Revision 2bc58db83ea4b78c2f03644a0408f0521a46f7f0 authored by Jameson Nash on 26 August 2015, 22:13:21 UTC, committed by Jameson Nash on 26 August 2015, 22:13:30 UTC
1 parent 8b95c0d
qr.jl
# 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)
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 : sub(a, 1:n - 1, 1:n - 1), b = i == 1 ? b : sub(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_approx_eq q'*full(q, thin = false) eye(n)
@test_approx_eq q*full(q, thin = false)' eye(n)
@test_approx_eq q*r a
@test_approx_eq_eps a*(qra\b) b 3000ε
@test_approx_eq full(qra) a
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_approx_eq q'*full(q, thin=false) eye(n)
@test_approx_eq q'*full(q) eye(n, n1)
@test_approx_eq q*r a[:,1:n1]
@test_approx_eq_eps q*b[1:n1] full(q)*b[1:n1] 100ε
@test_approx_eq_eps q*b full(q, thin=false)*b 100ε
@test_throws DimensionMismatch q*b[1:n1 + 1]
debug && println("(Automatic) Fat (pivoted) QR decomposition") # Pivoting is only implemented for BlasFloats
if eltya <: BlasFloat
@inferred qrfact(a, Val{true})
@inferred qr(a, Val{true})
end
qrpa = factorize(a[1:n1,:])
q,r = qrpa[:Q], qrpa[:R]
@test_throws KeyError qrpa[:Z]
if isa(qrpa,QRPivoted) p = qrpa[:p] end # Reconsider if pivoted QR gets implemented in julia
@test_approx_eq q'*full(q, thin=false) eye(n1)
@test_approx_eq q*full(q, thin=false)' eye(n1)
@test_approx_eq q*r isa(qrpa,QRPivoted) ? a[1:n1,p] : a[1:n1,:]
@test_approx_eq isa(qrpa, QRPivoted) ? q*r[:,invperm(p)] : q*r a[1:n1,:]
@test_approx_eq_eps a[1:n1,:]*(qrpa\b[1:n1]) b[1:n1] 5000ε
@test_approx_eq full(qrpa) a[1:5,:]
debug && println("(Automatic) Thin (pivoted) QR decomposition") # Pivoting is only implemented for BlasFloats
qrpa = factorize(a[:,1:n1])
q,r = qrpa[:Q], qrpa[:R]
@test_throws KeyError qrpa[:Z]
if isa(qrpa, QRPivoted) p = qrpa[:p] end # Reconsider if pivoted QR gets implemented in julia
@test_approx_eq q'*full(q, thin=false) eye(n)
@test_approx_eq q*full(q, thin=false)' eye(n)
@test_approx_eq q*r isa(qrpa, QRPivoted) ? a[:,p] : a[:,1:n1]
@test_approx_eq isa(qrpa, QRPivoted) ? q*r[:,invperm(p)] : q*r a[:,1:n1]
@test_approx_eq full(qrpa) a[:,1:5]
end
end
debug && println("Matmul with QR factorizations")
if eltya != Int
qrpa = factorize(a[:,1:n1])
q,r = qrpa[:Q], qrpa[:R]
@test_approx_eq A_mul_B!(full(q,thin=false)',q) eye(n)
@test_throws DimensionMismatch A_mul_B!(eye(eltya,n+1),q)
@test_approx_eq 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)
qra = qrfact(a[:,1:n1], Val{false})
q,r = qra[:Q], qra[:R]
@test_approx_eq A_mul_B!(full(q,thin=false)',q) eye(n)
@test_throws DimensionMismatch A_mul_B!(eye(eltya,n+1),q)
@test_approx_eq 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
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