1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath//===================================================== 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// File : blitz_LU_solve_interface.hh 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Author : L. Plagne <laurent.plagne@edf.fr)> 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) EDF R&D, lun sep 30 14:23:31 CEST 2002 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath//===================================================== 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This program is free software; you can redistribute it and/or 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// modify it under the terms of the GNU General Public License 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// as published by the Free Software Foundation; either version 2 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// of the License, or (at your option) any later version. 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This program is distributed in the hope that it will be useful, 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// but WITHOUT ANY WARRANTY; without even the implied warranty of 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// GNU General Public License for more details. 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// You should have received a copy of the GNU General Public License 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// along with this program; if not, write to the Free Software 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#ifndef BLITZ_LU_SOLVE_INTERFACE_HH 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#define BLITZ_LU_SOLVE_INTERFACE_HH 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include "blitz/array.h" 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <vector> 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan KamathBZ_USING_NAMESPACE(blitz) 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<class real> 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathclass blitz_LU_solve_interface : public blitz_interface<real> 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathpublic : 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename blitz_interface<real>::gene_matrix gene_matrix; 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename blitz_interface<real>::gene_vector gene_vector; 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef blitz::Array<int,1> Pivot_Vector; 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N) 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath pivot.resize(N); 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline static void free_Pivot_Vector(Pivot_Vector & pivot) 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return; 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline real matrix_vector_product_sliced(const gene_matrix & A, gene_vector B, int row, int col_start, int col_end) 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath real somme=0.; 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for (int j=col_start ; j<col_end+1 ; j++){ 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath somme+=A(row,j)*B(j); 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return somme; 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 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 ) 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath real somme=0.; 76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for (int j=col_start ; j<col_end+1 ; j++){ 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath somme+=A(row,j)*B(j+row_shift,col); 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return somme; 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline static void LU_factor(gene_matrix & LU, Pivot_Vector & pivot, int N) 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ASSERT( LU.rows()==LU.cols() ) ; 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int index_max = 0 ; 92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath real big = 0. ; 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath real theSum = 0. ; 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath real dum = 0. ; 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Get the implicit scaling information : 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath gene_vector ImplicitScaling( N ) ; 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for( int i=0; i<N; i++ ) { 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath big = 0. ; 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for( int j=0; j<N; j++ ) { 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if( abs( LU( i, j ) )>=big ) big = abs( LU( i, j ) ) ; 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if( big==0. ) { 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath INFOS( "blitz_LU_factor::Singular matrix" ) ; 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath exit( 0 ) ; 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ImplicitScaling( i ) = 1./big ; 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Loop over columns of Crout's method : 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for( int j=0; j<N; j++ ) { 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for( int i=0; i<j; i++ ) { 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath theSum = LU( i, j ) ; 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath theSum -= matrix_matrix_product_sliced(LU, i, 0, i-1, LU, 0, j) ; 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // theSum -= sum( LU( i, Range( fromStart, i-1 ) )*LU( Range( fromStart, i-1 ), j ) ) ; 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath LU( i, j ) = theSum ; 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Search for the largest pivot element : 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath big = 0. ; 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for( int i=j; i<N; i++ ) { 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath theSum = LU( i, j ) ; 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath theSum -= matrix_matrix_product_sliced(LU, i, 0, j-1, LU, 0, j) ; 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // theSum -= sum( LU( i, Range( fromStart, j-1 ) )*LU( Range( fromStart, j-1 ), j ) ) ; 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath LU( i, j ) = theSum ; 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if( (ImplicitScaling( i )*abs( theSum ))>=big ) { 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dum = ImplicitScaling( i )*abs( theSum ) ; 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath big = dum ; 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath index_max = i ; 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Interchanging rows and the scale factor : 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if( j!=index_max ) { 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for( int k=0; k<N; k++ ) { 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dum = LU( index_max, k ) ; 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath LU( index_max, k ) = LU( j, k ) ; 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath LU( j, k ) = dum ; 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ImplicitScaling( index_max ) = ImplicitScaling( j ) ; 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath pivot( j ) = index_max ; 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if ( LU( j, j )==0. ) LU( j, j ) = 1.e-20 ; 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Divide by the pivot element : 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if( j<N ) { 143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dum = 1./LU( j, j ) ; 144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for( int i=j+1; i<N; i++ ) LU( i, j ) *= dum ; 145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 147c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 148c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 149c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline static void LU_solve(const gene_matrix & LU, const Pivot_Vector pivot, gene_vector &B, gene_vector X, int N) 151c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 152c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 153c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Pour conserver le meme header, on travaille sur X, copie du second-membre B 154c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath X = B.copy() ; 155c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ASSERT( LU.rows()==LU.cols() ) ; 156c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath firstIndex indI ; 157c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Forward substitution : 158c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int ii = 0 ; 159c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath real theSum = 0. ; 160c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for( int i=0; i<N; i++ ) { 161c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int ip = pivot( i ) ; 162c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath theSum = X( ip ) ; 163c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // theSum = B( ip ) ; 164c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath X( ip ) = X( i ) ; 165c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // B( ip ) = B( i ) ; 166c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if( ii ) { 167c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath theSum -= matrix_vector_product_sliced(LU, X, i, ii-1, i-1) ; 168c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // theSum -= sum( LU( i, Range( ii-1, i-1 ) )*X( Range( ii-1, i-1 ) ) ) ; 169c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // theSum -= sum( LU( i, Range( ii-1, i-1 ) )*B( Range( ii-1, i-1 ) ) ) ; 170c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } else if( theSum ) { 171c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ii = i+1 ; 172c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 173c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath X( i ) = theSum ; 174c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // B( i ) = theSum ; 175c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 176c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Backsubstitution : 177c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for( int i=N-1; i>=0; i-- ) { 178c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath theSum = X( i ) ; 179c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // theSum = B( i ) ; 180c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath theSum -= matrix_vector_product_sliced(LU, X, i, i+1, N) ; 181c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // theSum -= sum( LU( i, Range( i+1, toEnd ) )*X( Range( i+1, toEnd ) ) ) ; 182c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // theSum -= sum( LU( i, Range( i+1, toEnd ) )*B( Range( i+1, toEnd ) ) ) ; 183c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Store a component of the solution vector : 184c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath X( i ) = theSum/LU( i, i ) ; 185c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // B( i ) = theSum/LU( i, i ) ; 186c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 187c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 188c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 189c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 190c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 191c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 192c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#endif 193