| //===================================================== |
| // 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 |