1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2012-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10 #define EIGEN_RUNTIME_NO_MALLOC
11 #include "main.h"
12 #include <limits>
13 #include <Eigen/Eigenvalues>
14 #include <Eigen/LU>
15
generalized_eigensolver_real(const MatrixType & m)16 template<typename MatrixType> void generalized_eigensolver_real(const MatrixType& m)
17 {
18 typedef typename MatrixType::Index Index;
19 /* this test covers the following files:
20 GeneralizedEigenSolver.h
21 */
22 Index rows = m.rows();
23 Index cols = m.cols();
24
25 typedef typename MatrixType::Scalar Scalar;
26 typedef std::complex<Scalar> ComplexScalar;
27 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
28
29 MatrixType a = MatrixType::Random(rows,cols);
30 MatrixType b = MatrixType::Random(rows,cols);
31 MatrixType a1 = MatrixType::Random(rows,cols);
32 MatrixType b1 = MatrixType::Random(rows,cols);
33 MatrixType spdA = a.adjoint() * a + a1.adjoint() * a1;
34 MatrixType spdB = b.adjoint() * b + b1.adjoint() * b1;
35
36 // lets compare to GeneralizedSelfAdjointEigenSolver
37 {
38 GeneralizedSelfAdjointEigenSolver<MatrixType> symmEig(spdA, spdB);
39 GeneralizedEigenSolver<MatrixType> eig(spdA, spdB);
40
41 VERIFY_IS_EQUAL(eig.eigenvalues().imag().cwiseAbs().maxCoeff(), 0);
42
43 VectorType realEigenvalues = eig.eigenvalues().real();
44 std::sort(realEigenvalues.data(), realEigenvalues.data()+realEigenvalues.size());
45 VERIFY_IS_APPROX(realEigenvalues, symmEig.eigenvalues());
46
47 // check eigenvectors
48 typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();
49 typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();
50 VERIFY_IS_APPROX(spdA*V, spdB*V*D);
51 }
52
53 // non symmetric case:
54 {
55 GeneralizedEigenSolver<MatrixType> eig(rows);
56 // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition
57 //Eigen::internal::set_is_malloc_allowed(false);
58 eig.compute(a,b);
59 //Eigen::internal::set_is_malloc_allowed(true);
60 for(Index k=0; k<cols; ++k)
61 {
62 Matrix<ComplexScalar,Dynamic,Dynamic> tmp = (eig.betas()(k)*a).template cast<ComplexScalar>() - eig.alphas()(k)*b;
63 if(tmp.size()>1 && tmp.norm()>(std::numeric_limits<Scalar>::min)())
64 tmp /= tmp.norm();
65 VERIFY_IS_MUCH_SMALLER_THAN( std::abs(tmp.determinant()), Scalar(1) );
66 }
67 // check eigenvectors
68 typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();
69 typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();
70 VERIFY_IS_APPROX(a*V, b*V*D);
71 }
72
73 // regression test for bug 1098
74 {
75 GeneralizedSelfAdjointEigenSolver<MatrixType> eig1(a.adjoint() * a,b.adjoint() * b);
76 eig1.compute(a.adjoint() * a,b.adjoint() * b);
77 GeneralizedEigenSolver<MatrixType> eig2(a.adjoint() * a,b.adjoint() * b);
78 eig2.compute(a.adjoint() * a,b.adjoint() * b);
79 }
80 }
81
test_eigensolver_generalized_real()82 void test_eigensolver_generalized_real()
83 {
84 for(int i = 0; i < g_repeat; i++) {
85 int s = 0;
86 CALL_SUBTEST_1( generalized_eigensolver_real(Matrix4f()) );
87 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
88 CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(s,s)) );
89
90 // some trivial but implementation-wise special cases
91 CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(1,1)) );
92 CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(2,2)) );
93 CALL_SUBTEST_3( generalized_eigensolver_real(Matrix<double,1,1>()) );
94 CALL_SUBTEST_4( generalized_eigensolver_real(Matrix2d()) );
95 TEST_SET_BUT_UNUSED_VARIABLE(s)
96 }
97 }
98