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