# This file is a part of Julia. License is MIT: http://julialang.org/license
debug = false
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
breal = randn(n,2)/2
bimg = randn(n,2)/2
for eltya in (Float32, Float64, Complex64, Complex128, BigFloat, 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 = a'+a # symmetric indefinite
apd = a'*a # symmetric positive-definite
ε = εa = eps(abs(float(one(eltya))))
for eltyb in (Float32, Float64, Complex64, Complex128, Int)
b = eltyb == Int ? rand(1:5, n, 2) : convert(Matrix{eltyb}, eltyb <: Complex ? complex.(breal, bimg) : breal)
εb = eps(abs(float(one(eltyb))))
ε = max(εa,εb)
α = rand(eltyb)
aα = fill(α,1,1)
@test qrfact(α)[:Q]*qrfact(α)[:R] ≈ qrfact(aα)[:Q]*qrfact(aα)[:R]
@test abs(qrfact(α)[:Q][1,1]) ≈ one(eltyb)
tab = promote_type(eltya,eltyb)
debug && println("\ntype of a: ", eltya, " type of b: ", eltyb, "\n")
debug && println("QR decomposition (without pivoting)")
for i = 1:2
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
qra = @inferred qrfact(a)
@inferred qr(a)
q, r = qra[:Q], qra[:R]
@test_throws KeyError qra[:Z]
@test q'*full(q, thin=false) ≈ eye(n)
@test q*full(q, thin=false)' ≈ eye(n)
@test q'*eye(n)' ≈ full(q, thin=false)'
@test full(q, thin=false)'q ≈ eye(n)
@test eye(n)'q' ≈ full(q, thin=false)'
@test q*r ≈ a
@test a*(qra\b) ≈ b atol=3000ε
@test full(qra) ≈ a
@test A_mul_Bc(eye(eltyb,size(q.factors,2)),q)*full(q,thin=false) ≈ eye(n) atol=5000ε
if eltya != Int
@test eye(eltyb,n)*q ≈ convert(AbstractMatrix{tab},q)
ac = copy(a)
@test qrfact!(a[:, 1:5])\b == qrfact!(view(ac, :, 1:5))\b
end
rstring = sprint(show,r)
qstring = sprint(show,q)
@test sprint(show,qra) == "$(typeof(qra)) with factors Q and R:\n$qstring\n$rstring"
debug && println("Thin QR decomposition (without pivoting)")
qra = @inferred qrfact(a[:,1:n1], Val{false})
@inferred qr(a[:,1:n1], Val{false})
q,r = qra[:Q], qra[:R]
@test_throws KeyError qra[:Z]
@test q'*full(q, thin=false) ≈ eye(n)
@test q'*full(q) ≈ eye(n,n1)
@test q*r ≈ a[:,1:n1]
@test q*b[1:n1] ≈ full(q)*b[1:n1] atol=100ε
@test q*b ≈ full(q,thin=false)*b atol=100ε
@test_throws DimensionMismatch q*b[1:n1 + 1]
@test_throws DimensionMismatch b[1:n1 + 1]*q'
@test A_mul_Bc(UpperTriangular(eye(eltyb,size(q.factors,2))),q)*full(q,thin=false) ≈ eye(n1,n) atol=5000ε
if eltya != Int
@test eye(eltyb,n)*q ≈ convert(AbstractMatrix{tab},q)
end
debug && println("(Automatic) Fat (pivoted) QR decomposition")
@inferred qrfact(a, Val{true})
@inferred qr(a, Val{true})
qrpa = factorize(a[1:n1,:])
q,r = qrpa[:Q], qrpa[:R]
@test_throws KeyError qrpa[:Z]
p = qrpa[:p]
@test q'*full(q, thin=false) ≈ eye(n1)
@test q*full(q, thin=false)' ≈ eye(n1)
@test (UpperTriangular(eye(eltya,size(q,2)))*q')*full(q, thin=false) ≈ eye(n1)
