eigen/test/eigensolver_selfadjoint.cpp
2010-06-10 00:19:45 +02:00

169 lines
6.5 KiB
C++

// 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 selfadjointeigensolver(const MatrixType& m)
{
/* this test covers the following files:
EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.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;
RealScalar largerEps = 10*test_precision<RealScalar>();
MatrixType a = MatrixType::Random(rows,cols);
MatrixType a1 = MatrixType::Random(rows,cols);
MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
MatrixType b = MatrixType::Random(rows,cols);
MatrixType b1 = MatrixType::Random(rows,cols);
MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
// generalized eigen pb
SelfAdjointEigenSolver<MatrixType> eiSymmGen(symmA, symmB);
#ifdef HAS_GSL
if (ei_is_same_type<RealScalar,double>::ret)
{
typedef GslTraits<Scalar> Gsl;
typename Gsl::Matrix gEvec=0, gSymmA=0, gSymmB=0;
typename GslTraits<RealScalar>::Vector gEval=0;
RealVectorType _eval;
MatrixType _evec;
convert<MatrixType>(symmA, gSymmA);
convert<MatrixType>(symmB, gSymmB);
convert<MatrixType>(symmA, gEvec);
gEval = GslTraits<RealScalar>::createVector(rows);
Gsl::eigen_symm(gSymmA, gEval, gEvec);
convert(gEval, _eval);
convert(gEvec, _evec);
// test gsl itself !
VERIFY((symmA * _evec).isApprox(_evec * _eval.asDiagonal(), largerEps));
// compare with eigen
VERIFY_IS_APPROX(_eval, eiSymm.eigenvalues());
VERIFY_IS_APPROX(_evec.cwiseAbs(), eiSymm.eigenvectors().cwiseAbs());
// generalized pb
Gsl::eigen_symm_gen(gSymmA, gSymmB, gEval, gEvec);
convert(gEval, _eval);
convert(gEvec, _evec);
// test GSL itself:
VERIFY((symmA * _evec).isApprox(symmB * (_evec * _eval.asDiagonal()), largerEps));
// compare with eigen
MatrixType normalized_eivec = eiSymmGen.eigenvectors()*eiSymmGen.eigenvectors().colwise().norm().asDiagonal().inverse();
VERIFY_IS_APPROX(_eval, eiSymmGen.eigenvalues());
VERIFY_IS_APPROX(_evec.cwiseAbs(), normalized_eivec.cwiseAbs());
Gsl::free(gSymmA);
Gsl::free(gSymmB);
GslTraits<RealScalar>::free(gEval);
Gsl::free(gEvec);
}
#endif
VERIFY_IS_EQUAL(eiSymm.info(), Success);
VERIFY((symmA * eiSymm.eigenvectors()).isApprox(
eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps));
VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);
VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);
VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
// generalized eigen problem Ax = lBx
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
VERIFY((symmA * eiSymmGen.eigenvectors()).isApprox(
symmB * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
MatrixType sqrtSymmA = eiSymm.operatorSqrt();
VERIFY_IS_APPROX(symmA, sqrtSymmA*sqrtSymmA);
VERIFY_IS_APPROX(sqrtSymmA, symmA*eiSymm.operatorInverseSqrt());
MatrixType id = MatrixType::Identity(rows, cols);
VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));
SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;
VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
eiSymmUninitialized.compute(symmA, false);
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
if (rows > 1)
{
// Test matrix with NaN
symmA(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmA);
VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
}
}
void test_eigensolver_selfadjoint()
{
for(int i = 0; i < g_repeat; i++) {
// very important to test a 3x3 matrix since we provide a special path for it
CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) );
CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) );
CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(10,10)) );
CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(19,19)) );
CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(17,17)) );
// some trivial but implementation-wise tricky cases
CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) );
CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) );
CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) );
CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) );
}
// Test problem size constructors
CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf>(10));
CALL_SUBTEST_8(Tridiagonalization<MatrixXf>(10));
}