1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@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 #include <Eigen/LU>
12 using namespace std;
13
14 template<typename MatrixType>
matrix_l1_norm(const MatrixType & m)15 typename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) {
16 return m.cwiseAbs().colwise().sum().maxCoeff();
17 }
18
lu_non_invertible()19 template<typename MatrixType> void lu_non_invertible()
20 {
21 typedef typename MatrixType::Index Index;
22 typedef typename MatrixType::RealScalar RealScalar;
23 /* this test covers the following files:
24 LU.h
25 */
26 Index rows, cols, cols2;
27 if(MatrixType::RowsAtCompileTime==Dynamic)
28 {
29 rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
30 }
31 else
32 {
33 rows = MatrixType::RowsAtCompileTime;
34 }
35 if(MatrixType::ColsAtCompileTime==Dynamic)
36 {
37 cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
38 cols2 = internal::random<int>(2,EIGEN_TEST_MAX_SIZE);
39 }
40 else
41 {
42 cols2 = cols = MatrixType::ColsAtCompileTime;
43 }
44
45 enum {
46 RowsAtCompileTime = MatrixType::RowsAtCompileTime,
47 ColsAtCompileTime = MatrixType::ColsAtCompileTime
48 };
49 typedef typename internal::kernel_retval_base<FullPivLU<MatrixType> >::ReturnType KernelMatrixType;
50 typedef typename internal::image_retval_base<FullPivLU<MatrixType> >::ReturnType ImageMatrixType;
51 typedef Matrix<typename MatrixType::Scalar, ColsAtCompileTime, ColsAtCompileTime>
52 CMatrixType;
53 typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, RowsAtCompileTime>
54 RMatrixType;
55
56 Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
57
58 // The image of the zero matrix should consist of a single (zero) column vector
59 VERIFY((MatrixType::Zero(rows,cols).fullPivLu().image(MatrixType::Zero(rows,cols)).cols() == 1));
60
61 MatrixType m1(rows, cols), m3(rows, cols2);
62 CMatrixType m2(cols, cols2);
63 createRandomPIMatrixOfRank(rank, rows, cols, m1);
64
65 FullPivLU<MatrixType> lu;
66
67 // The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank
68 // of singular values are either 0 or 1.
69 // So it's not clear at all that the epsilon should play any role there.
70 lu.setThreshold(RealScalar(0.01));
71 lu.compute(m1);
72
73 MatrixType u(rows,cols);
74 u = lu.matrixLU().template triangularView<Upper>();
75 RMatrixType l = RMatrixType::Identity(rows,rows);
76 l.block(0,0,rows,(std::min)(rows,cols)).template triangularView<StrictlyLower>()
77 = lu.matrixLU().block(0,0,rows,(std::min)(rows,cols));
78
79 VERIFY_IS_APPROX(lu.permutationP() * m1 * lu.permutationQ(), l*u);
80
81 KernelMatrixType m1kernel = lu.kernel();
82 ImageMatrixType m1image = lu.image(m1);
83
84 VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
85 VERIFY(rank == lu.rank());
86 VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
87 VERIFY(!lu.isInjective());
88 VERIFY(!lu.isInvertible());
89 VERIFY(!lu.isSurjective());
90 VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));
91 VERIFY(m1image.fullPivLu().rank() == rank);
92 VERIFY_IS_APPROX(m1 * m1.adjoint() * m1image, m1image);
93
94 m2 = CMatrixType::Random(cols,cols2);
95 m3 = m1*m2;
96 m2 = CMatrixType::Random(cols,cols2);
97 // test that the code, which does resize(), may be applied to an xpr
98 m2.block(0,0,m2.rows(),m2.cols()) = lu.solve(m3);
99 VERIFY_IS_APPROX(m3, m1*m2);
100
101 // test solve with transposed
102 m3 = MatrixType::Random(rows,cols2);
103 m2 = m1.transpose()*m3;
104 m3 = MatrixType::Random(rows,cols2);
105 lu.template _solve_impl_transposed<false>(m2, m3);
