qr_fullpivoting.cpp revision c981c48f5bc9aefeffc0bcb0cc3934c2fae179dd 
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  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
24  MatrixType m1;
25  createRandomPIMatrixOfRank(rank,rows,cols,m1);
26  FullPivHouseholderQR<MatrixType> qr(m1);
27  VERIFY(rank == qr.rank());
28  VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
29  VERIFY(!qr.isInjective());
30  VERIFY(!qr.isInvertible());
31  VERIFY(!qr.isSurjective());
32
33  MatrixType r = qr.matrixQR();
34
35  MatrixQType q = qr.matrixQ();
36  VERIFY_IS_UNITARY(q);
37
38  // FIXME need better way to construct trapezoid
39  for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
40
41  MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();
42
43  VERIFY_IS_APPROX(m1, c);
44
45  MatrixType m2 = MatrixType::Random(cols,cols2);
46  MatrixType m3 = m1*m2;
47  m2 = MatrixType::Random(cols,cols2);
48  m2 = qr.solve(m3);
49  VERIFY_IS_APPROX(m3, m1*m2);
50}
51
52template<typename MatrixType> void qr_invertible()
53{
54  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
55  typedef typename MatrixType::Scalar Scalar;
56
57  int size = internal::random<int>(10,50);
58
59  MatrixType m1(size, size), m2(size, size), m3(size, size);
60  m1 = MatrixType::Random(size,size);
61
62  if (internal::is_same<RealScalar,float>::value)
63  {
64    // let's build a matrix more stable to inverse
65    MatrixType a = MatrixType::Random(size,size*2);
66    m1 += a * a.adjoint();
67  }
68
69  FullPivHouseholderQR<MatrixType> qr(m1);
70  VERIFY(qr.isInjective());
71  VERIFY(qr.isInvertible());
72  VERIFY(qr.isSurjective());
73
74  m3 = MatrixType::Random(size,size);
75  m2 = qr.solve(m3);
76  VERIFY_IS_APPROX(m3, m1*m2);
77
78  // now construct a matrix with prescribed determinant
79  m1.setZero();
80  for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
81  RealScalar absdet = internal::abs(m1.diagonal().prod());
82  m3 = qr.matrixQ(); // get a unitary
83  m1 = m3 * m1 * m3;
84  qr.compute(m1);
85  VERIFY_IS_APPROX(absdet, qr.absDeterminant());
86  VERIFY_IS_APPROX(internal::log(absdet), qr.logAbsDeterminant());
87}
88
89template<typename MatrixType> void qr_verify_assert()
90{
91  MatrixType tmp;
92
93  FullPivHouseholderQR<MatrixType> qr;
94  VERIFY_RAISES_ASSERT(qr.matrixQR())
95  VERIFY_RAISES_ASSERT(qr.solve(tmp))
96  VERIFY_RAISES_ASSERT(qr.matrixQ())
97  VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
98  VERIFY_RAISES_ASSERT(qr.isInjective())
99  VERIFY_RAISES_ASSERT(qr.isSurjective())
100  VERIFY_RAISES_ASSERT(qr.isInvertible())
101  VERIFY_RAISES_ASSERT(qr.inverse())
102  VERIFY_RAISES_ASSERT(qr.absDeterminant())
103  VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
104}
105
106void test_qr_fullpivoting()
107{
108 for(int i = 0; i < 1; i++) {
109    // FIXME : very weird bug here
110//     CALL_SUBTEST(qr(Matrix2f()) );
111    CALL_SUBTEST_1( qr<MatrixXf>() );
112    CALL_SUBTEST_2( qr<MatrixXd>() );
113    CALL_SUBTEST_3( qr<MatrixXcd>() );
114  }
115
116  for(int i = 0; i < g_repeat; i++) {
117    CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
118    CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
119    CALL_SUBTEST_4( qr_invertible<MatrixXcf>() );
120    CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
121  }
122
123  CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());
124  CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());
125  CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
126  CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
127  CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());
128  CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
129
130  // Test problem size constructors
131  CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));
132}
133