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guarantee hermitian results in polar decompositions #143

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Merged
lkdvos merged 6 commits into from
Jan 5, 2026
Merged

guarantee hermitian results in polar decompositions #143

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68ecc19
guarantee hermitian results in polar
lkdvos Jan 5, 2026
d2dac21
update tests
lkdvos Jan 5, 2026
fb5b57f
fix double `@testset`
lkdvos Jan 5, 2026
6848da3
change to `syrk` convention
lkdvos Jan 5, 2026
d53b792
update changelog
lkdvos Jan 5, 2026
02f3366
some reshuffling to actually correctly dispatch
lkdvos Jan 5, 2026
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17 changes: 15 additions & 2 deletions src/implementations/polar.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -53,7 +53,7 @@ function left_polar!(A::AbstractMatrix, WP, alg::PolarViaSVD)
if !isempty(P)
S .= sqrt.(S)
SsqrtVᴴ = lmul!(S, Vᴴ)
P = mul!(P, SsqrtVᴴ', SsqrtVᴴ)
P = _mul_herm!(P, SsqrtVᴴ)
end
return (W, P)
end
Expand All @@ -65,11 +65,24 @@ function right_polar!(A::AbstractMatrix, PWᴴ, alg::PolarViaSVD)
if !isempty(P)
S .= sqrt.(S)
USsqrt = rmul!(U, S)
P = mul!(P, USsqrt, USsqrt')
P = _mul_herm!(P, USsqrt')
end
return (P, Wᴴ)
end

# Implement `mul!(C, A', A)` and guarantee the result is hermitian.
# For BLAS calls that dispatch to `syrk` or `herk` this works automatically
# for GPU this currently does not seem to be guaranteed so we manually project
function _mul_herm!(C, A)
mul!(C, A', A)
project_hermitian!(C)
return C
end
function _mul_herm!(C::YALAPACK.BlasMat{T}, A::YALAPACK.BlasMat{T}) where {T}
mul!(C, A', A)
return C
end

# Implementation via Newton
# --------------------------
function left_polar!(A::AbstractMatrix, WP, alg::PolarNewton)
Expand Down
12 changes: 4 additions & 8 deletions test/testsuite/polar.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -25,16 +25,14 @@ function test_left_polar(
@test eltype(P) == eltype(A) && size(P) == (size(A, 2), size(A, 2))
@test W * P ≈ A
@test isisometric(W)
@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P))
@test isposdef(project_hermitian!(P))
@test isposdef(P)

W2, P2 = @testinferred left_polar!(Ac, (W, P), alg)
@test W2 === W
@test P2 === P
@test W * P ≈ A
@test isisometric(W)
@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P))
@test isposdef(project_hermitian!(P))
@test isposdef(P)

noP = similar(P, (0, 0))
W2, P2 = @testinferred left_polar!(copy!(Ac, A), (W, noP), alg)
Expand Down Expand Up @@ -62,16 +60,14 @@ function test_right_polar(
@test eltype(P) == eltype(A) && size(P) == (size(A, 1), size(A, 1))
@test P * Wᴴ ≈ A
@test isisometric(Wᴴ; side = :right)
@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P))
@test isposdef(project_hermitian!(P))
@test isposdef(P)

P2, Wᴴ2 = @testinferred right_polar!(Ac, (P, Wᴴ), alg)
@test P2 === P
@test Wᴴ2 === Wᴴ
@test P * Wᴴ ≈ A
@test isisometric(Wᴴ; side = :right)
@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P))
@test isposdef(project_hermitian!(P))
@test isposdef(P)

noP = similar(P, (0, 0))
P2, Wᴴ2 = @testinferred right_polar!(copy!(Ac, A), (noP, Wᴴ), alg)
Expand Down
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