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::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
111void 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