solid #5b6078;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-macchiato .content table th{color:#b5c1f1}html.theme--catppuccin-macchiato .content table th:not([align]){text-align:inherit}html.theme--catppuccin-macchiato .content table thead td,html.theme--catppuccin-macchiato .content table thead th{border-width:0 0 2px;color:#b5c1f1}html.theme--catppuccin-macchiato .content table tfoot td,html.theme--catppuccin-macchiato .content table tfoot th{border-width:2px 0 0;color:#b5c1f1}html.theme--catppuccin-macchiato .content table tbody tr:last-child td,html.theme--catppuccin-macchiato .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-macchiato .content .tabs li+li{margin-top:0}html.theme--catppuccin-macchiato .content.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-macchiato .content.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .content.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .content.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-macchiato .icon.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-macchiato .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-macchiato .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-macchiato .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-macchiato .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-macchiato .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-macchiato .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-macchiato div.icon-text{display:flex}html.theme--catppuccin-macchiato .image,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-macchiato .image img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-macchiato .image img.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-macchiato .image.is-fullwidth,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-macchiato .image.is-square img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-macchiato .image.is-square .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-macchiato .image.is-1by1 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-macchiato .image.is-1by1 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-macchiato .image.is-5by4 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-macchiato .image.is-5by4 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-macchiato .image.is-4by3 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-macchiato .image.is-4by3 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-macchiato .image.is-3by2 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-macchiato .image.is-3by2 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-macchiato .image.is-5by3 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-macchiato .image.is-5by3 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-macchiato .image.is-16by9 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-macchiato .image.is-16by9 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-macchiato .image.is-2by1 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-macchiato .image.is-2by1 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-macchiato .image.is-3by1 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-macchiato .image.is-3by1 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by1 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select[disabled]:-moz-placeholder,html.theme--catppuccin-macchiato .textarea[disabled]:-moz-placeholder,html.theme--catppuccin-macchiato .input[disabled]:-moz-placeholder,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input[disabled]:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .select select:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .textarea:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .input:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input:-moz-placeholder{color:rgba(245,247,253,0.3)}html.theme--catppuccin-macchiato .select select[disabled]:-ms-input-placeholder,html.theme--catppuccin-macchiato .textarea[disabled]:-ms-input-placeholder,html.theme--catppuccin-macchiato .input[disabled]:-ms-input-placeholder,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input[disabled]:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .select select:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .textarea:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .input:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input:-ms-input-placeholder{color:rgba(245,247,253,0.3)}html.theme--catppuccin-macchiato .textarea,html.theme--catppuccin-macchiato .input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input{box-shadow:inset 0 0.0625em 0.125em rgba(10,10,10,0.05);max-width:100%;width:100%}html.theme--catppuccin-macchiato .textarea[readonly],html.theme--catppuccin-macchiato .input[readonly],html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input[readonly]{box-shadow:none}html.theme--catppuccin-macchiato 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form.docs-search>input.is-active{box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-macchiato .is-black.textarea,html.theme--catppuccin-macchiato .is-black.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black{border-color:#0a0a0a}html.theme--catppuccin-macchiato .is-black.textarea:focus,html.theme--catppuccin-macchiato .is-black.input:focus,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:focus,html.theme--catppuccin-macchiato .is-black.is-focused.textarea,html.theme--catppuccin-macchiato .is-black.is-focused.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--catppuccin-macchiato .is-black.textarea:active,html.theme--catppuccin-macchiato .is-black.input:active,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:active,html.theme--catppuccin-macchiato 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kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus:not(:active),html.theme--catppuccin-mocha .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(148,226,213,0.25)}html.theme--catppuccin-mocha .button.is-info:active,html.theme--catppuccin-mocha .button.is-info.is-active{background-color:#80ddcd;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:#94e2d5;box-shadow:none}html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.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--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.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--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.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--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.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--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .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--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .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--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .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--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .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--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #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--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .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--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha .content ul:not(:last-child),html.theme--catppuccin-mocha .content blockquote:not(:last-child),html.theme--catppuccin-mocha .content pre:not(:last-child),html.theme--catppuccin-mocha .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-mocha .content h1,html.theme--catppuccin-mocha .content h2,html.theme--catppuccin-mocha .content h3,html.theme--catppuccin-mocha .content h4,html.theme--catppuccin-mocha .content h5,html.theme--catppuccin-mocha .content h6{color:#cdd6f4;font-weight:600;line-height:1.125}html.theme--catppuccin-mocha .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-mocha .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-mocha .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-mocha .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-mocha .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-mocha .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-mocha .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-mocha .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-mocha .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-mocha .content blockquote{background-color:#181825;border-left:5px solid #585b70;padding:1.25em 1.5em}html.theme--catppuccin-mocha .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-mocha .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-mocha .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-mocha .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-mocha .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-mocha .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-mocha .content ul ul ul{list-style-type:square}html.theme--catppuccin-mocha .content dd{margin-left:2em}html.theme--catppuccin-mocha .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-mocha .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-mocha .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-mocha .content figure img{display:inline-block}html.theme--catppuccin-mocha .content figure figcaption{font-style:italic}html.theme--catppuccin-mocha .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-mocha .content sup,html.theme--catppuccin-mocha .content sub{font-size:75%}html.theme--catppuccin-mocha .content table{width:100%}html.theme--catppuccin-mocha .content table 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.content.is-normal{font-size:1rem}html.theme--catppuccin-mocha .content.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .content.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-mocha .icon.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-mocha .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-mocha .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-mocha .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-mocha .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-mocha .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-mocha .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-mocha div.icon-text{display:flex}html.theme--catppuccin-mocha .image,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-mocha .image img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-mocha .image img.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-mocha .image.is-fullwidth,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-mocha .image.is-square img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-mocha .image.is-square .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-mocha .image.is-1by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar 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.has-ratio,html.theme--catppuccin-mocha .image.is-5by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-mocha .image.is-5by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-mocha .image.is-16by9 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-mocha .image.is-16by9 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-mocha .image.is-2by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-mocha .image.is-2by1 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-mocha .image.is-3by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-mocha 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img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-mocha .image.is-3by5 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-mocha .image.is-9by16 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-mocha .image.is-9by16 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-mocha .image.is-1by2 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-mocha .image.is-1by2 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-mocha .image.is-1by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-mocha .image.is-1by3 .has-ratio,html.theme--catppuccin-mocha 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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:3px}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:#8c9b9d;border-color:#5e6d6f;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:#282f2f;border-color:#5e6d6f;color:#dbdee0;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 + 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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}@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 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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:#f2f2f2;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:#282f2f;border-left:5px solid #5e6d6f;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 #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}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:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}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 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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 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Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize 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 users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === 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 primaryLightTheme = null; + var primaryDarkTheme = 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. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = 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); + } + var activeTheme = null; + 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; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + 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; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/DifferentiationInterface/v0.6.18/assets/warner.js b/DifferentiationInterface/v0.6.18/assets/warner.js new file mode 100644 index 000000000..3f6f5d008 --- /dev/null +++ b/DifferentiationInterface/v0.6.18/assets/warner.js @@ -0,0 +1,52 @@ +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/DifferentiationInterface/v0.6.18/dev_guide/index.html b/DifferentiationInterface/v0.6.18/dev_guide/index.html new file mode 100644 index 000000000..3db78e66b --- /dev/null +++ b/DifferentiationInterface/v0.6.18/dev_guide/index.html @@ -0,0 +1,7 @@ + +Dev guide · DifferentiationInterface.jl
GitHub

Dev guide

This page is important reading if you want to contribute to DifferentiationInterface.jl. It is not part of the public API and the content below may become outdated, in which case you should refer to the source code as the ground truth.

General principles

The package is structured around 8 operators:

Most operators have 4 variants, which look like this in the first order: operator, operator!, value_and_operator, value_and_operator!.

New operator

To implement a new operator for an existing backend, you need to write 5 methods: 1 for preparation and 4 corresponding to the variants of the operator (see above). For first-order operators, you may also want to support in-place functions, which requires another 5 methods (defined on f! instead of f).

The method prepare_operator must output a prep object of the correct type. For instance, prepare_gradient(f, backend, x) must return a DifferentiationInterface.GradientPrep. Assuming you don't need any preparation for said operator, you can use the trivial prep that are already defined, like DifferentiationInterface.NoGradientPrep. Otherwise, define a custom struct like MyGradientPrep <: DifferentiationInterface.GradientPrep and put the necessary storage in there.

New backend

If you want to implement a new backend, for instance because you developed a new AD package called SuperDiff, please open a pull request to DifferentiationInterface.jl. Your AD package needs to be registered first.

Core code

In the main package, you should define a new struct SuperDiffBackend which subtypes ADTypes.AbstractADType, and endow it with the fields you need to parametrize your differentiation routines. You also have to define ADTypes.mode and DifferentiationInterface.inplace_support on SuperDiffBackend.

Info

In the end, this backend struct will need to be contributed to ADTypes.jl. However, putting it in the DifferentiationInterface.jl PR is a good first step for debugging.

In a package extension named DifferentiationInterfaceSuperDiffExt, you need to implement at least pushforward or pullback (and their variants). The exact requirements depend on the differentiation mode you chose:

backend modepushforward necessarypullback necessary
ADTypes.ForwardModeyesno
ADTypes.ReverseModenoyes
ADTypes.ForwardOrReverseModeyesyes
ADTypes.SymbolicModeyesyes

Every other operator can be deduced from these two, but you can gain efficiency by implementing additional operators.

Tests and docs

Once that is done, you need to add your new backend to the test suite. Test files should be gathered in a folder named SuperDiff inside DifferentiationInterface/test/Back. They should use DifferentiationInterfaceTest.jl to check correctness against the default scenarios. Take inspiration from the tests of other backends to write your own. To activate tests in CI, modify the test workflow and add your package to the list. To run the tests locally, replace the following line in DifferentiationInterface/test/runtests.jl

GROUP = get(ENV, "JULIA_DI_TEST_GROUP", "All")

with the much cheaper version

GROUP = get(ENV, "JULIA_DI_TEST_GROUP", "Back/SuperDiff")

but don't forget to switch it back before pushing.

Finally, you need to add your backend to the documentation, modifying every page that involves a list of backends (including the README.md).

diff --git a/DifferentiationInterface/v0.6.18/explanation/advanced/index.html b/DifferentiationInterface/v0.6.18/explanation/advanced/index.html new file mode 100644 index 000000000..be6982c3f --- /dev/null +++ b/DifferentiationInterface/v0.6.18/explanation/advanced/index.html @@ -0,0 +1,8 @@ + +Advanced features · DifferentiationInterface.jl
GitHub

Advanced features

Contexts

Additional arguments

For all operators provided DifferentiationInterface, there can be only one differentiated (or "active") argument, which we call x. However, the release v0.6 introduced the possibility of additional "context" arguments, which are not differentiated but still passed to the function after x.

Contexts can be useful if you have a function y = f(x, a, b, c, ...) or f!(y, x, a, b, c, ...) and you want derivatives of y with respect to x only. Another option would be creating a closure, but that is sometimes undesirable.

Types of contexts

Every context argument must be wrapped in a subtype of Context and come after the differentiated input x. Right now, there are two kinds of context: Constant and Cache.

Warning

This feature is still experimental and will not be supported by all backends. At the moment:

  • Constant is supported by all backends except symbolic ones
  • Cache is only supported by finite difference backends and AutoForwardDiff, but it is not yet optimized

Semantically, both of these calls compute the partial gradient of f(x, c) with respect to x, but they consider c differently:

gradient(f, backend, x, Constant(c))
+gradient(f, backend, x, Cache(c))

In the first call, c is kept unchanged throughout the function evaluation. In the second call, c can be mutated with values computed during the function.

Importantly, one can prepare an operator with an arbitrary value c' of the Constant (subject to the usual restrictions on preparation). The values in a provided Cache never matter anyway.

Sparsity

When faced with sparse Jacobian or Hessian matrices, one can take advantage of their sparsity pattern to speed up the computation. DifferentiationInterface does this automatically if you pass a backend of type AutoSparse.

Tip

To know more about sparse AD, read the survey What Color Is Your Jacobian? Graph Coloring for Computing Derivatives (Gebremedhin et al., 2005).

AutoSparse object

AutoSparse backends only support jacobian and hessian (as well as their variants), because other operators do not output matrices. An AutoSparse backend must be constructed from three ingredients:

  1. An underlying (dense) backend, which can be SecondOrder or anything from ADTypes.jl
  2. A sparsity pattern detector like:
  3. A coloring algorithm from SparseMatrixColorings.jl, such as:
Note

Symbolic backends have built-in sparsity handling, so AutoSparse(AutoSymbolics()) and AutoSparse(AutoFastDifferentiation()) do not need additional configuration for pattern detection or coloring.

Cost of sparse preparation

The preparation step of jacobian or hessian with an AutoSparse backend can be long, because it needs to detect the sparsity pattern and perform a matrix coloring. But after preparation, the more zeros are present in the matrix, the greater the speedup will be compared to dense differentiation.

Danger

The result of preparation for an AutoSparse backend cannot be reused if the sparsity pattern changes.

Tuning the coloring algorithm

The complexity of sparse Jacobians or Hessians grows with the number of distinct colors in a coloring of the sparsity pattern. To reduce this number of colors, GreedyColoringAlgorithm has two main settings: the order used for vertices and the decompression method. Depending on your use case, you may want to modify either of these options to increase performance. See the documentation of SparseMatrixColorings.jl for details.

Batch mode

Multiple tangents

The jacobian and hessian operators compute matrices by repeatedly applying lower-level operators (pushforward, pullback or hvp) to a set of tangents. The tangents usually correspond to basis elements of the appropriate vector space. We could call the lower-level operator on each tangent separately, but some packages (ForwardDiff.jl and Enzyme.jl) have optimized implementations to handle multiple tangents at once.

This behavior is often called "vector mode" AD, but we call it "batch mode" to avoid confusion with Julia's Vector type. As a matter of fact, the optimal batch size $B$ (number of simultaneous tangents) is usually very small, so tangents are passed within an NTuple and not a Vector. When the underlying vector space has dimension $N$, the operators jacobian and hessian process $\lceil N / B \rceil$ batches of size $B$ each.

Optimal batch size

For every backend which does not support batch mode, the batch size is set to $B = 1$. But for AutoForwardDiff and AutoEnzyme, more complicated rules apply. If the backend object has a pre-determined batch size $B_0$, then we always set $B = B_0$. In particular, this will throw errors when $N < B_0$. On the other hand, without a pre-determined batch size, we apply backend-specific heuristics to pick $B$ based on $N$.

diff --git a/DifferentiationInterface/v0.6.18/explanation/backends/index.html b/DifferentiationInterface/v0.6.18/explanation/backends/index.html new file mode 100644 index 000000000..c09287154 --- /dev/null +++ b/DifferentiationInterface/v0.6.18/explanation/backends/index.html @@ -0,0 +1,7 @@ + +Backends · DifferentiationInterface.jl
GitHub

Backends

List

We support the following dense backend choices from ADTypes.jl:

Features

Given a backend object, you can use:

  • check_available to know whether the required AD package is loaded
  • check_inplace to know whether the backend supports in-place functions (all backends support out-of-place functions)

In theory, all we need from each backend is either a pushforward or a pullback: we can deduce every other operator from these two. In practice, many AD backends have custom implementations for high-level operators like gradient or jacobian, which we reuse whenever possible.

