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Add sensitivities for pinv #174

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Add sensitivities for pinv #174

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7 changes: 7 additions & 0 deletions src/sensitivities/linalg/generic.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -128,3 +128,10 @@ function ∇(::typeof(exp), ::Type{Arg{1}}, p, Y, Ȳ, X::AbstractMatrix)
F = factorize(Uᵀ)
return real(F \ (Uᵀ * Ȳ / F .* Z) * Uᵀ)
end

# Ported from autograd, which uses https://mathoverflow.net/questions/25778/analytical-...
# formula-for-numerical-derivative-of-the-matrix-pseudo-inverse
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Please use the academic reference here as well:
Golub, Gene H., and Victor Pereyra. "The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate." SIAM Journal on numerical analysis 10.2 (1973): 413-432.

import LinearAlgebra: pinv
@explicit_intercepts pinv Tuple{AbstractMatrix{<:∇Scalar}}
∇(::typeof(pinv), ::Type{Arg{1}}, p, Y, Ȳ, A::AbstractMatrix) =
(-Y*Ȳ'*Y + Y*Y'*Ȳ*(I - A*Y) + (I - Y*A)*Ȳ*Y'*Y)'
10 changes: 10 additions & 0 deletions test/sensitivities/linalg/generic.jl
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Expand Up @@ -98,4 +98,14 @@
VA = randn(rng, n, n)
@test_throws ArgumentError check_errs(exp, randn(rng, n, n), A, VA)
end

@testset "pinv" begin
rng = MersenneTwister(12345)
for n in 3:5, m in 3:5
X = randn(rng, n, m)
VX = randn(rng, n, m)
Ȳ = randn(rng, m, n)
@test check_errs(pinv, Ȳ, X, VX)
end
end
end