mirror of
https://gitlab.com/libeigen/eigen.git
synced 2024-12-27 07:29:52 +08:00
98 lines
3.8 KiB
C++
98 lines
3.8 KiB
C++
// 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)
|
|
{
|
|
typedef typename MatrixType::Index Index;
|
|
/* 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);
|
|
}
|
|
}
|
|
|
|
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)
|
|
}
|
|
}
|