d2sdx2_1d.C
/*
* Copyright (c) 1999-2001 Philippe Grandclement
*
* This file is part of LORENE.
*
* LORENE 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.
*
* LORENE 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 LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
char d2sdx2_1d_C[] = "$Header: /cvsroot/Lorene/C++/Source/Non_class_members/Operators/d2sdx2_1d.C,v 1.7 2015/03/05 08:49:31 j_novak Exp $" ;
/*
* $Id: d2sdx2_1d.C,v 1.7 2015/03/05 08:49:31 j_novak Exp $
* $Log: d2sdx2_1d.C,v $
* Revision 1.7 2015/03/05 08:49:31 j_novak
* Implemented operators with Legendre bases.
*
* Revision 1.6 2014/10/13 08:53:23 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.5 2014/10/06 15:16:06 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.4 2007/12/11 15:28:18 jl_cornou
* Jacobi(0,2) polynomials partially implemented
*
* Revision 1.3 2002/10/16 15:05:54 j_novak
* *** empty log message ***
*
* Revision 1.2 2002/10/16 14:36:58 j_novak
* Reorganization of #include instructions of standard C++, in order to
* use experimental version 3 of gcc.
*
* Revision 1.1.1.1 2001/11/20 15:19:29 e_gourgoulhon
* LORENE
*
* Revision 2.4 1999/10/11 15:18:14 phil
* *** empty log message ***
*
* Revision 2.3 1999/10/11 14:27:06 phil
* initialisation des variables statiques
*
* Revision 2.2 1999/09/03 14:15:56 phil
* Correction termes 0 (/2)
*
* Revision 2.1 1999/07/08 09:53:13 phil
* correction gestion memoire
*
* Revision 2.0 1999/07/07 10:15:26 phil
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Source/Non_class_members/Operators/d2sdx2_1d.C,v 1.7 2015/03/05 08:49:31 j_novak Exp $
*
*/
#include <cstdlib>
#include "type_parite.h"
#include "headcpp.h"
#include "proto.h"
/*
* Routine appliquant l'operateur d2sdx2.
*
* Entree : tb contient les coefficients du developpement
* int nr : nombre de points en r.
*
* Sortie : tb contient d2sdx2
*
*/
//----------------------------------
// Routine pour les cas non prevus --
//----------------------------------
namespace Lorene {
void _d2sdx2_1d_pas_prevu(int nr, double* tb, double *xo) {
cout << "d2sdx2 pas prevu..." << endl ;
cout << "Nombre de points : " << nr << endl ;
cout << "Valeurs : " << tb << " " << xo <<endl ;
abort() ;
exit(-1) ;
}
//----------------
// cas R_CHEBU ---
//----------------
void _d2sdx2_1d_r_chebu(int nr, double* tb, double *xo)
{
// Variables statiques
static double* cx1 = 0x0 ;
static double* cx2 = 0x0 ;
static double* cx3 = 0x0 ;
static int nr_pre = 0 ;
// Test sur np pour initialisation eventuelle
if (nr > nr_pre) {
nr_pre = nr ;
if (cx1 != 0x0) delete [] cx1 ;
if (cx2 != 0x0) delete [] cx2 ;
if (cx3 != 0x0) delete [] cx3 ;
cx1 = new double [nr] ;
cx2 = new double [nr] ;
cx3 = new double [nr] ;
for (int i=0 ; i<nr ; i++) {
cx1[i] = (i+2)*(i+2)*(i+2) ;
cx2[i] = (i+2) ;
cx3[i] = i*i ;
}
}
double som1, som2 ;
xo[nr-1] = 0 ;
som1 = (nr-1)*(nr-1)*(nr-1) * tb[nr-1] ;
som2 = (nr-1) * tb[nr-1] ;
xo[nr-3] = som1 - (nr-3)*(nr-3)*som2 ;
for (int i = nr-5 ; i >= 0 ; i -= 2 ) {
som1 += cx1[i] * tb[i+2] ;
som2 += cx2[i] * tb[i+2] ;
xo[i] = som1 - cx3[i] * som2 ;
} // Fin de la premiere boucle sur r
xo[nr-2] = 0 ;
som1 = (nr-2)*(nr-2)*(nr-2) * tb[nr-2] ;
som2 = (nr-2) * tb[nr-2] ;
xo[nr-4] = som1 - (nr-4)*(nr-4)*som2 ;
