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
lu_non_invertible()14 template<typename MatrixType> void lu_non_invertible()
15 {
16 typedef typename MatrixType::Index Index;
17 typedef typename MatrixType::Scalar Scalar;
18 typedef typename MatrixType::RealScalar RealScalar;
19 /* this test covers the following files:
20 LU.h
21 */
22 Index rows, cols, cols2;
23 if(MatrixType::RowsAtCompileTime==Dynamic)
24 {
25 rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
26 }
27 else
28 {
29 rows = MatrixType::RowsAtCompileTime;
30 }
31 if(MatrixType::ColsAtCompileTime==Dynamic)
32 {
33 cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
34 cols2 = internal::random<int>(2,EIGEN_TEST_MAX_SIZE);
35 }
36 else
37 {
38 cols2 = cols = MatrixType::ColsAtCompileTime;
39 }
40
41 enum {
42 RowsAtCompileTime = MatrixType::RowsAtCompileTime,
43 ColsAtCompileTime = MatrixType::ColsAtCompileTime
44 };
45 typedef typename internal::kernel_retval_base<FullPivLU<MatrixType> >::ReturnType KernelMatrixType;
46 typedef typename internal::image_retval_base<FullPivLU<MatrixType> >::ReturnType ImageMatrixType;
47 typedef Matrix<typename MatrixType::Scalar, ColsAtCompileTime, ColsAtCompileTime>
48 CMatrixType;
49 typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, RowsAtCompileTime>
50 RMatrixType;
51
52 Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
53
54 // The image of the zero matrix should consist of a single (zero) column vector
55 VERIFY((MatrixType::Zero(rows,cols).fullPivLu().image(MatrixType::Zero(rows,cols)).cols() == 1));
56
57 MatrixType m1(rows, cols), m3(rows, cols2);
58 CMatrixType m2(cols, cols2);
59 createRandomPIMatrixOfRank(rank, rows, cols, m1);
60
61 FullPivLU<MatrixType> lu;
62
63 // The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank
64 // of singular values are either 0 or 1.
65 // So it's not clear at all that the epsilon should play any role there.
66 lu.setThreshold(RealScalar(0.01));
67 lu.compute(m1);
68
69 MatrixType u(rows,cols);
70 u = lu.matrixLU().template triangularView<Upper>();
71 RMatrixType l = RMatrixType::Identity(rows,rows);
72 l.block(0,0,rows,(std::min)(rows,cols)).template triangularView<StrictlyLower>()
73 = lu.matrixLU().block(0,0,rows,(std::min)(rows,cols));
74
75 VERIFY_IS_APPROX(lu.permutationP() * m1 * lu.permutationQ(), l*u);
76
77 KernelMatrixType m1kernel = lu.kernel();
78 ImageMatrixType m1image = lu.image(m1);
79
80 VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
81 VERIFY(rank == lu.rank());
82 VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
83 VERIFY(!lu.isInjective());
84 VERIFY(!lu.isInvertible());
85 VERIFY(!lu.isSurjective());
86 VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));
87 VERIFY(m1image.fullPivLu().rank() == rank);
88 VERIFY_IS_APPROX(m1 * m1.adjoint() * m1image, m1image);
89
90 m2 = CMatrixType::Random(cols,cols2);
91 m3 = m1*m2;
92 m2 = CMatrixType::Random(cols,cols2);
93 // test that the code, which does resize(), may be applied to an xpr
94 m2.block(0,0,m2.rows(),m2.cols()) = lu.solve(m3);
95 VERIFY_IS_APPROX(m3, m1*m2);
96 }
97
lu_invertible()98 template<typename MatrixType> void lu_invertible()
99 {
100 /* this test covers the following files:
101 LU.h
102 */
103 typedef typename MatrixType::Scalar Scalar;
104 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
105 int size = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
106
107 MatrixType m1(size, size), m2(size, size), m3(size, size);
