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