[Draft] Alternative rqa trend implementation respecting actual time stamps

src/RQADeforestation.jl

@@ -11,6 +11,7 @@ using TestItems
 
 export gdalcube, rqatrend
 
+include("weightedlinearregression.jl")
 include("metrics.jl")
 include("auxil.jl")
 include("rqatrend.jl")

src/rqatrend.jl

@@ -8,7 +8,6 @@ using Distances
 Compute the RQA trend metric for the datacube `cube` with the epsilon threshold `thresh`.
 """
 function rqatrend(cube; thresh=2, outpath=tempname() * ".zarr", overwrite=false, kwargs...)
-    @show outpath
     mapCube(rqatrend, cube, thresh; indims=InDims("Time"), outdims=OutDims(; outtype=Float32, path=outpath, overwrite, kwargs...))
 end
 
@@ -84,7 +83,6 @@ function rqatrend_impl(data; thresh=2, border=10, theiler=1, metric=CheckedEucli
     return 1000.0*(A \ b)[1]  # slope
 end
 
-
 @testitem "rqatrend_impl" begin
     import AllocCheck
     import Random
@@ -104,6 +102,64 @@ end
     @test isempty(AllocCheck.check_allocs(RQADeforestation.rqatrend_impl, Tuple{Vector{Union{Float64,Missing}}}))
 end
 
+function rqatrend_weightedonline(data, timeaxis; thresh=2, border=10, theiler=1, metric=CheckedEuclidean())
+    # simplified implementation of https://stats.stackexchange.com/a/370175 and https://github.com/joshday/OnlineStats.jl/blob/b89a99679b13e3047ff9c93a03c303c357931832/src/stats/linreg.jl
+    # x is the diagonal offset, y the percentage of local recurrence
+    # we compute the slope of a simple linear regression with bias from x to y
+    maxnum = last(timeaxis) - first(timeaxis)
+    start = 1
+    finish = length(data) - border
+    wf = WeightedFit()
+    for i in start:finish
+        data[i] === missing && continue
+        for j in i+theiler:finish
+            data[j] === missing && continue
+            y = Float64(evaluate(metric, data[i], data[j]) <= thresh)
+
+            x = Float64(timeaxis[j] - timeaxis[i])
+            weight = 1 / (maxnum - x)
+            wf = smoowthwlinfit(x, y, weight, wf)
+        end
+    end
+    b = finalizewlinreg(wf)[2]
+    return 1000.0 * b
+end
+
+@testitem "Weighted RQATrend with x values" begin
+    using RQADeforestation
+    using Distributions
+    using RecurrenceAnalysis
+    using Random, Test
+    Random.seed!(1234)
+    x = 1:200
+    noise = rand(Normal(0, 1), 200)
+    y1 = 2.0 .* sin.(x ./ 10) .+ noise
+    y2 = copy(noise)
+    y2[101:200] .-= 2
+
+    # rp1 = RecurrenceMatrix(y1, 0.2)
+    # rp2 = RecurrenceMatrix(y2, 0.2)
+    theiler = 1
+    border = 10
+
+    rqarange = (1+theiler):(200-border)
+
+    r1 = RQADeforestation.rqatrend_weightedonline(y2, x)
+    @test r1 == -2.66417434040921
+
+    # Add some missings
+    y2mis = collect(Union{Missing,Float64}, y2)
+    y2mis[10:20] .= missing
+    goodinds = (!ismissing).(y2mis)
+
+    r1miss = RQADeforestation.rqatrend_weightedonline(y2mis[goodinds], range(0, 1, length=length(y2mis))[goodinds])
+    r2miss = RQADeforestation.rqatrend_weightedonline(y2mis, range(0, 1, length=length(y2mis)))
+    @test r1miss == r2miss == -514.9110636319965
+end
+
+
+
+
 
 function tau_rr(y, d; thresh=2, metric=CheckedEuclidean())
     _thresh = convert(eltype(y), thresh)
@@ -137,11 +193,4 @@ end
 # assumes n is Int for optimal performance
 sumofsquares(n) = n*(n+1)*(2*n+1)/6
 
-"""
-    smooth(a, b, γ)
-
-Weighted average of `a` and `b` with weight `γ`.
 
-``(1 - γ) * a + γ * b``
-"""
-smooth(a, b, γ) = a + γ * (b - a)

src/weightedlinearregression.jl

@@ -0,0 +1,41 @@
+"""
+    smooth(a, b, γ)
+
+Weighted average of `a` and `b` with weight `γ`.
+
+``(1 - γ) * a + γ * b``
+"""
+smooth(a, b, γ) = a + γ * (b - a)
+
+struct WeightedFit
+    mx::Float64
+    my::Float64
+    mxx::Float64
+    mxy::Float64
+    mw::Float64
+    n::Int64
+end
+WeightedFit() = WeightedFit(0.0, 0.0, 0.0, 0.0, 0.0, 0)
+function finalizewlinreg(f::WeightedFit)
+    b = (f.mxy - f.mx * f.my) / (f.mxx - f.mx * f.mx)
+    a = f.my - b * f.mx
+    a, b
+end
+@inline function smoowthwlinfit(xi, yi, wi, f::WeightedFit)
+    n = f.n + 1
+    mw = smooth(f.mw, wi, inv(n))
+    updateweight = wi / (mw * n)
+    mx = smooth(f.mx, xi, updateweight)
+    my = smooth(f.my, yi, updateweight)
+    mxx = smooth(f.mxx, xi * xi, updateweight)
+    mxy = smooth(f.mxy, xi * yi, updateweight)
+    return WeightedFit(mx, my, mxx, mxy, mw, n)
+end
+
+function wlinreg(x, y, w)
+    f = WeightedFit()
+    @inbounds for i in eachindex(x, y, w)
+        f = smoowthwlinfit(x[i], y[i], w[i], f)
+    end
+    finalizewlinreg(f)
+end