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Specialized inv(F::SVD) #32126

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Merged
merged 4 commits into from
Aug 13, 2019
Merged

Specialized inv(F::SVD) #32126

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a96dd53
inv(F::SVD)
carstenbauer May 23, 2019
fde7233
throw SingularException
carstenbauer Jun 24, 2019
d6a3204
SingularException test
carstenbauer Jun 24, 2019
af761de
truncate
carstenbauer Aug 12, 2019
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8 changes: 8 additions & 0 deletions stdlib/LinearAlgebra/src/svd.jl
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Expand Up @@ -196,6 +196,14 @@ function ldiv!(A::SVD{T}, B::StridedVecOrMat) where T
view(A.Vt,1:k,:)' * (view(A.S,1:k) .\ (view(A.U,:,1:k)' * B))
end

function inv(F::SVD{T}) where T
@inbounds for i in eachindex(F.S)
iszero(F.S[i]) && throw(SingularException(i))
end
k = searchsortedlast(F.S, eps(T)*F.S[1], rev=true)
@views (F.S[1:k] .\ F.Vt[1:k, :])' * F.U[:,1:k]'
end

size(A::SVD, dim::Integer) = dim == 1 ? size(A.U, dim) : size(A.Vt, dim)
size(A::SVD) = (size(A, 1), size(A, 2))

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4 changes: 4 additions & 0 deletions stdlib/LinearAlgebra/test/svd.jl
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Expand Up @@ -31,6 +31,10 @@ using LinearAlgebra: BlasComplex, BlasFloat, BlasReal, QRPivoted
@test sf2.U*Diagonal(sf2.S)*sf2.Vt' ≊ m2

@test ldiv!([0., 0.], svd(Matrix(I, 2, 2)), [1., 1.]) ≊ [1., 1.]
@test inv(svd(Matrix(I, 2, 2))) ≈ I
@test inv(svd([1 2; 3 4])) ≈ [-2.0 1.0; 1.5 -0.5]
@test inv(svd([1 0 1; 0 1 0])) ≈ [0.5 0.0; 0.0 1.0; 0.5 0.0]
@test_throws SingularException inv(svd([0 0; 0 0]))
end

n = 10
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