cholmod.jl
# This file is a part of Julia. License is MIT: https://julialang.org/license
srand(123)
using Base.SparseArrays.CHOLMOD
using DelimitedFiles
# based on deps/SuiteSparse-4.0.2/CHOLMOD/Demo/
# chm_rdsp(joinpath(JULIA_HOME, "../../deps/SuiteSparse-4.0.2/CHOLMOD/Demo/Matrix/bcsstk01.tri"))
# because the file may not exist in binary distributions and when a system suitesparse library
# is used
## Result from C program
## ---------------------------------- cholmod_demo:
## norm (A,inf) = 3.57095e+09
## norm (A,1) = 3.57095e+09
## CHOLMOD sparse: A: 48-by-48, nz 224, upper. OK
## CHOLMOD dense: B: 48-by-1, OK
## bnorm 1.97917
## Analyze: flop 6009 lnz 489
## Factorizing A
## CHOLMOD factor: L: 48-by-48 simplicial, LDL'. nzmax 489. nz 489 OK
## Ordering: AMD fl/lnz 12.3 lnz/anz 2.2
## ints in L: 782, doubles in L: 489
## factor flops 6009 nnz(L) 489 (w/no amalgamation)
## nnz(A*A'): 224
## flops / nnz(L): 12.3
## nnz(L) / nnz(A): 2.2
## analyze cputime: 0.0000
## factor cputime: 0.0000 mflop: 0.0
## solve cputime: 0.0000 mflop: 0.0
## overall cputime: 0.0000 mflop: 0.0
## peak memory usage: 0 (MB)
## residual 2.5e-19 (|Ax-b|/(|A||x|+|b|))
## residual 1.3e-19 (|Ax-b|/(|A||x|+|b|)) after iterative refinement
## rcond 9.5e-06
A = CHOLMOD.Sparse(48, 48,
CHOLMOD.SuiteSparse_long[0,1,2,3,6,9,12,15,18,20,25,30,34,36,39,43,47,52,58,
62,67,71,77,84,90,93,95,98,103,106,110,115,119,123,130,136,142,146,150,155,
161,167,174,182,189,197,207,215,224], # zero-based column pointers
CHOLMOD.SuiteSparse_long[0,1,2,1,2,3,0,2,4,0,1,5,0,4,6,1,3,7,2,8,1,3,7,8,9,
0,4,6,8,10,5,6,7,11,6,12,7,11,13,8,10,13,14,9,13,14,15,8,10,12,14,16,7,11,
12,13,16,17,0,12,16,18,1,5,13,15,19,2,4,14,20,3,13,15,19,20,21,2,4,12,16,18,
20,22,1,5,17,18,19,23,0,5,24,1,25,2,3,26,2,3,25,26,27,4,24,28,0,5,24,29,6,
11,24,28,30,7,25,27,31,8,9,26,32,8,9,25,27,31,32,33,10,24,28,30,32,34,6,11,
29,30,31,35,12,17,30,36,13,31,35,37,14,15,32,34,38,14,15,33,37,38,39,16,32,
34,36,38,40,12,17,31,35,36,37,41,12,16,17,18,23,36,40,42,13,14,15,19,37,39,
43,13,14,15,20,21,38,43,44,13,14,15,20,21,37,39,43,44,45,12,16,17,22,36,40,
42,46,12,16,17,18,23,41,42,46,47],
[2.83226851852e6,1.63544753086e6,1.72436728395e6,-2.0e6,-2.08333333333e6,
1.00333333333e9,1.0e6,-2.77777777778e6,1.0675e9,2.08333333333e6,
5.55555555555e6,1.53533333333e9,-3333.33333333,-1.0e6,2.83226851852e6,
-6666.66666667,2.0e6,1.63544753086e6,-1.68e6,1.72436728395e6,-2.0e6,4.0e8,
2.0e6,-2.08333333333e6,1.00333333333e9,1.0e6,2.0e8,-1.0e6,-2.77777777778e6,
1.0675e9,-2.0e6,2.08333333333e6,5.55555555555e6,1.53533333333e9,-2.8e6,
2.8360994695e6,-30864.1975309,-5.55555555555e6,1.76741074446e6,
-15432.0987654,2.77777777778e6,517922.131816,3.89003806848e6,
-3.33333333333e6,4.29857058902e6,-2.6349902747e6,1.97572063531e9,
-2.77777777778e6,3.33333333333e8,-2.14928529451e6,2.77777777778e6,
1.52734651547e9,5.55555555555e6,6.66666666667e8,2.35916180402e6,
-5.55555555555e6,-1.09779731332e8,1.56411143711e9,-2.8e6,-3333.33333333,
1.0e6,2.83226851852e6,-30864.1975309,-5.55555555555e6,-6666.66666667,
-2.0e6,1.63544753086e6,-15432.0987654,2.77777777778e6,-1.68e6,
1.72436728395e6,-3.33333333333e6,2.0e6,4.0e8,-2.0e6,-2.08333333333e6,
1.00333333333e9,-2.77777777778e6,3.33333333333e8,-1.0e6,2.0e8,1.0e6,
2.77777777778e6,1.0675e9,5.55555555555e6,6.66666666667e8,-2.0e6,
2.08333333333e6,-5.55555555555e6,1.53533333333e9,-28935.1851852,
-2.08333333333e6,60879.6296296,-1.59791666667e6,3.37291666667e6,
-28935.1851852,2.08333333333e6,2.41171296296e6,-2.08333333333e6,
1.0e8,-2.5e6,-416666.666667,1.5e9,-833333.333333,1.25e6,5.01833333333e8,
