svd.jl
# This file is a part of Julia. License is MIT: http://julialang.org/license
using Base.Test
using Base.LinAlg: BlasComplex, BlasFloat, BlasReal, QRPivoted
n = 10
# Split n into 2 parts for tests needing two matrices
n1 = div(n, 2)
n2 = 2*n1
srand(1234321)
areal = randn(n,n)/2
aimg = randn(n,n)/2
a2real = randn(n,n)/2
a2img = randn(n,n)/2
@testset for eltya in (Float32, Float64, Complex64, Complex128, Int)
aa = eltya == Int ? rand(1:7, n, n) : convert(Matrix{eltya}, eltya <: Complex ? complex.(areal, aimg) : areal)
aa2 = eltya == Int ? rand(1:7, n, n) : convert(Matrix{eltya}, eltya <: Complex ? complex.(a2real, a2img) : a2real)
asym = aa'+aa # symmetric indefinite
apd = aa'*aa # symmetric positive-definite
@testset for atype in ("Array", "SubArray")
if atype == "Array"
a = aa
a2 = aa2
else
a = view(aa, 1:n, 1:n)
a2 = view(aa2, 1:n, 1:n)
end
ε = εa = eps(abs(float(one(eltya))))
usv = svdfact(a)
@testset "singular value decomposition" begin
@test usv[:S] === svdvals(usv)
@test usv[:U] * (Diagonal(usv[:S]) * usv[:Vt]) ≈ a
@test AbstractArray(usv) ≈ a
@test usv[:Vt]' ≈ usv[:V]
@test_throws KeyError usv[:Z]
b = rand(eltya,n)
@test usv\b ≈ a\b
if eltya <: BlasFloat
svdz = svdfact!(ones(eltya,0,0))
@test svdz[:U] ≈ eye(eltya,0,0)
@test svdz[:S] ≈ real(zeros(eltya,0))
@test svdz[:Vt] ≈ eye(eltya,0,0)
end
end
@testset "Generalized svd" begin
a_svd = a[1:n1, :]
gsvd = svdfact(a,a_svd)
@test gsvd[:U]*gsvd[:D1]*gsvd[:R]*gsvd[:Q]' ≈ a
@test gsvd[:V]*gsvd[:D2]*gsvd[:R]*gsvd[:Q]' ≈ a_svd
@test usv[:Vt]' ≈ usv[:V]
@test_throws KeyError usv[:Z]
@test_throws KeyError gsvd[:Z]
@test gsvd[:vals] ≈ svdvals(a,a_svd)
α = eltya == Int ? -1 : rand(eltya)
β = svdfact(α)
@test β[:S] == [abs(α)]
@test svdvals(α) == abs(α)
u,v,q,d1,d2,r0 = svd(a,a_svd)
@test u ≈ gsvd[:U]
@test v ≈ gsvd[:V]
@test d1 ≈ gsvd[:D1]
@test d2 ≈ gsvd[:D2]
@test q ≈ gsvd[:Q]
@test gsvd[:a].^2 + gsvd[:b].^2 ≈ ones(eltya,length(gsvd[:a]))
#testing the other layout for D1 & D2
b = rand(eltya,n,2*n)
c = rand(eltya,n,2*n)
gsvd = svdfact(b,c)
@test gsvd[:U]*gsvd[:D1]*gsvd[:R]*gsvd[:Q]' ≈ b
@test gsvd[:V]*gsvd[:D2]*gsvd[:R]*gsvd[:Q]' ≈ c
end
end
end