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
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 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 householder(const MatrixType& m)
{
static bool even = true;
even = !even;
/* this test covers the following files:
Householder.h
*/
Index rows = m.rows();
Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType;
typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;
Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols));
Scalar* tmp = &_tmp.coeffRef(0,0);
Scalar beta;
RealScalar alpha;
EssentialVectorType essential;
VectorType v1 = VectorType::Random(rows), v2;
v2 = v1;
v1.makeHouseholder(essential, beta, alpha);
v1.applyHouseholderOnTheLeft(essential,beta,tmp);
VERIFY_IS_APPROX(v1.norm(), v2.norm());
if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm());
v1 = VectorType::Random(rows);
v2 = v1;
v1.applyHouseholderOnTheLeft(essential,beta,tmp);
VERIFY_IS_APPROX(v1.norm(), v2.norm());
// reconstruct householder matrix:
SquareMatrixType id, H1, H2;
id.setIdentity(rows, rows);
H1 = H2 = id;
VectorType vv(rows);
vv << Scalar(1), essential;
H1.applyHouseholderOnTheLeft(essential, beta, tmp);
H2.applyHouseholderOnTheRight(essential, beta, tmp);
VERIFY_IS_APPROX(H1, H2);
VERIFY_IS_APPROX(H1, id - beta * vv*vv.adjoint());
MatrixType m1(rows, cols),
m2(rows, cols);
v1 = VectorType::Random(rows);
if(even) v1.tail(rows-1).setZero();
m1.colwise() = v1;
m2 = m1;
m1.col(0).makeHouseholder(essential, beta, alpha);
m1.applyHouseholderOnTheLeft(essential,beta,tmp);
VERIFY_IS_APPROX(m1.norm(), m2.norm());
if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm());
VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0)));
VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha);
v1 = VectorType::Random(rows);
if(even) v1.tail(rows-1).setZero();
SquareMatrixType m3(rows,rows), m4(rows,rows);
m3.rowwise() = v1.transpose();
m4 = m3;
m3.row(0).makeHouseholder(essential, beta, alpha);
m3.applyHouseholderOnTheRight(essential.conjugate(),beta,tmp);
VERIFY_IS_APPROX(m3.norm(), m4.norm());
if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());
VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0)));
VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha);
// test householder sequence on the left with a shift
Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0));
Index brows = rows - shift;
m1.setRandom(rows, cols);
HBlockMatrixType hbm = m1.block(shift,0,brows,cols);
HouseholderQR<HBlockMatrixType> qr(hbm);
m2 = m1;
m2.block(shift,0,brows,cols) = qr.matrixQR();
HCoeffsVectorType hc = qr.hCoeffs().conjugate();
HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc);
hseq.setLength(hc.size()).setShift(shift);
VERIFY(hseq.length() == hc.size());
VERIFY(hseq.shift() == shift);
MatrixType m5 = m2;
m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero();
VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly
m3 = hseq;
VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying
SquareMatrixType hseq_mat = hseq;
SquareMatrixType hseq_mat_conj = hseq.conjugate();
SquareMatrixType hseq_mat_adj = hseq.adjoint();
SquareMatrixType hseq_mat_trans = hseq.transpose();
SquareMatrixType m6 = SquareMatrixType::Random(rows, rows);
VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj);
VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj);
VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans);
VERIFY_IS_APPROX(hseq * m6, hseq_mat * m6);
VERIFY_IS_APPROX(hseq.adjoint() * m6, hseq_mat_adj * m6);
VERIFY_IS_APPROX(hseq.conjugate() * m6, hseq_mat_conj * m6);
VERIFY_IS_APPROX(hseq.transpose() * m6, hseq_mat_trans * m6);
VERIFY_IS_APPROX(m6 * hseq, m6 * hseq_mat);
VERIFY_IS_APPROX(m6 * hseq.adjoint(), m6 * hseq_mat_adj);
VERIFY_IS_APPROX(m6 * hseq.conjugate(), m6 * hseq_mat_conj);
VERIFY_IS_APPROX(m6 * hseq.transpose(), m6 * hseq_mat_trans);
// test householder sequence on the right with a shift
TMatrixType tm2 = m2.transpose();
HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc);
rhseq.setLength(hc.size()).setShift(shift);
VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly
m3 = rhseq;
VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying
}
EIGEN_DECLARE_TEST(householder)
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( householder(Matrix<double,2,2>()) );
CALL_SUBTEST_2( householder(Matrix<float,2,3>()) );
CALL_SUBTEST_3( householder(Matrix<double,3,5>()) );
CALL_SUBTEST_4( householder(Matrix<float,4,4>()) );
CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_8( householder(Matrix<double,1,1>()) );
}
}
|