Details

In the rough summary table below,

  • ✅ means that we reuse the custom implementation from the backend;
  • ❌ means that a custom implementation doesn't exist, so we use our default fallbacks;
  • 🔀 means it's complicated or not done yet.
pfpbdergradjachesshvpder2
AutoChainRules❌✅❌❌❌❌❌❌
AutoDiffractor✅❌❌❌❌❌❌❌
AutoEnzyme (forward)✅❌❌✅✅❌❌❌
AutoEnzyme (reverse)❌✅❌✅✅❌🔀❌
AutoFastDifferentiation✅✅✅✅✅✅✅✅
AutoFiniteDiff🔀❌✅✅✅✅❌❌
AutoFiniteDifferences🔀❌❌✅✅❌❌❌
AutoForwardDiff✅❌✅✅✅✅✅✅
AutoMooncake❌✅❌❌❌❌❌❌
AutoPolyesterForwardDiff🔀❌🔀✅✅🔀🔀🔀
AutoReverseDiff❌🔀❌✅✅✅❌❌
AutoSymbolics✅❌✅✅✅✅✅✅
AutoTracker❌✅❌✅❌❌❌❌
AutoZygote❌✅❌✅✅✅🔀❌

Moreover, each context type is supported by a specific subset of backends:

Constant
AutoChainRules✅
AutoDiffractor❌
AutoEnzyme (forward)✅
AutoEnzyme (reverse)✅
AutoFastDifferentiation❌
AutoFiniteDiff✅
AutoFiniteDifferences✅
AutoForwardDiff✅
AutoMooncake✅
AutoPolyesterForwardDiff✅
AutoReverseDiff✅
AutoSymbolics❌
AutoTracker✅
AutoZygote✅

Second order

For second-order operators like second_derivative, hessian and hvp, there are two main options. You can either use a single backend, or combine two of them within the SecondOrder struct:

backend = SecondOrder(outer_backend, inner_backend)

The inner backend will be called first, and the outer backend will differentiate the generated code. In general, using a forward outer backend over a reverse inner backend will yield the best performance.

Danger

Second-order AD is tricky, and many backend combinations will fail (even if you combine a backend with itself). Be ready to experiment and open issues if necessary.

Backend switch

The wrapper DifferentiateWith allows you to switch between backends. It takes a function f and specifies that f should be differentiated with the substitute backend of your choice, instead of whatever true backend the surrounding code is trying to use. In other words, when someone tries to differentiate dw = DifferentiateWith(f, substitute_backend) with true_backend, then substitute_backend steps in and true_backend does not dive into the function f itself. At the moment, DifferentiateWith only works when true_backend is either ForwardDiff.jl or a ChainRules.jl-compatible backend.

Implementations

What follows is a list of implementation details from the package extensions of DifferentiationInterface.jl It is not part of the public API or protected by semantic versioning, and it may become outdated. When in doubt, refer to the code itself.

ChainRulesCore

We only implement pullback, using the RuleConfig mechanism to call back into AD. Same-point preparation runs the forward sweep and returns the pullback closure.

Diffractor

We only implement pushforward.

Danger

The latest releases of Diffractor broke DifferentiationInterface.

Enzyme

Depending on the mode attribute inside AutoEnzyme, we implement either pushforward or pullback based on Enzyme.autodiff. When necessary, preparation chooses a number of chunks (for gradient and jacobian in forward mode, for jacobian only in reverse mode).

FastDifferentiation

For every operator, preparation generates an executable function from the symbolic expression of the differentiated function.

Warning

Preparation can be very slow for symbolic AD.

FiniteDiff

Whenever possible, preparation creates a cache object. Pushforward is implemented rather slowly using a closure.

FiniteDifferences

Nothing specific to mention.

ForwardDiff

We implement pushforward directly using Dual numbers, and preparation allocates the necessary space. For higher level operators, preparation creates a config object, which can be type-unstable.

PolyesterForwardDiff

Most operators fall back on AutoForwardDiff.

ReverseDiff

Wherever possible, preparation records a tape of the function's execution. This tape is computed from the arguments x and contexts... provided at preparation time. It is control-flow dependent, so only one branch is recorded at each if statement.

Danger

If your function has value-specific control flow (like if x[1] > 0 or if c == 1), you may get silently wrong results whenever it takes new branches that were not taken during preparation. You must make sure to run preparation with an input and contexts whose values trigger the correct control flow for future executions.

Symbolics

For all operators, preparation generates an executable function from the symbolic expression of the differentiated function.

Warning

Preparation can be very slow for symbolic AD.

Mooncake

For pullback, preparation builds the reverse rule of the function.

Tracker

We implement pullback based on Tracker.back. Same-point preparation runs the forward sweep and returns the pullback closure at x.

Zygote

We implement pullback based on Zygote.pullback. Same-point preparation runs the forward sweep and returns the pullback closure at x.

diff --git a/DifferentiationInterface/v0.6.18/explanation/operators/index.html b/DifferentiationInterface/v0.6.18/explanation/operators/index.html new file mode 100644 index 000000000..fdf92f35f --- /dev/null +++ b/DifferentiationInterface/v0.6.18/explanation/operators/index.html @@ -0,0 +1,8 @@ + +Operators · DifferentiationInterface.jl
GitHub

Operators

Tip

If there are some concepts you do not understand, take a look at the book The Elements of Differentiable Programming (Blondel and Roulet, 2024).

List of operators

Given a function f(x) = y, there are several differentiation operators available. The terminology depends on:

  • the type and shape of the input x
  • the type and shape of the output y
  • the order of differentiation

Below we list and describe all the operators we support.

Warning

The package is thoroughly tested with inputs and outputs of the following types: Float64, Vector{Float64} and Matrix{Float64}. We also expect it to work on most kinds of Number and AbstractArray variables. Beyond that, you are in uncharted territory. We voluntarily keep the type annotations minimal, so that passing more complex objects or custom structs might work in some cases, but we make no guarantees about that yet.

High-level operators

These operators are computed using only the input x.

operatororderinput xoutput yoperator result typeoperator result shape
derivative1NumberAnysimilar to ysize(y)
second_derivative2NumberAnysimilar to ysize(y)
gradient1AnyNumbersimilar to xsize(x)
jacobian1AbstractArrayAbstractArrayAbstractMatrix(length(y), length(x))
hessian2AbstractArrayNumberAbstractMatrix(length(x), length(x))

Low-level operators

These operators are computed using the input x and another argument t of type NTuple, which contains one or more tangents. You can think of tangents as perturbations propagated through the function; they live either in the same space as x or in the same space as y.

operatororderinput xoutput yelement type of toperator result typeoperator result shape
pushforward (JVP)1AnyAnysimilar to xsimilar to ysize(y)
pullback (VJP)1AnyAnysimilar to ysimilar to xsize(x)
hvp2AnyNumbersimilar to xsimilar to xsize(x)

Variants

Several variants of each operator are defined:

  • out-of-place operators return a new derivative object
  • in-place operators mutate the provided derivative object
out-of-placein-placeout-of-place + primalin-place + primal
derivativederivative!value_and_derivativevalue_and_derivative!
second_derivativesecond_derivative!value_derivative_and_second_derivativevalue_derivative_and_second_derivative!
gradientgradient!value_and_gradientvalue_and_gradient!
hessianhessian!value_gradient_and_hessianvalue_gradient_and_hessian!
jacobianjacobian!value_and_jacobianvalue_and_jacobian!
pushforwardpushforward!value_and_pushforwardvalue_and_pushforward!
pullbackpullback!value_and_pullbackvalue_and_pullback!
hvphvp!gradient_and_hvpgradient_and_hvp!

Mutation and signatures

Two kinds of functions are supported:

  • out-of-place functions f(x) = y
  • in-place functions f!(y, x) = nothing
Warning

In-place functions only work with pushforward, pullback, derivative and jacobian. The other operators hvp, gradient and hessian require scalar outputs, so it makes no sense to mutate the number y.

This results in various operator signatures (the necessary arguments and their order):

function signatureout-of-place operator (returns result)in-place operator (mutates result)
out-of-place function fop(f, backend, x, [t])op!(f, result, backend, x, [t])
in-place function f!op(f!, y, backend, x, [t])op!(f!, y, result, backend, x, [t])
Warning

The positional arguments between f/f! and backend are always mutated, regardless of the bang ! in the operator name. In particular, for in-place functions f!(y, x), every variant of every operator will mutate y.

Preparation

Principle

In many cases, AD can be accelerated if the function has been called at least once (e.g. to record a tape) or if some cache objects are pre-allocated. This preparation procedure is backend-specific, but we expose a common syntax to achieve it.

operatorpreparation (different point)preparation (same point)
derivativeprepare_derivative-
gradientprepare_gradient-
jacobianprepare_jacobian-
second_derivativeprepare_second_derivative-
hessianprepare_hessian-
pushforwardprepare_pushforwardprepare_pushforward_same_point
pullbackprepare_pullbackprepare_pullback_same_point
hvpprepare_hvpprepare_hvp_same_point

In addition, the preparation syntax depends on the number of arguments accepted by the function.

function signaturepreparation signature
out-of-place functionprepare_op(f, backend, x, [t])
in-place functionprepare_op(f!, y, backend, x, [t])

Preparation creates an object called prep which contains the the necessary information to speed up an operator and its variants. The idea is that you prepare only once, which can be costly, but then call the operator several times while reusing the same prep.

op(f, backend, x, [t])  # slow because it includes preparation
+op(f, prep, backend, x, [t])  # fast because it skips preparation
Warning

The prep object is the last argument before backend and it is always mutated, regardless of the bang ! in the operator name.

Reusing preparation

Deciding whether it is safe to reuse the results of preparation is not easy. Here are the general rules that we strive to implement:

For different-point preparation, the output prep of prepare_op(f, b, x, [t]) can be reused in op(f, prep, b, other_x, [other_t]), provided that:

  • the inputs x and other_x have the same types and sizes
  • the tangents in t and other_t have the same types and sizes

For same-point preparation, the output prep of prepare_op_same_point(f, b, x, [t]) can be reused in op(f, prep, b, x, other_t), provided that:

  • the input x remains exactly the same (as well as any Constant context)
  • the tangents in t and other_t have the same types and sizes
Warning

These rules hold for the majority of backends, but there are some exceptions. The most important exception is ReverseDiff and its taping mechanism, which is sensitive to control flow inside the function.

diff --git a/DifferentiationInterface/v0.6.18/index.html b/DifferentiationInterface/v0.6.18/index.html new file mode 100644 index 000000000..4bca1ee99 --- /dev/null +++ b/DifferentiationInterface/v0.6.18/index.html @@ -0,0 +1,23 @@ + +Home · DifferentiationInterface.jl
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DifferentiationInterface Logo

DifferentiationInterface

Build Status Coverage Code Style: Blue ColPrac: Contributor's Guide on Collaborative Practices for Community Packages DOI

PackageDocs
DifferentiationInterfaceStable Dev
DifferentiationInterfaceTestStable Dev

An interface to various automatic differentiation (AD) backends in Julia.

Goal

This package provides a unified syntax to differentiate functions, including:

  • First- and second-order operators (gradients, Jacobians, Hessians and more)
  • In-place and out-of-place differentiation
  • Preparation mechanism (e.g. to pre-allocate a cache or record a tape)
  • Built-in sparsity handling
  • Thorough validation on standard inputs and outputs (numbers, vectors, matrices)
  • Testing and benchmarking utilities accessible to users with DifferentiationInterfaceTest

Compatibility

We support the following backends defined by ADTypes.jl:

Note that in some cases, going through DifferentiationInterface.jl might be slower than a direct call to the backend's API. This is mostly true for Enzyme.jl, whose handling of activities and multiple arguments unlocks additional performance. We are working on this challenge, and welcome any suggestions or contributions. Meanwhile, if differentiation fails or takes too long, consider using Enzyme.jl directly.

Installation

To install the stable version of the package, run the following code in a Julia REPL:

using Pkg
+
+Pkg.add("DifferentiationInterface")

To install the development version, run this instead:

using Pkg
+
+Pkg.add(
+    url="https://github.com/JuliaDiff/DifferentiationInterface.jl",
+    subdir="DifferentiationInterface"
+)

Example

using DifferentiationInterface
+import ForwardDiff, Enzyme, Zygote  # AD backends you want to use 
+
+f(x) = sum(abs2, x)
+
+x = [1.0, 2.0]
+
+value_and_gradient(f, AutoForwardDiff(), x) # returns (5.0, [2.0, 4.0]) with ForwardDiff.jl
+value_and_gradient(f, AutoEnzyme(),      x) # returns (5.0, [2.0, 4.0]) with Enzyme.jl
+value_and_gradient(f, AutoZygote(),      x) # returns (5.0, [2.0, 4.0]) with Zygote.jl

To improve your performance by up to several orders of magnitude compared to this example, take a look at the tutorial and its section on operator preparation.

Citation

Please cite both DifferentiationInterface.jl and its inspiration AbstractDifferentiation.jl, using the provided CITATION.bib file.

