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
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "sparse.h"
template<typename Scalar> void
initSPD(double density,
Matrix<Scalar,Dynamic,Dynamic>& refMat,
SparseMatrix<Scalar>& sparseMat)
{
Matrix<Scalar,Dynamic,Dynamic> aux(refMat.rows(),refMat.cols());
initSparse(density,refMat,sparseMat);
refMat = refMat * refMat.adjoint();
for (int k=0; k<2; ++k)
{
initSparse(density,aux,sparseMat,ForceNonZeroDiag);
refMat += aux * aux.adjoint();
}
sparseMat.setZero();
for (int j=0 ; j<sparseMat.cols(); ++j)
for (int i=j ; i<sparseMat.rows(); ++i)
if (refMat(i,j)!=Scalar(0))
sparseMat.insert(i,j) = refMat(i,j);
sparseMat.finalize();
}
template<typename Scalar> void sparse_solvers(int rows, int cols)
{
double density = (std::max)(8./(rows*cols), 0.01);
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
// Scalar eps = 1e-6;
DenseVector vec1 = DenseVector::Random(rows);
std::vector<Vector2i> zeroCoords;
std::vector<Vector2i> nonzeroCoords;
// test triangular solver
{
DenseVector vec2 = vec1, vec3 = vec1;
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
// lower - dense
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2),
m2.template triangularView<Lower>().solve(vec3));
// upper - dense
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.template triangularView<Upper>().solve(vec2),
m2.template triangularView<Upper>().solve(vec3));
VERIFY_IS_APPROX(refMat2.conjugate().template triangularView<Upper>().solve(vec2),
m2.conjugate().template triangularView<Upper>().solve(vec3));
{
SparseMatrix<Scalar> cm2(m2);
//Index rows, Index cols, Index nnz, Index* outerIndexPtr, Index* innerIndexPtr, Scalar* valuePtr
MappedSparseMatrix<Scalar> mm2(rows, cols, cm2.nonZeros(), cm2.outerIndexPtr(), cm2.innerIndexPtr(), cm2.valuePtr());
VERIFY_IS_APPROX(refMat2.conjugate().template triangularView<Upper>().solve(vec2),
mm2.conjugate().template triangularView<Upper>().solve(vec3));
}
// lower - transpose
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Upper>().solve(vec2),
m2.transpose().template triangularView<Upper>().solve(vec3));
// upper - transpose
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Lower>().solve(vec2),
m2.transpose().template triangularView<Lower>().solve(vec3));
SparseMatrix<Scalar> matB(rows, rows);
DenseMatrix refMatB = DenseMatrix::Zero(rows, rows);
// lower - sparse
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular);
initSparse<Scalar>(density, refMatB, matB);
refMat2.template triangularView<Lower>().solveInPlace(refMatB);
m2.template triangularView<Lower>().solveInPlace(matB);
VERIFY_IS_APPROX(matB.toDense(), refMatB);
// upper - sparse
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular);
initSparse<Scalar>(density, refMatB, matB);
refMat2.template triangularView<Upper>().solveInPlace(refMatB);
m2.template triangularView<Upper>().solveInPlace(matB);
VERIFY_IS_APPROX(matB, refMatB);
// test deprecated API
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2),
m2.template triangularView<Lower>().solve(vec3));
}
}
void test_sparse_solvers()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1(sparse_solvers<double>(8, 8) );
int s = internal::random<int>(1,300);
CALL_SUBTEST_2(sparse_solvers<std::complex<double> >(s,s) );
CALL_SUBTEST_1(sparse_solvers<double>(s,s) );
}
}
|
