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using Tullio, Statistics | |
function tcov(x::AbstractMatrix; corrected=true, dims) | |
@assert dims==2 | |
pre = 1/(size(x,2)-corrected) | |
xbar=vec(mean(x, dims=2)) | |
@tullio Q[i,j] :=pre * (x[i,k] - xbar[i]) * (x[j,k] - xbar[j]) # verbose=true # sum(k) | |
end | |
mat = 100randn(4,5) # .+ im.*rand.(); # wrong for complex | |
mat2 = 100randn(4,5) | |
cov(mat; dims=2) | |
tcov(mat; dims=2) | |
mcov(mat; dims=2) | |
function mcov(x::AbstractMatrix; corrected=true, dims) | |
@assert dims==2 | |
pre = 1/(size(x,2)-corrected) | |
xcorr = x .- mean(x, dims=2) | |
z = pre * xcorr * adjoint(xcorr) # right for complex | |
end | |
function mcov(x::AbstractMatrix, y::AbstractMatrix; corrected=true, dims) | |
@assert dims==2 | |
pre = 1/(size(x,2)-corrected) | |
xcorr = x .- mean(x, dims=2) | |
ycorr = y .- mean(y, dims=2) | |
z = pre * xcorr * adjoint(ycorr) | |
end | |
mat = 100randn(4,5) .+ im.*rand.(); | |
mat2 = 100randn(4,5) .+ im.*rand.(); | |
cov(mat; dims=2) | |
mcov(mat; dims=2) | |
cov(mat, mat2; dims=2) | |
mcov(mat, mat2; dims=2) | |
using ChainRulesCore, Diffractor, ForwardDiff | |
function ChainRulesCore.rrule(::typeof(mcov), x::AbstractMatrix{T}; corrected=true, dims) where {T} | |
@assert dims==2 | |
pre = one(float(T))/(size(x,2) - corrected) | |
xcorr = x .- mean(x, dims=2) | |
z = pre * xcorr * adjoint(xcorr) | |
z, dz -> (NoTangent(), Hermitian(unthunk(dz)) * xcorr * 2pre) # not sure about complex case | |
end | |
ForwardDiff.gradient(x -> real(sum(sin, mcov(x; dims=2))), real(mat)) | |
Diffractor.gradient(x -> real(sum(sin, mcov(x; dims=2))), real(mat))[1] | |
function ChainRulesCore.rrule(::typeof(mcov), x::AbstractMatrix{T}, y::AbstractMatrix; corrected=true, dims) where {T} | |
@assert dims==2 | |
pre = one(float(T))/(size(x,2) - corrected) | |
xcorr = x .- mean(x, dims=2) | |
ycorr = y .- mean(y, dims=2) | |
z = pre * xcorr * adjoint(ycorr) | |
z, dz -> (NoTangent(), dz * ycorr * pre, adjoint(dz) * xcorr * pre) | |
end | |
ForwardDiff.gradient(x -> real(sum(sin, mcov(x, real(mat2); dims=2))), real(mat)) | |
Diffractor.gradient((x,y) -> real(sum(sin, mcov(x, y; dims=2))), real(mat), real(mat2))[1] | |
ForwardDiff.gradient(y -> real(sum(sin, mcov(real(mat), y; dims=2))), real(mat2)) | |
Diffractor.gradient((x,y) -> real(sum(sin, mcov(x, y; dims=2))), real(mat), real(mat2))[2] |
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