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However, same-point preparation must occur with the exact value that will be reused later.\n\nExample\n\njulia> using DifferentiationInterface\n\njulia> import ForwardDiff\n\njulia> f(x, c) = c * sum(abs2, x);\n\njulia> gradient(f, AutoForwardDiff(), [1.0, 2.0], Constant(10))\n2-element Vector{Float64}:\n 20.0\n 40.0\n\njulia> gradient(f, AutoForwardDiff(), [1.0, 2.0], Constant(100))\n2-element Vector{Float64}:\n 200.0\n 400.0\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.Cache","page":"API","title":"DifferentiationInterface.Cache","text":"Cache\n\nConcrete type of Context argument which can be mutated with active values during differentiation.\n\nThe initial values present inside the cache do not matter.\n\n\n\n\n\n","category":"type"},{"location":"api/#First-order","page":"API","title":"First order","text":"","category":"section"},{"location":"api/#Pushforward","page":"API","title":"Pushforward","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"prepare_pushforward\nprepare_pushforward_same_point\npushforward\npushforward!\nvalue_and_pushforward\nvalue_and_pushforward!","category":"page"},{"location":"api/#DifferentiationInterface.prepare_pushforward","page":"API","title":"DifferentiationInterface.prepare_pushforward","text":"prepare_pushforward(f, backend, x, tx, [contexts...]) -> prep\nprepare_pushforward(f!, y, backend, x, tx, [contexts...]) -> prep\n\nCreate a prep object that can be given to pushforward and its variants.\n\nwarning: Warning\nIf the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.prepare_pushforward_same_point","page":"API","title":"DifferentiationInterface.prepare_pushforward_same_point","text":"prepare_pushforward_same_point(f, backend, x, tx, [contexts...]) -> prep_same\nprepare_pushforward_same_point(f!, y, backend, x, tx, [contexts...]) -> prep_same\n\nCreate an prep_same object that can be given to pushforward and its variants if they are applied at the same point x and with the same contexts.\n\nwarning: Warning\nIf the function or the point changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.pushforward","page":"API","title":"DifferentiationInterface.pushforward","text":"pushforward(f, [prep,] backend, x, tx, [contexts...]) -> ty\npushforward(f!, y, [prep,] backend, x, tx, [contexts...]) -> ty\n\nCompute the pushforward of the function f at point x with a tuple of tangents tx.\n\nTo improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.\n\ntip: Tip\nPushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named jvp.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.pushforward!","page":"API","title":"DifferentiationInterface.pushforward!","text":"pushforward!(f, dy, [prep,] backend, x, tx, [contexts...]) -> ty\npushforward!(f!, y, dy, [prep,] backend, x, tx, [contexts...]) -> ty\n\nCompute the pushforward of the function f at point x with a tuple of tangents tx, overwriting ty.\n\nTo improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.\n\ntip: Tip\nPushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named jvp!.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_and_pushforward","page":"API","title":"DifferentiationInterface.value_and_pushforward","text":"value_and_pushforward(f, [prep,] backend, x, tx, [contexts...]) -> (y, ty)\nvalue_and_pushforward(f!, y, [prep,] backend, x, tx, [contexts...]) -> (y, ty)\n\nCompute the value and the pushforward of the function f at point x with a tuple of tangents tx.\n\nTo improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.\n\ntip: Tip\nPushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named value_and_jvp.\n\ninfo: Info\nRequired primitive for forward mode backends.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_and_pushforward!","page":"API","title":"DifferentiationInterface.value_and_pushforward!","text":"value_and_pushforward!(f, dy, [prep,] backend, x, tx, [contexts...]) -> (y, ty)\nvalue_and_pushforward!(f!, y, dy, [prep,] backend, x, tx, [contexts...]) -> (y, ty)\n\nCompute the value and the pushforward of the function f at point x with a tuple of tangents tx, overwriting ty.\n\nTo improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.\n\ntip: Tip\nPushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named value_and_jvp!.\n\n\n\n\n\n","category":"function"},{"location":"api/#Pullback","page":"API","title":"Pullback","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"prepare_pullback\nprepare_pullback_same_point\npullback\npullback!\nvalue_and_pullback\nvalue_and_pullback!","category":"page"},{"location":"api/#DifferentiationInterface.prepare_pullback","page":"API","title":"DifferentiationInterface.prepare_pullback","text":"prepare_pullback(f, backend, x, ty, [contexts...]) -> prep\nprepare_pullback(f!, y, backend, x, ty, [contexts...]) -> prep\n\nCreate a prep object that can be given to pullback and its variants.\n\nwarning: Warning\nIf the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.prepare_pullback_same_point","page":"API","title":"DifferentiationInterface.prepare_pullback_same_point","text":"prepare_pullback_same_point(f, backend, x, ty, [contexts...]) -> prep_same\nprepare_pullback_same_point(f!, y, backend, x, ty, [contexts...]) -> prep_same\n\nCreate an prep_same object that can be given to pullback and its variants if they are applied at the same point x and with the same contexts.\n\nwarning: Warning\nIf the function or the point changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.pullback","page":"API","title":"DifferentiationInterface.pullback","text":"pullback(f, [prep,] backend, x, ty, [contexts...]) -> tx\npullback(f!, y, [prep,] backend, x, ty, [contexts...]) -> tx\n\nCompute the pullback of the function f at point x with a tuple of tangents ty.\n\nTo improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.\n\ntip: Tip\nPullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named vjp.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.pullback!","page":"API","title":"DifferentiationInterface.pullback!","text":"pullback!(f, dx, [prep,] backend, x, ty, [contexts...]) -> tx\npullback!(f!, y, dx, [prep,] backend, x, ty, [contexts...]) -> tx\n\nCompute the pullback of the function f at point x with a tuple of tangents ty, overwriting dx.\n\nTo improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.\n\ntip: Tip\nPullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named vjp!.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_and_pullback","page":"API","title":"DifferentiationInterface.value_and_pullback","text":"value_and_pullback(f, [prep,] backend, x, ty, [contexts...]) -> (y, tx)\nvalue_and_pullback(f!, y, [prep,] backend, x, ty, [contexts...]) -> (y, tx)\n\nCompute the value and the pullback of the function f at point x with a tuple of tangents ty.\n\nTo improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.\n\ntip: Tip\nPullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named value_and_vjp.\n\ninfo: Info\nRequired primitive for reverse mode backends.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_and_pullback!","page":"API","title":"DifferentiationInterface.value_and_pullback!","text":"value_and_pullback!(f, dx, [prep,] backend, x, ty, [contexts...]) -> (y, tx)\nvalue_and_pullback!(f!, y, dx, [prep,] backend, x, ty, [contexts...]) -> (y, tx)\n\nCompute the value and the pullback of the function f at point x with a tuple of tangents ty, overwriting dx.\n\nTo improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.\n\ntip: Tip\nPullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named value_and_vjp!.\n\n\n\n\n\n","category":"function"},{"location":"api/#Derivative","page":"API","title":"Derivative","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"prepare_derivative\nderivative\nderivative!\nvalue_and_derivative\nvalue_and_derivative!","category":"page"},{"location":"api/#DifferentiationInterface.prepare_derivative","page":"API","title":"DifferentiationInterface.prepare_derivative","text":"prepare_derivative(f, backend, x, [contexts...]) -> prep\nprepare_derivative(f!, y, backend, x, [contexts...]) -> prep\n\nCreate a prep object that can be given to derivative and its variants.\n\nwarning: Warning\nIf the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.derivative","page":"API","title":"DifferentiationInterface.derivative","text":"derivative(f, [prep,] backend, x, [contexts...]) -> der\nderivative(f!, y, [prep,] backend, x, [contexts...]) -> der\n\nCompute the derivative of the function f at point x.\n\nTo improve performance via operator preparation, refer to prepare_derivative.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.derivative!","page":"API","title":"DifferentiationInterface.derivative!","text":"derivative!(f, der, [prep,] backend, x, [contexts...]) -> der\nderivative!(f!, y, der, [prep,] backend, x, [contexts...]) -> der\n\nCompute the derivative of the function f at point x, overwriting der.\n\nTo improve performance via operator preparation, refer to prepare_derivative.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_and_derivative","page":"API","title":"DifferentiationInterface.value_and_derivative","text":"value_and_derivative(f, [prep,] backend, x, [contexts...]) -> (y, der)\nvalue_and_derivative(f!, y, [prep,] backend, x, [contexts...]) -> (y, der)\n\nCompute the value and the derivative of the function f at point x.\n\nTo improve performance via operator preparation, refer to prepare_derivative.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_and_derivative!","page":"API","title":"DifferentiationInterface.value_and_derivative!","text":"value_and_derivative!(f, der, [prep,] backend, x, [contexts...]) -> (y, der)\nvalue_and_derivative!(f!, y, der, [prep,] backend, x, [contexts...]) -> (y, der)\n\nCompute the value and the derivative of the function f at point x, overwriting der.\n\nTo improve performance via operator preparation, refer to prepare_derivative.\n\n\n\n\n\n","category":"function"},{"location":"api/#Gradient","page":"API","title":"Gradient","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"prepare_gradient\ngradient\ngradient!\nvalue_and_gradient\nvalue_and_gradient!","category":"page"},{"location":"api/#DifferentiationInterface.prepare_gradient","page":"API","title":"DifferentiationInterface.prepare_gradient","text":"prepare_gradient(f, backend, x, [contexts...]) -> prep\n\nCreate a prep object that can be given to gradient and its variants.\n\nwarning: Warning\nIf the function changes in any way, the result of preparation will be invalidated, and you will need to run it again.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.gradient","page":"API","title":"DifferentiationInterface.gradient","text":"gradient(f, [prep,] backend, x, [contexts...]) -> grad\n\nCompute the gradient of the function f at point x.\n\nTo improve performance via operator preparation, refer to prepare_gradient.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.gradient!","page":"API","title":"DifferentiationInterface.gradient!","text":"gradient!(f, grad, [prep,] backend, x, [contexts...]) -> grad\n\nCompute the gradient of the function f at point x, overwriting grad.\n\nTo improve performance via operator preparation, refer to prepare_gradient.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_and_gradient","page":"API","title":"DifferentiationInterface.value_and_gradient","text":"value_and_gradient(f, [prep,] backend, x, [contexts...]) -> (y, grad)\n\nCompute the value and the gradient of the function f at point x.\n\nTo improve performance via operator preparation, refer to prepare_gradient.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_and_gradient!","page":"API","title":"DifferentiationInterface.value_and_gradient!","text":"value_and_gradient!(f, grad, [prep,] backend, x, [contexts...]) -> (y, grad)\n\nCompute the value and the gradient of the function f at point x, overwriting grad.\n\nTo improve performance via operator preparation, refer to prepare_gradient.\n\n\n\n\n\n","category":"function"},{"location":"api/#Jacobian","page":"API","title":"Jacobian","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"prepare_jacobian\njacobian\njacobian!\nvalue_and_jacobian\nvalue_and_jacobian!","category":"page"},{"location":"api/#DifferentiationInterface.prepare_jacobian","page":"API","title":"DifferentiationInterface.prepare_jacobian","text":"prepare_jacobian(f, backend, x, [contexts...]) -> prep\nprepare_jacobian(f!, y, backend, x, [contexts...]) -> prep\n\nCreate a prep object that can be given to jacobian and its variants.\n\nwarning: Warning\nIf the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.jacobian","page":"API","title":"DifferentiationInterface.jacobian","text":"jacobian(f, [prep,] backend, x, [contexts...]) -> jac\njacobian(f!, y, [prep,] backend, x, [contexts...]) -> jac\n\nCompute the Jacobian matrix of the function f at point x.\n\nTo improve performance via operator preparation, refer to prepare_jacobian.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.jacobian!","page":"API","title":"DifferentiationInterface.jacobian!","text":"jacobian!(f, jac, [prep,] backend, x, [contexts...]) -> jac\njacobian!(f!, y, jac, [prep,] backend, x, [contexts...]) -> jac\n\nCompute the Jacobian matrix of the function f at point x, overwriting jac.\n\nTo improve performance via operator preparation, refer to prepare_jacobian.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_and_jacobian","page":"API","title":"DifferentiationInterface.value_and_jacobian","text":"value_and_jacobian(f, [prep,] backend, x, [contexts...]) -> (y, jac)\nvalue_and_jacobian(f!, y, [prep,] backend, x, [contexts...]) -> (y, jac)\n\nCompute the value and the Jacobian matrix of the function f at point x.\n\nTo improve performance via operator preparation, refer to prepare_jacobian.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_and_jacobian!","page":"API","title":"DifferentiationInterface.value_and_jacobian!","text":"value_and_jacobian!(f, jac, [prep,] backend, x, [contexts...]) -> (y, jac)\nvalue_and_jacobian!(f!, y, jac, [prep,] backend, x, [contexts...]) -> (y, jac)\n\nCompute the value and the Jacobian matrix of the function f at point x, overwriting jac.\n\nTo improve performance via operator preparation, refer to prepare_jacobian.\n\n\n\n\n\n","category":"function"},{"location":"api/#Second-order","page":"API","title":"Second order","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"SecondOrder","category":"page"},{"location":"api/#DifferentiationInterface.SecondOrder","page":"API","title":"DifferentiationInterface.SecondOrder","text":"SecondOrder\n\nCombination of two backends for second-order differentiation.\n\ndanger: Danger\nSecondOrder backends do not support first-order operators.\n\nConstructor\n\nSecondOrder(outer_backend, inner_backend)\n\nFields\n\nouter::AbstractADType: backend for the outer differentiation\ninner::AbstractADType: backend for the inner differentiation\n\n\n\n\n\n","category":"type"},{"location":"api/#Second-derivative","page":"API","title":"Second derivative","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"prepare_second_derivative\nsecond_derivative\nsecond_derivative!\nvalue_derivative_and_second_derivative\nvalue_derivative_and_second_derivative!","category":"page"},{"location":"api/#DifferentiationInterface.prepare_second_derivative","page":"API","title":"DifferentiationInterface.prepare_second_derivative","text":"prepare_second_derivative(f, backend, x, [contexts...]) -> prep\n\nCreate a prep object that can be given to second_derivative and its variants.\n\nwarning: Warning\nIf the function changes in any way, the result of preparation will be invalidated, and you will need to run it again.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.second_derivative","page":"API","title":"DifferentiationInterface.second_derivative","text":"second_derivative(f, [prep,] backend, x, [contexts...]) -> der2\n\nCompute the second derivative of the function f at point x.\n\nTo improve performance via operator preparation, refer to prepare_second_derivative.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.second_derivative!","page":"API","title":"DifferentiationInterface.second_derivative!","text":"second_derivative!(f, der2, [prep,] backend, x, [contexts...]) -> der2\n\nCompute the second derivative of the function f at point x, overwriting der2.\n\nTo improve performance via operator preparation, refer to prepare_second_derivative.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_derivative_and_second_derivative","page":"API","title":"DifferentiationInterface.value_derivative_and_second_derivative","text":"value_derivative_and_second_derivative(f, [prep,] backend, x, [contexts...]) -> (y, der, der2)\n\nCompute the value, first derivative and second derivative of the function f at point x.\n\nTo improve performance via operator preparation, refer to prepare_second_derivative.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_derivative_and_second_derivative!","page":"API","title":"DifferentiationInterface.value_derivative_and_second_derivative!","text":"value_derivative_and_second_derivative!(f, der, der2, [prep,] backend, x, [contexts...]) -> (y, der, der2)\n\nCompute the value, first derivative and second derivative of the function f at point x, overwriting der and der2.\n\nTo improve performance via operator preparation, refer to prepare_second_derivative.\n\n\n\n\n\n","category":"function"},{"location":"api/#Hessian-vector-product","page":"API","title":"Hessian-vector product","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"prepare_hvp\nprepare_hvp_same_point\nhvp\nhvp!\ngradient_and_hvp\ngradient_and_hvp!","category":"page"},{"location":"api/#DifferentiationInterface.prepare_hvp","page":"API","title":"DifferentiationInterface.prepare_hvp","text":"prepare_hvp(f, backend, x, tx, [contexts...]) -> prep\n\nCreate a prep object that can be given to hvp and its variants.\n\nwarning: Warning\nIf the function changes in any way, the result of preparation will be invalidated, and you will need to run it again.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.prepare_hvp_same_point","page":"API","title":"DifferentiationInterface.prepare_hvp_same_point","text":"prepare_hvp_same_point(f, backend, x, tx, [contexts...]) -> prep_same\n\nCreate an prep_same object that can be given to hvp and its variants if they are applied at the same point x and with the same contexts.\n\nwarning: Warning\nIf the function or the point changes in any way, the result of preparation will be invalidated, and you will need to run it again.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.hvp","page":"API","title":"DifferentiationInterface.hvp","text":"hvp(f, [prep,] backend, x, tx, [contexts...]) -> tg\n\nCompute the Hessian-vector product of f at point x with a tuple of tangents tx.\n\nTo improve performance via operator preparation, refer to prepare_hvp and prepare_hvp_same_point.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.hvp!","page":"API","title":"DifferentiationInterface.hvp!","text":"hvp!(f, tg, [prep,] backend, x, tx, [contexts...]) -> tg\n\nCompute the Hessian-vector product of f at point x with a tuple of tangents tx, overwriting tg.\n\nTo improve performance via operator preparation, refer to prepare_hvp and prepare_hvp_same_point.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.gradient_and_hvp","page":"API","title":"DifferentiationInterface.gradient_and_hvp","text":"gradient_and_hvp(f, [prep,] backend, x, tx, [contexts...]) -> (grad, tg)\n\nCompute the gradient and the Hessian-vector product of f at point x with a tuple of tangents tx.\n\nTo improve performance via operator preparation, refer to prepare_hvp and prepare_hvp_same_point.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.gradient_and_hvp!","page":"API","title":"DifferentiationInterface.gradient_and_hvp!","text":"gradient_and_hvp!(f, grad, tg, [prep,] backend, x, tx, [contexts...]) -> (grad, tg)\n\nCompute the gradient and the Hessian-vector product of f at point x with a tuple of tangents tx, overwriting grad and tg.\n\nTo improve performance via operator preparation, refer to prepare_hvp and prepare_hvp_same_point.\n\n\n\n\n\n","category":"function"},{"location":"api/#Hessian","page":"API","title":"Hessian","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"prepare_hessian\nhessian\nhessian!\nvalue_gradient_and_hessian\nvalue_gradient_and_hessian!","category":"page"},{"location":"api/#DifferentiationInterface.prepare_hessian","page":"API","title":"DifferentiationInterface.prepare_hessian","text":"prepare_hessian(f, backend, x, [contexts...]) -> prep\n\nCreate a prep object that can be given to hessian and its variants.\n\nwarning: Warning\nIf the function changes in any way, the result of preparation will be invalidated, and you will need to run it again.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.hessian","page":"API","title":"DifferentiationInterface.hessian","text":"hessian(f, [prep,] backend, x, [contexts...]) -> hess\n\nCompute the Hessian matrix of the function f at point x.\n\nTo improve performance via operator preparation, refer to prepare_hessian.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.hessian!","page":"API","title":"DifferentiationInterface.hessian!","text":"hessian!(f, hess, [prep,] backend, x, [contexts...]) -> hess\n\nCompute the Hessian matrix of the function f at point x, overwriting hess.\n\nTo improve performance via operator preparation, refer to prepare_hessian.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_gradient_and_hessian","page":"API","title":"DifferentiationInterface.value_gradient_and_hessian","text":"value_gradient_and_hessian(f, [prep,] backend, x, [contexts...]) -> (y, grad, hess)\n\nCompute the value, gradient vector and Hessian matrix of the function f at point x.\n\nTo improve performance via operator preparation, refer to prepare_hessian.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.value_gradient_and_hessian!","page":"API","title":"DifferentiationInterface.value_gradient_and_hessian!","text":"value_gradient_and_hessian!(f, grad, hess, [prep,] backend, x, [contexts...]) -> (y, grad, hess)\n\nCompute the value, gradient vector and Hessian matrix of the function f at point x, overwriting grad and hess.\n\nTo improve performance via operator preparation, refer to prepare_hessian.\n\n\n\n\n\n","category":"function"},{"location":"api/#Utilities","page":"API","title":"Utilities","text":"","category":"section"},{"location":"api/#Backend-queries","page":"API","title":"Backend queries","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"check_available\ncheck_inplace\nDifferentiationInterface.outer\nDifferentiationInterface.inner","category":"page"},{"location":"api/#DifferentiationInterface.check_available","page":"API","title":"DifferentiationInterface.check_available","text":"check_available(backend)\n\nCheck whether backend is available (i.e. whether the extension is loaded).