2.08333333333e6,1.0e8,416666.666667,5.025e8,-28935.1851852,
-2.08333333333e6,-4166.66666667,-1.25e6,3.98587962963e6,-1.59791666667e6,
-8333.33333333,2.5e6,3.41149691358e6,-28935.1851852,2.08333333333e6,
-2.355e6,2.43100308642e6,-2.08333333333e6,1.0e8,-2.5e6,5.0e8,2.5e6,
-416666.666667,1.50416666667e9,-833333.333333,1.25e6,2.5e8,-1.25e6,
-3.47222222222e6,1.33516666667e9,2.08333333333e6,1.0e8,-2.5e6,
416666.666667,6.94444444444e6,2.16916666667e9,-28935.1851852,
-2.08333333333e6,-3.925e6,3.98587962963e6,-1.59791666667e6,
-38580.2469136,-6.94444444444e6,3.41149691358e6,-28935.1851852,
2.08333333333e6,-19290.1234568,3.47222222222e6,2.43100308642e6,
-2.08333333333e6,1.0e8,-4.16666666667e6,2.5e6,-416666.666667,
1.50416666667e9,-833333.333333,-3.47222222222e6,4.16666666667e8,
-1.25e6,3.47222222222e6,1.33516666667e9,2.08333333333e6,1.0e8,
6.94444444445e6,8.33333333333e8,416666.666667,-6.94444444445e6,
2.16916666667e9,-3830.95098171,1.14928529451e6,-275828.470683,
-28935.1851852,-2.08333333333e6,-4166.66666667,1.25e6,64710.5806113,
-131963.213599,-517922.131816,-2.29857058902e6,-1.59791666667e6,
-8333.33333333,-2.5e6,3.50487988027e6,-517922.131816,-2.16567078453e6,
551656.941366,-28935.1851852,2.08333333333e6,-2.355e6,517922.131816,
4.57738374749e6,2.29857058902e6,-551656.941367,4.8619365099e8,
-2.08333333333e6,1.0e8,2.5e6,5.0e8,-4.79857058902e6,134990.2747,
2.47238730198e9,-1.14928529451e6,2.29724661236e8,-5.57173510779e7,
-833333.333333,-1.25e6,2.5e8,2.39928529451e6,9.61679848804e8,275828.470683,
-5.57173510779e7,1.09411960038e7,2.08333333333e6,1.0e8,-2.5e6,
140838.195984,-1.09779731332e8,5.31278103775e8], 1)
@test CHOLMOD.norm_sparse(A, 0) ≈ 3.570948074697437e9
@test CHOLMOD.norm_sparse(A, 1) ≈ 3.570948074697437e9
@test_throws ArgumentError CHOLMOD.norm_sparse(A, 2)
@test CHOLMOD.isvalid(A)
B = A * ones(size(A,2))
chma = ldltfact(A) # LDL' form
@test CHOLMOD.isvalid(chma)
@test unsafe_load(pointer(chma)).is_ll == 0 # check that it is in fact an LDLt
x = chma\B
@test x ≈ ones(size(x))
@test nnz(ldltfact(A, perm=1:size(A,1))) > nnz(chma)
@test size(chma) == size(A)
chmal = CHOLMOD.FactorComponent(chma, :L)
@test size(chmal) == size(A)
@test size(chmal, 1) == size(A, 1)
chma = cholfact(A) # LL' form
@test CHOLMOD.isvalid(chma)
@test unsafe_load(pointer(chma)).is_ll == 1 # check that it is in fact an LLt
x = chma\B
@test x ≈ ones(size(x))
@test nnz(chma) == 489
@test nnz(cholfact(A, perm=1:size(A,1))) > nnz(chma)
@test size(chma) == size(A)
chmal = CHOLMOD.FactorComponent(chma, :L)
@test size(chmal) == size(A)
@test size(chmal, 1) == size(A, 1)
#lp_afiro example
afiro = CHOLMOD.Sparse(27, 51,
CHOLMOD.SuiteSparse_long[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
23,25,27,29,33,37,41,45,47,49,51,53,55,57,59,63,65,67,69,71,75,79,83,87,89,
91,93,95,97,99,101,102],
CHOLMOD.SuiteSparse_long[2,3,6,7,8,9,12,13,16,17,18,19,20,21,22,23,24,25,26,
0,1,2,23,0,3,0,21,1,25,4,5,6,24,4,5,7,24,4,5,8,24,4,5,9,24,6,20,7,20,8,20,9,
20,3,4,4,22,5,26,10,11,12,21,10,13,10,23,10,20,11,25,14,15,16,22,14,15,17,
22,14,15,18,22,14,15,19,22,16,20,17,20,18,20,19,20,13,15,15,24,14,26,15],
[1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,
1.0,-1.0,-1.06,1.0,0.301,1.0,-1.0,1.0,-1.0,1.0,1.0,-1.0,-1.06,1.0,0.301,
-1.0,-1.06,1.0,0.313,-1.0,-0.96,1.0,0.313,-1.0,-0.86,1.0,0.326,-1.0,2.364,
-1.0,2.386,-1.0,2.408,-1.0,2.429,1.4,1.0,1.0,-1.0,1.0,1.0,-1.0,-0.43,1.0,
0.109,1.0,-1.0,1.0,-1.0,1.0,-1.0,1.0,1.0,-0.43,1.0,1.0,0.109,-0.43,1.0,1.0,
0.108,-0.39,1.0,1.0,0.108,-0.37,1.0,1.0,0.107,-1.0,2.191,-1.0,2.219,-1.0,
