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 |
|
---|
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
|
---|