1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <[email protected]>
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 #include "solverbase.h"
13
qr(const MatrixType & m)14 template<typename MatrixType> void qr(const MatrixType& m)
15 {
16 Index rows = m.rows();
17 Index cols = m.cols();
18
19 typedef typename MatrixType::Scalar Scalar;
20 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
21
22 MatrixType a = MatrixType::Random(rows,cols);
23 HouseholderQR<MatrixType> qrOfA(a);
24
25 MatrixQType q = qrOfA.householderQ();
26 VERIFY_IS_UNITARY(q);
27
28 MatrixType r = qrOfA.matrixQR().template triangularView<Upper>();
29 VERIFY_IS_APPROX(a, qrOfA.householderQ() * r);
30 }
31
qr_fixedsize()32 template<typename MatrixType, int Cols2> void qr_fixedsize()
33 {
34 enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
35 typedef typename MatrixType::Scalar Scalar;
36 Matrix<Scalar,Rows,Cols> m1 = Matrix<Scalar,Rows,Cols>::Random();
37 HouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
38
39 Matrix<Scalar,Rows,Cols> r = qr.matrixQR();
40 // FIXME need better way to construct trapezoid
41 for(int i = 0; i < Rows; i++) for(int j = 0; j < Cols; j++) if(i>j) r(i,j) = Scalar(0);
42
43 VERIFY_IS_APPROX(m1, qr.householderQ() * r);
44
45 check_solverbase<Matrix<Scalar,Cols,Cols2>, Matrix<Scalar,Rows,Cols2> >(m1, qr, Rows, Cols, Cols2);
46 }
47
qr_invertible()48 template<typename MatrixType> void qr_invertible()
49 {
50 using std::log;
51 using std::abs;
52 using std::pow;
53 using std::max;
54 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
55 typedef typename MatrixType::Scalar Scalar;
56
57 STATIC_CHECK(( internal::is_same<typename HouseholderQR<MatrixType>::StorageIndex,int>::value ));
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*4);
68 m1 += a * a.adjoint();
69 }
70
71 HouseholderQR<MatrixType> qr(m1);
72
73 check_solverbase<MatrixType, MatrixType>(m1, qr, size, size, size);
74
75 // now construct a matrix with prescribed determinant
76 m1.setZero();
77 for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
78 RealScalar absdet = abs(m1.diagonal().prod());
79 m3 = qr.householderQ(); // get a unitary
80 m1 = m3 * m1 * m3;
81 qr.compute(m1);
82 VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
83 // This test is tricky if the determinant becomes too small.
84 // Since we generate random numbers with magnitude range [0,1], the average determinant is 0.5^size
85 VERIFY_IS_MUCH_SMALLER_THAN( abs(absdet-qr.absDeterminant()), numext::maxi(RealScalar(pow(0.5,size)),numext::maxi<RealScalar>(abs(absdet),abs(qr.absDeterminant()))) );
86
87 }
88
qr_verify_assert()89 template<typename MatrixType> void qr_verify_assert()
90 {
91 MatrixType tmp;
92
93 HouseholderQR<MatrixType> qr;
94 VERIFY_RAISES_ASSERT(qr.matrixQR())
95 VERIFY_RAISES_ASSERT(qr.solve(tmp))
96 VERIFY_RAISES_ASSERT(qr.transpose().solve(tmp))
97 VERIFY_RAISES_ASSERT(qr.adjoint().solve(tmp))
98 VERIFY_RAISES_ASSERT(qr.householderQ())
99 VERIFY_RAISES_ASSERT(qr.absDeterminant())
100 VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
101 }
102
EIGEN_DECLARE_TEST(qr)103 EIGEN_DECLARE_TEST(qr)
104 {
105 for(int i = 0; i < g_repeat; i++) {
106 CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
107 CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
108 CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() ));
109 CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() ));
110 CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() ));
111 CALL_SUBTEST_11( qr(Matrix<float,1,1>()) );
112 }
113
114 for(int i = 0; i < g_repeat; i++) {
115 CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
116 CALL_SUBTEST_6( qr_invertible<MatrixXd>() );
117 CALL_SUBTEST_7( qr_invertible<MatrixXcf>() );
118 CALL_SUBTEST_8( qr_invertible<MatrixXcd>() );
119 }
120
121 CALL_SUBTEST_9(qr_verify_assert<Matrix3f>());
122 CALL_SUBTEST_10(qr_verify_assert<Matrix3d>());
123 CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
124 CALL_SUBTEST_6(qr_verify_assert<MatrixXd>());
125 CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>());
126 CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>());
127
128 // Test problem size constructors
129 CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20));
130 }
131