1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2009-2010 Benoit Jacob <[email protected]>
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 static bool even = true;
16 even = !even;
17 /* this test covers the following files:
18 Householder.h
19 */
20 Index rows = m.rows();
21 Index cols = m.cols();
22
23 typedef typename MatrixType::Scalar Scalar;
24 typedef typename NumTraits<Scalar>::Real RealScalar;
25 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
26 typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;
27 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
28 typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType;
29 typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;
30
31 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;
32
33 Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols));
34 Scalar* tmp = &_tmp.coeffRef(0,0);
35
36 Scalar beta;
37 RealScalar alpha;
38 EssentialVectorType essential;
39
40 VectorType v1 = VectorType::Random(rows), v2;
41 v2 = v1;
42 v1.makeHouseholder(essential, beta, alpha);
43 v1.applyHouseholderOnTheLeft(essential,beta,tmp);
44 VERIFY_IS_APPROX(v1.norm(), v2.norm());
45 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm());
46 v1 = VectorType::Random(rows);
47 v2 = v1;
48 v1.applyHouseholderOnTheLeft(essential,beta,tmp);
49 VERIFY_IS_APPROX(v1.norm(), v2.norm());
50
51 // reconstruct householder matrix:
52 SquareMatrixType id, H1, H2;
53 id.setIdentity(rows, rows);
54 H1 = H2 = id;
55 VectorType vv(rows);
56 vv << Scalar(1), essential;
57 H1.applyHouseholderOnTheLeft(essential, beta, tmp);
58 H2.applyHouseholderOnTheRight(essential, beta, tmp);
59 VERIFY_IS_APPROX(H1, H2);
60 VERIFY_IS_APPROX(H1, id - beta * vv*vv.adjoint());
61
62 MatrixType m1(rows, cols),
63 m2(rows, cols);
64
65 v1 = VectorType::Random(rows);
66 if(even) v1.tail(rows-1).setZero();
67 m1.colwise() = v1;
68 m2 = m1;
69 m1.col(0).makeHouseholder(essential, beta, alpha);
70 m1.applyHouseholderOnTheLeft(essential,beta,tmp);
71 VERIFY_IS_APPROX(m1.norm(), m2.norm());
72 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm());
73 VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0)));
74 VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha);
75
76 v1 = VectorType::Random(rows);
77 if(even) v1.tail(rows-1).setZero();
78 SquareMatrixType m3(rows,rows), m4(rows,rows);
79 m3.rowwise() = v1.transpose();
80 m4 = m3;
81 m3.row(0).makeHouseholder(essential, beta, alpha);
82 m3.applyHouseholderOnTheRight(essential.conjugate(),beta,tmp);
83 VERIFY_IS_APPROX(m3.norm(), m4.norm());
84 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());
85 VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0)));
86 VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha);
87
88 // test householder sequence on the left with a shift
89
90 Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0));
91 Index brows = rows - shift;
92 m1.setRandom(rows, cols);
93 HBlockMatrixType hbm = m1.block(shift,0,brows,cols);
94 HouseholderQR<HBlockMatrixType> qr(hbm);
95 m2 = m1;
96 m2.block(shift,0,brows,cols) = qr.matrixQR();
97 HCoeffsVectorType hc = qr.hCoeffs().conjugate();
98 HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc);
99 hseq.setLength(hc.size()).setShift(shift);
100 VERIFY(hseq.length() == hc.size());
101 VERIFY(hseq.shift() == shift);
102
103 MatrixType m5 = m2;
104 m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero();
105 VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly
106 m3 = hseq;
107 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying
108
109 SquareMatrixType hseq_mat = hseq;
110 SquareMatrixType hseq_mat_conj = hseq.conjugate();
111 SquareMatrixType hseq_mat_adj = hseq.adjoint();
112 SquareMatrixType hseq_mat_trans = hseq.transpose();
113 SquareMatrixType m6 = SquareMatrixType::Random(rows, rows);
114 VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj);
115 VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj);
116 VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans);
117 VERIFY_IS_APPROX(hseq * m6, hseq_mat * m6);
118 VERIFY_IS_APPROX(hseq.adjoint() * m6, hseq_mat_adj * m6);
119 VERIFY_IS_APPROX(hseq.conjugate() * m6, hseq_mat_conj * m6);
120 VERIFY_IS_APPROX(hseq.transpose() * m6, hseq_mat_trans * m6);
121 VERIFY_IS_APPROX(m6 * hseq, m6 * hseq_mat);
122 VERIFY_IS_APPROX(m6 * hseq.adjoint(), m6 * hseq_mat_adj);
123 VERIFY_IS_APPROX(m6 * hseq.conjugate(), m6 * hseq_mat_conj);
124 VERIFY_IS_APPROX(m6 * hseq.transpose(), m6 * hseq_mat_trans);
125
126 // test householder sequence on the right with a shift
127
128 TMatrixType tm2 = m2.transpose();
129 HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc);
130 rhseq.setLength(hc.size()).setShift(shift);
131 VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly
132 m3 = rhseq;
133 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying
134 }
135
EIGEN_DECLARE_TEST(householder)136 EIGEN_DECLARE_TEST(householder)
137 {
138 for(int i = 0; i < g_repeat; i++) {
139 CALL_SUBTEST_1( householder(Matrix<double,2,2>()) );
140 CALL_SUBTEST_2( householder(Matrix<float,2,3>()) );
141 CALL_SUBTEST_3( householder(Matrix<double,3,5>()) );
142 CALL_SUBTEST_4( householder(Matrix<float,4,4>()) );
143 CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
144 CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
145 CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
146 CALL_SUBTEST_8( householder(Matrix<double,1,1>()) );
147 }
148 }
149