@test q*r ≈ (isa(qrpa,QRPivoted) ? a[1:n1,p] : a[1:n1,:])
@test q*r[:,invperm(p)] ≈ a[1:n1,:]
@test q*r*qrpa[:P].' ≈ a[1:n1,:]
@test a[1:n1,:]*(qrpa\b[1:n1]) ≈ b[1:n1] atol=5000ε
@test full(qrpa) ≈ a[1:5,:]
@test_throws DimensionMismatch q*b[1:n1+1]
@test_throws DimensionMismatch b[1:n1+1]*q'
if eltya != Int
@test eye(eltyb,n1)*q ≈ convert(AbstractMatrix{tab},q)
end
debug && println("(Automatic) Thin (pivoted) QR decomposition")
qrpa = factorize(a[:,1:n1])
q,r = qrpa[:Q], qrpa[:R]
@test_throws KeyError qrpa[:Z]
p = qrpa[:p]
@test q'*full(q, thin=false) ≈ eye(n)
@test q*full(q, thin=false)' ≈ eye(n)
@test q*r ≈ a[:,p]
@test q*r[:,invperm(p)] ≈ a[:,1:n1]
@test full(qrpa) ≈ a[:,1:5]
@test_throws DimensionMismatch q*b[1:n1+1]
@test_throws DimensionMismatch b[1:n1+1]*q'
@test A_mul_Bc(UpperTriangular(eye(eltyb,size(q.factors,2))),q)*full(q,thin=false) ≈ eye(n1,n) atol=5000ε
if eltya != Int
@test eye(eltyb,n)*q ≈ convert(AbstractMatrix{tab},q)
end
end
end
debug && println("Matmul with QR factorizations")
if eltya != Int
qrpa = factorize(a[:,1:n1])
q, r = qrpa[:Q], qrpa[:R]
@test A_mul_B!(full(q, thin=false)',q) ≈ eye(n)
@test_throws DimensionMismatch A_mul_B!(eye(eltya,n+1),q)
@test A_mul_Bc!(full(q, thin=false),q) ≈ eye(n)
@test_throws DimensionMismatch A_mul_Bc!(eye(eltya,n+1),q)
@test_throws BoundsError size(q,-1)
@test_throws DimensionMismatch Base.LinAlg.A_mul_B!(q,zeros(eltya,n1+1))
@test_throws DimensionMismatch Base.LinAlg.Ac_mul_B!(q,zeros(eltya,n1+1))
qra = qrfact(a[:,1:n1], Val{false})
q, r = qra[:Q], qra[:R]
@test A_mul_B!(full(q, thin=false)',q) ≈ eye(n)
@test_throws DimensionMismatch A_mul_B!(eye(eltya,n+1),q)
@test A_mul_Bc!(full(q, thin=false),q) ≈ eye(n)
@test_throws DimensionMismatch A_mul_Bc!(eye(eltya,n+1),q)
@test_throws BoundsError size(q,-1)
@test_throws DimensionMismatch q * eye(Int8,n+4)
end
end
end
# Because transpose(x) == x
@test_throws ErrorException transpose(qrfact(randn(3,3)))
@test_throws ErrorException ctranspose(qrfact(randn(3,3)))
@test_throws ErrorException transpose(qrfact(randn(3,3), Val{false}))
@test_throws ErrorException ctranspose(qrfact(randn(3,3), Val{false}))
@test_throws ErrorException transpose(qrfact(big.(randn(3,3))))
@test_throws ErrorException ctranspose(qrfact(big.(randn(3,3))))
# Issue 7304
let
A = [-√.5 -√.5; -√.5 √.5]
Q = full(qrfact(A)[:Q])
@test vecnorm(A-Q) < eps()
end
let
debug && println("qr on AbstractVector")
vr = [3.0, 4.0]
for Tr in (Float32, Float64)
for T in (Tr, Complex{Tr})
v = convert(Vector{T}, vr)
nv, nm = qr(v)
@test norm(nv - [0.6, 0.8], Inf) < eps(Tr)
@test nm == 5.0
end
end
end
@test qr(Int[]) == (Int[],1)
@test Base.LinAlg.qr!(Int[1]) == (Int[1],1)
B = rand(7,2)
@test (1:7)\B ≈ collect(1:7)\B
# Issue 16520
@test_throws DimensionMismatch ones(3,2)\(1:5)