137 lines
5.8 KiB
Julia
137 lines
5.8 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
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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)
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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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asym = a'+a # symmetric indefinite
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apd = a'*a # symmetric positive-definite
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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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εb = eps(abs(float(one(eltyb))))
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ε = max(εa,εb)
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α = rand(eltya)
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aα = fill(α,1,1)
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@test lqfact(α)[:L]*lqfact(α)[:Q] ≈ lqfact(aα)[:L]*lqfact(aα)[:Q]
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@test lq(α)[1]*lq(α)[2] ≈ lqfact(aα)[:L]*lqfact(aα)[:Q]
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@test abs(lqfact(α)[:Q][1,1]) ≈ one(eltya)
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tab = promote_type(eltya,eltyb)
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for i = 1:2
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let a = i == 1 ? a : view(a, 1:n - 1, 1:n - 1), b = i == 1 ? b : view(b, 1:n - 1), n = i == 1 ? n : n - 1
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lqa = lqfact(a)
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l,q = lqa[:L], lqa[:Q]
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qra = qrfact(a)
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@testset "Basic ops" begin
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@test size(lqa,1) == size(a,1)
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@test size(lqa,3) == 1
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@test size(lqa[:Q],3) == 1
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@test Base.LinAlg.getq(lqa) == lqa[:Q]
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@test_throws KeyError lqa[:Z]
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@test full(lqa') ≈ a'
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@test lqa * lqa' ≈ a * a'
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@test lqa' * lqa ≈ a' * a
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@test q*full(q, thin = false)' ≈ eye(eltya,n)
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@test l*q ≈ a
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@test full(lqa) ≈ a
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@test full(copy(lqa)) ≈ a
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lstring = sprint(show,l)
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qstring = sprint(show,q)
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@test sprint(show,lqa) == "$(typeof(lqa)) with factors L and Q:\n$lstring\n$qstring"
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end
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@testset "Binary ops" begin
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@test a*(lqa\b) ≈ b atol=3000ε
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@test lqa*b ≈ qra[:Q]*qra[:R]*b atol=3000ε
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@test A_mul_Bc(eye(eltyb,size(q.factors,2)),q)*full(q,thin=false) ≈ eye(n) atol=5000ε
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if eltya != Int
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@test eye(eltyb,n)*q ≈ convert(AbstractMatrix{tab},q)
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end
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@test q*b ≈ full(q,thin=false)*b atol=100ε
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@test q.'*b ≈ full(q,thin=false).'*b atol=100ε
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@test q'*b ≈ full(q,thin=false)'*b atol=100ε
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@test a*q ≈ a*full(q,thin=false) atol=100ε
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@test a*q.' ≈ a*full(q,thin=false).' atol=100ε
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@test a*q' ≈ a*full(q,thin=false)' atol=100ε
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@test a'*q ≈ a'*full(q,thin=false) atol=100ε
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@test a'*q' ≈ a'*full(q,thin=false)' atol=100ε
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@test_throws DimensionMismatch q*b[1:n1 + 1]
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@test_throws DimensionMismatch Ac_mul_B(q,ones(eltya,n+2,n+2))
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@test_throws DimensionMismatch ones(eltyb,n+2,n+2)*q
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if isa(a, DenseArray) && isa(b, DenseArray)
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# use this to test 2nd branch in mult code
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pad_a = vcat(eye(a), a)
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pad_b = hcat(eye(b), b)
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@test pad_a*q ≈ pad_a*full(q,thin=false) atol=100ε
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@test q.'*pad_b ≈ full(q,thin=false).'*pad_b atol=100ε
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@test q'*pad_b ≈ full(q,thin=false)'*pad_b atol=100ε
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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 "Matmul with LQ factorizations" begin
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lqa = lqfact(a[:,1:n1])
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l,q = lqa[:L], lqa[:Q]
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@test full(q)*full(q)' ≈ eye(eltya,n1)
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@test (full(q,thin=false)'*full(q,thin=false))[1:n1,:] ≈ eye(eltya,n1,n)
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@test_throws DimensionMismatch A_mul_B!(eye(eltya,n+1),q)
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@test Ac_mul_B!(q,full(q)) ≈ eye(eltya,n1)
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@test_throws DimensionMismatch A_mul_Bc!(eye(eltya,n+1),q)
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@test_throws BoundsError size(q,-1)
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end
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end
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end
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@testset "getindex on LQPackedQ (#23733)" begin
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function getqs(F::Base.LinAlg.LQ)
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implicitQ = F[:Q]
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explicitQ = A_mul_B!(implicitQ, eye(eltype(implicitQ), size(implicitQ.factors, 2)))
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return implicitQ, explicitQ
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end
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m, n = 3, 3 # thin Q 3-by-3, square Q 3-by-3
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implicitQ, explicitQ = getqs(lqfact(randn(m, n)))
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@test implicitQ[1, 1] == explicitQ[1, 1]
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@test implicitQ[m, 1] == explicitQ[m, 1]
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@test implicitQ[1, n] == explicitQ[1, n]
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@test implicitQ[m, n] == explicitQ[m, n]
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m, n = 3, 4 # thin Q 3-by-4, square Q 4-by-4
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implicitQ, explicitQ = getqs(lqfact(randn(m, n)))
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@test implicitQ[1, 1] == explicitQ[1, 1]
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@test implicitQ[m, 1] == explicitQ[m, 1]
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@test implicitQ[1, n] == explicitQ[1, n]
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@test implicitQ[m, n] == explicitQ[m, n]
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@test implicitQ[m+1, 1] == explicitQ[m+1, 1]
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@test implicitQ[m+1, n] == explicitQ[m+1, n]
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m, n = 4, 3 # thin Q 3-by-3, square Q 3-by-3
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implicitQ, explicitQ = getqs(lqfact(randn(m, n)))
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@test implicitQ[1, 1] == explicitQ[1, 1]
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@test implicitQ[n, 1] == explicitQ[n, 1]
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@test implicitQ[1, n] == explicitQ[1, n]
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@test implicitQ[n, n] == explicitQ[n, n]
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end
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