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
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// 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/>.
#ifndef EIGEN_NO_ASSERTION_CHECKING
#define EIGEN_NO_ASSERTION_CHECKING
#endif
#include "main.h"
#include <Eigen/Cholesky>
#include <Eigen/QR>
#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
for (int k=0; k<3; ++k)
{
MatrixType a1 = MatrixType::Random(rows,cols);
symm += a1 * a1.adjoint();
}
SquareMatrixType symmUp = symm.template triangularView<Upper>();
SquareMatrixType symmLo = symm.template triangularView<Lower>();
// to test if really Cholesky only uses the upper triangular part, uncomment the following
// FIXME: currently that fails !!
//symm.template part<StrictlyLower>().setZero();
#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
{
LLT<SquareMatrixType,Lower> chollo(symmLo);
VERIFY_IS_APPROX(symm, chollo.reconstructedMatrix());
vecX = chollo.solve(vecB);
VERIFY_IS_APPROX(symm * vecX, vecB);
matX = chollo.solve(matB);
VERIFY_IS_APPROX(symm * matX, matB);
// test the upper mode
LLT<SquareMatrixType,Upper> cholup(symmUp);
VERIFY_IS_APPROX(symm, cholup.reconstructedMatrix());
vecX = cholup.solve(vecB);
VERIFY_IS_APPROX(symm * vecX, vecB);
matX = cholup.solve(matB);
VERIFY_IS_APPROX(symm * matX, matB);
}
int sign = ei_random<int>()%2 ? 1 : -1;
if(sign == -1)
{
symm = -symm; // test a negative matrix
}
{
LDLT<SquareMatrixType,Lower> ldltlo(symm);
VERIFY_IS_APPROX(symm, ldltlo.reconstructedMatrix());
vecX = ldltlo.solve(vecB);
VERIFY_IS_APPROX(symm * vecX, vecB);
matX = ldltlo.solve(matB);
VERIFY_IS_APPROX(symm * matX, matB);
LDLT<SquareMatrixType,Upper> ldltup(symm);
VERIFY_IS_APPROX(symm, ldltup.reconstructedMatrix());
vecX = ldltup.solve(vecB);
VERIFY_IS_APPROX(symm * vecX, vecB);
matX = ldltup.solve(matB);
VERIFY_IS_APPROX(symm * matX, matB);
}
}
template<typename MatrixType> void cholesky_verify_assert()
{
MatrixType tmp;
LLT<MatrixType> llt;
VERIFY_RAISES_ASSERT(llt.matrixL())
VERIFY_RAISES_ASSERT(llt.solve(tmp))
VERIFY_RAISES_ASSERT(llt.solveInPlace(&tmp))
LDLT<MatrixType> ldlt;
VERIFY_RAISES_ASSERT(ldlt.matrixL())
VERIFY_RAISES_ASSERT(ldlt.permutationP())
VERIFY_RAISES_ASSERT(ldlt.vectorD())
VERIFY_RAISES_ASSERT(ldlt.isPositive())
VERIFY_RAISES_ASSERT(ldlt.isNegative())
VERIFY_RAISES_ASSERT(ldlt.solve(tmp))
VERIFY_RAISES_ASSERT(ldlt.solveInPlace(&tmp))
}
void test_cholesky()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( cholesky(Matrix<double,1,1>()) );
CALL_SUBTEST_2( cholesky(MatrixXd(1,1)) );
CALL_SUBTEST_3( cholesky(Matrix2d()) );
CALL_SUBTEST_4( cholesky(Matrix3f()) );
CALL_SUBTEST_5( cholesky(Matrix4d()) );
CALL_SUBTEST_2( cholesky(MatrixXd(200,200)) );
CALL_SUBTEST_6( cholesky(MatrixXcd(100,100)) );
}
CALL_SUBTEST_4( cholesky_verify_assert<Matrix3f>() );
CALL_SUBTEST_7( cholesky_verify_assert<Matrix3d>() );
CALL_SUBTEST_8( cholesky_verify_assert<MatrixXf>() );
CALL_SUBTEST_2( cholesky_verify_assert<MatrixXd>() );
// Test problem size constructors
CALL_SUBTEST_9( LLT<MatrixXf>(10) );
CALL_SUBTEST_9( LDLT<MatrixXf>(10) );
}
|
