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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <limits>
#include <Eigen/Eigenvalues>
#ifdef HAS_GSL
#include "gsl_helper.h"
#endif
template<typename MatrixType> void eigensolver(const MatrixType& m)
{
/* this test covers the following files:
EigenSolver.h
*/
int rows = m.rows();
int cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
MatrixType a = MatrixType::Random(rows,cols);
MatrixType a1 = MatrixType::Random(rows,cols);
MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
EigenSolver<MatrixType> ei0(symmA);
VERIFY_IS_EQUAL(ei0.info(), Success);
VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix());
VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()),
(ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal()));
EigenSolver<MatrixType> ei1(a);
VERIFY_IS_EQUAL(ei1.info(), Success);
VERIFY_IS_APPROX(a * ei1.pseudoEigenvectors(), ei1.pseudoEigenvectors() * ei1.pseudoEigenvalueMatrix());
VERIFY_IS_APPROX(a.template cast<Complex>() * ei1.eigenvectors(),
ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
VERIFY_IS_APPROX(a.eigenvalues(), ei1.eigenvalues());
EigenSolver<MatrixType> eiNoEivecs(a, false);
VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
VERIFY_IS_APPROX(ei1.pseudoEigenvalueMatrix(), eiNoEivecs.pseudoEigenvalueMatrix());
MatrixType id = MatrixType::Identity(rows, cols);
VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
if (rows > 2)
{
// Test matrix with NaN
a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
EigenSolver<MatrixType> eiNaN(a);
VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
}
}
template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
{
EigenSolver<MatrixType> eig;
VERIFY_RAISES_ASSERT(eig.eigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
VERIFY_RAISES_ASSERT(eig.eigenvalues());
MatrixType a = MatrixType::Random(m.rows(),m.cols());
eig.compute(a, false);
VERIFY_RAISES_ASSERT(eig.eigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
}
void test_eigensolver_generic()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( eigensolver(Matrix4f()) );
CALL_SUBTEST_2( eigensolver(MatrixXd(17,17)) );
// some trivial but implementation-wise tricky cases
CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) );
CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) );
CALL_SUBTEST_3( eigensolver(Matrix<double,1,1>()) );
CALL_SUBTEST_4( eigensolver(Matrix2d()) );
}
CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) );
CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(17,17)) );
CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<double,1,1>()) );
CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) );
// Test problem size constructors
CALL_SUBTEST_5(EigenSolver<MatrixXf>(10));
}
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