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+//=====================================================
+// File   :  blitz_LU_solve_interface.hh
+// Author :  L. Plagne <laurent.plagne@edf.fr)>        
+// Copyright (C) EDF R&D,  lun sep 30 14:23:31 CEST 2002
+//=====================================================
+// 
+// This program is free software; you can redistribute it and/or
+// modify it under the terms of the GNU General Public License
+// as published by the Free Software Foundation; either version 2
+// of the License, or (at your option) any later version.
+// 
+// This program is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+// You should have received a copy of the GNU General Public License
+// along with this program; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
+// 
+#ifndef BLITZ_LU_SOLVE_INTERFACE_HH
+#define BLITZ_LU_SOLVE_INTERFACE_HH
+
+#include "blitz/array.h"
+#include <vector>
+
+BZ_USING_NAMESPACE(blitz)
+
+template<class real>
+class blitz_LU_solve_interface : public blitz_interface<real>
+{
+
+public :
+
+  typedef typename blitz_interface<real>::gene_matrix gene_matrix;
+  typedef typename blitz_interface<real>::gene_vector gene_vector;
+
+  typedef blitz::Array<int,1> Pivot_Vector;
+
+  inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N)
+  {
+
+    pivot.resize(N);
+
+  }
+
+  inline static void free_Pivot_Vector(Pivot_Vector & pivot)
+  {
+    
+    return;
+
+  }
+
+
+  static inline real matrix_vector_product_sliced(const gene_matrix & A, gene_vector B, int row, int col_start, int col_end)
+  {
+    
+    real somme=0.;
+    
+    for (int j=col_start ; j<col_end+1 ; j++){
+	
+	somme+=A(row,j)*B(j);
+	
+    }
+
+    return somme;
+
+  }
+
+
+
+
+  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 )
+  {
+    
+    real somme=0.;
+    
+    for (int j=col_start ; j<col_end+1 ; j++){
+	
+	somme+=A(row,j)*B(j+row_shift,col);
+	
+    }
+
+    return somme;
+
+  }
+
+  inline static void LU_factor(gene_matrix & LU, Pivot_Vector & pivot, int N)
+  {
+
+    ASSERT( LU.rows()==LU.cols() ) ;
+    int index_max = 0 ;
+    real big = 0. ;
+    real theSum = 0. ;
+    real dum = 0. ;
+    // Get the implicit scaling information :
+    gene_vector ImplicitScaling( N ) ;
+    for( int i=0; i<N; i++ ) {
+      big = 0. ;
+      for( int j=0; j<N; j++ ) {
+	if( abs( LU( i, j ) )>=big ) big = abs( LU( i, j ) ) ;
+      }
+      if( big==0. ) {
+	INFOS( "blitz_LU_factor::Singular matrix" ) ;
+	exit( 0 ) ;
+      }
+      ImplicitScaling( i ) = 1./big ;
+    }
+    // Loop over columns of Crout's method :
+    for( int j=0; j<N; j++ ) {
+      for( int i=0; i<j; i++ ) {
+	theSum = LU( i, j ) ;
+	theSum -= matrix_matrix_product_sliced(LU, i, 0, i-1, LU, 0, j) ;
+	//	theSum -= sum( LU( i, Range( fromStart, i-1 ) )*LU( Range( fromStart, i-1 ), j ) ) ;
+	LU( i, j ) = theSum ;
+      }
+      
+      // Search for the largest pivot element :
+      big = 0. ;
+      for( int i=j; i<N; i++ ) {
+	theSum = LU( i, j ) ;
+	theSum -= matrix_matrix_product_sliced(LU, i, 0, j-1, LU, 0, j) ;
+	//	theSum -= sum( LU( i, Range( fromStart, j-1 ) )*LU( Range( fromStart, j-1 ), j ) ) ;
+	LU( i, j ) = theSum ;
+	if( (ImplicitScaling( i )*abs( theSum ))>=big ) {
+	  dum = ImplicitScaling( i )*abs( theSum ) ;
+	  big = dum ;
+	  index_max = i ;
+	}
+      }
+      // Interchanging rows and the scale factor :
+      if( j!=index_max ) {
+	for( int k=0; k<N; k++ ) {
+	  dum = LU( index_max, k ) ;
+	  LU( index_max, k ) = LU( j, k ) ;
+	  LU( j, k ) = dum ;
+	}
+	ImplicitScaling( index_max ) = ImplicitScaling( j ) ;
+      }
+      pivot( j ) = index_max ;
+      if ( LU( j, j )==0. ) LU( j, j ) = 1.e-20 ;
+      // Divide by the pivot element :
+      if( j<N ) {
+	dum = 1./LU( j, j ) ;
+	for( int i=j+1; i<N; i++ ) LU( i, j ) *= dum ;
+      }
+    }
+
+  }
+
+  inline static void LU_solve(const gene_matrix & LU, const Pivot_Vector pivot, gene_vector &B, gene_vector X, int N)
+  {
+
+    // Pour conserver le meme header, on travaille sur X, copie du second-membre B
+    X = B.copy() ;
+    ASSERT( LU.rows()==LU.cols() ) ;
+    firstIndex indI ;
+    // Forward substitution :
+    int ii = 0 ;
+    real theSum = 0. ;
+    for( int i=0; i<N; i++ ) {
+      int ip = pivot( i ) ;
+      theSum = X( ip ) ;
+      //      theSum = B( ip ) ;
+      X( ip ) = X( i ) ;
+      //      B( ip ) = B( i ) ;
+      if( ii ) {
+	theSum -= matrix_vector_product_sliced(LU, X, i, ii-1, i-1) ;
+	//	theSum -= sum( LU( i, Range( ii-1, i-1 ) )*X( Range( ii-1, i-1 ) ) ) ;
+	//	theSum -= sum( LU( i, Range( ii-1, i-1 ) )*B( Range( ii-1, i-1 ) ) ) ;
+      } else if( theSum ) {
+	ii = i+1 ;
+      }
+      X( i ) = theSum ;
+      //      B( i ) = theSum ;
+    }
+    // Backsubstitution :
+    for( int i=N-1; i>=0; i-- ) {
+      theSum = X( i ) ;
+      //      theSum = B( i ) ;
+      theSum -= matrix_vector_product_sliced(LU, X, i, i+1, N) ;
+      //      theSum -= sum( LU( i, Range( i+1, toEnd ) )*X( Range( i+1, toEnd ) ) ) ;
+      //      theSum -= sum( LU( i, Range( i+1, toEnd ) )*B( Range( i+1, toEnd ) ) ) ;
+      // Store a component of the solution vector :
+      X( i ) = theSum/LU( i, i ) ;
+      //      B( i ) = theSum/LU( i, i ) ;
+    }
+
+  }
+
+};
+
+#endif