1 // This file is triangularView of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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
12
13
triangular_square(const MatrixType & m)14 template<typename MatrixType> void triangular_square(const MatrixType& m)
15 {
16 typedef typename MatrixType::Scalar Scalar;
17 typedef typename NumTraits<Scalar>::Real RealScalar;
18 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
19
20 RealScalar largerEps = 10*test_precision<RealScalar>();
21
22 typename MatrixType::Index rows = m.rows();
23 typename MatrixType::Index cols = m.cols();
24
25 MatrixType m1 = MatrixType::Random(rows, cols),
26 m2 = MatrixType::Random(rows, cols),
27 m3(rows, cols),
28 m4(rows, cols),
29 r1(rows, cols),
30 r2(rows, cols);
31 VectorType v2 = VectorType::Random(rows);
32
33 MatrixType m1up = m1.template triangularView<Upper>();
34 MatrixType m2up = m2.template triangularView<Upper>();
35
36 if (rows*cols>1)
37 {
38 VERIFY(m1up.isUpperTriangular());
39 VERIFY(m2up.transpose().isLowerTriangular());
40 VERIFY(!m2.isLowerTriangular());
41 }
42
43 // VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
44
45 // test overloaded operator+=
46 r1.setZero();
47 r2.setZero();
48 r1.template triangularView<Upper>() += m1;
49 r2 += m1up;
50 VERIFY_IS_APPROX(r1,r2);
51
52 // test overloaded operator=
53 m1.setZero();
54 m1.template triangularView<Upper>() = m2.transpose() + m2;
55 m3 = m2.transpose() + m2;
56 VERIFY_IS_APPROX(m3.template triangularView<Lower>().transpose().toDenseMatrix(), m1);
57
58 // test overloaded operator=
59 m1.setZero();
60 m1.template triangularView<Lower>() = m2.transpose() + m2;
61 VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
62
63 VERIFY_IS_APPROX(m3.template triangularView<Lower>().conjugate().toDenseMatrix(),
64 m3.conjugate().template triangularView<Lower>().toDenseMatrix());
65
66 m1 = MatrixType::Random(rows, cols);
67 for (int i=0; i<rows; ++i)
68 while (numext::abs2(m1(i,i))<1e-1) m1(i,i) = internal::random<Scalar>();
69
70 Transpose<MatrixType> trm4(m4);
71 // test back and forward subsitution with a vector as the rhs
72 m3 = m1.template triangularView<Upper>();
73 VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(v2)), largerEps));
74 m3 = m1.template triangularView<Lower>();
75 VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(v2)), largerEps));
76 m3 = m1.template triangularView<Upper>();
77 VERIFY(v2.isApprox(m3 * (m1.template triangularView<Upper>().solve(v2)), largerEps));
78 m3 = m1.template triangularView<Lower>();
79 VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(v2)), largerEps));
80
81 // test back and forward subsitution with a matrix as the rhs
82 m3 = m1.template triangularView<Upper>();
83 VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(m2)), largerEps));
84 m3 = m1.template triangularView<Lower>();
85 VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(m2)), largerEps));
86 m3 = m1.template triangularView<Upper>();
87 VERIFY(m2.isApprox(m3 * (m1.template triangularView<Upper>().solve(m2)), largerEps));
88 m3 = m1.template triangularView<Lower>();
89 VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(m2)), largerEps));
90
91 // check M * inv(L) using in place API
92 m4 = m3;
93 m1.transpose().template triangularView<Eigen::Upper>().solveInPlace(trm4);
94 VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Lower>(), m3);
95
96 // check M * inv(U) using in place API
97 m3 = m1.template triangularView<Upper>();
98 m4 = m3;
99 m3.transpose().template triangularView<Eigen::Lower>().solveInPlace(trm4);
100 VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Upper>(), m3);
101
102 // check solve with unit diagonal
103 m3 = m1.template triangularView<UnitUpper>();
104 VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpper>().solve(m2)), largerEps));
105
106 // VERIFY(( m1.template triangularView<Upper>()
107 // * m2.template triangularView<Upper>()).isUpperTriangular());
108
109 // test swap
110 m1.setOnes();
111 m2.setZero();
112 m2.template triangularView<Upper>().swap(m1);
113 m3.setZero();
114 m3.template triangularView<Upper>().setOnes();
