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# This file is a part of Julia. License is MIT: https://julialang.org/license
module TestBunchKaufman
using Test, LinearAlgebra, Random
using LinearAlgebra: BlasComplex, BlasFloat, BlasReal, QRPivoted
using Base: getproperty
n = 10
# Split n into 2 parts for tests needing two matrices
n1 = div(n, 2)
n2 = 2*n1
Random.seed!(1234321)
areal = randn(n,n)/2
aimg = randn(n,n)/2
a2real = randn(n,n)/2
a2img = randn(n,n)/2
breal = randn(n,2)/2
bimg = randn(n,2)/2
@testset "$eltya argument A" for eltya in (Float32, Float64, ComplexF32, ComplexF64, Int)
a = eltya == Int ? rand(1:7, n, n) : convert(Matrix{eltya}, eltya <: Complex ? complex.(areal, aimg) : areal)
a2 = eltya == Int ? rand(1:7, n, n) : convert(Matrix{eltya}, eltya <: Complex ? complex.(a2real, a2img) : a2real)
asym = transpose(a) + a # symmetric indefinite
aher = a' + a # Hermitian indefinite
apd = a' * a # Positive-definite
for (a, a2, aher, apd) in ((a, a2, aher, apd),
(view(a, 1:n, 1:n),
view(a2, 1:n, 1:n),
view(aher, 1:n, 1:n),
view(apd , 1:n, 1:n)))
ε = εa = eps(abs(float(one(eltya))))
# check that factorize gives a Bunch-Kaufman
@test isa(factorize(asym), LinearAlgebra.BunchKaufman)
@test isa(factorize(aher), LinearAlgebra.BunchKaufman)
@testset "$uplo Bunch-Kaufman factor of indefinite matrix" for uplo in (:L, :U)
bc1 = bunchkaufman(Hermitian(aher, uplo))
@test LinearAlgebra.issuccess(bc1)
@test logabsdet(bc1)[1] ≈ log(abs(det(bc1)))
if eltya <: Real
@test logabsdet(bc1)[2] == sign(det(bc1))
else
@test logabsdet(bc1)[2] ≈ sign(det(bc1))
end
@test inv(bc1)*aher ≈ Matrix(I, n, n)
@testset for rook in (false, true)
@test inv(bunchkaufman(Symmetric(transpose(a) + a, uplo), rook))*(transpose(a) + a) ≈ Matrix(I, n, n)
if eltya <: BlasFloat
# test also bunchkaufman! without explicit type tag
# no bunchkaufman! method for Int ... yet
@test inv(bunchkaufman!(transpose(a) + a, rook))*(transpose(a) + a) ≈ Matrix(I, n, n)
end
@test size(bc1) == size(bc1.LD)
@test size(bc1, 1) == size(bc1.LD, 1)
@test size(bc1, 2) == size(bc1.LD, 2)
if eltya <: BlasReal
@test_throws ArgumentError bunchkaufman(a)
end
# Test extraction of factors
if eltya <: Real
@test getproperty(bc1, uplo)*bc1.D*getproperty(bc1, uplo)' ≈ aher[bc1.p, bc1.p]
@test getproperty(bc1, uplo)*bc1.D*getproperty(bc1, uplo)' ≈ bc1.P*aher*bc1.P'
end
bc1 = bunchkaufman(Symmetric(asym, uplo))
@test getproperty(bc1, uplo)*bc1.D*transpose(getproperty(bc1, uplo)) ≈ asym[bc1.p, bc1.p]
@test getproperty(bc1, uplo)*bc1.D*transpose(getproperty(bc1, uplo)) ≈ bc1.P*asym*transpose(bc1.P)
@test_throws ErrorException bc1.Z
@test_throws ArgumentError uplo == :L ? bc1.U : bc1.L
end
end
@testset "$eltyb argument B" for eltyb in (Float32, Float64, ComplexF32, ComplexF64, Int)
b = eltyb == Int ? rand(1:5, n, 2) : convert(Matrix{eltyb}, eltyb <: Complex ? complex.(breal, bimg) : breal)
for b in (b, view(b, 1:n, 1:2))
εb = eps(abs(float(one(eltyb))))
ε = max(εa,εb)
@testset "$uplo Bunch-Kaufman factor of indefinite matrix" for uplo in (:L, :U)
bc1 = bunchkaufman(Hermitian(aher, uplo))
@test aher*(bc1\b) ≈ b atol=1000ε
end
@testset "$uplo Bunch-Kaufman factors of a pos-def matrix" for uplo in (:U, :L)
@testset "rook pivoting: $rook" for rook in (false, true)
bc2 = bunchkaufman(Hermitian(apd, uplo), rook)
@test LinearAlgebra.issuccess(bc2)
bks = split(sprint(show, "text/plain", bc2), "\n")
@test bks[1] == summary(bc2)
@test bks[2] == "D factor:"
@test bks[4+n] == "$uplo factor:"
@test bks[6+2n] == "permutation:"
@test logdet(bc2) ≈ log(det(bc2))
@test logabsdet(bc2)[1] ≈ log(abs(det(bc2)))
@test logabsdet(bc2)[2] == sign(det(bc2))
@test inv(bc2)*apd ≈ Matrix(I, n, n)
@test apd*(bc2\b) ≈ b rtol=eps(cond(apd))
@test ishermitian(bc2) == !issymmetric(bc2)
end
end
end
end
end
end
@testset "Singular matrices" begin
R = Float64[1 0; 0 0]
C = ComplexF64[1 0; 0 0]
for A in (R, Symmetric(R), C, Hermitian(C))
@test_throws SingularException bunchkaufman(A)
@test_throws SingularException bunchkaufman!(copy(A))
@test_throws SingularException bunchkaufman(A; check = true)
@test_throws SingularException bunchkaufman!(copy(A); check = true)
@test !issuccess(bunchkaufman(A; check = false))
@test !issuccess(bunchkaufman!(copy(A); check = false))
end
F = bunchkaufman(R; check = false)
@test sprint(show, "text/plain", F) == "Failed factorization of type $(typeof(F))"
end
@testset "test example due to @timholy in PR 15354" begin
A = rand(6,5); A = complex(A'*A) # to avoid calling the real-lhs-complex-rhs method
F = cholesky(A);
v6 = rand(ComplexF64, 6)
v5 = view(v6, 1:5)
@test F\v5 == F\v6[1:5]
end
@test_throws DomainError logdet(bunchkaufman([-1 -1; -1 1]))
@test logabsdet(bunchkaufman([8 4; 4 2]; check = false))[1] == -Inf
@test isa(bunchkaufman(Symmetric(ones(0,0))), BunchKaufman) # 0x0 matrix
end # module TestBunchKaufman
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