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Add tests for polar decomposition for GPU (#83)
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‎test/amd/polar.jl‎

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using MatrixAlgebraKit
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using Test
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using TestExtras
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using StableRNGs
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using LinearAlgebra: LinearAlgebra, I, isposdef, Hermitian
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using MatrixAlgebraKit: PolarViaSVD
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using AMDGPU
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@testset "left_polar! for T = $T" for T in (Float32, Float64, ComplexF32, ComplexF64)
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rng = StableRNG(123)
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m = 54
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@testset "size ($m, $n)" for n in (37, m)
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k = min(m, n)
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svd_algs = (ROCSOLVER_QRIteration(), ROCSOLVER_Jacobi())
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@testset "algorithm $svd_alg" for svd_alg in svd_algs
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n < m && svd_alg isa ROCSOLVER_QRIteration && continue
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A = ROCArray(randn(rng, T, m, n))
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alg = PolarViaSVD(svd_alg)
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W, P = left_polar(A; alg)
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@test W isa ROCMatrix{T} && size(W) == (m, n)
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@test P isa ROCMatrix{T} && size(P) == (n, n)
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@test W * P ≈ A
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@test isisometric(W)
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# work around extremely strict Julia criteria for Hermiticity
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P)) && isposdef(Hermitian(P))
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Ac = similar(A)
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W2, P2 = @constinferred left_polar!(copy!(Ac, A), (W, P), alg)
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@test W2 === W
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@test P2 === P
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@test W * P ≈ A
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@test isisometric(W)
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# work around extremely strict Julia criteria for Hermiticity
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P)) && isposdef(Hermitian(P))
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noP = similar(P, (0, 0))
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W2, P2 = @constinferred left_polar!(copy!(Ac, A), (W, noP), alg)
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@test P2 === noP
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@test W2 === W
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@test isisometric(W)
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P = W' * A # compute P explicitly to verify W correctness
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P))
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@test isposdef(Hermitian(project_hermitian!(P)))
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end
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end
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end
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@testset "right_polar! for T = $T" for T in (Float32, Float64, ComplexF32, ComplexF64)
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rng = StableRNG(123)
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n = 54
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@testset "size ($m, $n)" for m in (37, n)
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k = min(m, n)
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svd_algs = (ROCSOLVER_QRIteration(), ROCSOLVER_Jacobi())
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@testset "algorithm $svd_alg" for svd_alg in svd_algs
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n > m && svd_alg isa ROCSOLVER_QRIteration && continue
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A = ROCArray(randn(rng, T, m, n))
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alg = PolarViaSVD(svd_alg)
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P, Wᴴ = right_polar(A; alg)
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@test Wᴴ isa ROCMatrix{T} && size(Wᴴ) == (m, n)
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@test P isa ROCMatrix{T} && size(P) == (m, m)
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@test P * Wᴴ ≈ A
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@test isisometric(Wᴴ; side = :right)
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# work around extremely strict Julia criteria for Hermiticity
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P)) && isposdef(Hermitian(P))
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Ac = similar(A)
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P2, Wᴴ2 = @constinferred right_polar!(copy!(Ac, A), (P, Wᴴ), alg)
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@test P2 === P
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@test Wᴴ2 === Wᴴ
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@test P * Wᴴ ≈ A
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@test isisometric(Wᴴ; side = :right)
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# work around extremely strict Julia criteria for Hermiticity
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P)) && isposdef(Hermitian(P))
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noP = similar(P, (0, 0))
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P2, Wᴴ2 = @constinferred right_polar!(copy!(Ac, A), (noP, Wᴴ), alg)
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@test P2 === noP
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@test Wᴴ2 === Wᴴ
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@test isisometric(Wᴴ; side = :right)
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P = A * Wᴴ' # compute P explicitly to verify W correctness
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P))
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@test isposdef(Hermitian(project_hermitian!(P)))
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end
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end
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end