2.249,-1.0,2.279,1.4,-1.0,1.0,-1.0,1.0,1.0,1.0], 0)
afiro2 = CHOLMOD.aat(afiro, CHOLMOD.SuiteSparse_long[0:50;], CHOLMOD.SuiteSparse_long(1))
CHOLMOD.change_stype!(afiro2, -1)
chmaf = cholfact(afiro2)
y = afiro'*ones(size(afiro,1))
sol = chmaf\(afiro*y) # least squares solution
@test CHOLMOD.isvalid(sol)
pred = afiro'*sol
@test norm(afiro * (convert(Matrix, y) - convert(Matrix, pred))) < 1e-8
let # Issue 9160
local A, B
A = sprand(10, 10, 0.1)
A = convert(SparseMatrixCSC{Float64,CHOLMOD.SuiteSparse_long}, A)
cmA = CHOLMOD.Sparse(A)
B = sprand(10, 10, 0.1)
B = convert(SparseMatrixCSC{Float64,CHOLMOD.SuiteSparse_long}, B)
cmB = CHOLMOD.Sparse(B)
# Ac_mul_B
@test sparse(cmA'*cmB) ≈ A'*B
# A_mul_Bc
@test sparse(cmA*cmB') ≈ A*B'
# A_mul_Ac
@test sparse(cmA*cmA') ≈ A*A'
# Ac_mul_A
@test sparse(cmA'*cmA) ≈ A'*A
# A_mul_Ac for symmetric A
A = 0.5*(A + A')
cmA = CHOLMOD.Sparse(A)
@test sparse(cmA*cmA') ≈ A*A'
end
# Issue #9915
@test speye(2)\speye(2) == eye(2)
# test eltype
@test eltype(Dense(ones(3))) == Float64
@test eltype(A) == Float64
@test eltype(chma) == Float64
# test Sparse constructor Symmetric and Hermitian input (and issymmetric and ishermitian)
ACSC = sprandn(10, 10, 0.3) + I
@test issymmetric(Sparse(Symmetric(ACSC, :L)))
@test issymmetric(Sparse(Symmetric(ACSC, :U)))
@test ishermitian(Sparse(Hermitian(complex(ACSC), :L)))
@test ishermitian(Sparse(Hermitian(complex(ACSC), :U)))
# test Sparse constructor for c_SparseVoid (and read_sparse)
mktempdir() do temp_dir
testfile = joinpath(temp_dir, "tmp.mtx")
writedlm(testfile, ["%%MatrixMarket matrix coordinate real symmetric","3 3 4","1 1 1","2 2 1","3 2 0.5","3 3 1"])
@test sparse(CHOLMOD.Sparse(testfile)) == [1 0 0;0 1 0.5;0 0.5 1]
rm(testfile)
writedlm(testfile, ["%%MatrixMarket matrix coordinate complex Hermitian",
"3 3 4","1 1 1.0 0.0","2 2 1.0 0.0","3 2 0.5 0.5","3 3 1.0 0.0"])
@test sparse(CHOLMOD.Sparse(testfile)) == [1 0 0;0 1 0.5-0.5im;0 0.5+0.5im 1]
rm(testfile)
writedlm(testfile, ["%%MatrixMarket matrix coordinate real symmetric","%3 3 4","1 1 1","2 2 1","3 2 0.5","3 3 1"])
@test_throws ArgumentError sparse(CHOLMOD.Sparse(testfile))
rm(testfile)
end
# test that Sparse(Ptr) constructor throws the right places
@test_throws ArgumentError CHOLMOD.Sparse(convert(Ptr{CHOLMOD.C_Sparse{Float64}}, C_NULL))
@test_throws ArgumentError CHOLMOD.Sparse(convert(Ptr{CHOLMOD.C_SparseVoid}, C_NULL))
## The struct pointer must be constructed by the library constructor and then modified afterwards to checks that the method throws
### illegal dtype (for now but should be supported at some point)
p = ccall((:cholmod_l_allocate_sparse, :libcholmod), Ptr{CHOLMOD.C_SparseVoid},
(Csize_t, Csize_t, Csize_t, Cint, Cint, Cint, Cint, Ptr{Void}),
1, 1, 1, true, true, 0, CHOLMOD.REAL, CHOLMOD.common_struct)
puint = convert(Ptr{UInt32}, p)
unsafe_store!(puint, CHOLMOD.SINGLE, 3*div(sizeof(Csize_t), 4) + 5*div(sizeof(Ptr{Void}), 4) + 4)
@test_throws CHOLMOD.CHOLMODException CHOLMOD.Sparse(p)
### illegal dtype
p = ccall((:cholmod_l_allocate_sparse, :libcholmod), Ptr{CHOLMOD.C_SparseVoid},
(Csize_t, Csize_t, Csize_t, Cint, Cint, Cint, Cint, Ptr{Void}),
1, 1, 1, true, true, 0, CHOLMOD.REAL, CHOLMOD.common_struct)
puint = convert(Ptr{UInt32}, p)
unsafe_store!(puint, 5, 3*div(sizeof(Csize_t), 4) + 5*div(sizeof(Ptr{Void}), 4) + 4)
@test_throws CHOLMOD.CHOLMODException CHOLMOD.Sparse(p)
### illegal xtype
p = ccall((:cholmod_l_allocate_sparse, :libcholmod), Ptr{CHOLMOD.C_SparseVoid},
(Csize_t, Csize_t, Csize_t, Cint, Cint, Cint, Cint, Ptr{Void}),
1, 1, 1, true, true, 0, CHOLMOD.REAL, CHOLMOD.common_struct)
