qr.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//
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 qr(const MatrixType& m)
14{
15  typedef typename MatrixType::Index Index;
16
17  Index rows = m.rows();
18  Index cols = m.cols();
19
20  typedef typename MatrixType::Scalar Scalar;
21  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
22  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
23
24  MatrixType a = MatrixType::Random(rows,cols);
25  HouseholderQR<MatrixType> qrOfA(a);
26
27  MatrixQType q = qrOfA.householderQ();
28  VERIFY_IS_UNITARY(q);
29
30  MatrixType r = qrOfA.matrixQR().template triangularView<Upper>();
31  VERIFY_IS_APPROX(a, qrOfA.householderQ() * r);
32}
33
34template<typename MatrixType, int Cols2> void qr_fixedsize()
35{
36  enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
37  typedef typename MatrixType::Scalar Scalar;
38  Matrix<Scalar,Rows,Cols> m1 = Matrix<Scalar,Rows,Cols>::Random();
39  HouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
40
41  Matrix<Scalar,Rows,Cols> r = qr.matrixQR();
42  // FIXME need better way to construct trapezoid
43  for(int i = 0; i < Rows; i++) for(int j = 0; j < Cols; j++) if(i>j) r(i,j) = Scalar(0);
44
45  VERIFY_IS_APPROX(m1, qr.householderQ() * r);
46
47  Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
48  Matrix<Scalar,Rows,Cols2> m3 = m1*m2;
49  m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
50  m2 = qr.solve(m3);
51  VERIFY_IS_APPROX(m3, m1*m2);
52}
53
54template<typename MatrixType> void qr_invertible()
55{
56  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
57  typedef typename MatrixType::Scalar Scalar;
58
59  int size = internal::random<int>(10,50);
60
61  MatrixType m1(size, size), m2(size, size), m3(size, size);
62  m1 = MatrixType::Random(size,size);
63
64  if (internal::is_same<RealScalar,float>::value)
65  {
66    // let's build a matrix more stable to inverse
67    MatrixType a = MatrixType::Random(size,size*2);
68    m1 += a * a.adjoint();
69  }
70
71  HouseholderQR<MatrixType> qr(m1);
72  m3 = MatrixType::Random(size,size);
73  m2 = qr.solve(m3);
74  VERIFY_IS_APPROX(m3, m1*m2);
75
76  // now construct a matrix with prescribed determinant
77  m1.setZero();
78  for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
79  RealScalar absdet = internal::abs(m1.diagonal().prod());
80  m3 = qr.householderQ(); // get a unitary
81  m1 = m3 * m1 * m3;
82  qr.compute(m1);
83  VERIFY_IS_APPROX(absdet, qr.absDeterminant());
84  VERIFY_IS_APPROX(internal::log(absdet), qr.logAbsDeterminant());
85}
86
87template<typename MatrixType> void qr_verify_assert()
88{
89  MatrixType tmp;
90
91  HouseholderQR<MatrixType> qr;
92  VERIFY_RAISES_ASSERT(qr.matrixQR())
93  VERIFY_RAISES_ASSERT(qr.solve(tmp))
94  VERIFY_RAISES_ASSERT(qr.householderQ())
95  VERIFY_RAISES_ASSERT(qr.absDeterminant())
96  VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
97}
98
99void test_qr()
100{
101  for(int i = 0; i < g_repeat; i++) {
102   CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
103   CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
104   CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() ));
105   CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() ));
106   CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() ));
107   CALL_SUBTEST_11( qr(Matrix<float,1,1>()) );
108  }
109
110  for(int i = 0; i < g_repeat; i++) {
111    CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
112    CALL_SUBTEST_6( qr_invertible<MatrixXd>() );
113    CALL_SUBTEST_7( qr_invertible<MatrixXcf>() );
114    CALL_SUBTEST_8( qr_invertible<MatrixXcd>() );
115  }
116
117  CALL_SUBTEST_9(qr_verify_assert<Matrix3f>());
118  CALL_SUBTEST_10(qr_verify_assert<Matrix3d>());
119  CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
120  CALL_SUBTEST_6(qr_verify_assert<MatrixXd>());
121  CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>());
122  CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>());
123
124  // Test problem size constructors
125  CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20));
126}
127