1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
5 // Copyright (C) 2010 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 #include <Eigen/LU>
15
16 /* Check that two column vectors are approximately equal upto permutations,
17 by checking that the k-th power sums are equal for k = 1, ..., vec1.rows() */
18 template<typename VectorType>
verify_is_approx_upto_permutation(const VectorType & vec1,const VectorType & vec2)19 void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)
20 {
21 typedef typename NumTraits<typename VectorType::Scalar>::Real RealScalar;
22
23 VERIFY(vec1.cols() == 1);
24 VERIFY(vec2.cols() == 1);
25 VERIFY(vec1.rows() == vec2.rows());
26 for (int k = 1; k <= vec1.rows(); ++k)
27 {
28 VERIFY_IS_APPROX(vec1.array().pow(RealScalar(k)).sum(), vec2.array().pow(RealScalar(k)).sum());
29 }
30 }
31
32
eigensolver(const MatrixType & m)33 template<typename MatrixType> void eigensolver(const MatrixType& m)
34 {
35 typedef typename MatrixType::Index Index;
36 /* this test covers the following files:
37 ComplexEigenSolver.h, and indirectly ComplexSchur.h
38 */
39 Index rows = m.rows();
40 Index cols = m.cols();
41
42 typedef typename MatrixType::Scalar Scalar;
43 typedef typename NumTraits<Scalar>::Real RealScalar;
44
45 MatrixType a = MatrixType::Random(rows,cols);
46 MatrixType symmA = a.adjoint() * a;
47
48 ComplexEigenSolver<MatrixType> ei0(symmA);
49 VERIFY_IS_EQUAL(ei0.info(), Success);
50 VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());
51
52 ComplexEigenSolver<MatrixType> ei1(a);
53 VERIFY_IS_EQUAL(ei1.info(), Success);
54 VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
55 // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus
56 // another algorithm so results may differ slightly
57 verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());
58
59 ComplexEigenSolver<MatrixType> ei2;
60 ei2.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
61 VERIFY_IS_EQUAL(ei2.info(), Success);
62 VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
63 VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
64 if (rows > 2) {
65 ei2.setMaxIterations(1).compute(a);
66 VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
67 VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
68 }
69
70 ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);
71 VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
72 VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
73
74 // Regression test for issue #66
75 MatrixType z = MatrixType::Zero(rows,cols);
76 ComplexEigenSolver<MatrixType> eiz(z);
77 VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());
78
79 MatrixType id = MatrixType::Identity(rows, cols);
80 VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
81
82 if (rows > 1)
83 {
84 // Test matrix with NaN
85 a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
86 ComplexEigenSolver<MatrixType> eiNaN(a);
87 VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
88 }
89 }
90
eigensolver_verify_assert(const MatrixType & m)91 template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
92 {
93 ComplexEigenSolver<MatrixType> eig;
94 VERIFY_RAISES_ASSERT(eig.eigenvectors());
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 }
101
test_eigensolver_complex()102 void test_eigensolver_complex()
103 {
104 int s = 0;
105 for(int i = 0; i < g_repeat; i++) {
106 CALL_SUBTEST_1( eigensolver(Matrix4cf()) );
107 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
108 CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) );
109 CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) );
110 CALL_SUBTEST_4( eigensolver(Matrix3f()) );
111 }
112 CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) );
113 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
114 CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) );
115 CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) );
116 CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) );
117
118 // Test problem size constructors
119 CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf> tmp(s));
120
121 TEST_SET_BUT_UNUSED_VARIABLE(s)
122 }
123