// 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>
//
// 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 <Eigen/QR>

#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;

  // 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().eval());

}

void test_eigensolver_generic()
{
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST( eigensolver(Matrix4f()) );
    CALL_SUBTEST( eigensolver(MatrixXd(17,17)) );

    // some trivial but implementation-wise tricky cases
    CALL_SUBTEST( eigensolver(MatrixXd(1,1)) );
    CALL_SUBTEST( eigensolver(MatrixXd(2,2)) );
    CALL_SUBTEST( eigensolver(Matrix<double,1,1>()) );
    CALL_SUBTEST( eigensolver(Matrix<double,2,2>()) );
  }
}