puint = convert(Ptr{UInt32}, p)
unsafe_store!(puint, 3, 3*div(sizeof(Csize_t), 4) + 5*div(sizeof(Ptr{Void}), 4) + 3)
@test_throws CHOLMOD.CHOLMODException CHOLMOD.Sparse(p)
### illegal itype
p = ccall((:cholmod_l_allocate_sparse, :libcholmod), Ptr{CHOLMOD.C_SparseVoid},
(Csize_t, Csize_t, Csize_t, Cint, Cint, Cint, Cint, Ptr{Void}),
1, 1, 1, true, true, 0, CHOLMOD.REAL, CHOLMOD.common_struct)
puint = convert(Ptr{UInt32}, p)
unsafe_store!(puint, CHOLMOD.INTLONG, 3*div(sizeof(Csize_t), 4) + 5*div(sizeof(Ptr{Void}), 4) + 2)
@test_throws CHOLMOD.CHOLMODException CHOLMOD.Sparse(p)
### illegal itype
p = ccall((:cholmod_l_allocate_sparse, :libcholmod), Ptr{CHOLMOD.C_SparseVoid},
(Csize_t, Csize_t, Csize_t, Cint, Cint, Cint, Cint, Ptr{Void}),
1, 1, 1, true, true, 0, CHOLMOD.REAL, CHOLMOD.common_struct)
puint = convert(Ptr{UInt32}, p)
unsafe_store!(puint, 5, 3*div(sizeof(Csize_t), 4) + 5*div(sizeof(Ptr{Void}), 4) + 2)
@test_throws CHOLMOD.CHOLMODException CHOLMOD.Sparse(p)
# Test Dense wrappers (only Float64 supported a present)
## High level interface
for elty in (Float64, Complex{Float64})
local A, b
if elty == Float64
A = randn(5, 5)
b = randn(5)
else
A = complex.(randn(5, 5), randn(5, 5))
b = complex.(randn(5), randn(5))
end
ADense = CHOLMOD.Dense(A)
bDense = CHOLMOD.Dense(b)
@test_throws BoundsError ADense[6, 1]
@test_throws BoundsError ADense[1, 6]
@test copy(ADense) == ADense
@test CHOLMOD.norm_dense(ADense, 1) ≈ norm(A, 1)
@test CHOLMOD.norm_dense(ADense, 0) ≈ norm(A, Inf)
@test_throws ArgumentError CHOLMOD.norm_dense(ADense, 2)
@test_throws ArgumentError CHOLMOD.norm_dense(ADense, 3)
@test CHOLMOD.norm_dense(bDense, 2) ≈ norm(b)
@test CHOLMOD.check_dense(bDense)
AA = CHOLMOD.eye(3)
unsafe_store!(convert(Ptr{Csize_t}, pointer(AA)), 2, 1) # change size, but not stride, of Dense
@test convert(Matrix, AA) == eye(2, 3)
end
## Low level interface
@test isa(CHOLMOD.zeros(3, 3, Float64), CHOLMOD.Dense{Float64})
@test isa(CHOLMOD.zeros(3, 3), CHOLMOD.Dense{Float64})
@test isa(CHOLMOD.zeros(3, 3, Float64), CHOLMOD.Dense{Float64})
@test isa(CHOLMOD.ones(3, 3), CHOLMOD.Dense{Float64})
@test isa(CHOLMOD.eye(3, 4, Float64), CHOLMOD.Dense{Float64})
@test isa(CHOLMOD.eye(3, 4), CHOLMOD.Dense{Float64})
@test isa(CHOLMOD.eye(3), CHOLMOD.Dense{Float64})
@test isa(CHOLMOD.copy_dense(CHOLMOD.eye(3)), CHOLMOD.Dense{Float64})
# Test Sparse and Factor
## test free_sparse!
p = ccall((:cholmod_l_allocate_sparse, :libcholmod), Ptr{CHOLMOD.C_Sparse{Float64}},
(Csize_t, Csize_t, Csize_t, Cint, Cint, Cint, Cint, Ptr{Void}),
1, 1, 1, true, true, 0, CHOLMOD.REAL, CHOLMOD.common_struct)
@test CHOLMOD.free_sparse!(p)
for elty in (Float64, Complex{Float64})
A1 = sparse([1:5; 1], [1:5; 2], elty == Float64 ? randn(6) : complex.(randn(6), randn(6)))
A2 = sparse([1:5; 1], [1:5; 2], elty == Float64 ? randn(6) : complex.(randn(6), randn(6)))
A1pd = A1'A1
A1Sparse = CHOLMOD.Sparse(A1)
A2Sparse = CHOLMOD.Sparse(A2)
A1pdSparse = CHOLMOD.Sparse(
A1pd.m,
A1pd.n,
Base.SparseArrays.decrement(A1pd.colptr),
Base.SparseArrays.decrement(A1pd.rowval),
A1pd.nzval)
## High level interface
@test isa(CHOLMOD.Sparse(3, 3, [0,1,3,4], [0,2,1,2], ones(4)), CHOLMOD.Sparse) # Sparse doesn't require columns to be sorted
@test_throws BoundsError A1Sparse[6, 1]
@test_throws BoundsError A1Sparse[1, 6]
@test sparse(A1Sparse) == A1
for i=1:size(A1, 1) A1[i, i] = real(A1[i, i]) end #Construct Hermitian matrix properly
@test CHOLMOD.sparse(CHOLMOD.Sparse(Hermitian(A1, :L))) == Hermitian(A1, :L)
@test CHOLMOD.sparse(CHOLMOD.Sparse(Hermitian(A1, :U))) == Hermitian(A1, :U)
