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
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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/>.
#include "main.h"
#include <Eigen/LU>
using namespace std;
template<typename MatrixType> void lu_non_invertible()
{
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
/* this test covers the following files:
LU.h
*/
Index rows, cols, cols2;
if(MatrixType::RowsAtCompileTime==Dynamic)
{
rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
}
else
{
rows = MatrixType::RowsAtCompileTime;
}
if(MatrixType::ColsAtCompileTime==Dynamic)
{
cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
cols2 = internal::random<int>(2,EIGEN_TEST_MAX_SIZE);
}
else
{
cols2 = cols = MatrixType::ColsAtCompileTime;
}
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime
};
typedef typename internal::kernel_retval_base<FullPivLU<MatrixType> >::ReturnType KernelMatrixType;
typedef typename internal::image_retval_base<FullPivLU<MatrixType> >::ReturnType ImageMatrixType;
typedef Matrix<typename MatrixType::Scalar, ColsAtCompileTime, ColsAtCompileTime>
CMatrixType;
typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, RowsAtCompileTime>
RMatrixType;
Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
// The image of the zero matrix should consist of a single (zero) column vector
VERIFY((MatrixType::Zero(rows,cols).fullPivLu().image(MatrixType::Zero(rows,cols)).cols() == 1));
MatrixType m1(rows, cols), m3(rows, cols2);
CMatrixType m2(cols, cols2);
createRandomPIMatrixOfRank(rank, rows, cols, m1);
FullPivLU<MatrixType> lu;
// The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank
// of singular values are either 0 or 1.
// So it's not clear at all that the epsilon should play any role there.
lu.setThreshold(RealScalar(0.01));
lu.compute(m1);
MatrixType u(rows,cols);
u = lu.matrixLU().template triangularView<Upper>();
RMatrixType l = RMatrixType::Identity(rows,rows);
l.block(0,0,rows,(std::min)(rows,cols)).template triangularView<StrictlyLower>()
= lu.matrixLU().block(0,0,rows,(std::min)(rows,cols));
VERIFY_IS_APPROX(lu.permutationP() * m1 * lu.permutationQ(), l*u);
KernelMatrixType m1kernel = lu.kernel();
ImageMatrixType m1image = lu.image(m1);
VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
VERIFY(rank == lu.rank());
VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
VERIFY(!lu.isInjective());
VERIFY(!lu.isInvertible());
VERIFY(!lu.isSurjective());
VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));
VERIFY(m1image.fullPivLu().rank() == rank);
VERIFY_IS_APPROX(m1 * m1.adjoint() * m1image, m1image);
m2 = CMatrixType::Random(cols,cols2);
m3 = m1*m2;
m2 = CMatrixType::Random(cols,cols2);
// test that the code, which does resize(), may be applied to an xpr
m2.block(0,0,m2.rows(),m2.cols()) = lu.solve(m3);
VERIFY_IS_APPROX(m3, m1*m2);
}
template<typename MatrixType> void lu_invertible()
{
/* this test covers the following files:
LU.h
*/
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
int size = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
MatrixType m1(size, size), m2(size, size), m3(size, size);
FullPivLU<MatrixType> lu;
lu.setThreshold(RealScalar(0.01));
do {
m1 = MatrixType::Random(size,size);
lu.compute(m1);
} while(!lu.isInvertible());
VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
VERIFY(0 == lu.dimensionOfKernel());
VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector
VERIFY(size == lu.rank());
VERIFY(lu.isInjective());
VERIFY(lu.isSurjective());
VERIFY(lu.isInvertible());
VERIFY(lu.image(m1).fullPivLu().isInvertible());
m3 = MatrixType::Random(size,size);
m2 = lu.solve(m3);
VERIFY_IS_APPROX(m3, m1*m2);
VERIFY_IS_APPROX(m2, lu.inverse()*m3);
}
template<typename MatrixType> void lu_partial_piv()
{
/* this test covers the following files:
PartialPivLU.h
*/
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
Index rows = internal::random<Index>(1,4);
Index cols = rows;
MatrixType m1(cols, rows);
m1.setRandom();
PartialPivLU<MatrixType> plu(m1);
VERIFY_IS_APPROX(m1, plu.reconstructedMatrix());
}
template<typename MatrixType> void lu_verify_assert()
{
MatrixType tmp;
FullPivLU<MatrixType> lu;
VERIFY_RAISES_ASSERT(lu.matrixLU())
VERIFY_RAISES_ASSERT(lu.permutationP())
VERIFY_RAISES_ASSERT(lu.permutationQ())
VERIFY_RAISES_ASSERT(lu.kernel())
VERIFY_RAISES_ASSERT(lu.image(tmp))
VERIFY_RAISES_ASSERT(lu.solve(tmp))
VERIFY_RAISES_ASSERT(lu.determinant())
VERIFY_RAISES_ASSERT(lu.rank())
VERIFY_RAISES_ASSERT(lu.dimensionOfKernel())
VERIFY_RAISES_ASSERT(lu.isInjective())
VERIFY_RAISES_ASSERT(lu.isSurjective())
VERIFY_RAISES_ASSERT(lu.isInvertible())
VERIFY_RAISES_ASSERT(lu.inverse())
PartialPivLU<MatrixType> plu;
VERIFY_RAISES_ASSERT(plu.matrixLU())
VERIFY_RAISES_ASSERT(plu.permutationP())
VERIFY_RAISES_ASSERT(plu.solve(tmp))
VERIFY_RAISES_ASSERT(plu.determinant())
VERIFY_RAISES_ASSERT(plu.inverse())
}
void test_lu()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( lu_non_invertible<Matrix3f>() );
CALL_SUBTEST_1( lu_verify_assert<Matrix3f>() );
CALL_SUBTEST_2( (lu_non_invertible<Matrix<double, 4, 6> >()) );
CALL_SUBTEST_2( (lu_verify_assert<Matrix<double, 4, 6> >()) );
CALL_SUBTEST_3( lu_non_invertible<MatrixXf>() );
CALL_SUBTEST_3( lu_invertible<MatrixXf>() );
CALL_SUBTEST_3( lu_verify_assert<MatrixXf>() );
CALL_SUBTEST_4( lu_non_invertible<MatrixXd>() );
CALL_SUBTEST_4( lu_invertible<MatrixXd>() );
CALL_SUBTEST_4( lu_partial_piv<MatrixXd>() );
CALL_SUBTEST_4( lu_verify_assert<MatrixXd>() );
CALL_SUBTEST_5( lu_non_invertible<MatrixXcf>() );
CALL_SUBTEST_5( lu_invertible<MatrixXcf>() );
CALL_SUBTEST_5( lu_verify_assert<MatrixXcf>() );
CALL_SUBTEST_6( lu_non_invertible<MatrixXcd>() );
CALL_SUBTEST_6( lu_invertible<MatrixXcd>() );
CALL_SUBTEST_6( lu_partial_piv<MatrixXcd>() );
CALL_SUBTEST_6( lu_verify_assert<MatrixXcd>() );
CALL_SUBTEST_7(( lu_non_invertible<Matrix<float,Dynamic,16> >() ));
// Test problem size constructors
CALL_SUBTEST_9( PartialPivLU<MatrixXf>(10) );
CALL_SUBTEST_9( FullPivLU<MatrixXf>(10, 20); );
}
}
|