\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.check_inplace","page":"API","title":"DifferentiationInterface.check_inplace","text":"check_inplace(backend)\n\nCheck whether backend supports differentiation of in-place functions.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.outer","page":"API","title":"DifferentiationInterface.outer","text":"outer(backend::SecondOrder)\nouter(backend::AbstractADType)\n\nReturn the outer backend of a SecondOrder object, tasked with differentiation at the second order.\n\nFor any other backend type, this function acts like the identity.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.inner","page":"API","title":"DifferentiationInterface.inner","text":"inner(backend::SecondOrder)\ninner(backend::AbstractADType)\n\nReturn the inner backend of a SecondOrder object, tasked with differentiation at the first order.\n\nFor any other backend type, this function acts like the identity.\n\n\n\n\n\n","category":"function"},{"location":"api/#Backend-switch","page":"API","title":"Backend switch","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"DifferentiateWith","category":"page"},{"location":"api/#DifferentiationInterface.DifferentiateWith","page":"API","title":"DifferentiationInterface.DifferentiateWith","text":"DifferentiateWith\n\nFunction wrapper that enforces differentiation with a \"substitute\" AD backend, possible different from the \"true\" AD backend that is called.\n\nFor instance, suppose a function f is not differentiable with Zygote because it involves mutation, but you know that it is differentiable with Enzyme. Then f2 = DifferentiateWith(f, AutoEnzyme()) is a new function that behaves like f, except that f2 is differentiable with Zygote (thanks to a chain rule which calls Enzyme under the hood). Moreover, any larger algorithm alg that calls f2 instead of f will also be differentiable with Zygote (as long as f was the only Zygote blocker).\n\ntip: Tip\nThis is mainly relevant for package developers who want to produce differentiable code at low cost, without writing the differentiation rules themselves. If you sprinkle a few DifferentiateWith in places where some AD backends may struggle, end users can pick from a wider variety of packages to differentiate your algorithms.\n\nwarning: Warning\nDifferentiateWith only supports out-of-place functions y = f(x) without additional context arguments. It only makes these functions differentiable if the true backend is either ForwardDiff or compatible with ChainRules. For any other true backend, the differentiation behavior is not altered by DifferentiateWith (it becomes a transparent wrapper).\n\nFields\n\nf: the function in question, with signature f(x)\nbackend::AbstractADType: the substitute backend to use for differentiation\n\nnote: Note\nFor the substitute AD backend to be called under the hood, its package needs to be loaded in addition to the package of the true AD backend.\n\nConstructor\n\nDifferentiateWith(f, backend)\n\nExample\n\njulia> using DifferentiationInterface\n\njulia> import FiniteDiff, ForwardDiff, Zygote\n\njulia> function f(x::Vector{Float64})\n a = Vector{Float64}(undef, 1) # type constraint breaks ForwardDiff\n a[1] = sum(abs2, x) # mutation breaks Zygote\n return a[1]\n end;\n\njulia> f2 = DifferentiateWith(f, AutoFiniteDiff());\n\njulia> f([3.0, 5.0]) == f2([3.0, 5.0])\ntrue\n\njulia> alg(x) = 7 * f2(x);\n\njulia> ForwardDiff.gradient(alg, [3.0, 5.0])\n2-element Vector{Float64}:\n 42.0\n 70.0\n\njulia> Zygote.gradient(alg, [3.0, 5.0])[1]\n2-element Vector{Float64}:\n 42.0\n 70.0\n\n\n\n\n\n","category":"type"},{"location":"api/#Sparsity-detection","page":"API","title":"Sparsity detection","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"DenseSparsityDetector","category":"page"},{"location":"api/#DifferentiationInterface.DenseSparsityDetector","page":"API","title":"DifferentiationInterface.DenseSparsityDetector","text":"DenseSparsityDetector\n\nSparsity pattern detector satisfying the detection API of ADTypes.jl.\n\nThe nonzeros in a Jacobian or Hessian are detected by computing the relevant matrix with dense AD, and thresholding the entries with a given tolerance (which can be numerically inaccurate). This process can be very slow, and should only be used if its output can be exploited multiple times to compute many sparse matrices.\n\ndanger: Danger\nIn general, the sparsity pattern you obtain can depend on the provided input x. If you want to reuse the pattern, make sure that it is input-agnostic.\n\nwarning: Warning\nDenseSparsityDetector functionality is now located in a package extension, please load the SparseArrays.jl standard library before you use it.\n\nFields\n\nbackend::AbstractADType is the dense AD backend used under the hood\natol::Float64 is the minimum magnitude of a matrix entry to be considered nonzero\n\nConstructor\n\nDenseSparsityDetector(backend; atol, method=:iterative)\n\nThe keyword argument method::Symbol can be either:\n\n:iterative: compute the matrix in a sequence of matrix-vector products (memory-efficient)\n:direct: compute the matrix all at once (memory-hungry but sometimes faster).\n\nNote that the constructor is type-unstable because method ends up being a type parameter of the DenseSparsityDetector object (this is not part of the API and might change).\n\nExamples\n\nusing ADTypes, DifferentiationInterface, SparseArrays\nimport ForwardDiff\n\ndetector = DenseSparsityDetector(AutoForwardDiff(); atol=1e-5, method=:direct)\n\nADTypes.jacobian_sparsity(diff, rand(5), detector)\n\n# output\n\n4×5 SparseMatrixCSC{Bool, Int64} with 8 stored entries:\n 1 1 ⋅ ⋅ ⋅\n ⋅ 1 1 ⋅ ⋅\n ⋅ ⋅ 1 1 ⋅\n ⋅ ⋅ ⋅ 1 1\n\nSometimes the sparsity pattern is input-dependent:\n\nADTypes.jacobian_sparsity(x -> [prod(x)], rand(2), detector)\n\n# output\n\n1×2 SparseMatrixCSC{Bool, Int64} with 2 stored entries:\n 1 1\n\nADTypes.jacobian_sparsity(x -> [prod(x)], [0, 1], detector)\n\n# output\n\n1×2 SparseMatrixCSC{Bool, Int64} with 1 stored entry:\n 1 ⋅\n\n\n\n\n\n","category":"type"},{"location":"api/#Internals","page":"API","title":"Internals","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"The following is not part of the public API.","category":"page"},{"location":"api/","page":"API","title":"API","text":"Modules = [DifferentiationInterface]\nPublic = false\nFilter = t -> !(Symbol(t) in [:outer, :inner])","category":"page"},{"location":"api/#DifferentiationInterface.AutoZeroForward","page":"API","title":"DifferentiationInterface.AutoZeroForward","text":"AutoZeroForward <: ADTypes.AbstractADType\n\nTrivial backend that sets all derivatives to zero. Used in testing and benchmarking.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.AutoZeroReverse","page":"API","title":"DifferentiationInterface.AutoZeroReverse","text":"AutoZeroReverse <: ADTypes.AbstractADType\n\nTrivial backend that sets all derivatives to zero. Used in testing and benchmarking.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.BatchSizeSettings","page":"API","title":"DifferentiationInterface.BatchSizeSettings","text":"BatchSizeSettings{B,singlebatch,aligned}\n\nConfiguration for the batch size deduced from a backend and a sample array of length N.\n\nType parameters\n\nB::Int: batch size\nsinglebatch::Bool: whether B > N\naligned::Bool: whether N % B == 0\n\nFields\n\nN::Int: array length\nA::Int: number of batches A = div(N, B, RoundUp)\nB_last::Int: size of the last batch (if aligned is false)\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.DerivativePrep","page":"API","title":"DifferentiationInterface.DerivativePrep","text":"DerivativePrep\n\nAbstract type for additional information needed by derivative and its variants.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.ForwardOverForward","page":"API","title":"DifferentiationInterface.ForwardOverForward","text":"ForwardOverForward\n\nTraits identifying second-order backends that compute HVPs in forward over forward mode (inefficient).\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.ForwardOverReverse","page":"API","title":"DifferentiationInterface.ForwardOverReverse","text":"ForwardOverReverse\n\nTraits identifying second-order backends that compute HVPs in forward over reverse mode.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.GradientPrep","page":"API","title":"DifferentiationInterface.GradientPrep","text":"GradientPrep\n\nAbstract type for additional information needed by gradient and its variants.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.HVPPrep","page":"API","title":"DifferentiationInterface.HVPPrep","text":"HVPPrep\n\nAbstract type for additional information needed by hvp and its variants.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.HessianPrep","page":"API","title":"DifferentiationInterface.HessianPrep","text":"HessianPrep\n\nAbstract type for additional information needed by hessian and its variants.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.InPlaceNotSupported","page":"API","title":"DifferentiationInterface.InPlaceNotSupported","text":"InPlaceNotSupported\n\nTrait identifying backends that do not support in-place functions f!(y, x).\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.InPlaceSupported","page":"API","title":"DifferentiationInterface.InPlaceSupported","text":"InPlaceSupported\n\nTrait identifying backends that support in-place functions f!(y, x).\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.JacobianPrep","page":"API","title":"DifferentiationInterface.JacobianPrep","text":"JacobianPrep\n\nAbstract type for additional information needed by jacobian and its variants.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PullbackFast","page":"API","title":"DifferentiationInterface.PullbackFast","text":"PullbackFast\n\nTrait identifying backends that support efficient pullbacks.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PullbackPrep","page":"API","title":"DifferentiationInterface.PullbackPrep","text":"PullbackPrep\n\nAbstract type for additional information needed by pullback and its variants.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PullbackSlow","page":"API","title":"DifferentiationInterface.PullbackSlow","text":"PullbackSlow\n\nTrait identifying backends that do not support efficient pullbacks.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PushforwardFast","page":"API","title":"DifferentiationInterface.PushforwardFast","text":"PushforwardFast\n\nTrait identifying backends that support efficient pushforwards.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PushforwardPrep","page":"API","title":"DifferentiationInterface.PushforwardPrep","text":"PushforwardPrep\n\nAbstract type for additional information needed by pushforward and its variants.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PushforwardSlow","page":"API","title":"DifferentiationInterface.PushforwardSlow","text":"PushforwardSlow\n\nTrait identifying backends that do not support efficient pushforwards.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.ReverseOverForward","page":"API","title":"DifferentiationInterface.ReverseOverForward","text":"ReverseOverForward\n\nTraits identifying second-order backends that compute HVPs in reverse over forward mode.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.ReverseOverReverse","page":"API","title":"DifferentiationInterface.ReverseOverReverse","text":"ReverseOverReverse\n\nTraits identifying second-order backends that compute HVPs in reverse over reverse mode.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.SecondDerivativePrep","page":"API","title":"DifferentiationInterface.SecondDerivativePrep","text":"SecondDerivativePrep\n\nAbstract type for additional information needed by second_derivative and its variants.\n\n\n\n\n\n","category":"type"},{"location":"api/#ADTypes.mode-Tuple{SecondOrder}","page":"API","title":"ADTypes.mode","text":"mode(backend::SecondOrder)\n\nReturn the outer mode of the second-order backend.\n\n\n\n\n\n","category":"method"},{"location":"api/#DifferentiationInterface.basis-Tuple{ADTypes.AbstractADType, AbstractArray, Any}","page":"API","title":"DifferentiationInterface.basis","text":"basis(backend, a::AbstractArray, i)\n\nConstruct the i-th standard basis array in the vector space of a with element type eltype(a).\n\nNote\n\nIf an AD backend benefits from a more specialized basis array implementation, this function can be extended on the backend type.\n\n\n\n\n\n","category":"method"},{"location":"api/#DifferentiationInterface.inplace_support-Tuple{ADTypes.AbstractADType}","page":"API","title":"DifferentiationInterface.inplace_support","text":"inplace_support(backend)\n\nReturn InPlaceSupported or InPlaceNotSupported in a statically predictable way.\n\n\n\n\n\n","category":"method"},{"location":"api/#DifferentiationInterface.multibasis-Tuple{ADTypes.AbstractADType, AbstractArray, Any}","page":"API","title":"DifferentiationInterface.multibasis","text":"multibasis(backend, a::AbstractArray, inds::AbstractVector)\n\nConstruct the sum of the i-th standard basis arrays in the vector space of a with element type eltype(a), for all i ∈ inds.\n\nNote\n\nIf an AD backend benefits from a more specialized basis array implementation, this function can be extended on the backend type.\n\n\n\n\n\n","category":"method"},{"location":"api/#DifferentiationInterface.prepare!_derivative","page":"API","title":"DifferentiationInterface.prepare!_derivative","text":"prepare!_derivative(f, prep, backend, x, [contexts...]) -> new_prep\nprepare!_derivative(f!, y, prep, backend, x, [contexts...]) -> new_prep\n\nSame behavior as prepare_derivative but can modify an existing prep object to avoid some allocations.\n\nThere is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.\n\ndanger: Danger\nFor efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.prepare!_gradient","page":"API","title":"DifferentiationInterface.prepare!_gradient","text":"prepare!_gradient(f, prep, backend, x, [contexts...]) -> new_prep\n\nSame behavior as prepare_gradient but can modify an existing prep object to avoid some allocations.\n\nThere is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.\n\ndanger: Danger\nFor efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.prepare!_hessian","page":"API","title":"DifferentiationInterface.prepare!_hessian","text":"prepare!_hessian(f, backend, x, [contexts...]) -> new_prep\n\nSame behavior as prepare_hessian but can modify an existing prep object to avoid some allocations.\n\nThere is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.\n\ndanger: Danger\nFor efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.prepare!_hvp","page":"API","title":"DifferentiationInterface.prepare!_hvp","text":"prepare!_hvp(f, backend, x, tx, [contexts...]) -> new_prep\n\nSame behavior as prepare_hvp but can modify an existing prep object to avoid some allocations.\n\nThere is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.\n\ndanger: Danger\nFor efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.prepare!_jacobian","page":"API","title":"DifferentiationInterface.prepare!_jacobian","text":"prepare!_jacobian(f, prep, backend, x, [contexts...]) -> new_prep\nprepare!_jacobian(f!, y, prep, backend, x, [contexts...]) -> new_prep\n\nSame behavior as prepare_jacobian but can modify an existing prep object to avoid some allocations.\n\nThere is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.\n\ndanger: Danger\nFor efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.prepare!_pullback","page":"API","title":"DifferentiationInterface.prepare!_pullback","text":"prepare!_pullback(f, prep, backend, x, ty, [contexts...]) -> new_prep\nprepare!_pullback(f!, y, prep, backend, x, ty, [contexts...]) -> new_prep\n\nSame behavior as prepare_pullback but can modify an existing prep object to avoid some allocations.\n\nThere is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.\n\ndanger: Danger\nFor efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.prepare!_pushforward","page":"API","title":"DifferentiationInterface.prepare!_pushforward","text":"prepare!_pushforward(f, prep, backend, x, tx, [contexts...]) -> new_prep\nprepare!_pushforward(f!, y, prep, backend, x, tx, [contexts...]) -> new_prep\n\nSame behavior as prepare_pushforward but can modify an existing prep object to avoid some allocations.\n\nThere is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.\n\ndanger: Danger\nFor efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.pullback_performance-Tuple{ADTypes.AbstractADType}","page":"API","title":"DifferentiationInterface.pullback_performance","text":"pullback_performance(backend)\n\nReturn PullbackFast or PullbackSlow in a statically predictable way.\n\n\n\n\n\n","category":"method"},{"location":"api/#DifferentiationInterface.pushforward_performance-Tuple{ADTypes.AbstractADType}","page":"API","title":"DifferentiationInterface.pushforward_performance","text":"pushforward_performance(backend)\n\nReturn PushforwardFast or PushforwardSlow in a statically predictable way.\n\n\n\n\n\n","category":"method"},{"location":"api/","page":"API","title":"API","text":"","category":"page"},{"location":"tutorials/advanced/#Advanced-tutorial","page":"Advanced tutorial","title":"Advanced tutorial","text":"","category":"section"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"We present contexts and sparsity handling with DifferentiationInterface.jl.","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"using BenchmarkTools\nusing DifferentiationInterface\nimport ForwardDiff, Zygote\nusing SparseConnectivityTracer: TracerSparsityDetector\nusing SparseMatrixColorings","category":"page"},{"location":"tutorials/advanced/#Contexts","page":"Advanced tutorial","title":"Contexts","text":"","category":"section"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"Assume you want differentiate a multi-argument function with respect to the first argument.","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"f_multiarg(x, c) = c * sum(abs2, x)\nnothing # hide","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"The first way, which works with every backend, is to create a closure:","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"f_singlearg(c) = x -> f_multiarg(x, c)\nnothing # hide","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"Let's see it in action:","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"backend = AutoForwardDiff()\nx = float.(1:3)\n\ngradient(f_singlearg(10), backend, x)","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"However, for performance reasons, it is sometimes preferrable to avoid closures and pass all arguments to the original function. We can do this by wrapping c into a Constant and giving this constant to the gradient operator.","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"gradient(f_multiarg, backend, x, Constant(10))","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"Preparation also works in this case, even if the constant changes before execution:","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"prep_other_constant = prepare_gradient(f_multiarg, backend, x, Constant(-1))\ngradient(f_multiarg, prep_other_constant, backend, x, Constant(10))","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"For additional arguments which act as mutated buffers, the Cache wrapper is the appropriate choice instead of Constant.","category":"page"},{"location":"tutorials/advanced/#Sparsity","page":"Advanced tutorial","title":"Sparsity","text":"","category":"section"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"Sparse AD is very useful when Jacobian or Hessian matrices have a lot of zeros. So let us write functions that satisfy this property.","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"f_sparse_vector(x::AbstractVector) = diff(x .^ 2) + diff(reverse(x .^ 2))\nf_sparse_scalar(x::AbstractVector) = sum(f_sparse_vector(x) .^ 2)\nnothing # hide","category":"page"},{"location":"tutorials/advanced/#Dense-backends","page":"Advanced tutorial","title":"Dense backends","text":"","category":"section"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"When we use the jacobian or hessian operator with a dense backend, we get a dense matrix with plenty of zeros.","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"x = float.(1:8);","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"dense_first_order_backend = AutoForwardDiff()\nJ_dense = jacobian(f_sparse_vector, dense_first_order_backend, x)","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"dense_second_order_backend = SecondOrder(AutoForwardDiff(), AutoZygote())\nH_dense = hessian(f_sparse_scalar, dense_second_order_backend, x)","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"The results are correct but the procedure is very slow. By using a sparse backend, we can get the runtime to increase with the number of nonzero elements, instead of the total number of elements.","category":"page"},{"location":"tutorials/advanced/#Sparse-backends","page":"Advanced tutorial","title":"Sparse backends","text":"","category":"section"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"Recipe to create a sparse backend: combine a dense backend, a sparsity detector and a compatible coloring algorithm inside AutoSparse. The following are reasonable defaults:","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"sparse_first_order_backend = AutoSparse(\n dense_first_order_backend;\n sparsity_detector=TracerSparsityDetector(),\n coloring_algorithm=GreedyColoringAlgorithm(),\n)\n\nsparse_second_order_backend = AutoSparse(\n dense_second_order_backend;\n sparsity_detector=TracerSparsityDetector(),\n coloring_algorithm=GreedyColoringAlgorithm(),\n)\nnothing # hide","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"Now the resulting matrices are sparse:","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"jacobian(f_sparse_vector, sparse_first_order_backend, x)","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"hessian(f_sparse_scalar, sparse_second_order_backend, x)","category":"page"},{"location":"tutorials/advanced/#Sparse-preparation","page":"Advanced tutorial","title":"Sparse preparation","text":"","category":"section"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"In the examples above, we didn't use preparation. Sparse preparation is more costly than dense preparation, but it is even more essential. Indeed, once preparation is done, sparse differentiation is much faster than dense differentiation, because it makes fewer calls to the underlying function.","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"Some result analysis functions from SparseMatrixColorings.jl can help you figure out what the preparation contains. First, it records the sparsity pattern itself (the one returned by the detector).","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"jac_prep = prepare_jacobian(f_sparse_vector, sparse_first_order_backend, x)\nsparsity_pattern(jac_prep)","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"In forward mode, each column of the sparsity pattern gets a color.","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"column_colors(jac_prep)","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"And the colors in turn define non-overlapping groups (for Jacobians at least, Hessians are a bit more complicated).","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"column_groups(jac_prep)","category":"page"},{"location":"tutorials/advanced/#Sparsity-speedup","page":"Advanced tutorial","title":"Sparsity speedup","text":"","category":"section"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"When preparation is used, the speedup due to sparsity becomes very visible in large dimensions.","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"xbig = rand(1000)\nnothing # hide","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"jac_prep_dense = prepare_jacobian(f_sparse_vector, dense_first_order_backend, zero(xbig))\n@benchmark jacobian($f_sparse_vector, $jac_prep_dense, $dense_first_order_backend, $xbig)","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"jac_prep_sparse = prepare_jacobian(f_sparse_vector, sparse_first_order_backend, zero(xbig))\n@benchmark jacobian($f_sparse_vector, $jac_prep_sparse, $sparse_first_order_backend, $xbig)","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"Better memory use can be achieved by pre-allocating the matrix from the preparation result (so that it has the correct structure).","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"jac_buffer = similar(sparsity_pattern(jac_prep_sparse), eltype(xbig))\n@benchmark jacobian!