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 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
45 typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
46 typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
47
48 MatrixType a = MatrixType::Random(rows,cols);
49 MatrixType symmA = a.adjoint() * a;
50
51 ComplexEigenSolver<MatrixType> ei0(symmA);
52 VERIFY_IS_EQUAL(ei0.info(), Success);
53 VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());
54
55 ComplexEigenSolver<MatrixType> ei1(a);
56 VERIFY_IS_EQUAL(ei1.info(), Success);
57 VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
58 // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus
59 // another algorithm so results may differ slightly
60 verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());
61
62 ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);
63 VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
64 VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
65
66 // Regression test for issue #66
67 MatrixType z = MatrixType::Zero(rows,cols);
68 ComplexEigenSolver<MatrixType> eiz(z);
69 VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());
70
71 MatrixType id = MatrixType::Identity(rows, cols);
72 VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
73
74 if (rows > 1)
75 {
76 // Test matrix with NaN
77 a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
78 ComplexEigenSolver<MatrixType> eiNaN(a);
79 VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
80 }
81 }
82
eigensolver_verify_assert(const MatrixType & m)83 template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
84 {
85 ComplexEigenSolver<MatrixType> eig;
86 VERIFY_RAISES_ASSERT(eig.eigenvectors());
87 VERIFY_RAISES_ASSERT(eig.eigenvalues());
88
89 MatrixType a = MatrixType::Random(m.rows(),m.cols());
90 eig.compute(a, false);
91 VERIFY_RAISES_ASSERT(eig.eigenvectors());
92 }
93
test_eigensolver_complex()94 void test_eigensolver_complex()
95 {
96 int s;
97 for(int i = 0; i < g_repeat; i++) {
98 CALL_SUBTEST_1( eigensolver(Matrix4cf()) );
99 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
100 CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) );
101 CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) );
102 CALL_SUBTEST_4( eigensolver(Matrix3f()) );
103 }
104
105 CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) );
106 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
107 CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) );
108 CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) );
109 CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) );
110
111 // Test problem size constructors
112 CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf>(s));
113
114 EIGEN_UNUSED_VARIABLE(s)
115 }
116