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WIP: add adjoint for eigen #327

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WIP: add adjoint for eigen #327

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18 changes: 18 additions & 0 deletions src/lib/array.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -403,6 +403,24 @@ end
(Ā, )
end

@adjoint function LinearAlgebra.eigen(A::AbstractMatrix)
eV = eigen(A)
e,V = eV
n = size(A,1)
eV, function (Δ)
Δe, ΔV = Δ
if ΔV === nothing
(inv(V)'*Diagonal(Δe)*V', )
elseif Δe === nothing
F = [i==j ? 0 : inv(e[j] - e[i]) for i=1:n, j=1:n]
(inv(V)'*(F .* (V'ΔV))*V', )
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@CarloLucibello CarloLucibello Sep 12, 2019

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Maybe this is more gpu friendly

F = inv.(e .- e')
F[diagind(F)] .= 0

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@baggepinnen baggepinnen Sep 12, 2019

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I was struggling to find the solution you hinted at with diagind, thanks!

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@CarloLucibello CarloLucibello Sep 12, 2019

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I wonder if it is safe to divide by zero on the gpu or it could throw an error

else
F = [i==j ? 0 : inv(e[j] - e[i]) for i=1:n, j=1:n]
(inv(V)'*(Diagonal(Δe) + F .* (V'ΔV))*V', )
end
end
end

Zygote.@adjoint function LinearAlgebra.tr(x::AbstractMatrix)
# x is a squre matrix checked by tr,
# so we could just use Eye(size(x, 1))
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12 changes: 12 additions & 0 deletions test/gradcheck.jl
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Expand Up @@ -352,6 +352,18 @@ end
end
end

@testset "eigen" begin
rng, N = MersenneTwister(6865931), 8
for i = 1:5
A = randn(rng, N, N)
@test gradtest(A->abs.(eigen(A).values), A)
@test gradcheck(A) do A
e = eigen(A)
sum(real.(e.values)) + sum(real.(e.vectors))
end
end
end

using Distances

Zygote.refresh()
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