‎test/cuda/polar.jl‎

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using MatrixAlgebraKit
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using Test
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using TestExtras
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using StableRNGs
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using LinearAlgebra: LinearAlgebra, I, isposdef, Hermitian
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using MatrixAlgebraKit: PolarViaSVD
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using CUDA
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@testset "left_polar! for T = $T" for T in (Float32, Float64, ComplexF32, ComplexF64)
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rng = StableRNG(123)
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m = 54
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@testset "size ($m, $n)" for n in (37, m)
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k = min(m, n)
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svd_algs = (CUSOLVER_QRIteration(), CUSOLVER_Jacobi())
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@testset "algorithm $svd_alg" for svd_alg in svd_algs
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n < m && svd_alg isa CUSOLVER_QRIteration && continue
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A = CuArray(randn(rng, T, m, n))
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alg = PolarViaSVD(svd_alg)
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W, P = left_polar(A; alg)
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@test W isa CuMatrix{T} && size(W) == (m, n)
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@test P isa CuMatrix{T} && size(P) == (n, n)
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@test W * P ≈ A
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@test isisometric(W)
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# work around extremely strict Julia criteria for Hermiticity
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P)) && isposdef(Hermitian(P))
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Ac = similar(A)
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W2, P2 = @constinferred left_polar!(copy!(Ac, A), (W, P), alg)
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@test W2 === W
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@test P2 === P
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@test W * P ≈ A
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@test isisometric(W)
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# work around extremely strict Julia criteria for Hermiticity
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P)) && isposdef(Hermitian(P))
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noP = similar(P, (0, 0))
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W2, P2 = @constinferred left_polar!(copy!(Ac, A), (W, noP), alg)
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@test P2 === noP
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@test W2 === W
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@test isisometric(W)
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P = W' * A # compute P explicitly to verify W correctness
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P))
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@test isposdef(Hermitian(project_hermitian!(P)))
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end
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end
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end
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@testset "right_polar! for T = $T" for T in (Float32, Float64, ComplexF32, ComplexF64)
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rng = StableRNG(123)
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n = 54
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@testset "size ($m, $n)" for m in (37, n)
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k = min(m, n)
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svd_algs = (CUSOLVER_QRIteration(), CUSOLVER_Jacobi())
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@testset "algorithm $svd_alg" for svd_alg in svd_algs
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n > m && svd_alg isa CUSOLVER_QRIteration && continue
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A = CuArray(randn(rng, T, m, n))
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alg = PolarViaSVD(svd_alg)
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P, Wᴴ = right_polar(A; alg)
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@test Wᴴ isa CuMatrix{T} && size(Wᴴ) == (m, n)
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@test P isa CuMatrix{T} && size(P) == (m, m)
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@test P * Wᴴ ≈ A
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@test isisometric(Wᴴ; side = :right)
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# work around extremely strict Julia criteria for Hermiticity
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P)) && isposdef(Hermitian(P))
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Ac = similar(A)
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P2, Wᴴ2 = @constinferred right_polar!(copy!(Ac, A), (P, Wᴴ), alg)
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@test P2 === P
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@test Wᴴ2 === Wᴴ
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@test P * Wᴴ ≈ A
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@test isisometric(Wᴴ; side = :right)
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# work around extremely strict Julia criteria for Hermiticity
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P)) && isposdef(Hermitian(P))
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noP = similar(P, (0, 0))
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P2, Wᴴ2 = @constinferred right_polar!(copy!(Ac, A), (noP, Wᴴ), alg)
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@test P2 === noP
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@test Wᴴ2 === Wᴴ
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@test isisometric(Wᴴ; side = :right)
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P = A * Wᴴ' # compute P explicitly to verify W correctness
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@test ishermitian(P; rtol = MatrixAlgebraKit.defaulttol(P))
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@test isposdef(Hermitian(project_hermitian!(P)))
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end
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end
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end

‎test/runtests.jl‎

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@safetestset "CUDA Hermitian Eigenvalue Decomposition" begin
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include("cuda/eigh.jl")
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end
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@safetestset "CUDA Polar Decomposition" begin
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include("cuda/polar.jl")
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end
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end
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using AMDGPU
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@safetestset "AMDGPU Hermitian Eigenvalue Decomposition" begin
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include("amd/eigh.jl")
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end
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@safetestset "AMDGPU Polar Decomposition" begin
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include("amd/polar.jl")
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end
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end

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