@test_throws ArgumentError convert(SparseMatrixCSC{elty,Int}, A1pdSparse)
if elty <: Real
@test_throws ArgumentError convert(Symmetric{Float64,SparseMatrixCSC{Float64,Int}}, A1Sparse)
else
@test_throws ArgumentError convert(Hermitian{Complex{Float64},SparseMatrixCSC{Complex{Float64},Int}}, A1Sparse)
end
@test copy(A1Sparse) == A1Sparse
@test size(A1Sparse, 3) == 1
if elty <: Real # multiplication only defined for real matrices in CHOLMOD
@test A1Sparse*A2Sparse ≈ A1*A2
@test_throws DimensionMismatch CHOLMOD.Sparse(A1[:,1:4])*A2Sparse
@test A1Sparse'A2Sparse ≈ A1'A2
@test A1Sparse*A2Sparse' ≈ A1*A2'
@test A1Sparse*A1Sparse ≈ A1*A1
@test A1Sparse'A1Sparse ≈ A1'A1
@test A1Sparse*A1Sparse' ≈ A1*A1'
@test A1pdSparse*A1pdSparse ≈ A1pd*A1pd
@test A1pdSparse'A1pdSparse ≈ A1pd'A1pd
@test A1pdSparse*A1pdSparse' ≈ A1pd*A1pd'
@test_throws DimensionMismatch A1Sparse*CHOLMOD.eye(4, 5, elty)
end
# Factor
@test_throws ArgumentError cholfact(A1)
@test_throws ArgumentError cholfact(A1)
@test_throws ArgumentError cholfact(A1, shift=1.0)
@test_throws ArgumentError ldltfact(A1)
@test_throws ArgumentError ldltfact(A1, shift=1.0)
@test_throws LinAlg.PosDefException cholfact(A1 + A1' - 2eigmax(Array(A1 + A1'))*I)\ones(size(A1, 1))
@test_throws LinAlg.PosDefException cholfact(A1 + A1', shift=-2eigmax(Array(A1 + A1')))\ones(size(A1, 1))
@test_throws ArgumentError ldltfact(A1 + A1' - 2real(A1[1,1])*I)\ones(size(A1, 1))
@test_throws ArgumentError ldltfact(A1 + A1', shift=-2real(A1[1,1]))\ones(size(A1, 1))
@test !isposdef(cholfact(A1 + A1' - 2eigmax(Array(A1 + A1'))*I))
@test !isposdef(cholfact(A1 + A1', shift=-2eigmax(Array(A1 + A1'))))
@test !LinAlg.issuccess(ldltfact(A1 + A1' - 2real(A1[1,1])*I))
@test !LinAlg.issuccess(ldltfact(A1 + A1', shift=-2real(A1[1,1])))
F = cholfact(A1pd)
tmp = IOBuffer()
show(tmp, F)
@test tmp.size > 0
@test isa(CHOLMOD.Sparse(F), CHOLMOD.Sparse{elty})
@test F\CHOLMOD.Sparse(sparse(ones(elty, 5))) ≈ A1pd\ones(5)
@test_throws DimensionMismatch F\CHOLMOD.Dense(ones(elty, 4))
@test_throws DimensionMismatch F\CHOLMOD.Sparse(sparse(ones(elty, 4)))
@test F'\ones(elty, 5) ≈ Array(A1pd)'\ones(5)
@test F'\sparse(ones(elty, 5)) ≈ Array(A1pd)'\ones(5)
@test F.'\ones(elty, 5) ≈ conj(A1pd)'\ones(elty, 5)
@test logdet(F) ≈ logdet(Array(A1pd))
@test det(F) == exp(logdet(F))
let # to test supernodal, we must use a larger matrix
Ftmp = sprandn(100,100,0.1)
Ftmp = Ftmp'Ftmp + I
@test logdet(cholfact(Ftmp)) ≈ logdet(Array(Ftmp))
end
@test logdet(ldltfact(A1pd)) ≈ logdet(Array(A1pd))
@test isposdef(A1pd)
@test !isposdef(A1)
@test !isposdef(A1 + A1' |> t -> t - 2eigmax(Array(t))*I)
if elty <: Real
@test CHOLMOD.issymmetric(Sparse(A1pd, 0))
@test CHOLMOD.Sparse(cholfact(Symmetric(A1pd, :L))) == CHOLMOD.Sparse(cholfact(A1pd))
F1 = CHOLMOD.Sparse(cholfact(Symmetric(A1pd, :L), shift=2))
F2 = CHOLMOD.Sparse(cholfact(A1pd, shift=2))
@test F1 == F2
@test CHOLMOD.Sparse(ldltfact(Symmetric(A1pd, :L))) == CHOLMOD.Sparse(ldltfact(A1pd))
F1 = CHOLMOD.Sparse(ldltfact(Symmetric(A1pd, :L), shift=2))
F2 = CHOLMOD.Sparse(ldltfact(A1pd, shift=2))
@test F1 == F2
else
@test !CHOLMOD.issymmetric(Sparse(A1pd, 0))
@test CHOLMOD.ishermitian(Sparse(A1pd, 0))
@test CHOLMOD.Sparse(cholfact(Hermitian(A1pd, :L))) == CHOLMOD.Sparse(cholfact(A1pd))
F1 = CHOLMOD.Sparse(cholfact(Hermitian(A1pd, :L), shift=2))
F2 = CHOLMOD.Sparse(cholfact(A1pd, shift=2))
@test F1 == F2
@test CHOLMOD.Sparse(ldltfact(Hermitian(A1pd, :L))) == CHOLMOD.Sparse(ldltfact(A1pd))
F1 = CHOLMOD.Sparse(ldltfact(Hermitian(A1pd, :L), shift=2))
F2 = CHOLMOD.Sparse(ldltfact(A1pd, shift=2))
