128 lines
4.4 KiB
Julia
128 lines
4.4 KiB
Julia
# This file is a part of Julia. License is MIT: https://julialang.org/license
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using Base.Test
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using Base.LinAlg: BlasComplex, BlasFloat, BlasReal, QRPivoted
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n = 10
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# Split n into 2 parts for tests needing two matrices
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n1 = div(n, 2)
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n2 = 2*n1
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srand(1234321)
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areal = randn(n,n)/2
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aimg = randn(n,n)/2
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a2real = randn(n,n)/2
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a2img = randn(n,n)/2
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breal = randn(n,2)/2
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bimg = randn(n,2)/2
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@testset for eltya in (Float32, Float64, Complex64, Complex128, Int)
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a = eltya == Int ? rand(1:7, n, n) : convert(Matrix{eltya}, eltya <: Complex ? complex.(areal, aimg) : areal)
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a2 = eltya == Int ? rand(1:7, n, n) : convert(Matrix{eltya}, eltya <: Complex ? complex.(a2real, a2img) : a2real)
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@testset for atype in ("Array", "SubArray")
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asym = a'+a # symmetric indefinite
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apd = a'*a # symmetric positive-definite
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if atype == "Array"
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a = a
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a2 = a2
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else
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a = view(a, 1:n, 1:n)
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a2 = view(a2, 1:n, 1:n)
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asym = view(asym, 1:n, 1:n)
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apd = view(apd, 1:n, 1:n)
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end
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ε = εa = eps(abs(float(one(eltya))))
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@testset for eltyb in (Float32, Float64, Complex64, Complex128, Int)
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b = eltyb == Int ? rand(1:5, n, 2) : convert(Matrix{eltyb}, eltyb <: Complex ? complex.(breal, bimg) : breal)
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@testset for btype in ("Array", "SubArray")
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if btype == "Array"
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b = b
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else
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b = view(b, 1:n, 1:2)
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end
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εb = eps(abs(float(one(eltyb))))
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ε = max(εa,εb)
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@testset "(Automatic) Bunch-Kaufman factor of indefinite matrix" begin
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bc1 = factorize(asym)
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@test logabsdet(bc1)[1] ≈ log(abs(det(bc1)))
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if eltya <: Real
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@test logabsdet(bc1)[2] == sign(det(bc1))
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else
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@test logabsdet(bc1)[2] ≈ sign(det(bc1))
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end
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@test inv(bc1)*asym ≈ eye(n)
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@test asym*(bc1\b) ≈ b atol=1000ε
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@testset for rook in (false, true)
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@test inv(bkfact(a.'+a, :U, true, rook))*(a.'+a) ≈ eye(n)
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@test size(bc1) == size(bc1.LD)
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@test size(bc1,1) == size(bc1.LD,1)
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@test size(bc1,2) == size(bc1.LD,2)
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if eltya <: BlasReal
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@test_throws ArgumentError bkfact(a)
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end
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end
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end
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@testset "Bunch-Kaufman factors of a pos-def matrix" begin
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@testset for rook in (false, true)
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bc2 = bkfact(apd, :U, issymmetric(apd), rook)
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@test logdet(bc2) ≈ log(det(bc2))
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@test logabsdet(bc2)[1] ≈ log(abs(det(bc2)))
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@test logabsdet(bc2)[2] == sign(det(bc2))
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@test inv(bc2)*apd ≈ eye(n)
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@test apd*(bc2\b) ≈ b atol=150000ε
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@test ishermitian(bc2) == !issymmetric(bc2)
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end
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end
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end
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end
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end
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end
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@testset "Bunch-Kaufman factors of a singular matrix" begin
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let As1 = ones(n, n)
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As2 = complex(ones(n, n))
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As3 = complex(ones(n, n))
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As3[end, 1] += im
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As3[1, end] -= im
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for As = (As1, As2, As3)
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@testset for Astype in ("Array", "SubArray")
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if Astype == "Array"
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As = As
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else
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As = view(As, 1:n, 1:n)
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end
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@testset for rook in (false, true)
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F = bkfact(As, :U, issymmetric(As), rook)
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@test det(F) == 0
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@test_throws LinAlg.SingularException inv(F)
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@test_throws LinAlg.SingularException F \ ones(size(As, 1))
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end
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end
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end
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end
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end
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# test example due to @timholy in PR 15354
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let
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A = rand(6,5); A = complex(A'*A) # to avoid calling the real-lhs-complex-rhs method
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F = cholfact(A);
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v6 = rand(Complex128, 6)
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v5 = view(v6, 1:5)
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@test F\v5 == F\v6[1:5]
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end
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@test_throws DomainError logdet(bkfact([-1 -1; -1 1]))
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@test logabsdet(bkfact([8 4; 4 2]))[1] == -Inf
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@test isa(bkfact(Symmetric(ones(0,0))), Base.LinAlg.BunchKaufman) # 0x0 matrix
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