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 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
qr_fixedsize()34 template<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
qr_invertible()54 template<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
qr_verify_assert()87 template<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
test_qr()99 void 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