108 FullPivLU<MatrixType> lu;
109 lu.setThreshold(RealScalar(0.01));
110 do {
111 m1 = MatrixType::Random(size,size);
112 lu.compute(m1);
113 } while(!lu.isInvertible());
114
115 VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
116 VERIFY(0 == lu.dimensionOfKernel());
117 VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector
118 VERIFY(size == lu.rank());
119 VERIFY(lu.isInjective());
120 VERIFY(lu.isSurjective());
121 VERIFY(lu.isInvertible());
122 VERIFY(lu.image(m1).fullPivLu().isInvertible());
123 m3 = MatrixType::Random(size,size);
124 m2 = lu.solve(m3);
125 VERIFY_IS_APPROX(m3, m1*m2);
126 VERIFY_IS_APPROX(m2, lu.inverse()*m3);
127 }
128
lu_partial_piv()129 template<typename MatrixType> void lu_partial_piv()
130 {
131 /* this test covers the following files:
132 PartialPivLU.h
133 */
134 typedef typename MatrixType::Index Index;
135 typedef typename MatrixType::Scalar Scalar;
136 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
137 Index rows = internal::random<Index>(1,4);
138 Index cols = rows;
139
140 MatrixType m1(cols, rows);
141 m1.setRandom();
142 PartialPivLU<MatrixType> plu(m1);
143
144 VERIFY_IS_APPROX(m1, plu.reconstructedMatrix());
145 }
146
lu_verify_assert()147 template<typename MatrixType> void lu_verify_assert()
148 {
149 MatrixType tmp;
150
151 FullPivLU<MatrixType> lu;
152 VERIFY_RAISES_ASSERT(lu.matrixLU())
153 VERIFY_RAISES_ASSERT(lu.permutationP())
154 VERIFY_RAISES_ASSERT(lu.permutationQ())
155 VERIFY_RAISES_ASSERT(lu.kernel())
156 VERIFY_RAISES_ASSERT(lu.image(tmp))
157 VERIFY_RAISES_ASSERT(lu.solve(tmp))
158 VERIFY_RAISES_ASSERT(lu.determinant())
159 VERIFY_RAISES_ASSERT(lu.rank())
160 VERIFY_RAISES_ASSERT(lu.dimensionOfKernel())
161 VERIFY_RAISES_ASSERT(lu.isInjective())
162 VERIFY_RAISES_ASSERT(lu.isSurjective())
163 VERIFY_RAISES_ASSERT(lu.isInvertible())
164 VERIFY_RAISES_ASSERT(lu.inverse())
165
166 PartialPivLU<MatrixType> plu;
167 VERIFY_RAISES_ASSERT(plu.matrixLU())
168 VERIFY_RAISES_ASSERT(plu.permutationP())
169 VERIFY_RAISES_ASSERT(plu.solve(tmp))
170 VERIFY_RAISES_ASSERT(plu.determinant())
171 VERIFY_RAISES_ASSERT(plu.inverse())
172 }
173
test_lu()174 void test_lu()
175 {
176 for(int i = 0; i < g_repeat; i++) {
177 CALL_SUBTEST_1( lu_non_invertible<Matrix3f>() );
178 CALL_SUBTEST_1( lu_verify_assert<Matrix3f>() );
179
180 CALL_SUBTEST_2( (lu_non_invertible<Matrix<double, 4, 6> >()) );
181 CALL_SUBTEST_2( (lu_verify_assert<Matrix<double, 4, 6> >()) );
182
183 CALL_SUBTEST_3( lu_non_invertible<MatrixXf>() );
184 CALL_SUBTEST_3( lu_invertible<MatrixXf>() );
185 CALL_SUBTEST_3( lu_verify_assert<MatrixXf>() );
186
187 CALL_SUBTEST_4( lu_non_invertible<MatrixXd>() );
188 CALL_SUBTEST_4( lu_invertible<MatrixXd>() );
189 CALL_SUBTEST_4( lu_partial_piv<MatrixXd>() );
190 CALL_SUBTEST_4( lu_verify_assert<MatrixXd>() );
191
192 CALL_SUBTEST_5( lu_non_invertible<MatrixXcf>() );
193 CALL_SUBTEST_5( lu_invertible<MatrixXcf>() );
194 CALL_SUBTEST_5( lu_verify_assert<MatrixXcf>() );
195
196 CALL_SUBTEST_6( lu_non_invertible<MatrixXcd>() );
197 CALL_SUBTEST_6( lu_invertible<MatrixXcd>() );
198 CALL_SUBTEST_6( lu_partial_piv<MatrixXcd>() );
199 CALL_SUBTEST_6( lu_verify_assert<MatrixXcd>() );
200
201 CALL_SUBTEST_7(( lu_non_invertible<Matrix<float,Dynamic,16> >() ));
202
203 // Test problem size constructors
204 CALL_SUBTEST_9( PartialPivLU<MatrixXf>(10) );
205 CALL_SUBTEST_9( FullPivLU<MatrixXf>(10, 20); );
206 }
207 }
208