1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
6//
7// This Source Code Form is subject to the terms of the Mozilla
8// Public License v. 2.0. If a copy of the MPL was not distributed
9// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11#include "main.h"
12#include <Eigen/QR>
13
14template<typename MatrixType> void qr()
15{
16  typedef typename MatrixType::Index Index;
17
18  Index rows = internal::random<Index>(20,200), cols = internal::random<int>(20,200), cols2 = internal::random<int>(20,200);
19  Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
20
21  typedef typename MatrixType::Scalar Scalar;
22  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
23  MatrixType m1;
24  createRandomPIMatrixOfRank(rank,rows,cols,m1);
25  FullPivHouseholderQR<MatrixType> qr(m1);
26  VERIFY(rank == qr.rank());
27  VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
28  VERIFY(!qr.isInjective());
29  VERIFY(!qr.isInvertible());
30  VERIFY(!qr.isSurjective());
31
32  MatrixType r = qr.matrixQR();
33
34  MatrixQType q = qr.matrixQ();
35  VERIFY_IS_UNITARY(q);
36
37  // FIXME need better way to construct trapezoid
38  for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
39
40  MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();
41
42  VERIFY_IS_APPROX(m1, c);
43
44  MatrixType m2 = MatrixType::Random(cols,cols2);
45  MatrixType m3 = m1*m2;
46  m2 = MatrixType::Random(cols,cols2);
47  m2 = qr.solve(m3);
48  VERIFY_IS_APPROX(m3, m1*m2);
49}
50
51template<typename MatrixType> void qr_invertible()
52{
53  using std::log;
54  using std::abs;
55  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
56  typedef typename MatrixType::Scalar Scalar;
57
58  int size = internal::random<int>(10,50);
59
60  MatrixType m1(size, size), m2(size, size), m3(size, size);
61  m1 = MatrixType::Random(size,size);
62
63  if (internal::is_same<RealScalar,float>::value)
64  {
65    // let's build a matrix more stable to inverse
66    MatrixType a = MatrixType::Random(size,size*2);
67    m1 += a * a.adjoint();
68  }
69
70  FullPivHouseholderQR<MatrixType> qr(m1);
71  VERIFY(qr.isInjective());
72  VERIFY(qr.isInvertible());
73  VERIFY(qr.isSurjective());
74
75  m3 = MatrixType::Random(size,size);
76  m2 = qr.solve(m3);
77  VERIFY_IS_APPROX(m3, m1*m2);
78
79  // now construct a matrix with prescribed determinant
80  m1.setZero();
81  for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
82  RealScalar absdet = abs(m1.diagonal().prod());
83  m3 = qr.matrixQ(); // get a unitary
84  m1 = m3 * m1 * m3;
85  qr.compute(m1);
86  VERIFY_IS_APPROX(absdet, qr.absDeterminant());
87  VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
88}
89
90template<typename MatrixType> void qr_verify_assert()
91{
92  MatrixType tmp;
93
94  FullPivHouseholderQR<MatrixType> qr;
95  VERIFY_RAISES_ASSERT(qr.matrixQR())
96  VERIFY_RAISES_ASSERT(qr.solve(tmp))
97  VERIFY_RAISES_ASSERT(qr.matrixQ())
98  VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
99  VERIFY_RAISES_ASSERT(qr.isInjective())
100  VERIFY_RAISES_ASSERT(qr.isSurjective())
101  VERIFY_RAISES_ASSERT(qr.isInvertible())
102  VERIFY_RAISES_ASSERT(qr.inverse())
103  VERIFY_RAISES_ASSERT(qr.absDeterminant())
104  VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
105}
106
107void test_qr_fullpivoting()
108{
109 for(int i = 0; i < 1; i++) {
110    // FIXME : very weird bug here
111//     CALL_SUBTEST(qr(Matrix2f()) );
112    CALL_SUBTEST_1( qr<MatrixXf>() );
113    CALL_SUBTEST_2( qr<MatrixXd>() );
114    CALL_SUBTEST_3( qr<MatrixXcd>() );
115  }
116
117  for(int i = 0; i < g_repeat; i++) {
118    CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
119    CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
120    CALL_SUBTEST_4( qr_invertible<MatrixXcf>() );
121    CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
122  }
123
124  CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());
125  CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());
126  CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
127  CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
128  CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());
129  CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
130
131  // Test problem size constructors
132  CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));
133  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(10,20)));
134  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(Matrix<float,10,20>::Random())));
135  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(20,10)));
136  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(Matrix<float,20,10>::Random())));
137}
138