[136] | 1 | //=====================================================
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| 2 | // File : blitz_LU_solve_interface.hh
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| 3 | // Author : L. Plagne <laurent.plagne@edf.fr)>
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| 4 | // Copyright (C) EDF R&D, lun sep 30 14:23:31 CEST 2002
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| 5 | //=====================================================
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| 6 | //
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| 7 | // This program is free software; you can redistribute it and/or
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| 8 | // modify it under the terms of the GNU General Public License
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| 9 | // as published by the Free Software Foundation; either version 2
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| 10 | // of the License, or (at your option) any later version.
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| 11 | //
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| 12 | // This program is distributed in the hope that it will be useful,
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| 13 | // but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 14 | // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 15 | // GNU General Public License for more details.
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| 16 | // You should have received a copy of the GNU General Public License
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| 17 | // along with this program; if not, write to the Free Software
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| 18 | // Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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| 19 | //
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| 20 | #ifndef BLITZ_LU_SOLVE_INTERFACE_HH
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| 21 | #define BLITZ_LU_SOLVE_INTERFACE_HH
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| 22 |
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| 23 | #include "blitz/array.h"
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| 24 | #include <vector>
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| 25 |
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| 26 | BZ_USING_NAMESPACE(blitz)
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| 27 |
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| 28 | template<class real>
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| 29 | class blitz_LU_solve_interface : public blitz_interface<real>
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| 30 | {
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| 31 |
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| 32 | public :
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| 33 |
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| 34 | typedef typename blitz_interface<real>::gene_matrix gene_matrix;
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| 35 | typedef typename blitz_interface<real>::gene_vector gene_vector;
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| 36 |
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| 37 | typedef blitz::Array<int,1> Pivot_Vector;
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| 38 |
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| 39 | inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N)
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| 40 | {
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| 41 |
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| 42 | pivot.resize(N);
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| 43 |
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| 44 | }
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| 45 |
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| 46 | inline static void free_Pivot_Vector(Pivot_Vector & pivot)
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| 47 | {
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| 48 |
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| 49 | return;
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| 50 |
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| 51 | }
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| 52 |
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| 53 |
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| 54 | static inline real matrix_vector_product_sliced(const gene_matrix & A, gene_vector B, int row, int col_start, int col_end)
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| 55 | {
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| 56 |
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| 57 | real somme=0.;
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| 58 |
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| 59 | for (int j=col_start ; j<col_end+1 ; j++){
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| 60 |
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| 61 | somme+=A(row,j)*B(j);
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| 62 |
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| 63 | }
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| 64 |
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| 65 | return somme;
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| 66 |
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| 67 | }
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| 68 |
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| 69 |
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| 70 |
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| 71 |
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| 72 | 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 )
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| 73 | {
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| 74 |
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| 75 | real somme=0.;
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| 76 |
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| 77 | for (int j=col_start ; j<col_end+1 ; j++){
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| 78 |
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| 79 | somme+=A(row,j)*B(j+row_shift,col);
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| 80 |
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| 81 | }
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| 82 |
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| 83 | return somme;
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| 84 |
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| 85 | }
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| 86 |
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| 87 | inline static void LU_factor(gene_matrix & LU, Pivot_Vector & pivot, int N)
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| 88 | {
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| 89 |
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| 90 | ASSERT( LU.rows()==LU.cols() ) ;
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| 91 | int index_max = 0 ;
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| 92 | real big = 0. ;
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| 93 | real theSum = 0. ;
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| 94 | real dum = 0. ;
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| 95 | // Get the implicit scaling information :
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| 96 | gene_vector ImplicitScaling( N ) ;
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| 97 | for( int i=0; i<N; i++ ) {
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| 98 | big = 0. ;
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| 99 | for( int j=0; j<N; j++ ) {
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| 100 | if( abs( LU( i, j ) )>=big ) big = abs( LU( i, j ) ) ;
