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// -*- c++ -*- (enables emacs c++ mode)
//===========================================================================
//
// Copyright (C) 2003-2008 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 2.1 of the License,  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
// or  FITNESS  FOR  A PARTICULAR PURPOSE.  See the GNU Lesser General Public
// License for more details.
// You  should  have received a copy of the GNU Lesser General Public License
// along  with  this program;  if not, write to the Free Software Foundation,
// Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA.
//
// As a special exception, you  may use  this file  as it is a part of a free
// software  library  without  restriction.  Specifically,  if   other  files
// instantiate  templates  or  use macros or inline functions from this file,
// or  you compile this  file  and  link  it  with other files  to produce an
// executable, this file  does  not  by itself cause the resulting executable
// to be covered  by the GNU Lesser General Public License.  This   exception
// does not  however  invalidate  any  other  reasons why the executable file
// might be covered by the GNU Lesser General Public License.
//
//===========================================================================

// This file is a modified version of lu.h from MTL.
// See http://osl.iu.edu/research/mtl/
// Following the corresponding Copyright notice.
//===========================================================================
//
// Copyright (c) 1997-2001, The Trustees of Indiana University.
// All rights reserved.
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
//    * Redistributions of source code must retain the above copyright
//      notice, this list of conditions and the following disclaimer.
//    * Redistributions in binary form must reproduce the above copyright
//      notice, this list of conditions and the following disclaimer in the
//      documentation and/or other materials provided with the distribution.
//    * Neither the name of the University of California, Berkeley nor the
//      names of its contributors may be used to endorse or promote products
//      derived from this software without specific prior written permission.
//
// THIS SOFTWARE  IS  PROVIDED  BY  THE TRUSTEES  OF  INDIANA UNIVERSITY  AND
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// DATA,  OR PROFITS;  OR BUSINESS  INTERRUPTION)  HOWEVER  CAUSED AND ON ANY
// THEORY  OF  LIABILITY,  WHETHER  IN  CONTRACT,  STRICT  LIABILITY, OR TORT
// (INCLUDING  NEGLIGENCE  OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
// THIS  SOFTWARE,  EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
//===========================================================================

/**@file gmm_dense_lu.h
   @author  Andrew Lumsdaine, Jeremy G. Siek, Lie-Quan Lee, Y. Renard
   @date June 5, 2003.
   @brief LU factorizations and determinant computation for dense matrices.
*/
#ifndef GMM_DENSE_LU_H
#define GMM_DENSE_LU_H

#include "gmm_dense_Householder.h"
#include "gmm_opt.h"

namespace gmm {


  /** LU Factorization of a general (dense) matrix (real or complex).
  
  This is the outer product (a level-2 operation) form of the LU
  Factorization with pivoting algorithm . This is equivalent to
  LAPACK's dgetf2. Also see "Matrix Computations" 3rd Ed.  by Golub
  and Van Loan section 3.2.5 and especially page 115.
  
  The pivot indices in ipvt are indexed starting from 1
  so that this is compatible with LAPACK (Fortran).
  */
  template <typename DenseMatrix, typename Pvector>
  size_type lu_factor(DenseMatrix& A, Pvector& ipvt) {
    typedef typename linalg_traits<DenseMatrix>::value_type T;
    typedef typename linalg_traits<Pvector>::value_type int_T;
    typedef typename number_traits<T>::magnitude_type R;
    size_type info(0), i, j, jp, M(mat_nrows(A)), N(mat_ncols(A));
    size_type NN = std::min(M, N);
    std::vector<T> c(M), r(N);
    
    GMM_ASSERT2(ipvt.size()+1 >= NN, "IPVT too small");
    for (i = 0; i+1 < NN; ++i) ipvt[i] = int_T(i);
      
    if (M || N) {
      for (j = 0; j+1 < NN; ++j) {
	R max = gmm::abs(A(j,j)); jp = j;
	for (i = j+1; i < M; ++i)		   /* find pivot.          */
	  if (gmm::abs(A(i,j)) > max) { jp = i; max = gmm::abs(A(i,j)); }
	ipvt[j] = int_T(jp + 1);
	
	if (max == R(0)) { info = j + 1; break; }
        if (jp != j) for (i = 0; i < N; ++i) std::swap(A(jp, i), A(j, i));
	
        for (i = j+1; i < M; ++i) { A(i, j) /= A(j,j); c[i-j-1] = -A(i, j); }
        for (i = j+1; i < N; ++i) r[i-j-1] = A(j, i);  // avoid the copy ?
	rank_one_update(sub_matrix(A, sub_interval(j+1, M-j-1),
				 sub_interval(j+1, N-j-1)), c, conjugated(r));
      }
      ipvt[j] = int_T(j + 1);
    }
    return info;
  }
  
