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
qr(const MatrixType & m)13 template<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
qr_fixedsize()33 template<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
qr_invertible()53 template<typename MatrixType> void qr_invertible()
54 {
55 using std::log;
56 using std::abs;
57 using std::pow;
58 using std::max;
59 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
60 typedef typename MatrixType::Scalar Scalar;
61
62 int size = internal::random<int>(10,50);
63
64 MatrixType m1(size, size), m2(size, size), m3(size, size);
65 m1 = MatrixType::Random(size,size);
66
67 if (internal::is_same<RealScalar,float>::value)
68 {
69 // let's build a matrix more stable to inverse
70 MatrixType a = MatrixType::Random(size,size*4);
71 m1 += a * a.adjoint();
72 }
73
74 HouseholderQR<MatrixType> qr(m1);
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.householderQ(); // get a unitary
84 m1 = m3 * m1 * m3;
85 qr.compute(m1);
86 VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
87 // This test is tricky if the determinant becomes too small.
88 // Since we generate random numbers with magnitude rrange [0,1], the average determinant is 0.5^size
89 VERIFY_IS_MUCH_SMALLER_THAN( abs(absdet-qr.absDeterminant()), numext::maxi(RealScalar(pow(0.5,size)),numext::maxi<RealScalar>(abs(absdet),abs(qr.absDeterminant()))) );
90
91 }
92
qr_verify_assert()93 template<typename MatrixType> void qr_verify_assert()
94 {
95 MatrixType tmp;
96
97 HouseholderQR<MatrixType> qr;
98 VERIFY_RAISES_ASSERT(qr.matrixQR())
99 VERIFY_RAISES_ASSERT(qr.solve(tmp))
100 VERIFY_RAISES_ASSERT(qr.householderQ())
101 VERIFY_RAISES_ASSERT(qr.absDeterminant())
102 VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
103 }
104
test_qr()105 void test_qr()
106 {
107 for(int i = 0; i < g_repeat; i++) {
108 CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
109 CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
110 CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() ));
111 CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() ));
112 CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() ));
113 CALL_SUBTEST_11( qr(Matrix<float,1,1>()) );
114 }
115
116 for(int i = 0; i < g_repeat; i++) {
117 CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
118 CALL_SUBTEST_6( qr_invertible<MatrixXd>() );
119 CALL_SUBTEST_7( qr_invertible<MatrixXcf>() );
120 CALL_SUBTEST_8( qr_invertible<MatrixXcd>() );
121 }
122
123 CALL_SUBTEST_9(qr_verify_assert<Matrix3f>());
124 CALL_SUBTEST_10(qr_verify_assert<Matrix3d>());
125 CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
126 CALL_SUBTEST_6(qr_verify_assert<MatrixXd>());
127 CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>());
128 CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>());
129
130 // Test problem size constructors
131 CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20));
132 }
133