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| 101 | }
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| 102 | if( big==0. ) {
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| 103 | INFOS( "blitz_LU_factor::Singular matrix" ) ;
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| 104 | exit( 0 ) ;
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| 105 | }
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| 106 | ImplicitScaling( i ) = 1./big ;
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| 107 | }
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| 108 | // Loop over columns of Crout's method :
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| 109 | for( int j=0; j<N; j++ ) {
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| 110 | for( int i=0; i<j; i++ ) {
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| 111 | theSum = LU( i, j ) ;
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| 112 | theSum -= matrix_matrix_product_sliced(LU, i, 0, i-1, LU, 0, j) ;
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| 113 | // theSum -= sum( LU( i, Range( fromStart, i-1 ) )*LU( Range( fromStart, i-1 ), j ) ) ;
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| 114 | LU( i, j ) = theSum ;
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| 115 | }
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| 116 |
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| 117 | // Search for the largest pivot element :
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| 118 | big = 0. ;
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| 119 | for( int i=j; i<N; i++ ) {
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| 120 | theSum = LU( i, j ) ;
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| 121 | theSum -= matrix_matrix_product_sliced(LU, i, 0, j-1, LU, 0, j) ;
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| 122 | // theSum -= sum( LU( i, Range( fromStart, j-1 ) )*LU( Range( fromStart, j-1 ), j ) ) ;
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| 123 | LU( i, j ) = theSum ;
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| 124 | if( (ImplicitScaling( i )*abs( theSum ))>=big ) {
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| 125 | dum = ImplicitScaling( i )*abs( theSum ) ;
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| 126 | big = dum ;
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| 127 | index_max = i ;
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| 128 | }
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| 129 | }
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| 130 | // Interchanging rows and the scale factor :
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| 131 | if( j!=index_max ) {
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| 132 | for( int k=0; k<N; k++ ) {
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| 133 | dum = LU( index_max, k ) ;
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| 134 | LU( index_max, k ) = LU( j, k ) ;
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| 135 | LU( j, k ) = dum ;
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| 136 | }
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| 137 | ImplicitScaling( index_max ) = ImplicitScaling( j ) ;
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| 138 | }
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| 139 | pivot( j ) = index_max ;
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| 140 | if ( LU( j, j )==0. ) LU( j, j ) = 1.e-20 ;
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| 141 | // Divide by the pivot element :
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| 142 | if( j<N ) {
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| 143 | dum = 1./LU( j, j ) ;
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| 144 | for( int i=j+1; i<N; i++ ) LU( i, j ) *= dum ;
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| 145 | }
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| 146 | }
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| 147 |
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| 148 | }
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| 149 |
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| 150 | inline static void LU_solve(const gene_matrix & LU, const Pivot_Vector pivot, gene_vector &B, gene_vector X, int N)
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| 151 | {
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| 152 |
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| 153 | // Pour conserver le meme header, on travaille sur X, copie du second-membre B
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| 154 | X = B.copy() ;
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| 155 | ASSERT( LU.rows()==LU.cols() ) ;
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| 156 | firstIndex indI ;
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| 157 | // Forward substitution :
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| 158 | int ii = 0 ;
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| 159 | real theSum = 0. ;
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| 160 | for( int i=0; i<N; i++ ) {
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| 161 | int ip = pivot( i ) ;
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| 162 | theSum = X( ip ) ;
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| 163 | // theSum = B( ip ) ;
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| 164 | X( ip ) = X( i ) ;
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| 165 | // B( ip ) = B( i ) ;
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| 166 | if( ii ) {
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| 167 | theSum -= matrix_vector_product_sliced(LU, X, i, ii-1, i-1) ;
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| 168 | // theSum -= sum( LU( i, Range( ii-1, i-1 ) )*X( Range( ii-1, i-1 ) ) ) ;
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| 169 | // theSum -= sum( LU( i, Range( ii-1, i-1 ) )*B( Range( ii-1, i-1 ) ) ) ;
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| 170 | } else if( theSum ) {
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| 171 | ii = i+1 ;
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| 172 | }
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| 173 | X( i ) = theSum ;
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| 174 | // B( i ) = theSum ;
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| 175 | }
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| 176 | // Backsubstitution :
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| 177 | for( int i=N-1; i>=0; i-- ) {
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| 178 | theSum = X( i ) ;
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| 179 | // theSum = B( i ) ;
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| 180 | theSum -= matrix_vector_product_sliced(LU, X, i, i+1, N) ;
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| 181 | // theSum -= sum( LU( i, Range( i+1, toEnd ) )*X( Range( i+1, toEnd ) ) ) ;
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| 182 | // theSum -= sum( LU( i, Range( i+1, toEnd ) )*B( Range( i+1, toEnd ) ) ) ;
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| 183 | // Store a component of the solution vector :
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| 184 | X( i ) = theSum/LU( i, i ) ;
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| 185 | // B( i ) = theSum/LU( i, i ) ;
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| 186 | }
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| 187 |
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| 188 | }
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| 189 |
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| 190 | };
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| 191 |
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| 192 | #endif
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