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
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#define EIGEN_NO_ASSERTION_CHECKING
#include "main.h"
#include <Eigen/Cholesky>
#include <Eigen/LU>
#ifdef HAS_GSL
#include "gsl_helper.h"
#endif
template<typename MatrixType> void cholesky(const MatrixType& m)
{
/* this test covers the following files:
LLT.h LDLT.h
*/
int rows = m.rows();
int cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
MatrixType a0 = MatrixType::Random(rows,cols);
VectorType vecB = VectorType::Random(rows), vecX(rows);
MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols);
SquareMatrixType symm = a0 * a0.adjoint();
// let's make sure the matrix is not singular or near singular
MatrixType a1 = MatrixType::Random(rows,cols);
symm += a1 * a1.adjoint();
#ifdef HAS_GSL
if (ei_is_same_type<RealScalar,double>::ret)
{
typedef GslTraits<Scalar> Gsl;
typename Gsl::Matrix gMatA=0, gSymm=0;
typename Gsl::Vector gVecB=0, gVecX=0;
convert<MatrixType>(symm, gSymm);
convert<MatrixType>(symm, gMatA);
convert<VectorType>(vecB, gVecB);
convert<VectorType>(vecB, gVecX);
Gsl::cholesky(gMatA);
Gsl::cholesky_solve(gMatA, gVecB, gVecX);
VectorType vecX(rows), _vecX, _vecB;
convert(gVecX, _vecX);
symm.llt().solve(vecB, &vecX);
Gsl::prod(gSymm, gVecX, gVecB);
convert(gVecB, _vecB);
// test gsl itself !
VERIFY_IS_APPROX(vecB, _vecB);
VERIFY_IS_APPROX(vecX, _vecX);
Gsl::free(gMatA);
Gsl::free(gSymm);
Gsl::free(gVecB);
Gsl::free(gVecX);
}
#endif
{
LDLT<SquareMatrixType> ldlt(symm);
VERIFY(ldlt.isPositiveDefinite());
VERIFY_IS_APPROX(symm, ldlt.matrixL() * ldlt.vectorD().asDiagonal() * ldlt.matrixL().adjoint());
ldlt.solve(vecB, &vecX);
VERIFY_IS_APPROX(symm * vecX, vecB);
ldlt.solve(matB, &matX);
VERIFY_IS_APPROX(symm * matX, matB);
}
{
LLT<SquareMatrixType> chol(symm);
VERIFY(chol.isPositiveDefinite());
VERIFY_IS_APPROX(symm, chol.matrixL() * chol.matrixL().adjoint());
chol.solve(vecB, &vecX);
VERIFY_IS_APPROX(symm * vecX, vecB);
chol.solve(matB, &matX);
VERIFY_IS_APPROX(symm * matX, matB);
}
#if 0 // cholesky is not rank-revealing anyway
// test isPositiveDefinite on non definite matrix
if (rows>4)
{
SquareMatrixType symm = a0.block(0,0,rows,cols-4) * a0.block(0,0,rows,cols-4).adjoint();
LLT<SquareMatrixType> chol(symm);
VERIFY(!chol.isPositiveDefinite());
LDLT<SquareMatrixType> cholnosqrt(symm);
VERIFY(!cholnosqrt.isPositiveDefinite());
}
#endif
}
void test_eigen2_cholesky()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( cholesky(Matrix<double,1,1>()) );
CALL_SUBTEST_2( cholesky(Matrix2d()) );
CALL_SUBTEST_3( cholesky(Matrix3f()) );
CALL_SUBTEST_4( cholesky(Matrix4d()) );
CALL_SUBTEST_5( cholesky(MatrixXcd(7,7)) );
CALL_SUBTEST_6( cholesky(MatrixXf(17,17)) );
CALL_SUBTEST_7( cholesky(MatrixXd(33,33)) );
}
#ifdef EIGEN_TEST_PART_6
MatrixXf m = MatrixXf::Zero(10,10);
VectorXf b = VectorXf::Zero(10);
VERIFY(!m.llt().isPositiveDefinite());
#endif
}
|