115 VERIFY_IS_APPROX(m2,m3);
116
117 }
118
119
triangular_rect(const MatrixType & m)120 template<typename MatrixType> void triangular_rect(const MatrixType& m)
121 {
122 typedef const typename MatrixType::Index Index;
123 typedef typename MatrixType::Scalar Scalar;
124 typedef typename NumTraits<Scalar>::Real RealScalar;
125 enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
126
127 Index rows = m.rows();
128 Index cols = m.cols();
129
130 MatrixType m1 = MatrixType::Random(rows, cols),
131 m2 = MatrixType::Random(rows, cols),
132 m3(rows, cols),
133 m4(rows, cols),
134 r1(rows, cols),
135 r2(rows, cols);
136
137 MatrixType m1up = m1.template triangularView<Upper>();
138 MatrixType m2up = m2.template triangularView<Upper>();
139
140 if (rows>1 && cols>1)
141 {
142 VERIFY(m1up.isUpperTriangular());
143 VERIFY(m2up.transpose().isLowerTriangular());
144 VERIFY(!m2.isLowerTriangular());
145 }
146
147 // test overloaded operator+=
148 r1.setZero();
149 r2.setZero();
150 r1.template triangularView<Upper>() += m1;
151 r2 += m1up;
152 VERIFY_IS_APPROX(r1,r2);
153
154 // test overloaded operator=
155 m1.setZero();
156 m1.template triangularView<Upper>() = 3 * m2;
157 m3 = 3 * m2;
158 VERIFY_IS_APPROX(m3.template triangularView<Upper>().toDenseMatrix(), m1);
159
160
161 m1.setZero();
162 m1.template triangularView<Lower>() = 3 * m2;
163 VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
164
165 m1.setZero();
166 m1.template triangularView<StrictlyUpper>() = 3 * m2;
167 VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpper>().toDenseMatrix(), m1);
168
169
170 m1.setZero();
171 m1.template triangularView<StrictlyLower>() = 3 * m2;
172 VERIFY_IS_APPROX(m3.template triangularView<StrictlyLower>().toDenseMatrix(), m1);
173 m1.setRandom();
174 m2 = m1.template triangularView<Upper>();
175 VERIFY(m2.isUpperTriangular());
176 VERIFY(!m2.isLowerTriangular());
177 m2 = m1.template triangularView<StrictlyUpper>();
178 VERIFY(m2.isUpperTriangular());
179 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
180 m2 = m1.template triangularView<UnitUpper>();
181 VERIFY(m2.isUpperTriangular());
182 m2.diagonal().array() -= Scalar(1);
183 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
184 m2 = m1.template triangularView<Lower>();
185 VERIFY(m2.isLowerTriangular());
186 VERIFY(!m2.isUpperTriangular());
187 m2 = m1.template triangularView<StrictlyLower>();
188 VERIFY(m2.isLowerTriangular());
189 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
190 m2 = m1.template triangularView<UnitLower>();
191 VERIFY(m2.isLowerTriangular());
192 m2.diagonal().array() -= Scalar(1);
193 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
194 // test swap
195 m1.setOnes();
196 m2.setZero();
197 m2.template triangularView<Upper>().swap(m1);
198 m3.setZero();
199 m3.template triangularView<Upper>().setOnes();
200 VERIFY_IS_APPROX(m2,m3);
201 }
202
bug_159()203 void bug_159()
204 {
205 Matrix3d m = Matrix3d::Random().triangularView<Lower>();
206 EIGEN_UNUSED_VARIABLE(m)
207 }
208
test_triangular()209 void test_triangular()
210 {
211 int maxsize = (std::min)(EIGEN_TEST_MAX_SIZE,20);
212 for(int i = 0; i < g_repeat ; i++)
213 {
214 int r = internal::random<int>(2,maxsize); TEST_SET_BUT_UNUSED_VARIABLE(r)
215 int c = internal::random<int>(2,maxsize); TEST_SET_BUT_UNUSED_VARIABLE(c)
216
217 CALL_SUBTEST_1( triangular_square(Matrix<float, 1, 1>()) );
218 CALL_SUBTEST_2( triangular_square(Matrix<float, 2, 2>()) );
219 CALL_SUBTEST_3( triangular_square(Matrix3d()) );
220 CALL_SUBTEST_4( triangular_square(Matrix<std::complex<float>,8, 8>()) );
221 CALL_SUBTEST_5( triangular_square(MatrixXcd(r,r)) );
222 CALL_SUBTEST_6( triangular_square(Matrix<float,Dynamic,Dynamic,RowMajor>(r, r)) );
223
224 CALL_SUBTEST_7( triangular_rect(Matrix<float, 4, 5>()) );
225 CALL_SUBTEST_8( triangular_rect(Matrix<double, 6, 2>()) );
226 CALL_SUBTEST_9( triangular_rect(MatrixXcf(r, c)) );
227 CALL_SUBTEST_5( triangular_rect(MatrixXcd(r, c)) );
228 CALL_SUBTEST_6( triangular_rect(Matrix<float,Dynamic,Dynamic,RowMajor>(r, c)) );
229 }
230
231 CALL_SUBTEST_1( bug_159() );
232 }
233