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
23  MatrixType a = MatrixType::Random(rows,cols);
24  HouseholderQR<MatrixType> qrOfA(a);
25
26  MatrixQType q = qrOfA.householderQ();
27  VERIFY_IS_UNITARY(q);
28
29  MatrixType r = qrOfA.matrixQR().template triangularView<Upper>();
30  VERIFY_IS_APPROX(a, qrOfA.householderQ() * r);
31}
32
33template<typename MatrixType, int Cols2> void qr_fixedsize()
34{
35  enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
36  typedef typename MatrixType::Scalar Scalar;
37  Matrix<Scalar,Rows,Cols> m1 = Matrix<Scalar,Rows,Cols>::Random();
38  HouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
39
40  Matrix<Scalar,Rows,Cols> r = qr.matrixQR();
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  VERIFY_IS_APPROX(m1, qr.householderQ() * r);
45
46  Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
47  Matrix<Scalar,Rows,Cols2> m3 = m1*m2;
48  m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
49  m2 = qr.solve(m3);
50  VERIFY_IS_APPROX(m3, m1*m2);
51}
52
53template<typename MatrixType> void qr_invertible()
54{
55  using std::log;
56  using std::abs;
57  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
58  typedef typename MatrixType::Scalar Scalar;
59
60  int size = internal::random<int>(10,50);
61
62  MatrixType m1(size, size), m2(size, size), m3(size, size);
63  m1 = MatrixType::Random(size,size);
64
65  if (internal::is_same<RealScalar,float>::value)
66  {
67    // let's build a matrix more stable to inverse
68    MatrixType a = MatrixType::Random(size,size*2);
69    m1 += a * a.adjoint();
70  }
71
72  HouseholderQR<MatrixType> qr(m1);
73  m3 = MatrixType::Random(size,size);
74  m2 = qr.solve(m3);
75  VERIFY_IS_APPROX(m3, m1*m2);
76
77  // now construct a matrix with prescribed determinant
78  m1.setZero();
79  for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
80  RealScalar absdet = abs(m1.diagonal().prod());
81  m3 = qr.householderQ(); // get a unitary
82  m1 = m3 * m1 * m3;
83  qr.compute(m1);
84  VERIFY_IS_APPROX(absdet, qr.absDeterminant());
85  VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
86}
87
88template<typename MatrixType> void qr_verify_assert()
89{
90  MatrixType tmp;
91
92  HouseholderQR<MatrixType> qr;
93  VERIFY_RAISES_ASSERT(qr.matrixQR())
94  VERIFY_RAISES_ASSERT(qr.solve(tmp))
95  VERIFY_RAISES_ASSERT(qr.householderQ())
96  VERIFY_RAISES_ASSERT(qr.absDeterminant())
97  VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
98}
99
100void test_qr()
101{
102  for(int i = 0; i < g_repeat; i++) {
103   CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
104   CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
105   CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() ));
106   CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() ));
107   CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() ));
108   CALL_SUBTEST_11( qr(Matrix<float,1,1>()) );
109  }
110
111  for(int i = 0; i < g_repeat; i++) {
112    CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
113    CALL_SUBTEST_6( qr_invertible<MatrixXd>() );
114    CALL_SUBTEST_7( qr_invertible<MatrixXcf>() );
115    CALL_SUBTEST_8( qr_invertible<MatrixXcd>() );
116  }
117
118  CALL_SUBTEST_9(qr_verify_assert<Matrix3f>());
119  CALL_SUBTEST_10(qr_verify_assert<Matrix3d>());
120  CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
121  CALL_SUBTEST_6(qr_verify_assert<MatrixXd>());
122  CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>());
123  CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>());
124
125  // Test problem size constructors
126  CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20));
127}
128