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  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
17
18  RealScalar largerEps = 10*test_precision<RealScalar>();
19
20  int rows = m.rows();
21  int cols = m.cols();
22
23  MatrixType m1 = MatrixType::Random(rows, cols),
24             m2 = MatrixType::Random(rows, cols),
25             m3(rows, cols),
26             m4(rows, cols),
27             r1(rows, cols),
28             r2(rows, cols),
29             mzero = MatrixType::Zero(rows, cols),
30             mones = MatrixType::Ones(rows, cols),
31             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
32                              ::Identity(rows, rows),
33             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
34                              ::Random(rows, rows);
35  VectorType v1 = VectorType::Random(rows),
36             v2 = VectorType::Random(rows),
37             vzero = VectorType::Zero(rows);
38
39  MatrixType m1up = m1.template part<Eigen::UpperTriangular>();
40  MatrixType m2up = m2.template part<Eigen::UpperTriangular>();
41
42  if (rows*cols>1)
43  {
44    VERIFY(m1up.isUpperTriangular());
45    VERIFY(m2up.transpose().isLowerTriangular());
46    VERIFY(!m2.isLowerTriangular());
47  }
48
49//   VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
50
51  // test overloaded operator+=
52  r1.setZero();
53  r2.setZero();
54  r1.template part<Eigen::UpperTriangular>() +=  m1;
55  r2 += m1up;
56  VERIFY_IS_APPROX(r1,r2);
57
58  // test overloaded operator=
59  m1.setZero();
60  m1.template part<Eigen::UpperTriangular>() = (m2.transpose() * m2).lazy();
61  m3 = m2.transpose() * m2;
62  VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>().transpose(), m1);
63
64  // test overloaded operator=
65  m1.setZero();
66  m1.template part<Eigen::LowerTriangular>() = (m2.transpose() * m2).lazy();
67  VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>(), m1);
68
69  VERIFY_IS_APPROX(m3.template part<Diagonal>(), m3.diagonal().asDiagonal());
70
71  m1 = MatrixType::Random(rows, cols);
72  for (int i=0; i<rows; ++i)
73    while (ei_abs2(m1(i,i))<1e-3) m1(i,i) = ei_random<Scalar>();
74
75  Transpose<MatrixType> trm4(m4);
76  // test back and forward subsitution
77  m3 = m1.template part<Eigen::LowerTriangular>();
78  VERIFY(m3.template marked<Eigen::LowerTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
79  VERIFY(m3.transpose().template marked<Eigen::UpperTriangular>()
80    .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
81  // check M * inv(L) using in place API
82  m4 = m3;
83  m3.transpose().template marked<Eigen::UpperTriangular>().solveTriangularInPlace(trm4);
84  VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
85
86  m3 = m1.template part<Eigen::UpperTriangular>();
87  VERIFY(m3.template marked<Eigen::UpperTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
88  VERIFY(m3.transpose().template marked<Eigen::LowerTriangular>()
89    .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
90  // check M * inv(U) using in place API
91  m4 = m3;
92  m3.transpose().template marked<Eigen::LowerTriangular>().solveTriangularInPlace(trm4);
93  VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
94
95  m3 = m1.template part<Eigen::UpperTriangular>();
96  VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::UpperTriangular>().solveTriangular(m2)), largerEps));
97  m3 = m1.template part<Eigen::LowerTriangular>();
98  VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::LowerTriangular>().solveTriangular(m2)), largerEps));
99
100  VERIFY((m1.template part<Eigen::UpperTriangular>() * m2.template part<Eigen::UpperTriangular>()).isUpperTriangular());
101
102  // test swap
103  m1.setOnes();
104  m2.setZero();
105  m2.template part<Eigen::UpperTriangular>().swap(m1);
106  m3.setZero();
107  m3.template part<Eigen::UpperTriangular>().setOnes();
108  VERIFY_IS_APPROX(m2,m3);
109
110}
111
112void selfadjoint()
113{
114  Matrix2i m;
115  m << 1, 2,
116       3, 4;
117
118  Matrix2i m1 = Matrix2i::Zero();
119  m1.part<SelfAdjoint>() = m;
120  Matrix2i ref1;
121  ref1 << 1, 2,
122          2, 4;
123  VERIFY(m1 == ref1);
124
125  Matrix2i m2 = Matrix2i::Zero();
126  m2.part<SelfAdjoint>() = m.part<UpperTriangular>();
127  Matrix2i ref2;
128  ref2 << 1, 2,
129          2, 4;
130  VERIFY(m2 == ref2);
131
132  Matrix2i m3 = Matrix2i::Zero();
133  m3.part<SelfAdjoint>() = m.part<LowerTriangular>();
134  Matrix2i ref3;
135  ref3 << 1, 0,
136          0, 4;
137  VERIFY(m3 == ref3);
138
139  // example inspired from bug 159
140  int array[] = {1, 2, 3, 4};
141  Matrix2i::Map(array).part<SelfAdjoint>() = Matrix2i::Random().part<LowerTriangular>();
142
143  std::cout << "hello\n" << array << std::endl;
144}
145
146void test_eigen2_triangular()
147{
148  CALL_SUBTEST_8( selfadjoint() );
149  for(int i = 0; i < g_repeat ; i++) {
150    CALL_SUBTEST_1( triangular(Matrix<float, 1, 1>()) );
151    CALL_SUBTEST_2( triangular(Matrix<float, 2, 2>()) );
152    CALL_SUBTEST_3( triangular(Matrix3d()) );
153    CALL_SUBTEST_4( triangular(MatrixXcf(4, 4)) );
154    CALL_SUBTEST_5( triangular(Matrix<std::complex<float>,8, 8>()) );
155    CALL_SUBTEST_6( triangular(MatrixXd(17,17)) );
156    CALL_SUBTEST_7( triangular(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) );
157  }
158}
159