1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
|
# 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!(12343210)
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
# test Base.iterate
ref_objs = (bc1.D, uplo == :L ? bc1.L : bc1.U, bc1.p)
for (bki, bkobj) in enumerate(bc1)
@test bkobj == ref_objs[bki]
end
if eltya <: BlasFloat
@test convert(LinearAlgebra.BunchKaufman{eltya}, bc1) === bc1
@test convert(LinearAlgebra.Factorization{eltya}, bc1) === bc1
if eltya <: BlasReal
@test convert(LinearAlgebra.Factorization{Float16}, bc1) == convert(LinearAlgebra.BunchKaufman{Float16}, bc1)
elseif eltya <: BlasComplex
@test convert(LinearAlgebra.Factorization{ComplexF16}, bc1) == convert(LinearAlgebra.BunchKaufman{ComplexF16}, bc1)
end
end
@test Base.propertynames(bc1) == (:p, :P, :L, :U, :D)
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
@testset "issue #32080" begin
A = Symmetric([-5 -9 9; -9 4 1; 9 1 2])
B = bunchkaufman(A, true)
@test B.U * B.D * B.U' ≈ A[B.p, B.p]
end
@test_throws DomainError logdet(bunchkaufman([-1 -1; -1 1]))
@test logabsdet(bunchkaufman([8 4; 4 2]; check = false))[1] == -Inf
@testset "0x0 matrix" begin
for ul in (:U, :L)
B = bunchkaufman(Symmetric(ones(0, 0), ul))
@test isa(B, BunchKaufman)
@test B.D == Tridiagonal([], [], [])
@test B.P == ones(0, 0)
@test B.p == []
if ul == :U
@test B.U == UnitUpperTriangular(ones(0, 0))
@test_throws ArgumentError B.L
else
@test B.L == UnitLowerTriangular(ones(0, 0))
@test_throws ArgumentError B.U
end
end
end
end # module TestBunchKaufman
|
