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      1 //=====================================================
      2 // File   :  blitz_LU_solve_interface.hh
      3 // Author :  L. Plagne <laurent.plagne (at) edf.fr)>
      4 // Copyright (C) EDF R&D,  lun sep 30 14:23:31 CEST 2002
      5 //=====================================================
      6 //
      7 // This program is free software; you can redistribute it and/or
      8 // modify it under the terms of the GNU General Public License
      9 // as published by the Free Software Foundation; either version 2
     10 // of the License, or (at your option) any later version.
     11 //
     12 // This program is distributed in the hope that it will be useful,
     13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
     14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     15 // GNU General Public License for more details.
     16 // You should have received a copy of the GNU General Public License
     17 // along with this program; if not, write to the Free Software
     18 // Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
     19 //
     20 #ifndef BLITZ_LU_SOLVE_INTERFACE_HH
     21 #define BLITZ_LU_SOLVE_INTERFACE_HH
     22 
     23 #include "blitz/array.h"
     24 #include <vector>
     25 
     26 BZ_USING_NAMESPACE(blitz)
     27 
     28 template<class real>
     29 class blitz_LU_solve_interface : public blitz_interface<real>
     30 {
     31 
     32 public :
     33 
     34   typedef typename blitz_interface<real>::gene_matrix gene_matrix;
     35   typedef typename blitz_interface<real>::gene_vector gene_vector;
     36 
     37   typedef blitz::Array<int,1> Pivot_Vector;
     38 
     39   inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N)
     40   {
     41 
     42     pivot.resize(N);
     43 
     44   }
     45 
     46   inline static void free_Pivot_Vector(Pivot_Vector & pivot)
     47   {
     48 
     49     return;
     50 
     51   }
     52 
     53 
     54   static inline real matrix_vector_product_sliced(const gene_matrix & A, gene_vector B, int row, int col_start, int col_end)
     55   {
     56 
     57     real somme=0.;
     58 
     59     for (int j=col_start ; j<col_end+1 ; j++){
     60 
     61 	somme+=A(row,j)*B(j);
     62 
     63     }
     64 
     65     return somme;
     66 
     67   }
     68 
     69 
     70 
     71 
     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 )
     73   {
     74 
     75     real somme=0.;
     76 
     77     for (int j=col_start ; j<col_end+1 ; j++){
     78 
     79 	somme+=A(row,j)*B(j+row_shift,col);
     80 
     81     }
     82 
     83     return somme;
     84 
     85   }
     86 
     87   inline static void LU_factor(gene_matrix & LU, Pivot_Vector & pivot, int N)
     88   {
     89 
     90     ASSERT( LU.rows()==LU.cols() ) ;
     91     int index_max = 0 ;
     92     real big = 0. ;
     93     real theSum = 0. ;
     94     real dum = 0. ;
     95     // Get the implicit scaling information :
     96     gene_vector ImplicitScaling( N ) ;
     97     for( int i=0; i<N; i++ ) {
     98       big = 0. ;
     99       for( int j=0; j<N; j++ ) {
    100 	if( abs( LU( i, j ) )>=big ) big = abs( LU( i, j ) ) ;
    101       }
    102       if( big==0. ) {
    103 	INFOS( "blitz_LU_factor::Singular matrix" ) ;
    104 	exit( 0 ) ;
    105       }
    106       ImplicitScaling( i ) = 1./big ;
    107     }
    108     // Loop over columns of Crout's method :
    109     for( int j=0; j<N; j++ ) {
    110       for( int i=0; i<j; i++ ) {
    111 	theSum = LU( i, j ) ;
    112 	theSum -= matrix_matrix_product_sliced(LU, i, 0, i-1, LU, 0, j) ;
    113 	//	theSum -= sum( LU( i, Range( fromStart, i-1 ) )*LU( Range( fromStart, i-1 ), j ) ) ;
    114 	LU( i, j ) = theSum ;
    115       }
    116 
    117       // Search for the largest pivot element :
    118       big = 0. ;
    119       for( int i=j; i<N; i++ ) {
    120 	theSum = LU( i, j ) ;
    121 	theSum -= matrix_matrix_product_sliced(LU, i, 0, j-1, LU, 0, j) ;
    122 	//	theSum -= sum( LU( i, Range( fromStart, j-1 ) )*LU( Range( fromStart, j-1 ), j ) ) ;
    123 	LU( i, j ) = theSum ;
    124 	if( (ImplicitScaling( i )*abs( theSum ))>=big ) {
    125 	  dum = ImplicitScaling( i )*abs( theSum ) ;
    126 	  big = dum ;
    127 	  index_max = i ;
    128 	}
    129       }
    130       // Interchanging rows and the scale factor :
    131       if( j!=index_max ) {
    132 	for( int k=0; k<N; k++ ) {
    133 	  dum = LU( index_max, k ) ;
    134 	  LU( index_max, k ) = LU( j, k ) ;
    135 	  LU( j, k ) = dum ;
    136 	}
    137 	ImplicitScaling( index_max ) = ImplicitScaling( j ) ;
    138       }
    139       pivot( j ) = index_max ;
    140       if ( LU( j, j )==0. ) LU( j, j ) = 1.e-20 ;
    141       // Divide by the pivot element :
    142       if( j<N ) {
    143 	dum = 1./LU( j, j ) ;
    144 	for( int i=j+1; i<N; i++ ) LU( i, j ) *= dum ;
    145       }
    146     }
    147 
    148   }
    149 
    150   inline static void LU_solve(const gene_matrix & LU, const Pivot_Vector pivot, gene_vector &B, gene_vector X, int N)
    151   {
    152 
    153     // Pour conserver le meme header, on travaille sur X, copie du second-membre B
    154     X = B.copy() ;
    155     ASSERT( LU.rows()==LU.cols() ) ;
    156     firstIndex indI ;
    157     // Forward substitution :
    158     int ii = 0 ;
    159     real theSum = 0. ;
    160     for( int i=0; i<N; i++ ) {
    161       int ip = pivot( i ) ;
    162       theSum = X( ip ) ;
    163       //      theSum = B( ip ) ;
    164       X( ip ) = X( i ) ;
    165       //      B( ip ) = B( i ) ;
    166       if( ii ) {
    167 	theSum -= matrix_vector_product_sliced(LU, X, i, ii-1, i-1) ;
    168 	//	theSum -= sum( LU( i, Range( ii-1, i-1 ) )*X( Range( ii-1, i-1 ) ) ) ;
    169 	//	theSum -= sum( LU( i, Range( ii-1, i-1 ) )*B( Range( ii-1, i-1 ) ) ) ;
    170       } else if( theSum ) {
    171 	ii = i+1 ;
    172       }
    173       X( i ) = theSum ;
    174       //      B( i ) = theSum ;
    175     }
    176     // Backsubstitution :
    177     for( int i=N-1; i>=0; i-- ) {
    178       theSum = X( i ) ;
    179       //      theSum = B( i ) ;
    180       theSum -= matrix_vector_product_sliced(LU, X, i, i+1, N) ;
    181       //      theSum -= sum( LU( i, Range( i+1, toEnd ) )*X( Range( i+1, toEnd ) ) ) ;
    182       //      theSum -= sum( LU( i, Range( i+1, toEnd ) )*B( Range( i+1, toEnd ) ) ) ;
    183       // Store a component of the solution vector :
    184       X( i ) = theSum/LU( i, i ) ;
    185       //      B( i ) = theSum/LU( i, i ) ;
    186     }
    187 
    188   }
    189 
    190 };
    191 
    192 #endif
    193