@test F1 == F2
end
### cholfact!/ldltfact!
F = cholfact(A1pd)
CHOLMOD.change_factor!(elty, false, false, true, true, F)
@test unsafe_load(pointer(F)).is_ll == 0
CHOLMOD.change_factor!(elty, true, false, true, true, F)
@test CHOLMOD.Sparse(cholfact!(copy(F), A1pd)) ≈ CHOLMOD.Sparse(F) # surprisingly, this can cause small ulp size changes so we cannot test exact equality
@test size(F, 2) == 5
@test size(F, 3) == 1
@test_throws ArgumentError size(F, 0)
F = cholfact(A1pdSparse, shift=2)
@test isa(CHOLMOD.Sparse(F), CHOLMOD.Sparse{elty})
@test CHOLMOD.Sparse(cholfact!(copy(F), A1pd, shift=2.0)) ≈ CHOLMOD.Sparse(F) # surprisingly, this can cause small ulp size changes so we cannot test exact equality
F = ldltfact(A1pd)
@test isa(CHOLMOD.Sparse(F), CHOLMOD.Sparse{elty})
@test CHOLMOD.Sparse(ldltfact!(copy(F), A1pd)) ≈ CHOLMOD.Sparse(F) # surprisingly, this can cause small ulp size changes so we cannot test exact equality
F = ldltfact(A1pdSparse, shift=2)
@test isa(CHOLMOD.Sparse(F), CHOLMOD.Sparse{elty})
@test CHOLMOD.Sparse(ldltfact!(copy(F), A1pd, shift=2.0)) ≈ CHOLMOD.Sparse(F) # surprisingly, this can cause small ulp size changes so we cannot test exact equality
@test isa(CHOLMOD.factor_to_sparse!(F), CHOLMOD.Sparse)
@test_throws CHOLMOD.CHOLMODException CHOLMOD.factor_to_sparse!(F)
## Low level interface
@test CHOLMOD.nnz(A1Sparse) == nnz(A1)
@test CHOLMOD.speye(5, 5, elty) == eye(elty, 5, 5)
@test CHOLMOD.spzeros(5, 5, 5, elty) == zeros(elty, 5, 5)
if elty <: Real
@test CHOLMOD.copy(A1Sparse, 0, 1) == A1Sparse
@test CHOLMOD.horzcat(A1Sparse, A2Sparse, true) == [A1 A2]
@test CHOLMOD.vertcat(A1Sparse, A2Sparse, true) == [A1; A2]
svec = ones(elty, 1)
@test CHOLMOD.scale!(CHOLMOD.Dense(svec), CHOLMOD.SCALAR, A1Sparse) == A1Sparse
svec = ones(elty, 5)
@test_throws DimensionMismatch CHOLMOD.scale!(CHOLMOD.Dense(svec), CHOLMOD.SCALAR, A1Sparse)
@test CHOLMOD.scale!(CHOLMOD.Dense(svec), CHOLMOD.ROW, A1Sparse) == A1Sparse
@test_throws DimensionMismatch CHOLMOD.scale!(CHOLMOD.Dense([svec; 1]), CHOLMOD.ROW, A1Sparse)
@test CHOLMOD.scale!(CHOLMOD.Dense(svec), CHOLMOD.COL, A1Sparse) == A1Sparse
@test_throws DimensionMismatch CHOLMOD.scale!(CHOLMOD.Dense([svec; 1]), CHOLMOD.COL, A1Sparse)
@test CHOLMOD.scale!(CHOLMOD.Dense(svec), CHOLMOD.SYM, A1Sparse) == A1Sparse
@test_throws DimensionMismatch CHOLMOD.scale!(CHOLMOD.Dense([svec; 1]), CHOLMOD.SYM, A1Sparse)
@test_throws DimensionMismatch CHOLMOD.scale!(CHOLMOD.Dense(svec), CHOLMOD.SYM, CHOLMOD.Sparse(A1[:,1:4]))
else
@test_throws MethodError CHOLMOD.copy(A1Sparse, 0, 1) == A1Sparse
@test_throws MethodError CHOLMOD.horzcat(A1Sparse, A2Sparse, true) == [A1 A2]
@test_throws MethodError CHOLMOD.vertcat(A1Sparse, A2Sparse, true) == [A1; A2]
end
if elty <: Real
@test CHOLMOD.ssmult(A1Sparse, A2Sparse, 0, true, true) ≈ A1*A2
@test CHOLMOD.aat(A1Sparse, [0:size(A1,2)-1;], 1) ≈ A1*A1'
@test CHOLMOD.aat(A1Sparse, [0:1;], 1) ≈ A1[:,1:2]*A1[:,1:2]'
@test CHOLMOD.copy(A1Sparse, 0, 1) == A1Sparse
end
@test CHOLMOD.Sparse(CHOLMOD.Dense(A1Sparse)) == A1Sparse
end
Af = float([4 12 -16; 12 37 -43; -16 -43 98])
As = sparse(Af)
Lf = float([2 0 0; 6 1 0; -8 5 3])
LDf = float([4 0 0; 3 1 0; -4 5 9]) # D is stored along the diagonal
L_f = float([1 0 0; 3 1 0; -4 5 1]) # L by itself in LDLt of Af
D_f = float([4 0 0; 0 1 0; 0 0 9])
# cholfact, no permutation
Fs = cholfact(As, perm=[1:3;])
@test Fs[:p] == [1:3;]
@test sparse(Fs[:L]) ≈ Lf
@test sparse(Fs) ≈ As
b = rand(3)
@test Fs\b ≈ Af\b
@test Fs[:UP]\(Fs[:PtL]\b) ≈ Af\b
@test Fs[:L]\b ≈ Lf\b
@test Fs[:U]\b ≈ Lf'\b
@test Fs[:L]'\b ≈ Lf'\b
@test Fs[:U]'\b ≈ Lf\b
@test Fs[:PtL]\b ≈ Lf\b
@test Fs[:UP]\b ≈ Lf'\b
@test Fs[:PtL]'\b ≈ Lf'\b
@test Fs[:UP]'\b ≈ Lf\b
@test_throws CHOLMOD.CHOLMODException Fs[:D]
@test_throws CHOLMOD.CHOLMODException Fs[:LD]
@test_throws CHOLMOD.CHOLMODException Fs[:DU]
@test_throws CHOLMOD.CHOLMODException Fs[:PLD]
@test_throws CHOLMOD.CHOLMODException Fs[:DUPt]
# cholfact, with permutation
p = [2,3,1]
p_inv = [3,1,2]
Fs = cholfact(As, perm=p)
@test Fs[:p] == p
