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
householder(const MatrixType & m)13 template<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::ColsAtCompileTime> RightSquareMatrixType;
33 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, Dynamic> VBlockMatrixType;
34 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;
35
36 Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols));
37 Scalar* tmp = &_tmp.coeffRef(0,0);
38
39 Scalar beta;
40 RealScalar alpha;
41 EssentialVectorType essential;
42
43 VectorType v1 = VectorType::Random(rows), v2;
44 v2 = v1;
45 v1.makeHouseholder(essential, beta, alpha);
46 v1.applyHouseholderOnTheLeft(essential,beta,tmp);
47 VERIFY_IS_APPROX(v1.norm(), v2.norm());
48 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm());
49 v1 = VectorType::Random(rows);
50 v2 = v1;
51 v1.applyHouseholderOnTheLeft(essential,beta,tmp);
52 VERIFY_IS_APPROX(v1.norm(), v2.norm());
53
54 MatrixType m1(rows, cols),
55 m2(rows, cols);
56
57 v1 = VectorType::Random(rows);
58 if(even) v1.tail(rows-1).setZero();
59 m1.colwise() = v1;
60 m2 = m1;
61 m1.col(0).makeHouseholder(essential, beta, alpha);
62 m1.applyHouseholderOnTheLeft(essential,beta,tmp);
63 VERIFY_IS_APPROX(m1.norm(), m2.norm());
64 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm());
65 VERIFY_IS_MUCH_SMALLER_THAN(internal::imag(m1(0,0)), internal::real(m1(0,0)));
66 VERIFY_IS_APPROX(internal::real(m1(0,0)), alpha);
67
68 v1 = VectorType::Random(rows);
69 if(even) v1.tail(rows-1).setZero();
70 SquareMatrixType m3(rows,rows), m4(rows,rows);
71 m3.rowwise() = v1.transpose();
72 m4 = m3;
73 m3.row(0).makeHouseholder(essential, beta, alpha);
74 m3.applyHouseholderOnTheRight(essential,beta,tmp);
75 VERIFY_IS_APPROX(m3.norm(), m4.norm());
76 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());
77 VERIFY_IS_MUCH_SMALLER_THAN(internal::imag(m3(0,0)), internal::real(m3(0,0)));
78 VERIFY_IS_APPROX(internal::real(m3(0,0)), alpha);
79
80 // test householder sequence on the left with a shift
81
82 Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0));
83 Index brows = rows - shift;
84 m1.setRandom(rows, cols);
85 HBlockMatrixType hbm = m1.block(shift,0,brows,cols);
86 HouseholderQR<HBlockMatrixType> qr(hbm);
87 m2 = m1;
88 m2.block(shift,0,brows,cols) = qr.matrixQR();
89 HCoeffsVectorType hc = qr.hCoeffs().conjugate();
90 HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc);
91 hseq.setLength(hc.size()).setShift(shift);
92 VERIFY(hseq.length() == hc.size());
93 VERIFY(hseq.shift() == shift);
94
95 MatrixType m5 = m2;
96 m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero();
97 VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly
98 m3 = hseq;
99 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying
100
101 // test householder sequence on the right with a shift
102
103 TMatrixType tm2 = m2.transpose();
104 HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc);
105 rhseq.setLength(hc.size()).setShift(shift);
106 VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly
107 m3 = rhseq;
108 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying
109 }
110
test_householder()111 void test_householder()
112 {
113 for(int i = 0; i < g_repeat; i++) {
114 CALL_SUBTEST_1( householder(Matrix<double,2,2>()) );
115 CALL_SUBTEST_2( householder(Matrix<float,2,3>()) );
116 CALL_SUBTEST_3( householder(Matrix<double,3,5>()) );
117 CALL_SUBTEST_4( householder(Matrix<float,4,4>()) );
118 CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
119 CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
120 CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
121 CALL_SUBTEST_8( householder(Matrix<double,1,1>()) );
122 }
123 }
124