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-rw-r--r--test/eigen2/eigen2_eigensolver.cpp146
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diff --git a/test/eigen2/eigen2_eigensolver.cpp b/test/eigen2/eigen2_eigensolver.cpp
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--- a/test/eigen2/eigen2_eigensolver.cpp
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-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra. Eigen itself is part of the KDE project.
-//
-// Copyright (C) 2008 Gael Guennebaud <g.gael@free.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/.
-
-#include "main.h"
-#include <Eigen/QR>
-
-#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.cwise().abs(), eiSymm.eigenvectors().cwise().abs());
-
- // 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((symmA * eiSymm.eigenvectors()).isApprox(
- eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps));
-
- // generalized eigen problem Ax = lBx
- 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());
-}
-
-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;
-
- // 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;
-
- EigenSolver<MatrixType> ei0(symmA);
- 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_APPROX(a * ei1.pseudoEigenvectors(), ei1.pseudoEigenvectors() * ei1.pseudoEigenvalueMatrix());
- VERIFY_IS_APPROX(a.template cast<Complex>() * ei1.eigenvectors(),
- ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
-
-}
-
-void test_eigen2_eigensolver()
-{
- 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(7,7)) );
- CALL_SUBTEST_4( selfadjointeigensolver(MatrixXcd(5,5)) );
- CALL_SUBTEST_5( selfadjointeigensolver(MatrixXd(19,19)) );
-
- CALL_SUBTEST_6( eigensolver(Matrix4f()) );
- CALL_SUBTEST_5( eigensolver(MatrixXd(17,17)) );
- }
-}
-