  /** LU Solve : Solve equation Ax=b, given an LU factored matrix.*/
  //  Thanks to Valient Gough for this routine!
  template <typename DenseMatrix, typename VectorB, typename VectorX,
	    typename Pvector>
  void lu_solve(const DenseMatrix &LU, const Pvector& pvector, 
		VectorX &x, const VectorB &b) {
    typedef typename linalg_traits<DenseMatrix>::value_type T;
    copy(b, x);
    for(size_type i = 0; i < pvector.size(); ++i) {
      size_type perm = pvector[i]-1;     // permutations stored in 1's offset
      if(i != perm) { T aux = x[i]; x[i] = x[perm]; x[perm] = aux; }
    }
    /* solve  Ax = b  ->  LUx = b  ->  Ux = L^-1 b.                        */
    lower_tri_solve(LU, x, true);
    upper_tri_solve(LU, x, false);
  }

  template <typename DenseMatrix, typename VectorB, typename VectorX>
  void lu_solve(const DenseMatrix &A, VectorX &x, const VectorB &b) {
    typedef typename linalg_traits<DenseMatrix>::value_type T;
    dense_matrix<T> B(mat_nrows(A), mat_ncols(A));
    std::vector<int> ipvt(mat_nrows(A));
    gmm::copy(A, B);
    size_type info = lu_factor(B, ipvt);
    GMM_ASSERT1(!info, "Singular system, pivot = " << info);
    lu_solve(B, ipvt, x, b);
  }
  
  template <typename DenseMatrix, typename VectorB, typename VectorX,
	    typename Pvector>
  void lu_solve_transposed(const DenseMatrix &LU, const Pvector& pvector, 
			   VectorX &x, const VectorB &b) {
    typedef typename linalg_traits<DenseMatrix>::value_type T;
    copy(b, x);
    lower_tri_solve(transposed(LU), x, false);
    upper_tri_solve(transposed(LU), x, true);
    for(size_type i = pvector.size(); i > 0; --i) {
      size_type perm = pvector[i-1]-1;    // permutations stored in 1's offset
      if(i-1 != perm) { T aux = x[i-1]; x[i-1] = x[perm]; x[perm] = aux; }
    }

  }


  ///@cond DOXY_SHOW_ALL_FUNCTIONS
  template <typename DenseMatrixLU, typename DenseMatrix, typename Pvector>
  void lu_inverse(const DenseMatrixLU& LU, const Pvector& pvector,
		  DenseMatrix& AInv, col_major) {
    typedef typename linalg_traits<DenseMatrixLU>::value_type T;
    std::vector<T> tmp(pvector.size(), T(0));
    std::vector<T> result(pvector.size());
    for(size_type i = 0; i < pvector.size(); ++i) {
      tmp[i] = T(1);
      lu_solve(LU, pvector, result, tmp);
      copy(result, mat_col(AInv, i));
      tmp[i] = T(0);
    }
  }

  template <typename DenseMatrixLU, typename DenseMatrix, typename Pvector>
  void lu_inverse(const DenseMatrixLU& LU, const Pvector& pvector,
		  DenseMatrix& AInv, row_major) {
    typedef typename linalg_traits<DenseMatrixLU>::value_type T;
    std::vector<T> tmp(pvector.size(), T(0));
    std::vector<T> result(pvector.size());
    for(size_type i = 0; i < pvector.size(); ++i) {
      tmp[i] = T(1); // to be optimized !!
      // on peut sur le premier tri solve reduire le systeme
      // et peut etre faire un solve sur une serie de vecteurs au lieu
      // de vecteur a vecteur (accumulation directe de l'inverse dans la
      // matrice au fur et a mesure du calcul ... -> evite la copie finale
      lu_solve_transposed(LU, pvector, result, tmp);
      copy(result, mat_row(AInv, i));
      tmp[i] = T(0);
    }
  }
  ///@endcond  

  /** Given an LU factored matrix, build the inverse of the matrix. */
  template <typename DenseMatrixLU, typename DenseMatrix, typename Pvector>
  void lu_inverse(const DenseMatrixLU& LU, const Pvector& pvector,
		  const DenseMatrix& AInv_) {
    DenseMatrix& AInv = const_cast<DenseMatrix&>(AInv_);
    lu_inverse(LU, pvector, AInv, typename principal_orientation_type<typename
	       linalg_traits<DenseMatrix>::sub_orientation>::potype());
  }

  /** Given a dense matrix, build the inverse of the matrix, and
      return the determinant */
  template <typename DenseMatrix>
  typename linalg_traits<DenseMatrix>::value_type
  lu_inverse(const DenseMatrix& A_) {
    typedef typename linalg_traits<DenseMatrix>::value_type T;
    DenseMatrix& A = const_cast<DenseMatrix&>(A_);
    dense_matrix<T> B(mat_nrows(A), mat_ncols(A));
    std::vector<int> ipvt(mat_nrows(A));
    gmm::copy(A, B);
    size_type info = lu_factor(B, ipvt);
    GMM_ASSERT1(!info, "Non invertible matrix, pivot = " << info);
    lu_inverse(B, ipvt, A);
    return lu_det(B, ipvt);
  }

  /** Compute the matrix determinant (via a LU factorization) */
  template <typename DenseMatrixLU, typename Pvector>
  typename linalg_traits<DenseMatrixLU>::value_type
  lu_det(const DenseMatrixLU& LU, const Pvector &pvector) {
    typedef typename linalg_traits<DenseMatrixLU>::value_type T;
    T det(1);
    for (size_type j = 0; j < std::min(mat_nrows(LU), mat_ncols(LU)); ++j)
      det *= LU(j,j);
    for(size_type i = 0; i < pvector.size(); ++i)
      if (i != size_type(pvector[i]-1)) { det = -det; }
    return det;
  }

  template <typename DenseMatrix>
  typename linalg_traits<DenseMatrix>::value_type
  lu_det(const DenseMatrix& A) {
    typedef typename linalg_traits<DenseMatrix>::value_type T;
    dense_matrix<T> B(mat_nrows(A), mat_ncols(A));
    std::vector<int> ipvt(mat_nrows(A));
    gmm::copy(A, B);
    lu_factor(B, ipvt);
    return lu_det(B, ipvt);
  }

}

#endif