($f_sparse_vector, $jac_buffer, $jac_prep_sparse, $sparse_first_order_backend, $xbig)","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"And for optimal speed, one should write non-allocating and type-stable functions.","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"function f_sparse_vector!(y::AbstractVector, x::AbstractVector)\n n = length(x)\n for i in eachindex(y)\n y[i] = abs2(x[i + 1]) - abs2(x[i]) + abs2(x[n - i]) - abs2(x[n - i + 1])\n end\n return nothing\nend\n\nybig = zeros(length(xbig) - 1)\nf_sparse_vector!(ybig, xbig)\nybig ≈ f_sparse_vector(xbig)","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"In this case, the sparse Jacobian should also become non-allocating (for our specific choice of backend).","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"jac_prep_sparse_nonallocating = prepare_jacobian(f_sparse_vector!, zero(ybig), sparse_first_order_backend, zero(xbig))\njac_buffer = similar(sparsity_pattern(jac_prep_sparse_nonallocating), eltype(xbig))\n@benchmark jacobian!($f_sparse_vector!, $ybig, $jac_buffer, $jac_prep_sparse_nonallocating, $sparse_first_order_backend, $xbig)","category":"page"},{"location":"tutorials/advanced/","page":"Advanced tutorial","title":"Advanced tutorial","text":"","category":"page"},{"location":"explanation/operators/#Operators","page":"Operators","title":"Operators","text":"","category":"section"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"tip: Tip\nIf there are some concepts you do not understand, take a look at the book The Elements of Differentiable Programming (Blondel and Roulet, 2024).","category":"page"},{"location":"explanation/operators/#List-of-operators","page":"Operators","title":"List of operators","text":"","category":"section"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"Given a function f(x) = y, there are several differentiation operators available. The terminology depends on:","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"the type and shape of the input x\nthe type and shape of the output y\nthe order of differentiation","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"Below we list and describe all the operators we support.","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"warning: Warning\nThe package is thoroughly tested with inputs and outputs of the following types: Float64, Vector{Float64} and Matrix{Float64}. We also expect it to work on most kinds of Number and AbstractArray variables. Beyond that, you are in uncharted territory. We voluntarily keep the type annotations minimal, so that passing more complex objects or custom structs might work in some cases, but we make no guarantees about that yet.","category":"page"},{"location":"explanation/operators/#High-level-operators","page":"Operators","title":"High-level operators","text":"","category":"section"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"These operators are computed using only the input x.","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"operator order input x output y operator result type operator result shape\nderivative 1 Number Any similar to y size(y)\nsecond_derivative 2 Number Any similar to y size(y)\ngradient 1 Any Number similar to x size(x)\njacobian 1 AbstractArray AbstractArray AbstractMatrix (length(y), length(x))\nhessian 2 AbstractArray Number AbstractMatrix (length(x), length(x))","category":"page"},{"location":"explanation/operators/#Low-level-operators","page":"Operators","title":"Low-level operators","text":"","category":"section"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"These operators are computed using the input x and another argument t of type NTuple, which contains one or more tangents. You can think of tangents as perturbations propagated through the function; they live either in the same space as x or in the same space as y.","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"operator order input x output y element type of t operator result type operator result shape\npushforward (JVP) 1 Any Any similar to x similar to y size(y)\npullback (VJP) 1 Any Any similar to y similar to x size(x)\nhvp 2 Any Number similar to x similar to x size(x)","category":"page"},{"location":"explanation/operators/#Variants","page":"Operators","title":"Variants","text":"","category":"section"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"Several variants of each operator are defined:","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"out-of-place operators return a new derivative object\nin-place operators mutate the provided derivative object","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"out-of-place in-place out-of-place + primal in-place + primal\nderivative derivative! value_and_derivative value_and_derivative!\nsecond_derivative second_derivative! value_derivative_and_second_derivative value_derivative_and_second_derivative!\ngradient gradient! value_and_gradient value_and_gradient!\nhessian hessian! value_gradient_and_hessian value_gradient_and_hessian!\njacobian jacobian! value_and_jacobian value_and_jacobian!\npushforward pushforward! value_and_pushforward value_and_pushforward!\npullback pullback! value_and_pullback value_and_pullback!\nhvp hvp! gradient_and_hvp gradient_and_hvp!","category":"page"},{"location":"explanation/operators/#Mutation-and-signatures","page":"Operators","title":"Mutation and signatures","text":"","category":"section"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"Two kinds of functions are supported:","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"out-of-place functions f(x) = y\nin-place functions f!(y, x) = nothing","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"warning: Warning\nIn-place functions only work with pushforward, pullback, derivative and jacobian. The other operators hvp, gradient and hessian require scalar outputs, so it makes no sense to mutate the number y.","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"This results in various operator signatures (the necessary arguments and their order):","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"function signature out-of-place operator (returns result) in-place operator (mutates result)\nout-of-place function f op(f, backend, x, [t]) op!(f, result, backend, x, [t])\nin-place function f! op(f!, y, backend, x, [t]) op!(f!, y, result, backend, x, [t])","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"warning: Warning\nThe positional arguments between f/f! and backend are always mutated, regardless of the bang ! in the operator name. In particular, for in-place functions f!(y, x), every variant of every operator will mutate y.","category":"page"},{"location":"explanation/operators/#Preparation","page":"Operators","title":"Preparation","text":"","category":"section"},{"location":"explanation/operators/#Principle","page":"Operators","title":"Principle","text":"","category":"section"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"In many cases, AD can be accelerated if the function has been called at least once (e.g. to record a tape) or if some cache objects are pre-allocated. This preparation procedure is backend-specific, but we expose a common syntax to achieve it.","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"operator preparation (different point) preparation (same point)\nderivative prepare_derivative -\ngradient prepare_gradient -\njacobian prepare_jacobian -\nsecond_derivative prepare_second_derivative -\nhessian prepare_hessian -\npushforward prepare_pushforward prepare_pushforward_same_point\npullback prepare_pullback prepare_pullback_same_point\nhvp prepare_hvp prepare_hvp_same_point","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"In addition, the preparation syntax depends on the number of arguments accepted by the function.","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"function signature preparation signature\nout-of-place function prepare_op(f, backend, x, [t])\nin-place function prepare_op(f!, y, backend, x, [t])","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"Preparation creates an object called prep which contains the the necessary information to speed up an operator and its variants. The idea is that you prepare only once, which can be costly, but then call the operator several times while reusing the same prep.","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"op(f, backend, x, [t]) # slow because it includes preparation\nop(f, prep, backend, x, [t]) # fast because it skips preparation","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"warning: Warning\nThe prep object is the last argument before backend and it is always mutated, regardless of the bang ! in the operator name.","category":"page"},{"location":"explanation/operators/#Reusing-preparation","page":"Operators","title":"Reusing preparation","text":"","category":"section"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"Deciding whether it is safe to reuse the results of preparation is not easy. Here are the general rules that we strive to implement:","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"For different-point preparation, the output prep of prepare_op(f, b, x, [t]) can be reused in op(f, prep, b, other_x, [other_t]), provided that:","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"the inputs x and other_x have the same types and sizes\nthe tangents in t and other_t have the same types and sizes","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"For same-point preparation, the output prep of prepare_op_same_point(f, b, x, [t]) can be reused in op(f, prep, b, x, other_t), provided that:","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"the input x remains exactly the same (as well as any Constant context)\nthe tangents in t and other_t have the same types and sizes","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"warning: Warning\nThese rules hold for the majority of backends, but there are some exceptions. The most important exception is ReverseDiff and its taping mechanism, which is sensitive to control flow inside the function.","category":"page"},{"location":"explanation/operators/","page":"Operators","title":"Operators","text":"","category":"page"},{"location":"dev_guide/#Dev-guide","page":"Dev guide","title":"Dev guide","text":"","category":"section"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"This page is important reading if you want to contribute to DifferentiationInterface.jl. It is not part of the public API and the content below may become outdated, in which case you should refer to the source code as the ground truth.","category":"page"},{"location":"dev_guide/#General-principles","page":"Dev guide","title":"General principles","text":"","category":"section"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"The package is structured around 8 operators:","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"derivative\nsecond_derivative\ngradient\njacobian\nhessian\npushforward\npullback\nhvp","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"Most operators have 4 variants, which look like this in the first order: operator, operator!, value_and_operator, value_and_operator!.","category":"page"},{"location":"dev_guide/#New-operator","page":"Dev guide","title":"New operator","text":"","category":"section"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"To implement a new operator for an existing backend, you need to write 5 methods: 1 for preparation and 4 corresponding to the variants of the operator (see above). For first-order operators, you may also want to support in-place functions, which requires another 5 methods (defined on f! instead of f).","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"The method prepare_operator must output a prep object of the correct type. For instance, prepare_gradient(f, backend, x) must return a DifferentiationInterface.GradientPrep. Assuming you don't need any preparation for said operator, you can use the trivial prep that are already defined, like DifferentiationInterface.NoGradientPrep. Otherwise, define a custom struct like MyGradientPrep <: DifferentiationInterface.GradientPrep and put the necessary storage in there.","category":"page"},{"location":"dev_guide/#New-backend","page":"Dev guide","title":"New backend","text":"","category":"section"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"If you want to implement a new backend, for instance because you developed a new AD package called SuperDiff, please open a pull request to DifferentiationInterface.jl. Your AD package needs to be registered first.","category":"page"},{"location":"dev_guide/#Core-code","page":"Dev guide","title":"Core code","text":"","category":"section"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"In the main package, you should define a new struct SuperDiffBackend which subtypes ADTypes.AbstractADType, and endow it with the fields you need to parametrize your differentiation routines. You also have to define ADTypes.mode and DifferentiationInterface.inplace_support on SuperDiffBackend.","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"info: Info\nIn the end, this backend struct will need to be contributed to ADTypes.jl. However, putting it in the DifferentiationInterface.jl PR is a good first step for debugging.","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"In a package extension named DifferentiationInterfaceSuperDiffExt, you need to implement at least pushforward or pullback (and their variants). The exact requirements depend on the differentiation mode you chose:","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"backend mode pushforward necessary pullback necessary\nADTypes.ForwardMode yes no\nADTypes.ReverseMode no yes\nADTypes.ForwardOrReverseMode yes yes\nADTypes.SymbolicMode yes yes","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"Every other operator can be deduced from these two, but you can gain efficiency by implementing additional operators.","category":"page"},{"location":"dev_guide/#Tests-and-docs","page":"Dev guide","title":"Tests and docs","text":"","category":"section"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"Once that is done, you need to add your new backend to the test suite. Test files should be gathered in a folder named SuperDiff inside DifferentiationInterface/test/Back. They should use DifferentiationInterfaceTest.jl to check correctness against the default scenarios. Take inspiration from the tests of other backends to write your own. To activate tests in CI, modify the test workflow and add your package to the list. To run the tests locally, replace the following line in DifferentiationInterface/test/runtests.jl","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"GROUP = get(ENV, \"JULIA_DI_TEST_GROUP\", \"All\")","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"with the much cheaper version","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"GROUP = get(ENV, \"JULIA_DI_TEST_GROUP\", \"Back/SuperDiff\")","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"but don't forget to switch it back before pushing.","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"Finally, you need to add your backend to the documentation, modifying every page that involves a list of backends (including the README.md).","category":"page"},{"location":"dev_guide/","page":"Dev guide","title":"Dev guide","text":"","category":"page"},{"location":"explanation/advanced/#Advanced-features","page":"Advanced features","title":"Advanced features","text":"","category":"section"},{"location":"explanation/advanced/#Contexts","page":"Advanced features","title":"Contexts","text":"","category":"section"},{"location":"explanation/advanced/#Additional-arguments","page":"Advanced features","title":"Additional arguments","text":"","category":"section"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"For all operators provided DifferentiationInterface, there can be only one differentiated (or \"active\") argument, which we call x. However, the release v0.6 introduced the possibility of additional \"context\" arguments, which are not differentiated but still passed to the function after x.","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"Contexts can be useful if you have a function y = f(x, a, b, c, ...) or f!(y, x, a, b, c, ...) and you want derivatives of y with respect to x only. Another option would be creating a closure, but that is sometimes undesirable.","category":"page"},{"location":"explanation/advanced/#Types-of-contexts","page":"Advanced features","title":"Types of contexts","text":"","category":"section"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"Every context argument must be wrapped in a subtype of Context and come after the differentiated input x. Right now, there are two kinds of context: Constant and Cache.","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"warning: Warning\nThis feature is still experimental and will not be supported by all backends. At the moment:Constant is supported by all backends except symbolic ones\nCache is only supported by finite difference backends and AutoForwardDiff, but it is not yet optimized","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"Semantically, both of these calls compute the partial gradient of f(x, c) with respect to x, but they consider c differently:","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"gradient(f, backend, x, Constant(c))\ngradient(f, backend, x, Cache(c))","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"In the first call, c is kept unchanged throughout the function evaluation. In the second call, c can be mutated with values computed during the function.","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"Importantly, one can prepare an operator with an arbitrary value c' of the Constant (subject to the usual restrictions on preparation). The values in a provided Cache never matter anyway.","category":"page"},{"location":"explanation/advanced/#Sparsity","page":"Advanced features","title":"Sparsity","text":"","category":"section"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"When faced with sparse Jacobian or Hessian matrices, one can take advantage of their sparsity pattern to speed up the computation. DifferentiationInterface does this automatically if you pass a backend of type AutoSparse.","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"tip: Tip\nTo know more about sparse AD, read the survey What Color Is Your Jacobian? Graph Coloring for Computing Derivatives (Gebremedhin et al., 2005).","category":"page"},{"location":"explanation/advanced/#AutoSparse-object","page":"Advanced features","title":"AutoSparse object","text":"","category":"section"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"AutoSparse backends only support jacobian and hessian (as well as their variants), because other operators do not output matrices. An AutoSparse backend must be constructed from three ingredients:","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"An underlying (dense) backend, which can be SecondOrder or anything from ADTypes.jl\nA sparsity pattern detector like:\nTracerSparsityDetector from SparseConnectivityTracer.jl\nSymbolicsSparsityDetector from Symbolics.jl\nDenseSparsityDetector from DifferentiationInterface.jl (beware that this detector only gives a locally valid pattern)\nKnownJacobianSparsityDetector or KnownHessianSparsityDetector from ADTypes.jl (if you already know the pattern)\nA coloring algorithm from SparseMatrixColorings.jl, such as:\nGreedyColoringAlgorithm (our generic recommendation)\nConstantColoringAlgorithm (if you have already computed the optimal coloring and always want to return it)","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"note: Note\nSymbolic backends have built-in sparsity handling, so AutoSparse(AutoSymbolics()) and AutoSparse(AutoFastDifferentiation()) do not need additional configuration for pattern detection or coloring.","category":"page"},{"location":"explanation/advanced/#Cost-of-sparse-preparation","page":"Advanced features","title":"Cost of sparse preparation","text":"","category":"section"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"The preparation step of jacobian or hessian with an AutoSparse backend can be long, because it needs to detect the sparsity pattern and perform a matrix coloring. But after preparation, the more zeros are present in the matrix, the greater the speedup will be compared to dense differentiation.","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"danger: Danger\nThe result of preparation for an AutoSparse backend cannot be reused if the sparsity pattern changes.","category":"page"},{"location":"explanation/advanced/#Tuning-the-coloring-algorithm","page":"Advanced features","title":"Tuning the coloring algorithm","text":"","category":"section"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"The complexity of sparse Jacobians or Hessians grows with the number of distinct colors in a coloring of the sparsity pattern. To reduce this number of colors, GreedyColoringAlgorithm has two main settings: the order used for vertices and the