test/eigen2/eigen2_eigensolver.cpp

// 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)) );
  }
}