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
qr()14 template<typename MatrixType> void qr()
15 {
16 Index max_size = EIGEN_TEST_MAX_SIZE;
17 Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);
18 Index rows = internal::random<Index>(min_size,max_size),
19 cols = internal::random<Index>(min_size,max_size),
20 cols2 = internal::random<Index>(min_size,max_size),
21 rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
22
23 typedef typename MatrixType::Scalar Scalar;
24 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
25 MatrixType m1;
26 createRandomPIMatrixOfRank(rank,rows,cols,m1);
27 FullPivHouseholderQR<MatrixType> qr(m1);
28 VERIFY_IS_EQUAL(rank, qr.rank());
29 VERIFY_IS_EQUAL(cols - qr.rank(), qr.dimensionOfKernel());
30 VERIFY(!qr.isInjective());
31 VERIFY(!qr.isInvertible());
32 VERIFY(!qr.isSurjective());
33
34 MatrixType r = qr.matrixQR();
35
36 MatrixQType q = qr.matrixQ();
37 VERIFY_IS_UNITARY(q);
38
39 // FIXME need better way to construct trapezoid
40 for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
41
42 MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();
43
44 VERIFY_IS_APPROX(m1, c);
45
46 // stress the ReturnByValue mechanism
47 MatrixType tmp;
48 VERIFY_IS_APPROX(tmp.noalias() = qr.matrixQ() * r, (qr.matrixQ() * r).eval());
49
50 MatrixType m2 = MatrixType::Random(cols,cols2);
51 MatrixType m3 = m1*m2;
52 m2 = MatrixType::Random(cols,cols2);
53 m2 = qr.solve(m3);
54 VERIFY_IS_APPROX(m3, m1*m2);
55
56 {
57 Index size = rows;
58 do {
59 m1 = MatrixType::Random(size,size);
60 qr.compute(m1);
61 } while(!qr.isInvertible());
62 MatrixType m1_inv = qr.inverse();
63 m3 = m1 * MatrixType::Random(size,cols2);
64 m2 = qr.solve(m3);
65 VERIFY_IS_APPROX(m2, m1_inv*m3);
66 }
67 }
68
qr_invertible()69 template<typename MatrixType> void qr_invertible()
70 {
71 using std::log;
72 using std::abs;
73 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
74 typedef typename MatrixType::Scalar Scalar;
75
76 Index max_size = numext::mini(50,EIGEN_TEST_MAX_SIZE);
77 Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);
78 Index size = internal::random<Index>(min_size,max_size);
79
80 MatrixType m1(size, size), m2(size, size), m3(size, size);
81 m1 = MatrixType::Random(size,size);
82
83 if (internal::is_same<RealScalar,float>::value)
84 {
85 // let's build a matrix more stable to inverse
86 MatrixType a = MatrixType::Random(size,size*2);
87 m1 += a * a.adjoint();
88 }
89
90 FullPivHouseholderQR<MatrixType> qr(m1);
91 VERIFY(qr.isInjective());
92 VERIFY(qr.isInvertible());
93 VERIFY(qr.isSurjective());
94
95 m3 = MatrixType::Random(size,size);
96 m2 = qr.solve(m3);
97 VERIFY_IS_APPROX(m3, m1*m2);
98
99 // now construct a matrix with prescribed determinant
100 m1.setZero();
101 for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
102 RealScalar absdet = abs(m1.diagonal().prod());
103 m3 = qr.matrixQ(); // get a unitary
104 m1 = m3 * m1 * m3;
105 qr.compute(m1);
106 VERIFY_IS_APPROX(absdet, qr.absDeterminant());
107 VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
108 }
109
qr_verify_assert()110 template<typename MatrixType> void qr_verify_assert()
111 {
112 MatrixType tmp;
113
114 FullPivHouseholderQR<MatrixType> qr;
115 VERIFY_RAISES_ASSERT(qr.matrixQR())
116 VERIFY_RAISES_ASSERT(qr.solve(tmp))
117 VERIFY_RAISES_ASSERT(qr.matrixQ())
118 VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
119 VERIFY_RAISES_ASSERT(qr.isInjective())
120 VERIFY_RAISES_ASSERT(qr.isSurjective())
121 VERIFY_RAISES_ASSERT(qr.isInvertible())
122 VERIFY_RAISES_ASSERT(qr.inverse())
123 VERIFY_RAISES_ASSERT(qr.absDeterminant())
124 VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
125 }
126
test_qr_fullpivoting()127 void test_qr_fullpivoting()
128 {
129 for(int i = 0; i < 1; i++) {
130 // FIXME : very weird bug here
131 // CALL_SUBTEST(qr(Matrix2f()) );
132 CALL_SUBTEST_1( qr<MatrixXf>() );
133 CALL_SUBTEST_2( qr<MatrixXd>() );
134 CALL_SUBTEST_3( qr<MatrixXcd>() );
135 }
136
137 for(int i = 0; i < g_repeat; i++) {
138 CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
139 CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
140 CALL_SUBTEST_4( qr_invertible<MatrixXcf>() );
141 CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
142 }
143
144 CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());
145 CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());
146 CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
147 CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
148 CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());
149 CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
150
151 // Test problem size constructors
152 CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));
153 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(10,20)));
154 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(Matrix<float,10,20>::Random())));
155 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(20,10)));
156 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(Matrix<float,20,10>::Random())));
157 }
158