decompression method. Depending on your use case, you may want to modify either of these options to increase performance. See the documentation of SparseMatrixColorings.jl for details.","category":"page"},{"location":"explanation/advanced/#Batch-mode","page":"Advanced features","title":"Batch mode","text":"","category":"section"},{"location":"explanation/advanced/#Multiple-tangents","page":"Advanced features","title":"Multiple tangents","text":"","category":"section"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"The jacobian and hessian operators compute matrices by repeatedly applying lower-level operators (pushforward, pullback or hvp) to a set of tangents. The tangents usually correspond to basis elements of the appropriate vector space. We could call the lower-level operator on each tangent separately, but some packages (ForwardDiff.jl and Enzyme.jl) have optimized implementations to handle multiple tangents at once.","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"This behavior is often called \"vector mode\" AD, but we call it \"batch mode\" to avoid confusion with Julia's Vector type. As a matter of fact, the optimal batch size B (number of simultaneous tangents) is usually very small, so tangents are passed within an NTuple and not a Vector. When the underlying vector space has dimension N, the operators jacobian and hessian process lceil N B rceil batches of size B each.","category":"page"},{"location":"explanation/advanced/#Optimal-batch-size","page":"Advanced features","title":"Optimal batch size","text":"","category":"section"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"For every backend which does not support batch mode, the batch size is set to B = 1. But for AutoForwardDiff and AutoEnzyme, more complicated rules apply. If the backend object has a pre-determined batch size B_0, then we always set B = B_0. In particular, this will throw errors when N B_0. On the other hand, without a pre-determined batch size, we apply backend-specific heuristics to pick B based on N.","category":"page"},{"location":"explanation/advanced/","page":"Advanced features","title":"Advanced features","text":"","category":"page"},{"location":"","page":"Home","title":"Home","text":"(Image: DifferentiationInterface Logo)","category":"page"},{"location":"#DifferentiationInterface","page":"Home","title":"DifferentiationInterface","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"(Image: Build Status) (Image: Coverage) (Image: Code Style: Blue) (Image: ColPrac: Contributor's Guide on Collaborative Practices for Community Packages) (Image: DOI)","category":"page"},{"location":"","page":"Home","title":"Home","text":"Package Docs\nDifferentiationInterface (Image: Stable) (Image: Dev)\nDifferentiationInterfaceTest (Image: Stable) (Image: Dev)","category":"page"},{"location":"","page":"Home","title":"Home","text":"An interface to various automatic differentiation (AD) backends in Julia.","category":"page"},{"location":"#Goal","page":"Home","title":"Goal","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"This package provides a unified syntax to differentiate functions, including:","category":"page"},{"location":"","page":"Home","title":"Home","text":"First- and second-order operators (gradients, Jacobians, Hessians and more)\nIn-place and out-of-place differentiation\nPreparation mechanism (e.g. to pre-allocate a cache or record a tape)\nBuilt-in sparsity handling\nThorough validation on standard inputs and outputs (numbers, vectors, matrices)\nTesting and benchmarking utilities accessible to users with DifferentiationInterfaceTest","category":"page"},{"location":"#Compatibility","page":"Home","title":"Compatibility","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"We support the following backends defined by ADTypes.jl:","category":"page"},{"location":"","page":"Home","title":"Home","text":"ChainRulesCore.jl\nDiffractor.jl\nEnzyme.jl\nFastDifferentiation.jl\nFiniteDiff.jl\nFiniteDifferences.jl\nForwardDiff.jl\nMooncake.jl\nPolyesterForwardDiff.jl\nReverseDiff.jl\nSymbolics.jl\nTracker.jl\nZygote.jl","category":"page"},{"location":"","page":"Home","title":"Home","text":"Note that in some cases, going through DifferentiationInterface.jl might be slower than a direct call to the backend's API. This is mostly true for Enzyme.jl, whose handling of activities and multiple arguments unlocks additional performance. We are working on this challenge, and welcome any suggestions or contributions. Meanwhile, if differentiation fails or takes too long, consider using Enzyme.jl directly.","category":"page"},{"location":"#Installation","page":"Home","title":"Installation","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"To install the stable version of the package, run the following code in a Julia REPL:","category":"page"},{"location":"","page":"Home","title":"Home","text":"using Pkg\n\nPkg.add(\"DifferentiationInterface\")","category":"page"},{"location":"","page":"Home","title":"Home","text":"To install the development version, run this instead:","category":"page"},{"location":"","page":"Home","title":"Home","text":"using Pkg\n\nPkg.add(\n url=\"https://github.com/JuliaDiff/DifferentiationInterface.jl\",\n subdir=\"DifferentiationInterface\"\n)","category":"page"},{"location":"#Example","page":"Home","title":"Example","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"using DifferentiationInterface\nimport ForwardDiff, Enzyme, Zygote # AD backends you want to use \n\nf(x) = sum(abs2, x)\n\nx = [1.0, 2.0]\n\nvalue_and_gradient(f, AutoForwardDiff(), x) # returns (5.0, [2.0, 4.0]) with ForwardDiff.jl\nvalue_and_gradient(f, AutoEnzyme(), x) # returns (5.0, [2.0, 4.0]) with Enzyme.jl\nvalue_and_gradient(f, AutoZygote(), x) # returns (5.0, [2.0, 4.0]) with Zygote.jl","category":"page"},{"location":"","page":"Home","title":"Home","text":"To improve your performance by up to several orders of magnitude compared to this example, take a look at the tutorial and its section on operator preparation.","category":"page"},{"location":"#Citation","page":"Home","title":"Citation","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Please cite both DifferentiationInterface.jl and its inspiration AbstractDifferentiation.jl, using the provided CITATION.bib file.","category":"page"},{"location":"","page":"Home","title":"Home","text":"","category":"page"},{"location":"explanation/backends/#Backends","page":"Backends","title":"Backends","text":"","category":"section"},{"location":"explanation/backends/#List","page":"Backends","title":"List","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"We support the following dense backend choices from ADTypes.jl:","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"AutoChainRules\nAutoDiffractor\nAutoEnzyme\nAutoFastDifferentiation\nAutoFiniteDiff\nAutoFiniteDifferences\nAutoForwardDiff\nAutoMooncake\nAutoPolyesterForwardDiff\nAutoReverseDiff\nAutoSymbolics\nAutoTracker\nAutoZygote","category":"page"},{"location":"explanation/backends/#Features","page":"Backends","title":"Features","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"Given a backend object, you can use:","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"check_available to know whether the required AD package is loaded\ncheck_inplace to know whether the backend supports in-place functions (all backends support out-of-place functions)","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"In theory, all we need from each backend is either a pushforward or a pullback: we can deduce every other operator from these two. In practice, many AD backends have custom implementations for high-level operators like gradient or jacobian, which we reuse whenever possible.","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"details: Details\nIn the rough summary table below,✅ means that we reuse the custom implementation from the backend;\n❌ means that a custom implementation doesn't exist, so we use our default fallbacks;\n🔀 means it's complicated or not done yet. pf pb der grad jac hess hvp der2\nAutoChainRules ❌ ✅ ❌ ❌ ❌ ❌ ❌ ❌\nAutoDiffractor ✅ ❌ ❌ ❌ ❌ ❌ ❌ ❌\nAutoEnzyme (forward) ✅ ❌ ❌ ✅ ✅ ❌ ❌ ❌\nAutoEnzyme (reverse) ❌ ✅ ❌ ✅ ✅ ❌ 🔀 ❌\nAutoFastDifferentiation ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅\nAutoFiniteDiff 🔀 ❌ ✅ ✅ ✅ ✅ ❌ ❌\nAutoFiniteDifferences 🔀 ❌ ❌ ✅ ✅ ❌ ❌ ❌\nAutoForwardDiff ✅ ❌ ✅ ✅ ✅ ✅ ✅ ✅\nAutoMooncake ❌ ✅ ❌ ❌ ❌ ❌ ❌ ❌\nAutoPolyesterForwardDiff 🔀 ❌ 🔀 ✅ ✅ 🔀 🔀 🔀\nAutoReverseDiff ❌ 🔀 ❌ ✅ ✅ ✅ ❌ ❌\nAutoSymbolics ✅ ❌ ✅ ✅ ✅ ✅ ✅ ✅\nAutoTracker ❌ ✅ ❌ ✅ ❌ ❌ ❌ ❌\nAutoZygote ❌ ✅ ❌ ✅ ✅ ✅ 🔀 ❌","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"Moreover, each context type is supported by a specific subset of backends:","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":" Constant\nAutoChainRules ✅\nAutoDiffractor ❌\nAutoEnzyme (forward) ✅\nAutoEnzyme (reverse) ✅\nAutoFastDifferentiation ❌\nAutoFiniteDiff ✅\nAutoFiniteDifferences ✅\nAutoForwardDiff ✅\nAutoMooncake ✅\nAutoPolyesterForwardDiff ✅\nAutoReverseDiff ✅\nAutoSymbolics ❌\nAutoTracker ✅\nAutoZygote ✅","category":"page"},{"location":"explanation/backends/#Second-order","page":"Backends","title":"Second order","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"For second-order operators like second_derivative, hessian and hvp, there are two main options. You can either use a single backend, or combine two of them within the SecondOrder struct:","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"backend = SecondOrder(outer_backend, inner_backend)","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"The inner backend will be called first, and the outer backend will differentiate the generated code. In general, using a forward outer backend over a reverse inner backend will yield the best performance.","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"danger: Danger\nSecond-order AD is tricky, and many backend combinations will fail (even if you combine a backend with itself). Be ready to experiment and open issues if necessary.","category":"page"},{"location":"explanation/backends/#Backend-switch","page":"Backends","title":"Backend switch","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"The wrapper DifferentiateWith allows you to switch between backends. It takes a function f and specifies that f should be differentiated with the substitute backend of your choice, instead of whatever true backend the surrounding code is trying to use. In other words, when someone tries to differentiate dw = DifferentiateWith(f, substitute_backend) with true_backend, then substitute_backend steps in and true_backend does not dive into the function f itself. At the moment, DifferentiateWith only works when true_backend is either ForwardDiff.jl or a ChainRules.jl-compatible backend.","category":"page"},{"location":"explanation/backends/#Implementations","page":"Backends","title":"Implementations","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"What follows is a list of implementation details from the package extensions of DifferentiationInterface.jl It is not part of the public API or protected by semantic versioning, and it may become outdated. When in doubt, refer to the code itself.","category":"page"},{"location":"explanation/backends/#ChainRulesCore","page":"Backends","title":"ChainRulesCore","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"We only implement pullback, using the RuleConfig mechanism to call back into AD. Same-point preparation runs the forward sweep and returns the pullback closure.","category":"page"},{"location":"explanation/backends/#Diffractor","page":"Backends","title":"Diffractor","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"We only implement pushforward.","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"danger: Danger\nThe latest releases of Diffractor broke DifferentiationInterface.","category":"page"},{"location":"explanation/backends/#Enzyme","page":"Backends","title":"Enzyme","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"Depending on the mode attribute inside AutoEnzyme, we implement either pushforward or pullback based on Enzyme.autodiff. When necessary, preparation chooses a number of chunks (for gradient and jacobian in forward mode, for jacobian only in reverse mode).","category":"page"},{"location":"explanation/backends/#FastDifferentiation","page":"Backends","title":"FastDifferentiation","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"For every operator, preparation generates an executable function from the symbolic expression of the differentiated function.","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"warning: Warning\nPreparation can be very slow for symbolic AD.","category":"page"},{"location":"explanation/backends/#FiniteDiff","page":"Backends","title":"FiniteDiff","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"Whenever possible, preparation creates a cache object. Pushforward is implemented rather slowly using a closure.","category":"page"},{"location":"explanation/backends/#FiniteDifferences","page":"Backends","title":"FiniteDifferences","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"Nothing specific to mention.","category":"page"},{"location":"explanation/backends/#ForwardDiff","page":"Backends","title":"ForwardDiff","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"We implement pushforward directly using Dual numbers, and preparation allocates the necessary space. For higher level operators, preparation creates a config object, which can be type-unstable.","category":"page"},{"location":"explanation/backends/#PolyesterForwardDiff","page":"Backends","title":"PolyesterForwardDiff","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"Most operators fall back on AutoForwardDiff.","category":"page"},{"location":"explanation/backends/#ReverseDiff","page":"Backends","title":"ReverseDiff","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"Wherever possible, preparation records a tape of the function's execution. This tape is computed from the arguments x and contexts... provided at preparation time. It is control-flow dependent, so only one branch is recorded at each if statement.","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"danger: Danger\nIf your function has value-specific control flow (like if x[1] > 0 or if c == 1), you may get silently wrong results whenever it takes new branches that were not taken during preparation. You must make sure to run preparation with an input and contexts whose values trigger the correct control flow for future executions.","category":"page"},{"location":"explanation/backends/#Symbolics","page":"Backends","title":"Symbolics","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"For all operators, preparation generates an executable function from the symbolic expression of the differentiated function.","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"warning: Warning\nPreparation can be very slow for symbolic AD.","category":"page"},{"location":"explanation/backends/#Mooncake","page":"Backends","title":"Mooncake","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"For pullback, preparation builds the reverse rule of the function.","category":"page"},{"location":"explanation/backends/#Tracker","page":"Backends","title":"Tracker","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"We implement pullback based on Tracker.back. Same-point preparation runs the forward sweep and returns the pullback closure at x.","category":"page"},{"location":"explanation/backends/#Zygote","page":"Backends","title":"Zygote","text":"","category":"section"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"We implement pullback based on Zygote.pullback. Same-point preparation runs the forward sweep and returns the pullback closure at x.","category":"page"},{"location":"explanation/backends/","page":"Backends","title":"Backends","text":"","category":"page"},{"location":"tutorials/basic/#Basic-tutorial","page":"Basic tutorial","title":"Basic tutorial","text":"","category":"section"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"We present the main features of DifferentiationInterface.jl.","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"using DifferentiationInterface","category":"page"},{"location":"tutorials/basic/#Computing-a-gradient","page":"Basic tutorial","title":"Computing a gradient","text":"","category":"section"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"A common use case of automatic differentiation (AD) is optimizing real-valued functions with first- or second-order methods. Let's define a simple objective (the squared norm) and a random input vector","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"f(x) = sum(abs2, x)","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"x = collect(1.0:5.0)","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"To compute its gradient, we need to choose a \"backend\", i.e. an AD package to call under the hood. Most backend types are defined by ADTypes.jl and re-exported by DifferentiationInterface.jl.","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"ForwardDiff.jl is very generic and efficient for low-dimensional inputs, so it's a good starting point:","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"import ForwardDiff\n\nbackend = AutoForwardDiff()","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"tip: Tip\nTo avoid name conflicts, load AD packages with import instead of using. Indeed, most AD packages also export operators like gradient and jacobian, but you only want to use the ones from DifferentiationInterface.jl.","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"Now you can use the following syntax to compute the gradient:","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"gradient(f, backend, x)","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"Was that fast? BenchmarkTools.jl helps you answer that question.","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"using BenchmarkTools\n\n@benchmark gradient($f, $backend, $x)","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"Not bad, but you can do better.","category":"page"},{"location":"tutorials/basic/#Overwriting-a-gradient","page":"Basic tutorial","title":"Overwriting a gradient","text":"","category":"section"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"Since you know how much space your gradient will occupy (the same as your input x), you can pre-allocate that memory and offer it to AD. Some backends get a speed boost from this trick.","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"grad = similar(x)\ngradient!(f, grad, backend, x)\ngrad # has been mutated","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"The bang indicates that one of the arguments of gradient! might be mutated. More precisely, our convention is that every positional argument between the function and the backend is mutated.","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"@benchmark gradient!($f, $grad, $backend, $x)","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"For some reason the in-place version is not much better than your first attempt. However, it makes fewer allocations, thanks to the gradient vector you provided. Don't worry, you can get even more performance.","category":"page"},{"location":"tutorials/basic/#Preparing-for-multiple-gradients","page":"Basic tutorial","title":"Preparing for multiple gradients","text":"","category":"section"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"Internally, ForwardDiff.jl creates some data structures to keep track of things. These objects can be reused between gradient computations, even on different input values. We abstract away the preparation step behind a backend-agnostic syntax:","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"prep = prepare_gradient(f, backend, zero(x))","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"You don't need to know what this object is, you just need to pass it to the gradient operator. Note that preparation does not depend on the actual components of the vector x, just on its type and size. You can thus reuse the prep for different values of the input.","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"grad = similar(x)\ngradient!(f, grad, prep, backend, x)\ngrad # has been mutated","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"Preparation makes the gradient computation much faster, and (in this case) allocation-free.","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"@benchmark gradient!($f, $grad, $prep, $backend, $x)","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"Beware that the prep object is nearly always mutated by differentiation operators, even though it is given as the last positional argument.","category":"page"},{"location":"tutorials/basic/#Switching-backends","page":"Basic tutorial","title":"Switching backends","text":"","category":"section"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"The whole point of DifferentiationInterface.jl is that you can easily experiment with different AD solutions. Typically, for gradients, reverse mode AD might be a better fit, so let's try Zygote.jl!","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"import Zygote\n\nbackend2 = AutoZygote()","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"Once the backend is created, things run smoothly with exactly the same syntax as before:","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"gradient(f, backend2, x)","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"And you can run the same benchmarks to see what you gained (although such a small input may not be realistic):","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"prep2 = prepare_gradient(f, backend2, zero(x))\n\n@benchmark gradient!($f, $grad, $prep2, $backend2, $x)","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"In short, DifferentiationInterface.jl allows for easy testing and comparison of AD backends. If you want to go further, check out the documentation of DifferentiationInterfaceTest.jl. This related package provides benchmarking utilities to compare backends and help you select the one that is best suited for your problem.","category":"page"},{"location":"tutorials/basic/","page":"Basic tutorial","title":"Basic tutorial","text":"","category":"page"}] +} diff --git a/DifferentiationInterface/v0.6.18/siteinfo.js b/DifferentiationInterface/v0.6.18/siteinfo.js new file mode 100644 index 000000000..ca291afcf --- /dev/null +++ b/DifferentiationInterface/v0.6.18/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.6.18"; diff --git a/DifferentiationInterface/v0.6.18/tutorials/advanced/index.html b/DifferentiationInterface/v0.6.18/tutorials/advanced/index.html new file mode 100644 index 000000000..939ad47af --- /dev/null +++ b/DifferentiationInterface/v0.6.18/tutorials/advanced/index.html @@ -0,0 +1,146 @@ + +Advanced tutorial · DifferentiationInterface.jl
GitHub

