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 rows = internal::random<Index>(20,200), cols = internal::random<int>(20,200), cols2 = internal::random<int>(20,200);
19 Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
20
21 typedef typename MatrixType::Scalar Scalar;
22 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
23 MatrixType m1;
24 createRandomPIMatrixOfRank(rank,rows,cols,m1);
25 FullPivHouseholderQR<MatrixType> qr(m1);
26 VERIFY(rank == qr.rank());
27 VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
28 VERIFY(!qr.isInjective());
29 VERIFY(!qr.isInvertible());
30 VERIFY(!qr.isSurjective());
31
32 MatrixType r = qr.matrixQR();
33
34 MatrixQType q = qr.matrixQ();
35 VERIFY_IS_UNITARY(q);
36
37 // FIXME need better way to construct trapezoid
38 for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
39
40 MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();
41
42 VERIFY_IS_APPROX(m1, c);
43
44 MatrixType m2 = MatrixType::Random(cols,cols2);
45 MatrixType m3 = m1*m2;
46 m2 = MatrixType::Random(cols,cols2);
47 m2 = qr.solve(m3);
48 VERIFY_IS_APPROX(m3, m1*m2);
49 }
50
qr_invertible()51 template<typename MatrixType> void qr_invertible()
52 {
53 using std::log;
54 using std::abs;
55 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
56 typedef typename MatrixType::Scalar Scalar;
57
58 int size = internal::random<int>(10,50);
59
60 MatrixType m1(size, size), m2(size, size), m3(size, size);
61 m1 = MatrixType::Random(size,size);
62
63 if (internal::is_same<RealScalar,float>::value)
64 {
65 // let's build a matrix more stable to inverse
66 MatrixType a = MatrixType::Random(size,size*2);
67 m1 += a * a.adjoint();
68 }
69
70 FullPivHouseholderQR<MatrixType> qr(m1);
71 VERIFY(qr.isInjective());
72 VERIFY(qr.isInvertible());
73 VERIFY(qr.isSurjective());
74
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.matrixQ(); // get a unitary
84 m1 = m3 * m1 * m3;
85 qr.compute(m1);
86 VERIFY_IS_APPROX(absdet, qr.absDeterminant());
87 VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
88 }
89
qr_verify_assert()90 template<typename MatrixType> void qr_verify_assert()
91 {
92 MatrixType tmp;
93
94 FullPivHouseholderQR<MatrixType> qr;
95 VERIFY_RAISES_ASSERT(qr.matrixQR())
96 VERIFY_RAISES_ASSERT(qr.solve(tmp))
97 VERIFY_RAISES_ASSERT(qr.matrixQ())
98 VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
99 VERIFY_RAISES_ASSERT(qr.isInjective())
100 VERIFY_RAISES_ASSERT(qr.isSurjective())
101 VERIFY_RAISES_ASSERT(qr.isInvertible())
102 VERIFY_RAISES_ASSERT(qr.inverse())
103 VERIFY_RAISES_ASSERT(qr.absDeterminant())
104 VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
105 }
106
test_qr_fullpivoting()107 void test_qr_fullpivoting()
108 {
109 for(int i = 0; i < 1; i++) {
110 // FIXME : very weird bug here
111 // CALL_SUBTEST(qr(Matrix2f()) );
112 CALL_SUBTEST_1( qr<MatrixXf>() );
113 CALL_SUBTEST_2( qr<MatrixXd>() );
114 CALL_SUBTEST_3( qr<MatrixXcd>() );
115 }
116
117 for(int i = 0; i < g_repeat; i++) {
118 CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
119 CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
120 CALL_SUBTEST_4( qr_invertible<MatrixXcf>() );
121 CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
122 }
123
124 CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());
125 CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());
126 CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
127 CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
128 CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());
129 CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
130
131 // Test problem size constructors
132 CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));
133 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(10,20)));
134 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(Matrix<float,10,20>::Random())));
135 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(20,10)));
136 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(Matrix<float,20,10>::Random())));
137 }
138