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
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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 "main.h"
#include <Eigen/QR>
template<typename MatrixType> void qr()
{
typedef typename MatrixType::Index Index;
Index rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols2 = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
typedef typename MatrixType::Scalar Scalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
MatrixType m1;
createRandomPIMatrixOfRank(rank,rows,cols,m1);
ColPivHouseholderQR<MatrixType> qr(m1);
VERIFY(rank == qr.rank());
VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
VERIFY(!qr.isInjective());
VERIFY(!qr.isInvertible());
VERIFY(!qr.isSurjective());
MatrixQType q = qr.householderQ();
VERIFY_IS_UNITARY(q);
MatrixType r = qr.matrixQR().template triangularView<Upper>();
MatrixType c = q * r * qr.colsPermutation().inverse();
VERIFY_IS_APPROX(m1, c);
MatrixType m2 = MatrixType::Random(cols,cols2);
MatrixType m3 = m1*m2;
m2 = MatrixType::Random(cols,cols2);
m2 = qr.solve(m3);
VERIFY_IS_APPROX(m3, m1*m2);
}
template<typename MatrixType, int Cols2> void qr_fixedsize()
{
enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
typedef typename MatrixType::Scalar Scalar;
int rank = internal::random<int>(1, (std::min)(int(Rows), int(Cols))-1);
Matrix<Scalar,Rows,Cols> m1;
createRandomPIMatrixOfRank(rank,Rows,Cols,m1);
ColPivHouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
VERIFY(rank == qr.rank());
VERIFY(Cols - qr.rank() == qr.dimensionOfKernel());
VERIFY(qr.isInjective() == (rank == Rows));
VERIFY(qr.isSurjective() == (rank == Cols));
VERIFY(qr.isInvertible() == (qr.isInjective() && qr.isSurjective()));
Matrix<Scalar,Rows,Cols> r = qr.matrixQR().template triangularView<Upper>();
Matrix<Scalar,Rows,Cols> c = qr.householderQ() * r * qr.colsPermutation().inverse();
VERIFY_IS_APPROX(m1, c);
Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
Matrix<Scalar,Rows,Cols2> m3 = m1*m2;
m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
m2 = qr.solve(m3);
VERIFY_IS_APPROX(m3, m1*m2);
}
template<typename MatrixType> void qr_invertible()
{
using std::log;
using std::abs;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef typename MatrixType::Scalar Scalar;
int size = internal::random<int>(10,50);
MatrixType m1(size, size), m2(size, size), m3(size, size);
m1 = MatrixType::Random(size,size);
if (internal::is_same<RealScalar,float>::value)
{
// let's build a matrix more stable to inverse
MatrixType a = MatrixType::Random(size,size*2);
m1 += a * a.adjoint();
}
ColPivHouseholderQR<MatrixType> qr(m1);
m3 = MatrixType::Random(size,size);
m2 = qr.solve(m3);
//VERIFY_IS_APPROX(m3, m1*m2);
// now construct a matrix with prescribed determinant
m1.setZero();
for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
RealScalar absdet = abs(m1.diagonal().prod());
m3 = qr.householderQ(); // get a unitary
m1 = m3 * m1 * m3;
qr.compute(m1);
VERIFY_IS_APPROX(absdet, qr.absDeterminant());
VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
}
template<typename MatrixType> void qr_verify_assert()
{
MatrixType tmp;
ColPivHouseholderQR<MatrixType> qr;
VERIFY_RAISES_ASSERT(qr.matrixQR())
VERIFY_RAISES_ASSERT(qr.solve(tmp))
VERIFY_RAISES_ASSERT(qr.householderQ())
VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
VERIFY_RAISES_ASSERT(qr.isInjective())
VERIFY_RAISES_ASSERT(qr.isSurjective())
VERIFY_RAISES_ASSERT(qr.isInvertible())
VERIFY_RAISES_ASSERT(qr.inverse())
VERIFY_RAISES_ASSERT(qr.absDeterminant())
VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}
void test_qr_colpivoting()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( qr<MatrixXf>() );
CALL_SUBTEST_2( qr<MatrixXd>() );
CALL_SUBTEST_3( qr<MatrixXcd>() );
CALL_SUBTEST_4(( qr_fixedsize<Matrix<float,3,5>, 4 >() ));
CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,6,2>, 3 >() ));
CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,1,1>, 1 >() ));
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
CALL_SUBTEST_6( qr_invertible<MatrixXcf>() );
CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
}
CALL_SUBTEST_7(qr_verify_assert<Matrix3f>());
CALL_SUBTEST_8(qr_verify_assert<Matrix3d>());
CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
CALL_SUBTEST_6(qr_verify_assert<MatrixXcf>());
CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
// Test problem size constructors
CALL_SUBTEST_9(ColPivHouseholderQR<MatrixXf>(10, 20));
}
|
