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1 //=====================================================
2 // File   :  blitz_LU_solve_interface.hh
3 // Author :  L. Plagne <laurent.plagne@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 
new_Pivot_Vector(Pivot_Vector & pivot,int N)39   inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N)
40   {
41 
42     pivot.resize(N);
43 
44   }
45 
free_Pivot_Vector(Pivot_Vector & pivot)46   inline static void free_Pivot_Vector(Pivot_Vector & pivot)
47   {
48 
49     return;
50 
51   }
52 
53 
matrix_vector_product_sliced(const gene_matrix & A,gene_vector B,int row,int col_start,int col_end)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 
matrix_matrix_product_sliced(gene_matrix & A,int row,int col_start,int col_end,gene_matrix & B,int row_shift,int col)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 
LU_factor(gene_matrix & LU,Pivot_Vector & pivot,int N)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 
LU_solve(const gene_matrix & LU,const Pivot_Vector pivot,gene_vector & B,gene_vector X,int N)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