blitz_LU_solve_interface.hh
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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>
30 {
31 
32 public :
33 
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
blitz_LU_solve_interface::gene_vector
blitz_interface< real >::gene_vector gene_vector
Definition: blitz_LU_solve_interface.hh:35
col
m col(1)
blitz_LU_solve_interface::matrix_vector_product_sliced
static real matrix_vector_product_sliced(const gene_matrix &A, gene_vector B, int row, int col_start, int col_end)
Definition: blitz_LU_solve_interface.hh:54
blitz_interface::gene_vector
blitz::Array< real, 1 > gene_vector
Definition: blitz_interface.hh:44
B
Definition: test_numpy_dtypes.cpp:299
blitz_LU_solve_interface::new_Pivot_Vector
static void new_Pivot_Vector(Pivot_Vector &pivot, int N)
Definition: blitz_LU_solve_interface.hh:39
E1::B
@ B
X
#define X
Definition: icosphere.cpp:20
blitz_LU_solve_interface::LU_factor
static void LU_factor(gene_matrix &LU, Pivot_Vector &pivot, int N)
Definition: blitz_LU_solve_interface.hh:87
blitz_interface
Definition: blitz_interface.hh:34
blitz_LU_solve_interface::Pivot_Vector
blitz::Array< int, 1 > Pivot_Vector
Definition: blitz_LU_solve_interface.hh:37
A
Definition: test_numpy_dtypes.cpp:298
j
std::ptrdiff_t j
Definition: tut_arithmetic_redux_minmax.cpp:2
blitz_LU_solve_interface
Definition: blitz_LU_solve_interface.hh:29
E1::A
@ A
ASSERT
#define ASSERT(expression)
Definition: ccolamd.c:872
blitz_LU_solve_interface::free_Pivot_Vector
static void free_Pivot_Vector(Pivot_Vector &pivot)
Definition: blitz_LU_solve_interface.hh:46
INFOS
#define INFOS(chain)
Definition: 3rdparty/Eigen/bench/btl/generic_bench/utils/utilities.h:22
row
m row(1)
big
static double big
Definition: igam.c:119
blitz_LU_solve_interface::matrix_matrix_product_sliced
static real matrix_matrix_product_sliced(gene_matrix &A, int row, int col_start, int col_end, gene_matrix &B, int row_shift, int col)
Definition: blitz_LU_solve_interface.hh:72
blitz_LU_solve_interface::gene_matrix
blitz_interface< real >::gene_matrix gene_matrix
Definition: blitz_LU_solve_interface.hh:34
blitz_LU_solve_interface::LU_solve
static void LU_solve(const gene_matrix &LU, const Pivot_Vector pivot, gene_vector &B, gene_vector X, int N)
Definition: blitz_LU_solve_interface.hh:150
abs
#define abs(x)
Definition: datatypes.h:17
N
#define N
Definition: igam.h:9
blitz_interface::gene_matrix
blitz::Array< real, 2 > gene_matrix
Definition: blitz_interface.hh:43
real
Definition: main.h:100
i
int i
Definition: BiCGSTAB_step_by_step.cpp:9


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