1*bf2c3715SXin Li // This file is part of Eigen, a lightweight C++ template library
2*bf2c3715SXin Li // for linear algebra.
3*bf2c3715SXin Li //
4*bf2c3715SXin Li // Copyright (C) 2012-2016 Gael Guennebaud <[email protected]>
5*bf2c3715SXin Li //
6*bf2c3715SXin Li // This Source Code Form is subject to the terms of the Mozilla
7*bf2c3715SXin Li // Public License v. 2.0. If a copy of the MPL was not distributed
8*bf2c3715SXin Li // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9*bf2c3715SXin Li
10*bf2c3715SXin Li #define EIGEN_RUNTIME_NO_MALLOC
11*bf2c3715SXin Li #include "main.h"
12*bf2c3715SXin Li #include <limits>
13*bf2c3715SXin Li #include <Eigen/Eigenvalues>
14*bf2c3715SXin Li #include <Eigen/LU>
15*bf2c3715SXin Li
generalized_eigensolver_real(const MatrixType & m)16*bf2c3715SXin Li template<typename MatrixType> void generalized_eigensolver_real(const MatrixType& m)
17*bf2c3715SXin Li {
18*bf2c3715SXin Li /* this test covers the following files:
19*bf2c3715SXin Li GeneralizedEigenSolver.h
20*bf2c3715SXin Li */
21*bf2c3715SXin Li Index rows = m.rows();
22*bf2c3715SXin Li Index cols = m.cols();
23*bf2c3715SXin Li
24*bf2c3715SXin Li typedef typename MatrixType::Scalar Scalar;
25*bf2c3715SXin Li typedef std::complex<Scalar> ComplexScalar;
26*bf2c3715SXin Li typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
27*bf2c3715SXin Li
28*bf2c3715SXin Li MatrixType a = MatrixType::Random(rows,cols);
29*bf2c3715SXin Li MatrixType b = MatrixType::Random(rows,cols);
30*bf2c3715SXin Li MatrixType a1 = MatrixType::Random(rows,cols);
31*bf2c3715SXin Li MatrixType b1 = MatrixType::Random(rows,cols);
32*bf2c3715SXin Li MatrixType spdA = a.adjoint() * a + a1.adjoint() * a1;
33*bf2c3715SXin Li MatrixType spdB = b.adjoint() * b + b1.adjoint() * b1;
34*bf2c3715SXin Li
35*bf2c3715SXin Li // lets compare to GeneralizedSelfAdjointEigenSolver
36*bf2c3715SXin Li {
37*bf2c3715SXin Li GeneralizedSelfAdjointEigenSolver<MatrixType> symmEig(spdA, spdB);
38*bf2c3715SXin Li GeneralizedEigenSolver<MatrixType> eig(spdA, spdB);
39*bf2c3715SXin Li
40*bf2c3715SXin Li VERIFY_IS_EQUAL(eig.eigenvalues().imag().cwiseAbs().maxCoeff(), 0);
41*bf2c3715SXin Li
42*bf2c3715SXin Li VectorType realEigenvalues = eig.eigenvalues().real();
43*bf2c3715SXin Li std::sort(realEigenvalues.data(), realEigenvalues.data()+realEigenvalues.size());
44*bf2c3715SXin Li VERIFY_IS_APPROX(realEigenvalues, symmEig.eigenvalues());
45*bf2c3715SXin Li
46*bf2c3715SXin Li // check eigenvectors
47*bf2c3715SXin Li typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();
48*bf2c3715SXin Li typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();
49*bf2c3715SXin Li VERIFY_IS_APPROX(spdA*V, spdB*V*D);
50*bf2c3715SXin Li }
51*bf2c3715SXin Li
52*bf2c3715SXin Li // non symmetric case:
53*bf2c3715SXin Li {
54*bf2c3715SXin Li GeneralizedEigenSolver<MatrixType> eig(rows);
55*bf2c3715SXin Li // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition
56*bf2c3715SXin Li //Eigen::internal::set_is_malloc_allowed(false);
57*bf2c3715SXin Li eig.compute(a,b);
58*bf2c3715SXin Li //Eigen::internal::set_is_malloc_allowed(true);
59*bf2c3715SXin Li for(Index k=0; k<cols; ++k)
60*bf2c3715SXin Li {
61*bf2c3715SXin Li Matrix<ComplexScalar,Dynamic,Dynamic> tmp = (eig.betas()(k)*a).template cast<ComplexScalar>() - eig.alphas()(k)*b;
62*bf2c3715SXin Li if(tmp.size()>1 && tmp.norm()>(std::numeric_limits<Scalar>::min)())
63*bf2c3715SXin Li tmp /= tmp.norm();
64*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN( std::abs(tmp.determinant()), Scalar(1) );
65*bf2c3715SXin Li }
66*bf2c3715SXin Li // check eigenvectors
67*bf2c3715SXin Li typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();
68*bf2c3715SXin Li typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();
69*bf2c3715SXin Li VERIFY_IS_APPROX(a*V, b*V*D);
70*bf2c3715SXin Li }
71*bf2c3715SXin Li
72*bf2c3715SXin Li // regression test for bug 1098
73*bf2c3715SXin Li {
74*bf2c3715SXin Li GeneralizedSelfAdjointEigenSolver<MatrixType> eig1(a.adjoint() * a,b.adjoint() * b);
75*bf2c3715SXin Li eig1.compute(a.adjoint() * a,b.adjoint() * b);
76*bf2c3715SXin Li GeneralizedEigenSolver<MatrixType> eig2(a.adjoint() * a,b.adjoint() * b);
77*bf2c3715SXin Li eig2.compute(a.adjoint() * a,b.adjoint() * b);
78*bf2c3715SXin Li }
79*bf2c3715SXin Li
80*bf2c3715SXin Li // check without eigenvectors
81*bf2c3715SXin Li {
82*bf2c3715SXin Li GeneralizedEigenSolver<MatrixType> eig1(spdA, spdB, true);
83*bf2c3715SXin Li GeneralizedEigenSolver<MatrixType> eig2(spdA, spdB, false);
84*bf2c3715SXin Li VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues());
85*bf2c3715SXin Li }
86*bf2c3715SXin Li }
87*bf2c3715SXin Li
EIGEN_DECLARE_TEST(eigensolver_generalized_real)88*bf2c3715SXin Li EIGEN_DECLARE_TEST(eigensolver_generalized_real)
89*bf2c3715SXin Li {
90*bf2c3715SXin Li for(int i = 0; i < g_repeat; i++) {
91*bf2c3715SXin Li int s = 0;
92*bf2c3715SXin Li CALL_SUBTEST_1( generalized_eigensolver_real(Matrix4f()) );
93*bf2c3715SXin Li s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
94*bf2c3715SXin Li CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(s,s)) );
95*bf2c3715SXin Li
96*bf2c3715SXin Li // some trivial but implementation-wise special cases
97*bf2c3715SXin Li CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(1,1)) );
98*bf2c3715SXin Li CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(2,2)) );
99*bf2c3715SXin Li CALL_SUBTEST_3( generalized_eigensolver_real(Matrix<double,1,1>()) );
100*bf2c3715SXin Li CALL_SUBTEST_4( generalized_eigensolver_real(Matrix2d()) );
101*bf2c3715SXin Li TEST_SET_BUT_UNUSED_VARIABLE(s)
102*bf2c3715SXin Li }
103*bf2c3715SXin Li }
104