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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#define EIGEN_RUNTIME_NO_MALLOC
#include "main.h"
#include <limits>
#include <Eigen/Eigenvalues>
#include <Eigen/LU>
template<typename MatrixType> void generalized_eigensolver_real(const MatrixType& m)
{
/* this test covers the following files:
GeneralizedEigenSolver.h
*/
Index rows = m.rows();
Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef std::complex<Scalar> ComplexScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
MatrixType a = MatrixType::Random(rows,cols);
MatrixType b = MatrixType::Random(rows,cols);
MatrixType a1 = MatrixType::Random(rows,cols);
MatrixType b1 = MatrixType::Random(rows,cols);
MatrixType spdA = a.adjoint() * a + a1.adjoint() * a1;
MatrixType spdB = b.adjoint() * b + b1.adjoint() * b1;
// lets compare to GeneralizedSelfAdjointEigenSolver
{
GeneralizedSelfAdjointEigenSolver<MatrixType> symmEig(spdA, spdB);
GeneralizedEigenSolver<MatrixType> eig(spdA, spdB);
VERIFY_IS_EQUAL(eig.eigenvalues().imag().cwiseAbs().maxCoeff(), 0);
VectorType realEigenvalues = eig.eigenvalues().real();
std::sort(realEigenvalues.data(), realEigenvalues.data()+realEigenvalues.size());
VERIFY_IS_APPROX(realEigenvalues, symmEig.eigenvalues());
// check eigenvectors
typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();
typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();
VERIFY_IS_APPROX(spdA*V, spdB*V*D);
}
// non symmetric case:
{
GeneralizedEigenSolver<MatrixType> eig(rows);
// TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition
//Eigen::internal::set_is_malloc_allowed(false);
eig.compute(a,b);
//Eigen::internal::set_is_malloc_allowed(true);
for(Index k=0; k<cols; ++k)
{
Matrix<ComplexScalar,Dynamic,Dynamic> tmp = (eig.betas()(k)*a).template cast<ComplexScalar>() - eig.alphas()(k)*b;
if(tmp.size()>1 && tmp.norm()>(std::numeric_limits<Scalar>::min)())
tmp /= tmp.norm();
VERIFY_IS_MUCH_SMALLER_THAN( std::abs(tmp.determinant()), Scalar(1) );
}
// check eigenvectors
typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();
typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();
VERIFY_IS_APPROX(a*V, b*V*D);
}
// regression test for bug 1098
{
GeneralizedSelfAdjointEigenSolver<MatrixType> eig1(a.adjoint() * a,b.adjoint() * b);
eig1.compute(a.adjoint() * a,b.adjoint() * b);
GeneralizedEigenSolver<MatrixType> eig2(a.adjoint() * a,b.adjoint() * b);
eig2.compute(a.adjoint() * a,b.adjoint() * b);
}
// check without eigenvectors
{
GeneralizedEigenSolver<MatrixType> eig1(spdA, spdB, true);
GeneralizedEigenSolver<MatrixType> eig2(spdA, spdB, false);
VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues());
}
}
void test_eigensolver_generalized_real()
{
for(int i = 0; i < g_repeat; i++) {
int s = 0;
CALL_SUBTEST_1( generalized_eigensolver_real(Matrix4f()) );
s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(s,s)) );
// some trivial but implementation-wise special cases
CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(1,1)) );
CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(2,2)) );
CALL_SUBTEST_3( generalized_eigensolver_real(Matrix<double,1,1>()) );
CALL_SUBTEST_4( generalized_eigensolver_real(Matrix2d()) );
TEST_SET_BUT_UNUSED_VARIABLE(s)
}
}
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