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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