1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
5 // Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11 #include "main.h"
12 #include <limits>
13 #include <Eigen/Eigenvalues>
14
eigensolver(const MatrixType & m)15 template<typename MatrixType> void eigensolver(const MatrixType& m)
16 {
17 typedef typename MatrixType::Index Index;
18 /* this test covers the following files:
19 EigenSolver.h
20 */
21 Index rows = m.rows();
22 Index cols = m.cols();
23
24 typedef typename MatrixType::Scalar Scalar;
25 typedef typename NumTraits<Scalar>::Real RealScalar;
26 typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
27 typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
28
29 MatrixType a = MatrixType::Random(rows,cols);
30 MatrixType a1 = MatrixType::Random(rows,cols);
31 MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
32
33 EigenSolver<MatrixType> ei0(symmA);
34 VERIFY_IS_EQUAL(ei0.info(), Success);
35 VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix());
36 VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()),
37 (ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal()));
38
39 EigenSolver<MatrixType> ei1(a);
40 VERIFY_IS_EQUAL(ei1.info(), Success);
41 VERIFY_IS_APPROX(a * ei1.pseudoEigenvectors(), ei1.pseudoEigenvectors() * ei1.pseudoEigenvalueMatrix());
42 VERIFY_IS_APPROX(a.template cast<Complex>() * ei1.eigenvectors(),
43 ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
44 VERIFY_IS_APPROX(ei1.eigenvectors().colwise().norm(), RealVectorType::Ones(rows).transpose());
45 VERIFY_IS_APPROX(a.eigenvalues(), ei1.eigenvalues());
46
47 EigenSolver<MatrixType> ei2;
48 ei2.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
49 VERIFY_IS_EQUAL(ei2.info(), Success);
50 VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
51 VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
52 if (rows > 2) {
53 ei2.setMaxIterations(1).compute(a);
54 VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
55 VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
56 }
57
58 EigenSolver<MatrixType> eiNoEivecs(a, false);
59 VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
60 VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
61 VERIFY_IS_APPROX(ei1.pseudoEigenvalueMatrix(), eiNoEivecs.pseudoEigenvalueMatrix());
62
63 MatrixType id = MatrixType::Identity(rows, cols);
64 VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
65
66 if (rows > 2 && rows < 20)
67 {
68 // Test matrix with NaN
69 a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
70 EigenSolver<MatrixType> eiNaN(a);
71 VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
72 }
73
74 // regression test for bug 1098
75 {
76 EigenSolver<MatrixType> eig(a.adjoint() * a);
77 eig.compute(a.adjoint() * a);
78 }
79
80 // regression test for bug 478
81 {
82 a.setZero();
83 EigenSolver<MatrixType> ei3(a);
84 VERIFY_IS_EQUAL(ei3.info(), Success);
85 VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));
86 VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());
87 }
88 }
89
eigensolver_verify_assert(const MatrixType & m)90 template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
91 {
92 EigenSolver<MatrixType> eig;
93 VERIFY_RAISES_ASSERT(eig.eigenvectors());
94 VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
95 VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
96 VERIFY_RAISES_ASSERT(eig.eigenvalues());
97
98 MatrixType a = MatrixType::Random(m.rows(),m.cols());
99 eig.compute(a, false);
100 VERIFY_RAISES_ASSERT(eig.eigenvectors());
101 VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
102 }
103
test_eigensolver_generic()104 void test_eigensolver_generic()
105 {
106 int s = 0;
107 for(int i = 0; i < g_repeat; i++) {
108 CALL_SUBTEST_1( eigensolver(Matrix4f()) );
109 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
110 CALL_SUBTEST_2( eigensolver(MatrixXd(s,s)) );
111 TEST_SET_BUT_UNUSED_VARIABLE(s)
112
113 // some trivial but implementation-wise tricky cases
114 CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) );
115 CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) );
116 CALL_SUBTEST_3( eigensolver(Matrix<double,1,1>()) );
117 CALL_SUBTEST_4( eigensolver(Matrix2d()) );
118 }
119
120 CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) );
121 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
122 CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(s,s)) );
123 CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<double,1,1>()) );
124 CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) );
125
126 // Test problem size constructors
127 CALL_SUBTEST_5(EigenSolver<MatrixXf> tmp(s));
128
129 // regression test for bug 410
130 CALL_SUBTEST_2(
131 {
132 MatrixXd A(1,1);
133 A(0,0) = std::sqrt(-1.); // is Not-a-Number
134 Eigen::EigenSolver<MatrixXd> solver(A);
135 VERIFY_IS_EQUAL(solver.info(), NumericalIssue);
136 }
137 );
138
139 #ifdef EIGEN_TEST_PART_2
140 {
141 // regression test for bug 793
142 MatrixXd a(3,3);
143 a << 0, 0, 1,
144 1, 1, 1,
145 1, 1e+200, 1;
146 Eigen::EigenSolver<MatrixXd> eig(a);
147 double scale = 1e-200; // scale to avoid overflow during the comparisons
148 VERIFY_IS_APPROX(a * eig.pseudoEigenvectors()*scale, eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()*scale);
149 VERIFY_IS_APPROX(a * eig.eigenvectors()*scale, eig.eigenvectors() * eig.eigenvalues().asDiagonal()*scale);
150 }
151 {
152 // check a case where all eigenvalues are null.
153 MatrixXd a(2,2);
154 a << 1, 1,
155 -1, -1;
156 Eigen::EigenSolver<MatrixXd> eig(a);
157 VERIFY_IS_APPROX(eig.pseudoEigenvectors().squaredNorm(), 2.);
158 VERIFY_IS_APPROX((a * eig.pseudoEigenvectors()).norm()+1., 1.);
159 VERIFY_IS_APPROX((eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()).norm()+1., 1.);
160 VERIFY_IS_APPROX((a * eig.eigenvectors()).norm()+1., 1.);
161 VERIFY_IS_APPROX((eig.eigenvectors() * eig.eigenvalues().asDiagonal()).norm()+1., 1.);
162 }
163 #endif
164
165 TEST_SET_BUT_UNUSED_VARIABLE(s)
166 }
167