Afp = Af[p,p]
Lfp = cholfact(Afp)[:L]
@test sparse(Fs[:L]) ≈ Lfp
@test sparse(Fs) ≈ As
b = rand(3)
@test Fs\b ≈ Af\b
@test Fs[:UP]\(Fs[:PtL]\b) ≈ Af\b
@test Fs[:L]\b ≈ Lfp\b
@test Fs[:U]'\b ≈ Lfp\b
@test Fs[:U]\b ≈ Lfp'\b
@test Fs[:L]'\b ≈ Lfp'\b
@test Fs[:PtL]\b ≈ Lfp\b[p]
@test Fs[:UP]\b ≈ (Lfp'\b)[p_inv]
@test Fs[:PtL]'\b ≈ (Lfp'\b)[p_inv]
@test Fs[:UP]'\b ≈ Lfp\b[p]
@test_throws CHOLMOD.CHOLMODException Fs[:PL]
@test_throws CHOLMOD.CHOLMODException Fs[:UPt]
@test_throws CHOLMOD.CHOLMODException Fs[:D]
@test_throws CHOLMOD.CHOLMODException Fs[:LD]
@test_throws CHOLMOD.CHOLMODException Fs[:DU]
@test_throws CHOLMOD.CHOLMODException Fs[:PLD]
@test_throws CHOLMOD.CHOLMODException Fs[:DUPt]
# ldltfact, no permutation
Fs = ldltfact(As, perm=[1:3;])
@test Fs[:p] == [1:3;]
@test sparse(Fs[:LD]) ≈ LDf
@test sparse(Fs) ≈ As
b = rand(3)
@test Fs\b ≈ Af\b
@test Fs[:UP]\(Fs[:PtLD]\b) ≈ Af\b
@test Fs[:DUP]\(Fs[:PtL]\b) ≈ Af\b
@test Fs[:L]\b ≈ L_f\b
@test Fs[:U]\b ≈ L_f'\b
@test Fs[:L]'\b ≈ L_f'\b
@test Fs[:U]'\b ≈ L_f\b
@test Fs[:PtL]\b ≈ L_f\b
@test Fs[:UP]\b ≈ L_f'\b
@test Fs[:PtL]'\b ≈ L_f'\b
@test Fs[:UP]'\b ≈ L_f\b
@test Fs[:D]\b ≈ D_f\b
@test Fs[:D]'\b ≈ D_f\b
@test Fs[:LD]\b ≈ D_f\(L_f\b)
@test Fs[:DU]'\b ≈ D_f\(L_f\b)
@test Fs[:LD]'\b ≈ L_f'\(D_f\b)
@test Fs[:DU]\b ≈ L_f'\(D_f\b)
@test Fs[:PtLD]\b ≈ D_f\(L_f\b)
@test Fs[:DUP]'\b ≈ D_f\(L_f\b)
@test Fs[:PtLD]'\b ≈ L_f'\(D_f\b)
@test Fs[:DUP]\b ≈ L_f'\(D_f\b)
# ldltfact, with permutation
Fs = ldltfact(As, perm=p)
@test Fs[:p] == p
@test sparse(Fs) ≈ As
b = rand(3)
Asp = As[p,p]
LDp = sparse(ldltfact(Asp, perm=[1,2,3])[:LD])
# LDp = sparse(Fs[:LD])
Lp, dp = Base.SparseArrays.CHOLMOD.getLd!(copy(LDp))
Dp = spdiagm(dp)
@test Fs\b ≈ Af\b
@test Fs[:UP]\(Fs[:PtLD]\b) ≈ Af\b
@test Fs[:DUP]\(Fs[:PtL]\b) ≈ Af\b
@test Fs[:L]\b ≈ Lp\b
@test Fs[:U]\b ≈ Lp'\b
@test Fs[:L]'\b ≈ Lp'\b
@test Fs[:U]'\b ≈ Lp\b
@test Fs[:PtL]\b ≈ Lp\b[p]
@test Fs[:UP]\b ≈ (Lp'\b)[p_inv]
@test Fs[:PtL]'\b ≈ (Lp'\b)[p_inv]
@test Fs[:UP]'\b ≈ Lp\b[p]
@test Fs[:LD]\b ≈ Dp\(Lp\b)
@test Fs[:DU]'\b ≈ Dp\(Lp\b)
@test Fs[:LD]'\b ≈ Lp'\(Dp\b)
@test Fs[:DU]\b ≈ Lp'\(Dp\b)
@test Fs[:PtLD]\b ≈ Dp\(Lp\b[p])
@test Fs[:DUP]'\b ≈ Dp\(Lp\b[p])
@test Fs[:PtLD]'\b ≈ (Lp'\(Dp\b))[p_inv]
@test Fs[:DUP]\b ≈ (Lp'\(Dp\b))[p_inv]
@test_throws CHOLMOD.CHOLMODException Fs[:DUPt]
@test_throws CHOLMOD.CHOLMODException Fs[:PLD]
# Issue 11745 - row and column pointers were not sorted in sparse(Factor)
let A = Float64[10 1 1 1; 1 10 0 0; 1 0 10 0; 1 0 0 10]
@test sparse(cholfact(sparse(A))) ≈ A
end
gc()
# Issue 11747 - Wrong show method defined for FactorComponent
let v = cholfact(sparse(Float64[ 10 1 1 1; 1 10 0 0; 1 0 10 0; 1 0 0 10]))[:L]
for s in (sprint(show, MIME("text/plain"), v), sprint(show, v))
@test contains(s, "method: simplicial")
@test !contains(s, "#undef")
end
end
# Element promotion and type inference
@inferred cholfact(As)\ones(Int, size(As, 1))
@inferred ldltfact(As)\ones(Int, size(As, 1))
# Issue 14076
@test cholfact(sparse([1,2,3,4], [1,2,3,4], Float32[1,4,16,64]))\[1,4,16,64] == ones(4)
# Issue 14134
A = SparseArrays.CHOLMOD.Sparse(sprandn(10,5,0.1) + I |> t -> t't)
b = IOBuffer()
serialize(b, A)
seekstart(b)
Anew = deserialize(b)
@test_throws ArgumentError show(Anew)
@test_throws ArgumentError size(Anew)
@test_throws ArgumentError Anew[1]
@test_throws ArgumentError Anew[2,1]
F = cholfact(A)
serialize(b, F)
seekstart(b)
Fnew = deserialize(b)
@test_throws ArgumentError Fnew\ones(5)
@test_throws ArgumentError show(Fnew)
@test_throws ArgumentError size(Fnew)
@test_throws ArgumentError diag(Fnew)
@test_throws ArgumentError logdet(Fnew)
# Issue with promotion during conversion to CHOLMOD.Dense
@test SparseArrays.CHOLMOD.Dense(ones(Float32, 5)) == ones(5, 1)
@test SparseArrays.CHOLMOD.Dense(ones(Int, 5)) == ones(5, 1)
@test SparseArrays.CHOLMOD.Dense(ones(Complex{Float32}, 5, 2)) == ones(5, 2)
# Further issue with promotion #14894
@test cholfact(speye(Float16, 5))\ones(5) == ones(5)
@test cholfact(Symmetric(speye(Float16, 5)))\ones(5) == ones(5)
