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 typedef typename MatrixType::Index Index;
17
18 Index max_size = EIGEN_TEST_MAX_SIZE;
19 Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);
20 Index rows = internal::random<Index>(min_size,max_size),
21 cols = internal::random<Index>(min_size,max_size),
22 cols2 = internal::random<Index>(min_size,max_size),
23 rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
24
25 typedef typename MatrixType::Scalar Scalar;
26 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
27 MatrixType m1;
28 createRandomPIMatrixOfRank(rank,rows,cols,m1);
29 FullPivHouseholderQR<MatrixType> qr(m1);
30 VERIFY_IS_EQUAL(rank, qr.rank());
31 VERIFY_IS_EQUAL(cols - qr.rank(), qr.dimensionOfKernel());
32 VERIFY(!qr.isInjective());
33 VERIFY(!qr.isInvertible());
34 VERIFY(!qr.isSurjective());
35
36 MatrixType r = qr.matrixQR();
37
38 MatrixQType q = qr.matrixQ();
39 VERIFY_IS_UNITARY(q);
40
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 MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();
45
46 VERIFY_IS_APPROX(m1, c);
47
48 // stress the ReturnByValue mechanism
49 MatrixType tmp;
50 VERIFY_IS_APPROX(tmp.noalias() = qr.matrixQ() * r, (qr.matrixQ() * r).eval());
51
52 MatrixType m2 = MatrixType::Random(cols,cols2);
53 MatrixType m3 = m1*m2;
54 m2 = MatrixType::Random(cols,cols2);
55 m2 = qr.solve(m3);
56 VERIFY_IS_APPROX(m3, m1*m2);
57
58 {
59 Index size = rows;
60 do {
61 m1 = MatrixType::Random(size,size);
62 qr.compute(m1);
63 } while(!qr.isInvertible());
64 MatrixType m1_inv = qr.inverse();
65 m3 = m1 * MatrixType::Random(size,cols2);
66 m2 = qr.solve(m3);
67 VERIFY_IS_APPROX(m2, m1_inv*m3);
68 }
69 }
70
qr_invertible()71 template<typename MatrixType> void qr_invertible()
72 {
73 using std::log;
74 using std::abs;
75 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
76 typedef typename MatrixType::Scalar Scalar;
77
78 Index max_size = numext::mini(50,EIGEN_TEST_MAX_SIZE);
79 Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);
80 Index size = internal::random<Index>(min_size,max_size);
81
82 MatrixType m1(size, size), m2(size, size), m3(size, size);
83 m1 = MatrixType::Random(size,size);
84
85 if (internal::is_same<RealScalar,float>::value)
86 {
87 // let's build a matrix more stable to inverse
88 MatrixType a = MatrixType::Random(size,size*2);
89 m1 += a * a.adjoint();
90 }
91
92 FullPivHouseholderQR<MatrixType> qr(m1);
93 VERIFY(qr.isInjective());
94 VERIFY(qr.isInvertible());
95 VERIFY(qr.isSurjective());
96
97 m3 = MatrixType::Random(size,size);
98 m2 = qr.solve(m3);
99 VERIFY_IS_APPROX(m3, m1*m2);
100
101 // now construct a matrix with prescribed determinant
102 m1.setZero();
103 for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
104 RealScalar absdet = abs(m1.diagonal().prod());
105 m3 = qr.matrixQ(); // get a unitary
106 m1 = m3 * m1 * m3;
107 qr.compute(m1);
108 VERIFY_IS_APPROX(absdet, qr.absDeterminant());
109 VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
110 }
111
qr_verify_assert()112 template<typename MatrixType> void qr_verify_assert()
113 {
114 MatrixType tmp;
115
116 FullPivHouseholderQR<MatrixType> qr;
117 VERIFY_RAISES_ASSERT(qr.matrixQR())
118 VERIFY_RAISES_ASSERT(qr.solve(tmp))
119 VERIFY_RAISES_ASSERT(qr.matrixQ())
120 VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
121 VERIFY_RAISES_ASSERT(qr.isInjective())
122 VERIFY_RAISES_ASSERT(qr.isSurjective())
123 VERIFY_RAISES_ASSERT(qr.isInvertible())
124 VERIFY_RAISES_ASSERT(qr.inverse())
125 VERIFY_RAISES_ASSERT(qr.absDeterminant())
126 VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
127 }
128
test_qr_fullpivoting()129 void test_qr_fullpivoting()
130 {
131 for(int i = 0; i < 1; i++) {
132 // FIXME : very weird bug here
133 // CALL_SUBTEST(qr(Matrix2f()) );
134 CALL_SUBTEST_1( qr<MatrixXf>() );
135 CALL_SUBTEST_2( qr<MatrixXd>() );
136 CALL_SUBTEST_3( qr<MatrixXcd>() );
137 }
138
139 for(int i = 0; i < g_repeat; i++) {
140 CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
141 CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
142 CALL_SUBTEST_4( qr_invertible<MatrixXcf>() );
143 CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
144 }
145
146 CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());
147 CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());
148 CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
149 CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
150 CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());
151 CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
152
153 // Test problem size constructors
154 CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));
155 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(10,20)));
156 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(Matrix<float,10,20>::Random())));
157 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(20,10)));
158 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(Matrix<float,20,10>::Random())));
159 }
160