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
12template<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
102void 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
136void 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