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svd for Adjoint and Transpose #27916

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Merged
merged 1 commit into from
Jul 4, 2018
Merged

svd for Adjoint and Transpose #27916

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8 changes: 8 additions & 0 deletions stdlib/LinearAlgebra/src/svd.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -132,6 +132,14 @@ function svd(x::Integer; full::Bool = false, thin::Union{Bool,Nothing} = nothing
end
return svd(float(x), full = full)
end
function svd(A::Adjoint; full::Bool = false)
s = svd(A.parent, full = full)
return SVD(s.Vt', s.S, s.U')
end
function svd(A::Transpose; full::Bool = false)
s = svd(A.parent, full = full)
return SVD(transpose(s.Vt), s.S, transpose(s.U))
end

function getproperty(F::SVD, d::Symbol)
if d == :V
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20 changes: 20 additions & 0 deletions stdlib/LinearAlgebra/test/svd.jl
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Expand Up @@ -69,6 +69,26 @@ a2img = randn(n,n)/2
@test svdz.Vt ≈ Matrix{eltya}(I, 0, 0)
end
end
usv = svd(a')
@testset "singular value decomposition of adjoint" begin
@test usv.S === svdvals(usv)
@test usv.U * (Diagonal(usv.S) * usv.Vt) ≈ a'
@test convert(Array, usv) ≈ a'
@test usv.Vt' ≈ usv.V
@test_throws ErrorException usv.Z
b = rand(eltya,n)
@test usv\b ≈ a'\b
end
usv = svd(transpose(a))
@testset "singular value decomposition of transpose" begin
@test usv.S === svdvals(usv)
@test usv.U * (Diagonal(usv.S) * usv.Vt) ≈ transpose(a)
@test convert(Array, usv) ≈ transpose(a)
@test usv.Vt' ≈ usv.V
@test_throws ErrorException usv.Z
b = rand(eltya,n)
@test usv\b ≈ transpose(a)\b
end
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@StefanKarpinski StefanKarpinski Jul 5, 2018 •
edited
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I would think that the most obvious tests here would be these:

svd(a').U == svd(a).V
svd(a').S == svd(a).S
svd(a').V == svd(a).U

Is there some reason not to test this directly? I realize that the precise U and V matrices are not well defined in many cases but it seems unlikely that this will ever break in this case, no?

@testset "Generalized svd" begin
a_svd = a[1:n1, :]
gsvd = svd(a,a_svd)
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