1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra. Eigen itself is part of the KDE project.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@gmail.com>
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
triangular(const MatrixType & m)12 template<typename MatrixType> void triangular(const MatrixType& m)
13 {
14 typedef typename MatrixType::Scalar Scalar;
15 typedef typename NumTraits<Scalar>::Real RealScalar;
16
17 RealScalar largerEps = 10*test_precision<RealScalar>();
18
19 int rows = m.rows();
20 int cols = m.cols();
21
22 MatrixType m1 = MatrixType::Random(rows, cols),
23 m2 = MatrixType::Random(rows, cols),
24 m3(rows, cols),
25 m4(rows, cols),
26 r1(rows, cols),
27 r2(rows, cols);
28
29 MatrixType m1up = m1.template part<Eigen::UpperTriangular>();
30 MatrixType m2up = m2.template part<Eigen::UpperTriangular>();
31
32 if (rows*cols>1)
33 {
34 VERIFY(m1up.isUpperTriangular());
35 VERIFY(m2up.transpose().isLowerTriangular());
36 VERIFY(!m2.isLowerTriangular());
37 }
38
39 // VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
40
41 // test overloaded operator+=
42 r1.setZero();
43 r2.setZero();
44 r1.template part<Eigen::UpperTriangular>() += m1;
45 r2 += m1up;
46 VERIFY_IS_APPROX(r1,r2);
47
48 // test overloaded operator=
49 m1.setZero();
50 m1.template part<Eigen::UpperTriangular>() = (m2.transpose() * m2).lazy();
51 m3 = m2.transpose() * m2;
52 VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>().transpose(), m1);
53
54 // test overloaded operator=
55 m1.setZero();
56 m1.template part<Eigen::LowerTriangular>() = (m2.transpose() * m2).lazy();
57 VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>(), m1);
58
59 VERIFY_IS_APPROX(m3.template part<Diagonal>(), m3.diagonal().asDiagonal());
60
61 m1 = MatrixType::Random(rows, cols);
62 for (int i=0; i<rows; ++i)
63 while (ei_abs2(m1(i,i))<1e-3) m1(i,i) = ei_random<Scalar>();
64
65 Transpose<MatrixType> trm4(m4);
66 // test back and forward subsitution
67 m3 = m1.template part<Eigen::LowerTriangular>();
68 VERIFY(m3.template marked<Eigen::LowerTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
69 VERIFY(m3.transpose().template marked<Eigen::UpperTriangular>()
70 .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
71 // check M * inv(L) using in place API
72 m4 = m3;
73 m3.transpose().template marked<Eigen::UpperTriangular>().solveTriangularInPlace(trm4);
74 VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
75
76 m3 = m1.template part<Eigen::UpperTriangular>();
77 VERIFY(m3.template marked<Eigen::UpperTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
78 VERIFY(m3.transpose().template marked<Eigen::LowerTriangular>()
79 .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
80 // check M * inv(U) using in place API
81 m4 = m3;
82 m3.transpose().template marked<Eigen::LowerTriangular>().solveTriangularInPlace(trm4);
83 VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
84
85 m3 = m1.template part<Eigen::UpperTriangular>();
86 VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::UpperTriangular>().solveTriangular(m2)), largerEps));
87 m3 = m1.template part<Eigen::LowerTriangular>();
88 VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::LowerTriangular>().solveTriangular(m2)), largerEps));
89
90 VERIFY((m1.template part<Eigen::UpperTriangular>() * m2.template part<Eigen::UpperTriangular>()).isUpperTriangular());
91
92 // test swap
93 m1.setOnes();
94 m2.setZero();
95 m2.template part<Eigen::UpperTriangular>().swap(m1);
96 m3.setZero();
97 m3.template part<Eigen::UpperTriangular>().setOnes();
98 VERIFY_IS_APPROX(m2,m3);
99
100 }
101
selfadjoint()102 void selfadjoint()
103 {
104 Matrix2i m;
105 m << 1, 2,
106 3, 4;
107
108 Matrix2i m1 = Matrix2i::Zero();
109 m1.part<SelfAdjoint>() = m;
110 Matrix2i ref1;
111 ref1 << 1, 2,
112 2, 4;
113 VERIFY(m1 == ref1);
114
115 Matrix2i m2 = Matrix2i::Zero();
116 m2.part<SelfAdjoint>() = m.part<UpperTriangular>();
117 Matrix2i ref2;
118 ref2 << 1, 2,
119 2, 4;
120 VERIFY(m2 == ref2);
121
122 Matrix2i m3 = Matrix2i::Zero();
123 m3.part<SelfAdjoint>() = m.part<LowerTriangular>();
124 Matrix2i ref3;
125 ref3 << 1, 0,
126 0, 4;
127 VERIFY(m3 == ref3);
128
129 // example inspired from bug 159
130 int array[] = {1, 2, 3, 4};
131 Matrix2i::Map(array).part<SelfAdjoint>() = Matrix2i::Random().part<LowerTriangular>();
132
133 std::cout << "hello\n" << array << std::endl;
134 }
135
test_eigen2_triangular()136 void test_eigen2_triangular()
137 {
138 CALL_SUBTEST_8( selfadjoint() );
139 for(int i = 0; i < g_repeat ; i++) {
140 CALL_SUBTEST_1( triangular(Matrix<float, 1, 1>()) );
141 CALL_SUBTEST_2( triangular(Matrix<float, 2, 2>()) );
142 CALL_SUBTEST_3( triangular(Matrix3d()) );
143 CALL_SUBTEST_4( triangular(MatrixXcf(4, 4)) );
144 CALL_SUBTEST_5( triangular(Matrix<std::complex<float>,8, 8>()) );
145 CALL_SUBTEST_6( triangular(MatrixXd(17,17)) );
146 CALL_SUBTEST_7( triangular(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) );
147 }
148 }
149