source: pacpussensors/trunk/Vislab/lib3dv-1.2.0/lib3dv/eigen/test/householder.cpp

Last change on this file was 136, checked in by ldecherf, 8 years ago

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1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
5//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10#include "main.h"
11#include <Eigen/QR>
12
13template<typename MatrixType> void householder(const MatrixType& m)
14{
15 typedef typename MatrixType::Index Index;
16 static bool even = true;
17 even = !even;
18 /* this test covers the following files:
19 Householder.h
20 */
21 Index rows = m.rows();
22 Index cols = m.cols();
23
24 typedef typename MatrixType::Scalar Scalar;
25 typedef typename NumTraits<Scalar>::Real RealScalar;
26 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
27 typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;
28 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
29 typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType;
30 typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;
31
32 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;
33
34 Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols));
35 Scalar* tmp = &_tmp.coeffRef(0,0);
36
37 Scalar beta;
38 RealScalar alpha;
39 EssentialVectorType essential;
40
41 VectorType v1 = VectorType::Random(rows), v2;
42 v2 = v1;
43 v1.makeHouseholder(essential, beta, alpha);
44 v1.applyHouseholderOnTheLeft(essential,beta,tmp);
45 VERIFY_IS_APPROX(v1.norm(), v2.norm());
46 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm());
47 v1 = VectorType::Random(rows);
48 v2 = v1;
49 v1.applyHouseholderOnTheLeft(essential,beta,tmp);
50 VERIFY_IS_APPROX(v1.norm(), v2.norm());
51
52 MatrixType m1(rows, cols),
53 m2(rows, cols);
54
55 v1 = VectorType::Random(rows);
56 if(even) v1.tail(rows-1).setZero();
57 m1.colwise() = v1;
58 m2 = m1;
59 m1.col(0).makeHouseholder(essential, beta, alpha);
60 m1.applyHouseholderOnTheLeft(essential,beta,tmp);
61 VERIFY_IS_APPROX(m1.norm(), m2.norm());
62 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm());
63 VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0)));
64 VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha);
65
66 v1 = VectorType::Random(rows);
67 if(even) v1.tail(rows-1).setZero();
68 SquareMatrixType m3(rows,rows), m4(rows,rows);
69 m3.rowwise() = v1.transpose();
70 m4 = m3;
71 m3.row(0).makeHouseholder(essential, beta, alpha);
72 m3.applyHouseholderOnTheRight(essential,beta,tmp);
73 VERIFY_IS_APPROX(m3.norm(), m4.norm());
74 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());
75 VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0)));
76 VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha);
77
78 // test householder sequence on the left with a shift
79
80 Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0));
81 Index brows = rows - shift;
82 m1.setRandom(rows, cols);
83 HBlockMatrixType hbm = m1.block(shift,0,brows,cols);
84 HouseholderQR<HBlockMatrixType> qr(hbm);
85 m2 = m1;
86 m2.block(shift,0,brows,cols) = qr.matrixQR();
87 HCoeffsVectorType hc = qr.hCoeffs().conjugate();
88 HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc);
89 hseq.setLength(hc.size()).setShift(shift);
90 VERIFY(hseq.length() == hc.size());
91 VERIFY(hseq.shift() == shift);
92
93 MatrixType m5 = m2;
94 m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero();
95 VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly
96 m3 = hseq;
97 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying
98
99 SquareMatrixType hseq_mat = hseq;
100 SquareMatrixType hseq_mat_conj = hseq.conjugate();
101 SquareMatrixType hseq_mat_adj = hseq.adjoint();
102 SquareMatrixType hseq_mat_trans = hseq.transpose();
103 SquareMatrixType m6 = SquareMatrixType::Random(rows, rows);
104 VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj);
105 VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj);
106 VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans);
107 VERIFY_IS_APPROX(hseq_mat * m6, hseq_mat * m6);
108 VERIFY_IS_APPROX(hseq_mat.adjoint() * m6, hseq_mat_adj * m6);
109 VERIFY_IS_APPROX(hseq_mat.conjugate() * m6, hseq_mat_conj * m6);
110 VERIFY_IS_APPROX(hseq_mat.transpose() * m6, hseq_mat_trans * m6);
111 VERIFY_IS_APPROX(m6 * hseq_mat, m6 * hseq_mat);
112 VERIFY_IS_APPROX(m6 * hseq_mat.adjoint(), m6 * hseq_mat_adj);
113 VERIFY_IS_APPROX(m6 * hseq_mat.conjugate(), m6 * hseq_mat_conj);
114 VERIFY_IS_APPROX(m6 * hseq_mat.transpose(), m6 * hseq_mat_trans);
115
116 // test householder sequence on the right with a shift
117
118 TMatrixType tm2 = m2.transpose();
119 HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc);
120 rhseq.setLength(hc.size()).setShift(shift);
121 VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly
122 m3 = rhseq;
123 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying
124}
125
126void test_householder()
127{
128 for(int i = 0; i < g_repeat; i++) {
129 CALL_SUBTEST_1( householder(Matrix<double,2,2>()) );
130 CALL_SUBTEST_2( householder(Matrix<float,2,3>()) );
131 CALL_SUBTEST_3( householder(Matrix<double,3,5>()) );
132 CALL_SUBTEST_4( householder(Matrix<float,4,4>()) );
133 CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
134 CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
135 CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
136 CALL_SUBTEST_8( householder(Matrix<double,1,1>()) );
137 }
138}
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