Advanced tutorial

We present contexts and sparsity handling with DifferentiationInterface.jl.

using BenchmarkTools
+using DifferentiationInterface
+import ForwardDiff, Zygote
+using SparseConnectivityTracer: TracerSparsityDetector
+using SparseMatrixColorings

Contexts

Assume you want differentiate a multi-argument function with respect to the first argument.

f_multiarg(x, c) = c * sum(abs2, x)

The first way, which works with every backend, is to create a closure:

f_singlearg(c) = x -> f_multiarg(x, c)

Let's see it in action:

backend = AutoForwardDiff()
+x = float.(1:3)
+
+gradient(f_singlearg(10), backend, x)
3-element Vector{Float64}:
+ 20.0
+ 40.0
+ 60.0

However, for performance reasons, it is sometimes preferrable to avoid closures and pass all arguments to the original function. We can do this by wrapping c into a Constant and giving this constant to the gradient operator.

gradient(f_multiarg, backend, x, Constant(10))
3-element Vector{Float64}:
+ 20.0
+ 40.0
+ 60.0

Preparation also works in this case, even if the constant changes before execution:

prep_other_constant = prepare_gradient(f_multiarg, backend, x, Constant(-1))
+gradient(f_multiarg, prep_other_constant, backend, x, Constant(10))
3-element Vector{Float64}:
+ 20.0
+ 40.0
+ 60.0

For additional arguments which act as mutated buffers, the Cache wrapper is the appropriate choice instead of Constant.

Sparsity

Sparse AD is very useful when Jacobian or Hessian matrices have a lot of zeros. So let us write functions that satisfy this property.

f_sparse_vector(x::AbstractVector) = diff(x .^ 2) + diff(reverse(x .^ 2))
+f_sparse_scalar(x::AbstractVector) = sum(f_sparse_vector(x) .^ 2)

Dense backends

When we use the jacobian or hessian operator with a dense backend, we get a dense matrix with plenty of zeros.

x = float.(1:8);
8-element Vector{Float64}:
+ 1.0
+ 2.0
+ 3.0
+ 4.0
+ 5.0
+ 6.0
+ 7.0
+ 8.0
dense_first_order_backend = AutoForwardDiff()
+J_dense = jacobian(f_sparse_vector, dense_first_order_backend, x)
7×8 Matrix{Float64}:
+ -2.0   4.0   0.0   0.0    0.0    0.0   14.0  -16.0
+  0.0  -4.0   6.0   0.0    0.0   12.0  -14.0    0.0
+  0.0   0.0  -6.0   8.0   10.0  -12.0    0.0    0.0
+  0.0   0.0   0.0   0.0    0.0    0.0    0.0    0.0
+  0.0   0.0   6.0  -8.0  -10.0   12.0    0.0    0.0
+  0.0   4.0  -6.0   0.0    0.0  -12.0   14.0    0.0
+  2.0  -4.0   0.0   0.0    0.0    0.0  -14.0   16.0
dense_second_order_backend = SecondOrder(AutoForwardDiff(), AutoZygote())
+H_dense = hessian(f_sparse_scalar, dense_second_order_backend, x)
8×8 Matrix{Float64}:
+  112.0   -32.0     0.0     0.0     0.0     0.0  -112.0   128.0
+  -32.0    96.0   -96.0     0.0     0.0  -192.0   448.0  -256.0
+    0.0   -96.0   256.0  -192.0  -240.0   576.0  -336.0     0.0
+    0.0     0.0  -192.0   224.0   320.0  -384.0     0.0     0.0
+    0.0     0.0  -240.0   320.0   368.0  -480.0     0.0     0.0
+    0.0  -192.0   576.0  -384.0  -480.0  1120.0  -672.0     0.0
+ -112.0   448.0  -336.0     0.0     0.0  -672.0  1536.0  -896.0
+  128.0  -256.0     0.0     0.0     0.0     0.0  -896.0  1120.0

The results are correct but the procedure is very slow. By using a sparse backend, we can get the runtime to increase with the number of nonzero elements, instead of the total number of elements.

Sparse backends

Recipe to create a sparse backend: combine a dense backend, a sparsity detector and a compatible coloring algorithm inside AutoSparse. The following are reasonable defaults:

sparse_first_order_backend = AutoSparse(
+    dense_first_order_backend;
+    sparsity_detector=TracerSparsityDetector(),
+    coloring_algorithm=GreedyColoringAlgorithm(),
+)
+
+sparse_second_order_backend = AutoSparse(
+    dense_second_order_backend;
+    sparsity_detector=TracerSparsityDetector(),
+    coloring_algorithm=GreedyColoringAlgorithm(),
+)

Now the resulting matrices are sparse:

jacobian(f_sparse_vector, sparse_first_order_backend, x)
7×8 SparseArrays.SparseMatrixCSC{Float64, Int64} with 26 stored entries:
+ -2.0   4.0    ⋅     ⋅      ⋅      ⋅    14.0  -16.0
+   ⋅   -4.0   6.0    ⋅      ⋅    12.0  -14.0     ⋅ 
+   ⋅     ⋅   -6.0   8.0   10.0  -12.0     ⋅      ⋅ 
+   ⋅     ⋅     ⋅    0.0    0.0     ⋅      ⋅      ⋅ 
+   ⋅     ⋅    6.0  -8.0  -10.0   12.0     ⋅      ⋅ 
+   ⋅    4.0  -6.0    ⋅      ⋅   -12.0   14.0     ⋅ 
+  2.0  -4.0    ⋅     ⋅      ⋅      ⋅   -14.0   16.0
hessian(f_sparse_scalar, sparse_second_order_backend, x)
8×8 SparseArrays.SparseMatrixCSC{Float64, Int64} with 40 stored entries:
+  112.0   -32.0      ⋅       ⋅       ⋅       ⋅   -112.0   128.0
+  -32.0    96.0   -96.0      ⋅       ⋅   -192.0   448.0  -256.0
+     ⋅    -96.0   256.0  -192.0  -240.0   576.0  -336.0      ⋅ 
+     ⋅       ⋅   -192.0   224.0   320.0  -384.0      ⋅       ⋅ 
+     ⋅       ⋅   -240.0   320.0   368.0  -480.0      ⋅       ⋅ 
+     ⋅   -192.0   576.0  -384.0  -480.0  1120.0  -672.0      ⋅ 
+ -112.0   448.0  -336.0      ⋅       ⋅   -672.0  1536.0  -896.0
+  128.0  -256.0      ⋅       ⋅       ⋅       ⋅   -896.0  1120.0

Sparse preparation

In the examples above, we didn't use preparation. Sparse preparation is more costly than dense preparation, but it is even more essential. Indeed, once preparation is done, sparse differentiation is much faster than dense differentiation, because it makes fewer calls to the underlying function.

