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
26BZ_USING_NAMESPACE(blitz)
27
28template<class real>
29class blitz_LU_solve_interface : public blitz_interface<real>
30{
31
32public :
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