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//=====================================================
// File : blitz_LU_solve_interface.hh
// Author : L. Plagne <laurent.plagne@edf.fr)>
// Copyright (C) EDF R&D, lun sep 30 14:23:31 CEST 2002
//=====================================================
//
// This program 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.
//
// 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 General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
//
#ifndef BLITZ_LU_SOLVE_INTERFACE_HH
#define BLITZ_LU_SOLVE_INTERFACE_HH
#include "blitz/array.h"
#include <vector>
BZ_USING_NAMESPACE(blitz)
template<class real>
class blitz_LU_solve_interface : public blitz_interface<real>
{
public :
typedef typename blitz_interface<real>::gene_matrix gene_matrix;
typedef typename blitz_interface<real>::gene_vector gene_vector;
typedef blitz::Array<int,1> Pivot_Vector;
inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N)
{
pivot.resize(N);
}
inline static void free_Pivot_Vector(Pivot_Vector & pivot)
{
return;
}
static inline real matrix_vector_product_sliced(const gene_matrix & A, gene_vector B, int row, int col_start, int col_end)
{
real somme=0.;
for (int j=col_start ; j<col_end+1 ; j++){
somme+=A(row,j)*B(j);
}
return somme;
}
static inline real matrix_matrix_product_sliced(gene_matrix & A, int row, int col_start, int col_end, gene_matrix & B, int row_shift, int col )
{
real somme=0.;
for (int j=col_start ; j<col_end+1 ; j++){
somme+=A(row,j)*B(j+row_shift,col);
}
return somme;
}
inline static void LU_factor(gene_matrix & LU, Pivot_Vector & pivot, int N)
{
ASSERT( LU.rows()==LU.cols() ) ;
int index_max = 0 ;
real big = 0. ;
real theSum = 0. ;
real dum = 0. ;
// Get the implicit scaling information :
gene_vector ImplicitScaling( N ) ;
for( int i=0; i<N; i++ ) {
big = 0. ;
for( int j=0; j<N; j++ ) {
if( abs( LU( i, j ) )>=big ) big = abs( LU( i, j ) ) ;
}
if( big==0. ) {
INFOS( "blitz_LU_factor::Singular matrix" ) ;
exit( 0 ) ;
}
ImplicitScaling( i ) = 1./big ;
}
// Loop over columns of Crout's method :
for( int j=0; j<N; j++ ) {
for( int i=0; i<j; i++ ) {
theSum = LU( i, j ) ;
theSum -= matrix_matrix_product_sliced(LU, i, 0, i-1, LU, 0, j) ;
// theSum -= sum( LU( i, Range( fromStart, i-1 ) )*LU( Range( fromStart, i-1 ), j ) ) ;
LU( i, j ) = theSum ;
}
// Search for the largest pivot element :
big = 0. ;
for( int i=j; i<N; i++ ) {
theSum = LU( i, j ) ;
theSum -= matrix_matrix_product_sliced(LU, i, 0, j-1, LU, 0, j) ;
// theSum -= sum( LU( i, Range( fromStart, j-1 ) )*LU( Range( fromStart, j-1 ), j ) ) ;
LU( i, j ) = theSum ;
if( (ImplicitScaling( i )*abs( theSum ))>=big ) {
dum = ImplicitScaling( i )*abs( theSum ) ;
big = dum ;
index_max = i ;
}
}
// Interchanging rows and the scale factor :
if( j!=index_max ) {
for( int k=0; k<N; k++ ) {
dum = LU( index_max, k ) ;
LU( index_max, k ) = LU( j, k ) ;
LU( j, k ) = dum ;
}
ImplicitScaling( index_max ) = ImplicitScaling( j ) ;
}
pivot( j ) = index_max ;
if ( LU( j, j )==0. ) LU( j, j ) = 1.e-20 ;
// Divide by the pivot element :
if( j<N ) {
dum = 1./LU( j, j ) ;
for( int i=j+1; i<N; i++ ) LU( i, j ) *= dum ;
}
}
}
inline static void LU_solve(const gene_matrix & LU, const Pivot_Vector pivot, gene_vector &B, gene_vector X, int N)
{
// Pour conserver le meme header, on travaille sur X, copie du second-membre B
X = B.copy() ;
ASSERT( LU.rows()==LU.cols() ) ;
firstIndex indI ;
// Forward substitution :
int ii = 0 ;
real theSum = 0. ;
for( int i=0; i<N; i++ ) {
int ip = pivot( i ) ;
theSum = X( ip ) ;
// theSum = B( ip ) ;
X( ip ) = X( i ) ;
// B( ip ) = B( i ) ;
if( ii ) {
theSum -= matrix_vector_product_sliced(LU, X, i, ii-1, i-1) ;
// theSum -= sum( LU( i, Range( ii-1, i-1 ) )*X( Range( ii-1, i-1 ) ) ) ;
// theSum -= sum( LU( i, Range( ii-1, i-1 ) )*B( Range( ii-1, i-1 ) ) ) ;
} else if( theSum ) {
ii = i+1 ;
}
X( i ) = theSum ;
// B( i ) = theSum ;
}
// Backsubstitution :
for( int i=N-1; i>=0; i-- ) {
theSum = X( i ) ;
// theSum = B( i ) ;
theSum -= matrix_vector_product_sliced(LU, X, i, i+1, N) ;
// theSum -= sum( LU( i, Range( i+1, toEnd ) )*X( Range( i+1, toEnd ) ) ) ;
// theSum -= sum( LU( i, Range( i+1, toEnd ) )*B( Range( i+1, toEnd ) ) ) ;
// Store a component of the solution vector :
X( i ) = theSum/LU( i, i ) ;
// B( i ) = theSum/LU( i, i ) ;
}
}
};
#endif
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