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 max_size = EIGEN_TEST_MAX_SIZE;
19  Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);
20  Index rows  = internal::random<Index>(min_size,max_size),
21        cols  = internal::random<Index>(min_size,max_size),
22        cols2 = internal::random<Index>(min_size,max_size),
23        rank  = internal::random<Index>(1, (std::min)(rows, cols)-1);
24
25  typedef typename MatrixType::Scalar Scalar;
26  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
27  MatrixType m1;
28  createRandomPIMatrixOfRank(rank,rows,cols,m1);
29  FullPivHouseholderQR<MatrixType> qr(m1);
30  VERIFY_IS_EQUAL(rank, qr.rank());
31  VERIFY_IS_EQUAL(cols - qr.rank(), qr.dimensionOfKernel());
32  VERIFY(!qr.isInjective());
33  VERIFY(!qr.isInvertible());
34  VERIFY(!qr.isSurjective());
35
36  MatrixType r = qr.matrixQR();
37
38  MatrixQType q = qr.matrixQ();
39  VERIFY_IS_UNITARY(q);
40
41  // FIXME need better way to construct trapezoid
42  for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
43
44  MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();
45
46  VERIFY_IS_APPROX(m1, c);
47
48  // stress the ReturnByValue mechanism
49  MatrixType tmp;
50  VERIFY_IS_APPROX(tmp.noalias() = qr.matrixQ() * r, (qr.matrixQ() * r).eval());
51
52  MatrixType m2 = MatrixType::Random(cols,cols2);
53  MatrixType m3 = m1*m2;
54  m2 = MatrixType::Random(cols,cols2);
55  m2 = qr.solve(m3);
56  VERIFY_IS_APPROX(m3, m1*m2);
57
58  {
59    Index size = rows;
60    do {
61      m1 = MatrixType::Random(size,size);
62      qr.compute(m1);
63    } while(!qr.isInvertible());
64    MatrixType m1_inv = qr.inverse();
65    m3 = m1 * MatrixType::Random(size,cols2);
66    m2 = qr.solve(m3);
67    VERIFY_IS_APPROX(m2, m1_inv*m3);
68  }
69}
70
71template<typename MatrixType> void qr_invertible()
72{
73  using std::log;
74  using std::abs;
75  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
76  typedef typename MatrixType::Scalar Scalar;
77
78  Index max_size = numext::mini(50,EIGEN_TEST_MAX_SIZE);
79  Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);
80  Index size = internal::random<Index>(min_size,max_size);
81
82  MatrixType m1(size, size), m2(size, size), m3(size, size);
83  m1 = MatrixType::Random(size,size);
84
85  if (internal::is_same<RealScalar,float>::value)
86  {
87    // let's build a matrix more stable to inverse
88    MatrixType a = MatrixType::Random(size,size*2);
89    m1 += a * a.adjoint();
90  }
91
92  FullPivHouseholderQR<MatrixType> qr(m1);
93  VERIFY(qr.isInjective());
94  VERIFY(qr.isInvertible());
95  VERIFY(qr.isSurjective());
96
97  m3 = MatrixType::Random(size,size);
98  m2 = qr.solve(m3);
99  VERIFY_IS_APPROX(m3, m1*m2);
100
101  // now construct a matrix with prescribed determinant
102  m1.setZero();
103  for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
104  RealScalar absdet = abs(m1.diagonal().prod());
105  m3 = qr.matrixQ(); // get a unitary
106  m1 = m3 * m1 * m3;
107  qr.compute(m1);
108  VERIFY_IS_APPROX(absdet, qr.absDeterminant());
109  VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
110}
111
112template<typename MatrixType> void qr_verify_assert()
113{
114  MatrixType tmp;
115
116  FullPivHouseholderQR<MatrixType> qr;
117  VERIFY_RAISES_ASSERT(qr.matrixQR())
118  VERIFY_RAISES_ASSERT(qr.solve(tmp))
119  VERIFY_RAISES_ASSERT(qr.matrixQ())
120  VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
121  VERIFY_RAISES_ASSERT(qr.isInjective())
122  VERIFY_RAISES_ASSERT(qr.isSurjective())
123  VERIFY_RAISES_ASSERT(qr.isInvertible())
124  VERIFY_RAISES_ASSERT(qr.inverse())
125  VERIFY_RAISES_ASSERT(qr.absDeterminant())
126  VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
127}
128
129void test_qr_fullpivoting()
130{
131 for(int i = 0; i < 1; i++) {
132    // FIXME : very weird bug here
133//     CALL_SUBTEST(qr(Matrix2f()) );
134    CALL_SUBTEST_1( qr<MatrixXf>() );
135    CALL_SUBTEST_2( qr<MatrixXd>() );
136    CALL_SUBTEST_3( qr<MatrixXcd>() );
137  }
138
139  for(int i = 0; i < g_repeat; i++) {
140    CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
141    CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
142    CALL_SUBTEST_4( qr_invertible<MatrixXcf>() );
143    CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
144  }
145
146  CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());
147  CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());
148  CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
149  CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
150  CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());
151  CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
152
153  // Test problem size constructors
154  CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));
155  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(10,20)));
156  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(Matrix<float,10,20>::Random())));
157  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(20,10)));
158  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(Matrix<float,20,10>::Random())));
159}
160