// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 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 <Eigen/Eigenvalues>

template<typename Scalar,int Size> void hessenberg(int size = Size)
{
  typedef Matrix<Scalar,Size,Size> MatrixType;

  // Test basic functionality: A = U H U* and H is Hessenberg
  for(int counter = 0; counter < g_repeat; ++counter) {
    MatrixType m = MatrixType::Random(size,size);
    HessenbergDecomposition<MatrixType> hess(m);
    VERIFY_IS_APPROX(m, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint());
    MatrixType H = hess.matrixH();
    for(int row = 2; row < size; ++row) {
      for(int col = 0; col < row-1; ++col) {
	VERIFY(H(row,col) == (typename MatrixType::Scalar)0);
      }
    }
  }

  // Test whether compute() and constructor returns same result
  MatrixType A = MatrixType::Random(size, size);
  HessenbergDecomposition<MatrixType> cs1;
  cs1.compute(A);
  HessenbergDecomposition<MatrixType> cs2(A);
  VERIFY_IS_EQUAL(cs1.matrixQ(), cs2.matrixQ());
  VERIFY_IS_EQUAL(cs1.matrixH(), cs2.matrixH());

  // TODO: Add tests for packedMatrix() and householderCoefficients()
}

void test_hessenberg()
{
  CALL_SUBTEST_1(( hessenberg<std::complex<double>,1>() ));
  CALL_SUBTEST_2(( hessenberg<std::complex<double>,2>() ));
  CALL_SUBTEST_3(( hessenberg<std::complex<float>,4>() ));
  CALL_SUBTEST_4(( hessenberg<float,Dynamic>(ei_random<int>(1,320)) ));
  CALL_SUBTEST_5(( hessenberg<std::complex<double>,Dynamic>(ei_random<int>(1,320)) ));
}