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