106 VERIFY_IS_APPROX(m2, m1.transpose()*m3);
107 m3 = MatrixType::Random(rows,cols2);
108 m3 = lu.transpose().solve(m2);
109 VERIFY_IS_APPROX(m2, m1.transpose()*m3);
110
111 // test solve with conjugate transposed
112 m3 = MatrixType::Random(rows,cols2);
113 m2 = m1.adjoint()*m3;
114 m3 = MatrixType::Random(rows,cols2);
115 lu.template _solve_impl_transposed<true>(m2, m3);
116 VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
117 m3 = MatrixType::Random(rows,cols2);
118 m3 = lu.adjoint().solve(m2);
119 VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
120 }
121
lu_invertible()122 template<typename MatrixType> void lu_invertible()
123 {
124 /* this test covers the following files:
125 LU.h
126 */
127 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
128 Index size = MatrixType::RowsAtCompileTime;
129 if( size==Dynamic)
130 size = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
131
132 MatrixType m1(size, size), m2(size, size), m3(size, size);
133 FullPivLU<MatrixType> lu;
134 lu.setThreshold(RealScalar(0.01));
135 do {
136 m1 = MatrixType::Random(size,size);
137 lu.compute(m1);
138 } while(!lu.isInvertible());
139
140 VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
141 VERIFY(0 == lu.dimensionOfKernel());
142 VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector
143 VERIFY(size == lu.rank());
144 VERIFY(lu.isInjective());
145 VERIFY(lu.isSurjective());
146 VERIFY(lu.isInvertible());
147 VERIFY(lu.image(m1).fullPivLu().isInvertible());
148 m3 = MatrixType::Random(size,size);
149 m2 = lu.solve(m3);
150 VERIFY_IS_APPROX(m3, m1*m2);
151 MatrixType m1_inverse = lu.inverse();
152 VERIFY_IS_APPROX(m2, m1_inverse*m3);
153
154 RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse);
155 const RealScalar rcond_est = lu.rcond();
156 // Verify that the estimated condition number is within a factor of 10 of the
157 // truth.
158 VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);
159
160 // test solve with transposed
161 lu.template _solve_impl_transposed<false>(m3, m2);
162 VERIFY_IS_APPROX(m3, m1.transpose()*m2);
163 m3 = MatrixType::Random(size,size);
164 m3 = lu.transpose().solve(m2);
165 VERIFY_IS_APPROX(m2, m1.transpose()*m3);
166
167 // test solve with conjugate transposed
168 lu.template _solve_impl_transposed<true>(m3, m2);
169 VERIFY_IS_APPROX(m3, m1.adjoint()*m2);
170 m3 = MatrixType::Random(size,size);
171 m3 = lu.adjoint().solve(m2);
172 VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
173
174 // Regression test for Bug 302
175 MatrixType m4 = MatrixType::Random(size,size);
176 VERIFY_IS_APPROX(lu.solve(m3*m4), lu.solve(m3)*m4);
177 }
178
lu_partial_piv()179 template<typename MatrixType> void lu_partial_piv()
180 {
181 /* this test covers the following files:
182 PartialPivLU.h
183 */
184 typedef typename MatrixType::Index Index;
185 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
186 Index size = internal::random<Index>(1,4);
187
188 MatrixType m1(size, size), m2(size, size), m3(size, size);
189 m1.setRandom();
190 PartialPivLU<MatrixType> plu(m1);
191
192 VERIFY_IS_APPROX(m1, plu.reconstructedMatrix());
193
194 m3 = MatrixType::Random(size,size);
195 m2 = plu.solve(m3);
196 VERIFY_IS_APPROX(m3, m1*m2);
197 MatrixType m1_inverse = plu.inverse();
198 VERIFY_IS_APPROX(m2, m1_inverse*m3);
199
200 RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse);
201 const RealScalar rcond_est = plu.rcond();
202 // Verify that the estimate is within a factor of 10 of the truth.