@test cholfact(Hermitian(speye(Complex{Float16}, 5)))\ones(5) == ones(Complex{Float64}, 5)
@test_throws MethodError cholfact(speye(BigFloat, 5))
@test_throws MethodError cholfact(Symmetric(speye(BigFloat, 5)))
@test_throws MethodError cholfact(Hermitian(speye(Complex{BigFloat}, 5)))
# test \ for Factor and StridedVecOrMat
let x = rand(5),
A = cholfact(sparse(diagm(x.\1)))
@test A\view(ones(10),1:2:10) ≈ x
@test A\view(eye(5,5),:,:) ≈ diagm(x)
end
# Real factorization and complex rhs
let A = sprandn(5, 5, 0.4) |> t -> t't + I,
B = complex.(randn(5, 2), randn(5, 2))
@test cholfact(A)\B ≈ A\B
end
# Make sure that ldltfact performs an LDLt (Issue #19032)
let m = 400, n = 500,
A = sprandn(m, n, .2),
M = [speye(n) A'; A -speye(m)],
b = M * ones(m + n),
F = ldltfact(M),
s = unsafe_load(pointer(F))
@test s.is_super == 0
@test F\b ≈ ones(m + n)
end
# Test that \ and '\ and .'\ work for Symmetric and Hermitian. This is just
# a dispatch exercise so it doesn't matter that the complex matrix has
# zero imaginary parts
let Apre = sprandn(10, 10, 0.2) - I
for A in (Symmetric(Apre), Hermitian(Apre),
Symmetric(Apre + 10I), Hermitian(Apre + 10I),
Hermitian(complex(Apre)), Hermitian(complex(Apre) + 10I))
local A, x, b
x = ones(10)
b = A*x
@test x ≈ A\b
@test A.'\b ≈ A'\b
end
end
# Check that Symmetric{SparseMatrixCSC} can be constructed from CHOLMOD.Sparse
let A = sprandn(10, 10, 0.1),
B = SparseArrays.CHOLMOD.Sparse(A),
C = B'B
# Change internal representation to symmetric (upper/lower)
o = fieldoffset(CHOLMOD.C_Sparse{eltype(C)}, find(fieldnames(CHOLMOD.C_Sparse{eltype(C)}) .== :stype)[1])
for uplo in (1, -1)
unsafe_store!(Ptr{Int8}(pointer(C)), uplo, Int(o) + 1)
@test convert(Symmetric{Float64,SparseMatrixCSC{Float64,Int}}, C) == Symmetric(A'A)
end
end
@testset "Check inputs to Sparse. Related to #20024" for A_ in (
SparseMatrixCSC(2, 2, [1, 2], CHOLMOD.SuiteSparse_long[], Float64[]),
SparseMatrixCSC(2, 2, [1, 2, 3], CHOLMOD.SuiteSparse_long[1], Float64[]),
SparseMatrixCSC(2, 2, [1, 2, 3], CHOLMOD.SuiteSparse_long[], Float64[1.0]),
SparseMatrixCSC(2, 2, [1, 2, 3], CHOLMOD.SuiteSparse_long[1], Float64[1.0]))
@test_throws ArgumentError CHOLMOD.Sparse(size(A_)..., A_.colptr .- 1, A_.rowval .- 1, A_.nzval)
@test_throws ArgumentError CHOLMOD.Sparse(A_)
end
@testset "sparse right multiplication of Symmetric and Hermitian matrices #21431" begin
@test issparse(speye(2)*speye(2)*speye(2))
for T in (Symmetric, Hermitian)
@test issparse(speye(2)*T(speye(2))*speye(2))
@test issparse(speye(2)*(T(speye(2))*speye(2)))
@test issparse((speye(2)*T(speye(2)))*speye(2))
end
end
#Test sparse low rank update for cholesky decomposion
A = SparseMatrixCSC{Float64,CHOLMOD.SuiteSparse_long}(10, 5, [1,3,6,8,10,13], [6,7,1,2,9,3,5,1,7,6,7,9],
[-0.138843, 2.99571, -0.556814, 0.669704, -1.39252, 1.33814,
1.02371, -0.502384, 1.10686, 0.262229, -1.6935, 0.525239])
AtA = A'*A;
C0 = [1., 2., 0, 0, 0]
#Test both cholfact and LDLt with and without automatic permutations
for F in (cholfact(AtA), cholfact(AtA, perm=1:5), ldltfact(AtA), ldltfact(AtA, perm=1:5))
local F
B0 = F\ones(5)
#Test both sparse/dense and vectors/matrices
for Ctest in (C0, sparse(C0), [C0 2*C0], sparse([C0 2*C0]))
local B, C, F1
C = copy(Ctest)
F1 = copy(F)
B = (AtA+C*C')\ones(5)
#Test update
F11 = CHOLMOD.lowrankupdate(F1, C)
@test Array(sparse(F11)) ≈ AtA+C*C'
@test F11\ones(5) ≈ B
#Make sure we get back the same factor again
F10 = CHOLMOD.lowrankdowndate(F11, C)
@test Array(sparse(F10)) ≈ AtA
@test F10\ones(5) ≈ B0
#Test in-place update
CHOLMOD.lowrankupdate!(F1, C)
@test Array(sparse(F1)) ≈ AtA+C*C'
@test F1\ones(5) ≈ B
#Test in-place downdate
CHOLMOD.lowrankdowndate!(F1, C)
@test Array(sparse(F1)) ≈ AtA
@test F1\ones(5) ≈ B0
@test C == Ctest #Make sure C didn't change
end
end
@testset "Issue #22335" begin
local A, F
A = speye(3)
@test LinAlg.issuccess(cholfact(A))
A[3, 3] = -1
F = cholfact(A)
@test !LinAlg.issuccess(F)
@test LinAlg.issuccess(ldltfact!(F, A))
A[3, 3] = 1
@test A[:, 3:-1:1]\ones(3) == [1, 1, 1]
end