Some result analysis functions from SparseMatrixColorings.jl can help you figure out what the preparation contains. First, it records the sparsity pattern itself (the one returned by the detector).

jac_prep = prepare_jacobian(f_sparse_vector, sparse_first_order_backend, x)
+sparsity_pattern(jac_prep)
7×8 SparseArrays.SparseMatrixCSC{Bool, Int64} with 26 stored entries:
+ 1  1  ⋅  ⋅  ⋅  ⋅  1  1
+ ⋅  1  1  ⋅  ⋅  1  1  ⋅
+ ⋅  ⋅  1  1  1  1  ⋅  ⋅
+ ⋅  ⋅  ⋅  1  1  ⋅  ⋅  ⋅
+ ⋅  ⋅  1  1  1  1  ⋅  ⋅
+ ⋅  1  1  ⋅  ⋅  1  1  ⋅
+ 1  1  ⋅  ⋅  ⋅  ⋅  1  1

In forward mode, each column of the sparsity pattern gets a color.

column_colors(jac_prep)
8-element Vector{Int64}:
+ 1
+ 2
+ 1
+ 2
+ 3
+ 4
+ 3
+ 4

And the colors in turn define non-overlapping groups (for Jacobians at least, Hessians are a bit more complicated).

column_groups(jac_prep)
4-element Vector{SubArray{Int64, 1, Vector{Int64}, Tuple{UnitRange{Int64}}, true}}:
+ [1, 3]
+ [2, 4]
+ [5, 7]
+ [6, 8]

Sparsity speedup

When preparation is used, the speedup due to sparsity becomes very visible in large dimensions.

xbig = rand(1000)
jac_prep_dense = prepare_jacobian(f_sparse_vector, dense_first_order_backend, zero(xbig))
+@benchmark jacobian($f_sparse_vector, $jac_prep_dense, $dense_first_order_backend, $xbig)
BenchmarkTools.Trial: 436 samples with 1 evaluation.
+ Range (min … max):   4.645 ms … 163.316 ms  ┊ GC (min … max):  9.04% … 96.90%
+ Time  (median):      5.256 ms               ┊ GC (median):    15.82%
+ Time  (mean ± σ):   11.678 ms ±  26.198 ms  ┊ GC (mean ± σ):  48.62% ± 19.91%
+
+  █▂                                                            
+  ██▇█▆▁██▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▅▅▁▁▁▁▁▆ ▆
+  4.65 ms       Histogram: log(frequency) by time       160 ms <
+
+ Memory estimate: 57.63 MiB, allocs estimate: 1515.
jac_prep_sparse = prepare_jacobian(f_sparse_vector, sparse_first_order_backend, zero(xbig))
+@benchmark jacobian($f_sparse_vector, $jac_prep_sparse, $sparse_first_order_backend, $xbig)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
+ Range (min … max):  21.530 μs …  4.192 ms  ┊ GC (min … max):  0.00% … 98.76%
+ Time  (median):     27.461 μs              ┊ GC (median):     0.00%
+ Time  (mean ± σ):   36.130 μs ± 80.223 μs  ┊ GC (mean ± σ):  12.69% ±  7.31%
+
+   █▇▆▆                                                        
+  ▅████▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▁▁▂▂▂▂▁▁▁▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▁▁▁▁▁▁▂▂▃▂ ▃
+  21.5 μs         Histogram: frequency by time         139 μs <
+
+ Memory estimate: 305.31 KiB, allocs estimate: 27.

Better memory use can be achieved by pre-allocating the matrix from the preparation result (so that it has the correct structure).

jac_buffer = similar(sparsity_pattern(jac_prep_sparse), eltype(xbig))
+@benchmark jacobian!($f_sparse_vector, $jac_buffer, $jac_prep_sparse, $sparse_first_order_backend, $xbig)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
+ Range (min … max):  18.414 μs …  4.334 ms  ┊ GC (min … max):  0.00% … 98.82%
+ Time  (median):     23.869 μs              ┊ GC (median):     0.00%
+ Time  (mean ± σ):   31.194 μs ± 81.547 μs  ┊ GC (mean ± σ):  10.42% ±  5.96%
+
+  ▅▆▆█▆▃▂▁▁                                               ▂▃▂ ▂
+  █████████▆▅▇▆▆▅▅▅▅▆▄▅▁▁▁▁▁▁▁▁▁▁▁▁▃▁▁▁▁▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▇███ █
+  18.4 μs      Histogram: log(frequency) by time       110 μs <
+
+ Memory estimate: 234.75 KiB, allocs estimate: 18.

And for optimal speed, one should write non-allocating and type-stable functions.

function f_sparse_vector!(y::AbstractVector, x::AbstractVector)
+    n = length(x)
+    for i in eachindex(y)
+        y[i] = abs2(x[i + 1]) - abs2(x[i]) + abs2(x[n - i]) - abs2(x[n - i + 1])
+    end
+    return nothing
+end
+
+ybig = zeros(length(xbig) - 1)
+f_sparse_vector!(ybig, xbig)
+ybig ≈ f_sparse_vector(xbig)
true

In this case, the sparse Jacobian should also become non-allocating (for our specific choice of backend).

jac_prep_sparse_nonallocating = prepare_jacobian(f_sparse_vector!, zero(ybig), sparse_first_order_backend, zero(xbig))
+jac_buffer = similar(sparsity_pattern(jac_prep_sparse_nonallocating), eltype(xbig))
+@benchmark jacobian!($f_sparse_vector!, $ybig, $jac_buffer, $jac_prep_sparse_nonallocating, $sparse_first_order_backend, $xbig)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
+ Range (min … max):  12.864 μs …  33.142 μs  ┊ GC (min … max): 0.00% … 0.00%
+ Time  (median):     13.135 μs               ┊ GC (median):    0.00%
+ Time  (mean ± σ):   13.222 μs ± 832.350 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%
+
+    ▁█▇                                                         
+  ▂▄███▆▂▂▂▂▂▂▂▂▂▂▂▁▁▂▂▂▂▂▁▁▁▁▁▂▁▁▁▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▁▂▁▂▂▂▂▂▂▂▂▂ ▂
+  12.9 μs         Histogram: frequency by time         17.1 μs <
+
+ Memory estimate: 0 bytes, allocs estimate: 0.
diff --git a/DifferentiationInterface/v0.6.18/tutorials/basic/index.html b/DifferentiationInterface/v0.6.18/tutorials/basic/index.html new file mode 100644 index 000000000..1ab3e21ae --- /dev/null +++ b/DifferentiationInterface/v0.6.18/tutorials/basic/index.html @@ -0,0 +1,80 @@ + +Basic tutorial · DifferentiationInterface.jl
GitHub

Basic tutorial

We present the main features of DifferentiationInterface.jl.

using DifferentiationInterface

Computing a gradient

A common use case of automatic differentiation (AD) is optimizing real-valued functions with first- or second-order methods. Let's define a simple objective (the squared norm) and a random input vector

f(x) = sum(abs2, x)
f (generic function with 1 method)
x = collect(1.0:5.0)
5-element Vector{Float64}:
+ 1.0
+ 2.0
+ 3.0
+ 4.0
+ 5.0

To compute its gradient, we need to choose a "backend", i.e. an AD package to call under the hood. Most backend types are defined by ADTypes.jl and re-exported by DifferentiationInterface.jl.

ForwardDiff.jl is very generic and efficient for low-dimensional inputs, so it's a good starting point:

import ForwardDiff
+
+backend = AutoForwardDiff()
AutoForwardDiff()
Tip

To avoid name conflicts, load AD packages with import instead of using. Indeed, most AD packages also export operators like gradient and jacobian, but you only want to use the ones from DifferentiationInterface.jl.

Now you can use the following syntax to compute the gradient:

gradient(f, backend, x)
5-element Vector{Float64}:
+  2.0
+  4.0
+  6.0
+  8.0
+ 10.0

Was that fast? BenchmarkTools.jl helps you answer that question.

using BenchmarkTools
+
+@benchmark gradient($f, $backend, $x)
BenchmarkTools.Trial: 10000 samples with 89 evaluations.
+ Range (min … max):  817.933 ns … 297.241 μs  ┊ GC (min … max): 0.00% … 99.58%
+ Time  (median):       1.132 μs               ┊ GC (median):    0.00%
+ Time  (mean ± σ):     1.143 μs ±   4.545 μs  ┊ GC (mean ± σ):  7.60% ±  1.99%
+
+  ▆▅▆▆▃              ▁▆▇█▆▄▂   ▁▁                               ▂
+  ██████▇▇▇▇█▇▇▆▅▃▄▃▆████████████▇█▆▄▄▅▃▅▄▃▅▄▃▁▁▄▁▁▃▃▃▅▄▅▄▄▆▆▇▇ █
+  818 ns        Histogram: log(frequency) by time        1.7 μs <
+
+ Memory estimate: 848 bytes, allocs estimate: 6.

Not bad, but you can do better.

Overwriting a gradient

Since you know how much space your gradient will occupy (the same as your input x), you can pre-allocate that memory and offer it to AD. Some backends get a speed boost from this trick.

grad = similar(x)
+gradient!(f, grad, backend, x)
+grad  # has been mutated
5-element Vector{Float64}:
+  2.0
+  4.0
+  6.0
+  8.0
+ 10.0

The bang indicates that one of the arguments of gradient! might be mutated. More precisely, our convention is that every positional argument between the function and the backend is mutated.

@benchmark gradient!($f, $grad, $backend, $x)
BenchmarkTools.Trial: 10000 samples with 196 evaluations.
+ Range (min … max):  484.117 ns … 122.520 μs  ┊ GC (min … max): 0.00% … 99.43%
+ Time  (median):     682.495 ns               ┊ GC (median):    0.00%
+ Time  (mean ± σ):   649.678 ns ±   1.924 μs  ┊ GC (mean ± σ):  6.72% ±  3.23%
+
+  ▄█▇▃                                 ▄▆▇▇▆▄▂                  ▂
+  █████▆▅▄▃▁▆▇█▆▇▆▅▅▅▃▃▅▅█▆▅▅▄▄▁▁▁▃▅▁▁█████████▆▅▆▇███▇▇▇▆▆▆▆▆▆ █
+  484 ns        Histogram: log(frequency) by time        800 ns <
+
+ Memory estimate: 528 bytes, allocs estimate: 3.

For some reason the in-place version is not much better than your first attempt. However, it makes fewer allocations, thanks to the gradient vector you provided. Don't worry, you can get even more performance.

Preparing for multiple gradients

Internally, ForwardDiff.jl creates some data structures to keep track of things. These objects can be reused between gradient computations, even on different input values. We abstract away the preparation step behind a backend-agnostic syntax:

prep = prepare_gradient(f, backend, zero(x))
DifferentiationInterfaceForwardDiffExt.ForwardDiffGradientPrep{ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(Main.f), Float64}, Float64, 5, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.f), Float64}, Float64, 5}}}}(ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(Main.f), Float64}, Float64, 5, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.f), Float64}, Float64, 5}}}((Partials(1.0, 0.0, 0.0, 0.0, 0.0), Partials(0.0, 1.0, 0.0, 0.0, 0.0), Partials(0.0, 0.0, 1.0, 0.0, 0.0), Partials(0.0, 0.0, 0.0, 1.0, 0.0), Partials(0.0, 0.0, 0.0, 0.0, 1.0)), ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.f), Float64}, Float64, 5}[Dual{ForwardDiff.Tag{typeof(Main.f), Float64}}(1.0,1.0,0.0,0.0,0.0,0.0), Dual{ForwardDiff.Tag{typeof(Main.f), Float64}}(2.0,0.0,1.0,0.0,0.0,0.0), Dual{ForwardDiff.Tag{typeof(Main.f), Float64}}(3.0,0.0,0.0,1.0,0.0,0.0), Dual{ForwardDiff.Tag{typeof(Main.f), Float64}}(4.0,0.0,0.0,0.0,1.0,0.0), Dual{ForwardDiff.Tag{typeof(Main.f), Float64}}(5.0,0.0,0.0,0.0,0.0,1.0)]))

You don't need to know what this object is, you just need to pass it to the gradient operator. Note that preparation does not depend on the actual components of the vector x, just on its type and size. You can thus reuse the prep for different values of the input.

grad = similar(x)
+gradient!(f, grad, prep, backend, x)
+grad  # has been mutated
5-element Vector{Float64}:
+  2.0
+  4.0
+  6.0
+  8.0
+ 10.0

Preparation makes the gradient computation much faster, and (in this case) allocation-free.

@benchmark gradient!($f, $grad, $prep, $backend, $x)
BenchmarkTools.Trial: 10000 samples with 995 evaluations.
+ Range (min … max):  27.307 ns … 54.131 ns  ┊ GC (min … max): 0.00% … 0.00%
+ Time  (median):     27.880 ns              ┊ GC (median):    0.00%
+ Time  (mean ± σ):   28.394 ns ±  2.084 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%
+
+  ▃▆▇█▇▇▅▃                                              ▁▂▃▁  ▂
+  █████████▆▅▄▁▃▄▅▄▆▅▄▃▃▄▄▃▁▁▃▃▃▃▁▁▄▃▃▃▁▁▁▁▃▄▁▄▄▆▆▆▆▇█▇█████▇ █
+  27.3 ns      Histogram: log(frequency) by time      36.4 ns <
+
+ Memory estimate: 0 bytes, allocs estimate: 0.

Beware that the prep object is nearly always mutated by differentiation operators, even though it is given as the last positional argument.

Switching backends

The whole point of DifferentiationInterface.jl is that you can easily experiment with different AD solutions. Typically, for gradients, reverse mode AD might be a better fit, so let's try Zygote.jl!

import Zygote
+
+backend2 = AutoZygote()
AutoZygote()

Once the backend is created, things run smoothly with exactly the same syntax as before:

gradient(f, backend2, x)
5-element Vector{Float64}:
+  2.0
+  4.0
+  6.0
+  8.0
+ 10.0

And you can run the same benchmarks to see what you gained (although such a small input may not be realistic):

prep2 = prepare_gradient(f, backend2, zero(x))
+
+@benchmark gradient!($f, $grad, $prep2, $backend2, $x)
BenchmarkTools.Trial: 10000 samples with 993 evaluations.
+ Range (min … max):  34.474 ns …  28.168 μs  ┊ GC (min … max):  0.00% … 99.73%
+ Time  (median):     59.174 ns               ┊ GC (median):     0.00%
+ Time  (mean ± σ):   63.957 ns ± 486.132 ns  ┊ GC (mean ± σ):  14.77% ±  1.95%
+
+  ▂█                            ▁▁▂                             
+  ██▆▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▁▂▂▂▁▂▂▁▂▂▄███▅▃▂▂▂▂▂▂▂▃▄▅▆▆▅▄▃▂▂▂▂▂▂▂▂▂▂ ▃
+  34.5 ns         Histogram: frequency by time         81.7 ns <
+
+ Memory estimate: 96 bytes, allocs estimate: 2.

In short, DifferentiationInterface.jl allows for easy testing and comparison of AD backends. If you want to go further, check out the documentation of DifferentiationInterfaceTest.jl. This related package provides benchmarking utilities to compare backends and help you select the one that is best suited for your problem.

diff --git a/DifferentiationInterface/versions.js b/DifferentiationInterface/versions.js index 205fed628..216bc8769 100644 --- a/DifferentiationInterface/versions.js +++ b/DifferentiationInterface/versions.js @@ -8,5 +8,5 @@ var DOC_VERSIONS = [ "v0.1", "dev", ]; -var DOCUMENTER_NEWEST = "v0.6.17"; +var DOCUMENTER_NEWEST = "v0.6.18"; var DOCUMENTER_STABLE = "stable";