203 VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);
204
205 // test solve with transposed
206 plu.template _solve_impl_transposed<false>(m3, m2);
207 VERIFY_IS_APPROX(m3, m1.transpose()*m2);
208 m3 = MatrixType::Random(size,size);
209 m3 = plu.transpose().solve(m2);
210 VERIFY_IS_APPROX(m2, m1.transpose()*m3);
211
212 // test solve with conjugate transposed
213 plu.template _solve_impl_transposed<true>(m3, m2);
214 VERIFY_IS_APPROX(m3, m1.adjoint()*m2);
215 m3 = MatrixType::Random(size,size);
216 m3 = plu.adjoint().solve(m2);
217 VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
218 }
219
lu_verify_assert()220 template<typename MatrixType> void lu_verify_assert()
221 {
222 MatrixType tmp;
223
224 FullPivLU<MatrixType> lu;
225 VERIFY_RAISES_ASSERT(lu.matrixLU())
226 VERIFY_RAISES_ASSERT(lu.permutationP())
227 VERIFY_RAISES_ASSERT(lu.permutationQ())
228 VERIFY_RAISES_ASSERT(lu.kernel())
229 VERIFY_RAISES_ASSERT(lu.image(tmp))
230 VERIFY_RAISES_ASSERT(lu.solve(tmp))
231 VERIFY_RAISES_ASSERT(lu.determinant())
232 VERIFY_RAISES_ASSERT(lu.rank())
233 VERIFY_RAISES_ASSERT(lu.dimensionOfKernel())
234 VERIFY_RAISES_ASSERT(lu.isInjective())
235 VERIFY_RAISES_ASSERT(lu.isSurjective())
236 VERIFY_RAISES_ASSERT(lu.isInvertible())
237 VERIFY_RAISES_ASSERT(lu.inverse())
238
239 PartialPivLU<MatrixType> plu;
240 VERIFY_RAISES_ASSERT(plu.matrixLU())
241 VERIFY_RAISES_ASSERT(plu.permutationP())
242 VERIFY_RAISES_ASSERT(plu.solve(tmp))
243 VERIFY_RAISES_ASSERT(plu.determinant())
244 VERIFY_RAISES_ASSERT(plu.inverse())
245 }
246
test_lu()247 void test_lu()
248 {
249 for(int i = 0; i < g_repeat; i++) {
250 CALL_SUBTEST_1( lu_non_invertible<Matrix3f>() );
251 CALL_SUBTEST_1( lu_invertible<Matrix3f>() );
252 CALL_SUBTEST_1( lu_verify_assert<Matrix3f>() );
253
254 CALL_SUBTEST_2( (lu_non_invertible<Matrix<double, 4, 6> >()) );
255 CALL_SUBTEST_2( (lu_verify_assert<Matrix<double, 4, 6> >()) );
256
257 CALL_SUBTEST_3( lu_non_invertible<MatrixXf>() );
258 CALL_SUBTEST_3( lu_invertible<MatrixXf>() );
259 CALL_SUBTEST_3( lu_verify_assert<MatrixXf>() );
260
261 CALL_SUBTEST_4( lu_non_invertible<MatrixXd>() );
262 CALL_SUBTEST_4( lu_invertible<MatrixXd>() );
263 CALL_SUBTEST_4( lu_partial_piv<MatrixXd>() );
264 CALL_SUBTEST_4( lu_verify_assert<MatrixXd>() );
265
266 CALL_SUBTEST_5( lu_non_invertible<MatrixXcf>() );
267 CALL_SUBTEST_5( lu_invertible<MatrixXcf>() );
268 CALL_SUBTEST_5( lu_verify_assert<MatrixXcf>() );
269
270 CALL_SUBTEST_6( lu_non_invertible<MatrixXcd>() );
271 CALL_SUBTEST_6( lu_invertible<MatrixXcd>() );
272 CALL_SUBTEST_6( lu_partial_piv<MatrixXcd>() );
273 CALL_SUBTEST_6( lu_verify_assert<MatrixXcd>() );
274
275 CALL_SUBTEST_7(( lu_non_invertible<Matrix<float,Dynamic,16> >() ));
276
277 // Test problem size constructors
278 CALL_SUBTEST_9( PartialPivLU<MatrixXf>(10) );
279 CALL_SUBTEST_9( FullPivLU<MatrixXf>(10, 20); );
280 }
281 }
282