/usr/share/julia/test/linalg/lu.jl is in julia-common 0.4.7-6.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 | # This file is a part of Julia. License is MIT: http://julialang.org/license
debug = false
using Base.Test
import Base.LinAlg.BlasInt, Base.LinAlg.BlasFloat
n = 10
# Split n into 2 parts for tests needing two matrices
n1 = div(n, 2)
n2 = 2*n1
srand(1234321)
a = rand(n,n)
areal = randn(n,n)/2
aimg = randn(n,n)/2
breal = randn(n,2)/2
bimg = randn(n,2)/2
creal = randn(n)/2
cimg = randn(n)/2
dureal = randn(n-1)/2
duimg = randn(n-1)/2
dlreal = randn(n-1)/2
dlimg = randn(n-1)/2
dreal = randn(n)/2
dimg = randn(n)/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)
d = eltya == Int ? Tridiagonal(rand(1:7, n-1), rand(1:7, n), rand(1:7, n-1)) : convert(Tridiagonal{eltya}, eltya <: Complex ? Tridiagonal(complex(dlreal, dlimg), complex(dreal, dimg), complex(dureal, duimg)) : Tridiagonal(dlreal, dreal, dureal))
ε = εa = eps(abs(float(one(eltya))))
if eltya <: BlasFloat
num = rand(eltya)
@test lu(num) == (one(eltya),num,1)
@test_approx_eq full(lufact(num)) eltya[num]
end
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)
c = eltyb == Int ? rand(1:5, n) : convert(Vector{eltyb}, eltyb <: Complex ? complex(creal, cimg) : creal)
εb = eps(abs(float(one(eltyb))))
ε = max(εa,εb)
debug && println("(Automatic) Square LU decomposition")
κ = cond(a,1)
lua = factorize(a)
@test_throws KeyError lua[:Z]
l,u,p = lua[:L], lua[:U], lua[:p]
ll,ul,pl = lu(a)
@test_approx_eq ll * ul a[pl,:]
@test_approx_eq l*u a[p,:]
@test_approx_eq (l*u)[invperm(p),:] a
@test_approx_eq a * inv(lua) eye(n)
@test norm(a*(lua\b) - b, 1) < ε*κ*n*2 # Two because the right hand side has two columns
@test norm(a'*(lua'\b) - b, 1) < ε*κ*n*2 # Two because the right hand side has two columns
@test norm(a'*(lua'\a') - a', 1) < ε*κ*n^2
@test norm(a*(lua\c) - c, 1) < ε*κ*n # c is a vector
@test norm(a'*(lua'\c) - c, 1) < ε*κ*n # c is a vector
@test_approx_eq full(lua) a
if eltya <: Real && eltyb <: Real
@test norm(a.'*(lua.'\b) - b,1) < ε*κ*n*2 # Two because the right hand side has two columns
@test norm(a.'*(lua.'\c) - c,1) < ε*κ*n
end
if eltya <: BlasFloat && eltyb <: BlasFloat
e = rand(eltyb,n,n)
@test norm(e/lua - e/a,1) < ε*κ*n^2
end
debug && println("Tridiagonal LU")
κd = cond(full(d),1)
lud = lufact(d)
@test lufact(lud) == lud
@test_throws KeyError lud[:Z]
@test_approx_eq lud[:L]*lud[:U] lud[:P]*full(d)
@test_approx_eq lud[:L]*lud[:U] full(d)[lud[:p],:]
@test_approx_eq full(lud) d
@test norm(d*(lud\b) - b, 1) < ε*κd*n*2 # Two because the right hand side has two columns
if eltya <: Real
@test norm((lud.'\b) - full(d.')\b, 1) < ε*κd*n*2 # Two because the right hand side has two columns
end
if eltya <: Complex
@test norm((lud'\b) - full(d')\b, 1) < ε*κd*n*2 # Two because the right hand side has two columns
end
f = zeros(eltyb, n+1)
@test_throws DimensionMismatch lud\f
@test_throws DimensionMismatch lud.'\f
@test_throws DimensionMismatch lud'\f
if eltya <: BlasFloat && eltyb <: BlasFloat
e = rand(eltyb,n,n)
@test norm(e/lud - e/d,1) < ε*κ*n^2
@test norm((lud.'\e') - full(d.')\e',1) < ε*κd*n^2
#test singular
du = rand(eltya,n-1)
dl = rand(eltya,n-1)
dd = rand(eltya,n)
dd[1] = zero(eltya)
du[1] = zero(eltya)
dl[1] = zero(eltya)
zT = Tridiagonal(dl,dd,du)
@test lufact(zT).info == 1
end
debug && println("Thin LU")
lua = @inferred lufact(a[:,1:n1])
@test_approx_eq lua[:L]*lua[:U] lua[:P]*a[:,1:n1]
debug && println("Fat LU")
lua = lufact(a[1:n1,:])
@test_approx_eq lua[:L]*lua[:U] lua[:P]*a[1:n1,:]
end
end
# test conversion routine
a = Tridiagonal(rand(9),rand(10),rand(9))
fa = full(a)
falu = lufact(fa)
alu = lufact(a)
falu = convert(typeof(falu),alu)
@test full(alu) == fa
# Test rational matrices
## Integrate in general tests when more linear algebra is implemented in julia
a = convert(Matrix{Rational{BigInt}}, rand(1:10//1,n,n))/n
b = rand(1:10,n,2)
@inferred lufact(a)
lua = factorize(a)
l,u,p = lua[:L], lua[:U], lua[:p]
@test_approx_eq l*u a[p,:]
@test_approx_eq l[invperm(p),:]*u a
@test_approx_eq a * inv(lua) eye(n)
@test_approx_eq a*(lua\b) b
@test_approx_eq @inferred(det(a)) det(Array{Float64}(a))
## Hilbert Matrix (very ill conditioned)
## Testing Rational{BigInt} and BigFloat version
nHilbert = 50
H = Rational{BigInt}[1//(i+j-1) for i = 1:nHilbert,j = 1:nHilbert]
Hinv = Rational{BigInt}[(-1)^(i+j)*(i+j-1)*binomial(nHilbert+i-1,nHilbert-j)*binomial(nHilbert+j-1,nHilbert-i)*binomial(i+j-2,i-1)^2 for i = big(1):nHilbert,j=big(1):nHilbert]
@test inv(H) == Hinv
with_bigfloat_precision(2^10) do
@test norm(Array{Float64}(inv(float(H)) - float(Hinv))) < 1e-100
end
# Test balancing in eigenvector calculations
for elty in (Float32, Float64, Complex64, Complex128)
A = convert(Matrix{elty}, [ 3.0 -2.0 -0.9 2*eps(real(one(elty)));
-2.0 4.0 1.0 -eps(real(one(elty)));
-eps(real(one(elty)))/4 eps(real(one(elty)))/2 -1.0 0;
-0.5 -0.5 0.1 1.0])
F = eigfact(A, permute=false, scale=false)
eig(A, permute=false, scale=false)
@test_approx_eq F[:vectors]*Diagonal(F[:values])/F[:vectors] A
F = eigfact(A)
# @test norm(F[:vectors]*Diagonal(F[:values])/F[:vectors] - A) > 0.01
end
@test @inferred(logdet(Complex64[1.0f0 0.5f0; 0.5f0 -1.0f0])) === 0.22314355f0 + 3.1415927f0im
@test_throws DomainError logdet([1 1; 1 -1])
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