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 (internal::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 typedef Matrix<Scalar, Rows, 1> VectorType;
127 typedef Matrix<Scalar, Rows, Rows> RMatrixType;
128
129
130 Index rows = m.rows();
131 Index cols = m.cols();
132
133 MatrixType m1 = MatrixType::Random(rows, cols),
134 m2 = MatrixType::Random(rows, cols),
135 m3(rows, cols),
136 m4(rows, cols),
137 r1(rows, cols),
138 r2(rows, cols);
139
140 MatrixType m1up = m1.template triangularView<Upper>();
141 MatrixType m2up = m2.template triangularView<Upper>();
142
143 if (rows>1 && cols>1)
144 {
145 VERIFY(m1up.isUpperTriangular());
146 VERIFY(m2up.transpose().isLowerTriangular());
147 VERIFY(!m2.isLowerTriangular());
148 }
149
150 // test overloaded operator+=
151 r1.setZero();
152 r2.setZero();
153 r1.template triangularView<Upper>() += m1;
154 r2 += m1up;
155 VERIFY_IS_APPROX(r1,r2);
156
157 // test overloaded operator=
158 m1.setZero();
159 m1.template triangularView<Upper>() = 3 * m2;
160 m3 = 3 * m2;
161 VERIFY_IS_APPROX(m3.template triangularView<Upper>().toDenseMatrix(), m1);
162
163
164 m1.setZero();
165 m1.template triangularView<Lower>() = 3 * m2;
166 VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
167
168 m1.setZero();
169 m1.template triangularView<StrictlyUpper>() = 3 * m2;
170 VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpper>().toDenseMatrix(), m1);
171
172
173 m1.setZero();
174 m1.template triangularView<StrictlyLower>() = 3 * m2;
175 VERIFY_IS_APPROX(m3.template triangularView<StrictlyLower>().toDenseMatrix(), m1);
176 m1.setRandom();
177 m2 = m1.template triangularView<Upper>();
178 VERIFY(m2.isUpperTriangular());
179 VERIFY(!m2.isLowerTriangular());
180 m2 = m1.template triangularView<StrictlyUpper>();
181 VERIFY(m2.isUpperTriangular());
182 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
183 m2 = m1.template triangularView<UnitUpper>();
184 VERIFY(m2.isUpperTriangular());
185 m2.diagonal().array() -= Scalar(1);
186 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
187 m2 = m1.template triangularView<Lower>();
188 VERIFY(m2.isLowerTriangular());
189 VERIFY(!m2.isUpperTriangular());
190 m2 = m1.template triangularView<StrictlyLower>();
191 VERIFY(m2.isLowerTriangular());
192 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
193 m2 = m1.template triangularView<UnitLower>();
194 VERIFY(m2.isLowerTriangular());
195 m2.diagonal().array() -= Scalar(1);
196 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
197 // test swap
198 m1.setOnes();
199 m2.setZero();
200 m2.template triangularView<Upper>().swap(m1);
201 m3.setZero();
202 m3.template triangularView<Upper>().setOnes();
203 VERIFY_IS_APPROX(m2,m3);
204 }
205
bug_159()206 void bug_159()
207 {
208 Matrix3d m = Matrix3d::Random().triangularView<Lower>();
209 EIGEN_UNUSED_VARIABLE(m)
210 }
211
test_triangular()212 void test_triangular()
213 {
214 int maxsize = (std::min)(EIGEN_TEST_MAX_SIZE,20);
215 for(int i = 0; i < g_repeat ; i++)
216 {
217 int r = internal::random<int>(2,maxsize); EIGEN_UNUSED_VARIABLE(r);
218 int c = internal::random<int>(2,maxsize); EIGEN_UNUSED_VARIABLE(c);
219
220 CALL_SUBTEST_1( triangular_square(Matrix<float, 1, 1>()) );
221 CALL_SUBTEST_2( triangular_square(Matrix<float, 2, 2>()) );
222 CALL_SUBTEST_3( triangular_square(Matrix3d()) );
223 CALL_SUBTEST_4( triangular_square(Matrix<std::complex<float>,8, 8>()) );
224 CALL_SUBTEST_5( triangular_square(MatrixXcd(r,r)) );
225 CALL_SUBTEST_6( triangular_square(Matrix<float,Dynamic,Dynamic,RowMajor>(r, r)) );
226
227 CALL_SUBTEST_7( triangular_rect(Matrix<float, 4, 5>()) );
228 CALL_SUBTEST_8( triangular_rect(Matrix<double, 6, 2>()) );
229 CALL_SUBTEST_9( triangular_rect(MatrixXcf(r, c)) );
230 CALL_SUBTEST_5( triangular_rect(MatrixXcd(r, c)) );
231 CALL_SUBTEST_6( triangular_rect(Matrix<float,Dynamic,Dynamic,RowMajor>(r, c)) );
232 }
233
234 CALL_SUBTEST_1( bug_159() );
235 }
236