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#ifndef _RHEO_TINY_LU_H
#define _RHEO_TINY_LU_H
///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; 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.
///
/// Rheolef 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 General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
/// 
/// =========================================================================

#include "rheolef/tiny_matvec.h"

// first step: LU factorization
// ----------------------------
// with partial pivoting
//
// references :
//  P. Lascaux, R. Theodor
//  "Analyse numerique matricielle
//   appliquee a l'art de l'ingenieur",
//  page 242,
//  Masson, 1986
//

namespace rheolef { 
template <class T>
void
lu (tiny_matrix<T>& a, tiny_vector<size_t>& piv)
{
	typedef size_t size_type;
	const size_type n = a.nrow();
	if (n == 0) return;

	// initialize permutation table
	for (size_type i = 0; i < n; i++)
	    piv [i] = i;

	// factorize in 'n' steps
        for (size_type k = 0; k < n-1; k++) {

	    // we search the largest element of th k-th
	    // line, that has not yet been pivot-line
	    T amax = abs(a(piv[k],k));
	    size_type jmax = k;

	    for (size_type i = k+1; i < n; i++) {
		if (abs(a(piv[i],k)) > amax) {
		    amax = abs(a(piv[i],k));
		    jmax = i;
		}
	    }
	    // largest element is in piv[jmax] line
	    // we permut indexes
	    size_type i = piv [k];
	    piv [k] = piv [jmax];
	    piv [jmax] = i;
	    
	    // and invert the pivot
	    if (1 + a(piv[k],k) == 1) { // a (piv[k],k) < zero machine
		error_macro ("lu: unisolvence failed on pivot " << k);
	    }
	    T pivinv = 1./a(piv[k],k);

	    // modify lines that has not yet been
	    // pivot-lines
	    for (size_type i = k+1; i < n; i++) {

		T c = a(piv[i],k) * pivinv;
		a(piv[i],k) = c;
		for (size_type j = k+1; j < n; j++) 
		    a(piv [i],j)  -=  c * a(piv[k],j);
	    }
	}
}
// second step: one-column resolution
// ----------------------------------
template <class T>
void
solve (tiny_matrix<T>& a, tiny_vector<size_t>& piv, 
    const tiny_vector<T>& b, tiny_vector<T>& x)
{
	typedef size_t size_type;
	const size_type n = a.nrow();
	if (n == 0) return;

	// solve Ly = piv(b); y is stored in x
	for (size_type i = 0; i < n; i++) {

	    T c = 0;
	    for (size_type j = 0; j < i; j++)

		c += a(piv[i],j) * x [j];

	    x [i] = b [piv[i]] - c;
	}
	// solve Ux = y; x contains y as input and x as output
	for (int i = n-1; i >= 0; i--) {

	    T c = 0;
	    for (size_type j = i+1; j < n; j++)

		c += a(piv[i],j) * x [j];

	    x [i] = (x [i] - c) / a(piv[i],i);
	}
}
// ---------------------------------
// third step : matrix inversion
// NOTE: the a matrix is destroyed !
// ---------------------------------

template <class T>
void
invert (tiny_matrix<T>& a, tiny_matrix<T>& inv_a)
{
    typedef size_t size_type;
    const size_type n = a.nrow();

    // performs the gauss factorization:  M = L.U
    tiny_vector<size_t> piv (n);
    lu (a, piv);
    
    // invert M in B, column by colomn
    tiny_vector<T> column (n);
    tiny_vector<T> x (n);
    inv_a.resize (n,n);

    for (size_type j = 0; j < n; j++) {

	for (size_type i = 0; i < n; i++) 
	    column [i] = 0;
	column [j] = 1;

	solve (a, piv, column, x);

	for (size_type i = 0; i < n; i++) 
	  inv_a (i,j) = x [i];
    }
}
template <class T>
void
put (std::ostream& out, std::string name, const tiny_matrix<T>& a)
{
    typedef size_t size_type;
    out << name << "(" << a.nrow() << "," << a.ncol() << ")" << std::endl;

    for (size_type i = 0; i < a.nrow(); i++) {
      for (size_type j = 0; j < a.ncol(); j++) {
	 out << name << "(" << i << "," << j << ") = " << a(i,j) << std::endl;
      }
    }
}
}// namespace rheolef
#endif // _RHEO_TINY_LU_H