/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================

 Copyright (C) 2003-2017 Yves Renard

 This file is a part of GetFEM++

 GetFEM++  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 along with the GCC Runtime Library
 Exception either version 3.1 or (at your option) any later version.
 This program  is  distributed  in  the  hope  that it will be useful,  but
 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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 License and GCC Runtime Library Exception for more details.
 You  should  have received a copy of the GNU Lesser General Public License
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 As a special exception, you  may use  this file  as it is a part of a free
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===========================================================================*/

/** @file gmm_dense_sylvester.h
    @author  Yves Renard <Yves.Renard@insa-lyon.fr>
    @date June 5, 2003.
    @brief Sylvester equation solver.
*/
#ifndef GMM_DENSE_SYLVESTER_H
#define GMM_DENSE_SYLVESTER_H

#include "gmm_kernel.h"

namespace gmm {

  /* ********************************************************************* */
  /*   Kronecker system matrix.                                            */
  /* ********************************************************************* */
  template <typename MAT1, typename MAT2, typename MAT3>
  void kron(const MAT1 &m1, const MAT2 &m2, const MAT3 &m3_,
	    bool init = true) {
    MAT3 &m3 = const_cast<MAT3 &>(m3_);
    size_type m = mat_nrows(m1), n = mat_ncols(m1);
    size_type l = mat_nrows(m2), k = mat_ncols(m2);

    GMM_ASSERT2(mat_nrows(m3) == m*l && mat_ncols(m3) == n*k,
		"dimensions mismatch");

    for (size_type i = 0; i < m; ++i)
      for (size_type j = 0; j < m; ++j)
	if (init)
	  gmm::copy(gmm::scaled(m2, m1(i,j)),
		    gmm::sub_matrix(m3, sub_interval(l*i, l),
				    sub_interval(k*j, k)));
	else
	  gmm::add(gmm::scaled(m2, m1(i,j)),
		    gmm::sub_matrix(m3, sub_interval(l*i, l),
				    sub_interval(k*j, k)));
  }
	

  /* ********************************************************************* */
  /*   Copy a matrix into a vector.                                        */
  /* ********************************************************************* */

  template <typename MAT, typename VECT>
  colmatrix_to_vector(const MAT &A, VECT &v, col_major) {
    size_type m = mat_nrows(A), n = mat_ncols(A);
    GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
    for (size_type i = 0; i < n; ++i)
      gmm::copy(mat_col(A, i), sub_vector(v, sub_interval(i*m, m)));
  }

  template <typename MAT, typename VECT>
  colmatrix_to_vector(const MAT &A, VECT &v, row_and_col)
  { colmatrix_to_vector(A, v, col_major()); }

  template <typename MAT, typename VECT>
  colmatrix_to_vector(const MAT &A, VECT &v, col_and_row)
  { colmatrix_to_vector(A, v, col_major()); }

  template <typename MAT, typename VECT>
  colmatrix_to_vector(const MAT &A, VECT &v, row_major) {
    size_type m = mat_nrows(mat), n = mat_ncols(A);
    GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
    for (size_type i = 0; i < m; ++i)
      gmm::copy(mat_row(A, i), sub_vector(v, sub_slice(i, n, m)));
  }

  template <typename MAT, typename VECT> inline
  colmatrix_to_vector(const MAT &A, const VECT &v_) {
    VECT &v = const_cast<VECT &>(v_);
    colmatrix_to_vector(A, v, typename linalg_traits<MAT>::sub_orientation());
  }


  /* ********************************************************************* */
  /*   Copy a vector into a matrix.                                        */
  /* ********************************************************************* */

  template <typename MAT, typename VECT>
  vector_to_colmatrix(const VECT &v, MAT &A, col_major) {
    size_type m = mat_nrows(A), n = mat_ncols(A);
    GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
    for (size_type i = 0; i < n; ++i)
      gmm::copy(sub_vector(v, sub_interval(i*m, m)), mat_col(A, i));
  }

  template <typename MAT, typename VECT>
  vector_to_colmatrix(const VECT &v, MAT &A, row_and_col)
  { vector_to_colmatrix(v, A, col_major()); }

  template <typename MAT, typename VECT>
  vector_to_colmatrix(const VECT &v, MAT &A, col_and_row)
  { vector_to_colmatrix(v, A, col_major()); }

  template <typename MAT, typename VECT>
  vector_to_colmatrix(const VECT &v, MAT &A, row_major) {
    size_type m = mat_nrows(mat), n = mat_ncols(A);
    GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
    for (size_type i = 0; i < m; ++i)
      gmm::copy(sub_vector(v, sub_slice(i, n, m)), mat_row(A, i));
  }

  template <typename MAT, typename VECT> inline
  vector_to_colmatrix(const VECT &v, const MAT &A_) {
    MAT &A = const_cast<MAT &>(A_);
    vector_to_colmatrix(v, A, typename linalg_traits<MAT>::sub_orientation());
  }

  /* ********************************************************************* */
  /*   Solve sylvester equation.                                           */
  /* ********************************************************************* */

  // very prohibitive solver, to be replaced ... 
  template <typename MAT1, typename MAT2, typename MAT3, typename MAT4 >
  void sylvester(const MAT1 &m1, const MAT2 &m2, const MAT3 &m3,
		 const MAT4 &m4_) {
    typedef typename linalg_traits<Mat>::value_type T;
    
    MAT3 &m4 = const_cast<MAT4 &>(m4_);
    size_type m = mat_nrows(m1), n = mat_ncols(m1);
    size_type l = mat_nrows(m2), k = mat_ncols(m2);
    
    GMM_ASSERT2(m == n && l == k && m == mat_nrows(m3) &&
		l == mat_ncols(m3) && m == mat_nrows(m4) && l == mat_ncols(m4),
		"dimensions mismatch");

    gmm::dense_matrix<T> akronb(m*l, m*l);
    gmm::dense_matrix<T> idm(m, m), idl(l,l);
    gmm::copy(identity_matrix(), idm);
    gmm::copy(identity_matrix(), idl);
    std::vector<T> x(m*l), c(m*l);
    
    kron(idl, m1, akronb);
    kron(gmm::transposed(m2), idm, akronb, false);

    colmatrix_to_vector(m3, c);
    lu_solve(akronb, c, x);
    vector_to_colmatrix(x, m4);

  }
}

#endif