for (int i = nr-6 ; i >= 0 ; i -= 2 ) {
som1 += cx1[i] * tb[i+2] ;
som2 += cx2[i] * tb[i+2] ;
xo[i] = som1 - cx3[i] * som2 ;
} // Fin de la deuxieme boucle sur r
xo[0] *= 0.5 ;
}
//---------------
// cas R_CHEB ---
//---------------
void _d2sdx2_1d_r_cheb(int nr, double* tb, double *xo)
{
// Variables statiques
static double* cx1 = 0x0 ;
static double* cx2 = 0x0 ;
static double* cx3 = 0x0 ;
static int nr_pre = 0 ;
// Test sur np pour initialisation eventuelle
if (nr > nr_pre) {
nr_pre = nr ;
if (cx1 != 0x0) delete [] cx1 ;
if (cx2 != 0x0) delete [] cx2 ;
if (cx3 != 0x0) delete [] cx3 ;
cx1 = new double [nr] ;
cx2 = new double [nr] ;
cx3 = new double [nr] ;
for (int i=0 ; i<nr ; i++) {
cx1[i] = (i+2)*(i+2)*(i+2) ;
cx2[i] = (i+2) ;
cx3[i] = i*i ;
}
}
double som1, som2 ;
xo[nr-1] = 0 ;
som1 = (nr-1)*(nr-1)*(nr-1) * tb[nr-1] ;
som2 = (nr-1) * tb[nr-1] ;
xo[nr-3] = som1 - (nr-3)*(nr-3)*som2 ;
for (int i = nr-5 ; i >= 0 ; i -= 2 ) {
som1 += cx1[i] * tb[i+2] ;
som2 += cx2[i] * tb[i+2] ;
xo[i] = som1 - cx3[i] * som2 ;
} // Fin de la premiere boucle sur r
xo[nr-2] = 0 ;
som1 = (nr-2)*(nr-2)*(nr-2) * tb[nr-2] ;
som2 = (nr-2) * tb[nr-2] ;
xo[nr-4] = som1 - (nr-4)*(nr-4)*som2 ;
for (int i = nr-6 ; i >= 0 ; i -= 2 ) {
som1 += cx1[i] * tb[i+2] ;
som2 += cx2[i] * tb[i+2] ;
xo[i] = som1 - cx3[i] * som2 ;
} // Fin de la deuxieme boucle sur r
xo[0] *= .5 ;
}
//----------------
// cas R_JACO02 --
//----------------
void _d2sdx2_1d_r_jaco02(int nr, double* tb, double *xo)
{
dsdx_1d(nr, &tb, R_JACO02 >> TRA_R) ;
dsdx_1d(nr, &tb, R_JACO02 >> TRA_R) ;
for (int i = 0 ; i<nr ; i++) {
xo[i] = tb[i] ;
}
}
//-----------------
// cas R_CHEBP ---
//----------------
void _d2sdx2_1d_r_chebp(int nr, double* tb, double *xo)
{
// Variables statiques
static double* cx1 = 0x0 ;
static double* cx2 = 0x0 ;
static double* cx3 = 0x0 ;
static int nr_pre = 0 ;
// Test sur np pour initialisation eventuelle
if (nr > nr_pre) {
nr_pre = nr ;
if (cx1 != 0x0) delete [] cx1 ;
if (cx2 != 0x0) delete [] cx2 ;
if (cx3 != 0x0) delete [] cx3 ;
cx1 = new double [nr] ;
cx2 = new double [nr] ;
cx3 = new double [nr] ;
for (int i=0 ; i<nr ; i++) {
cx1[i] = 8*(i+1)*(i+1)*(i+1) ;
cx2[i] = 2*(i+1) ;
cx3[i] = 4*i*i ;
}
}
double som1, som2 ;
xo[nr-1] = 0 ;
som1 = 8*(nr-1)*(nr-1)*(nr-1) * tb[nr-1] ;
som2 = 2*(nr-1) * tb[nr-1] ;
xo[nr-2] = som1 - 4*(nr-2)*(nr-2)*som2 ;
for (int i = nr-3 ; i >= 0 ; i-- ) {
som1 += cx1[i] * tb[i+1] ;
som2 += cx2[i] * tb[i+1] ;
xo[i] = som1 - cx3[i] * som2 ;
} // Fin de la boucle sur r
xo[0] *= .5 ;
}
//---------------
// cas R_CHEBI --
//---------------
void _d2sdx2_1d_r_chebi(int nr, double* tb, double *xo)
{
// Variables statiques
static double* cx1 = 0x0 ;
static double* cx2 = 0x0 ;
static double* cx3 = 0x0 ;
static int nr_pre = 0 ;
// Test sur np pour initialisation eventuelle
if (nr > nr_pre) {
nr_pre = nr ;
if (cx1 != 0x0) delete [] cx1 ;
if (cx2 != 0x0) delete [] cx2 ;
if (cx3 != 0x0) delete [] cx3 ;
cx1 = new double [nr] ;
cx2 = new double [nr] ;
cx3 = new double [nr] ;
for (int i=0 ; i<nr ; i++) {
cx1[i] = (2*i+3)*(2*i+3)*(2*i+3) ;
cx2[i] = (2*i+3) ;
cx3[i] = (2*i+1)*(2*i+1) ;
}
}
// pt. sur le tableau de double resultat
double som1, som2 ;
xo[nr-1] = 0 ;
som1 = (2*nr-1)*(2*nr-1)*(2*nr-1) * tb[nr-1] ;
som2 = (2*nr-1) * tb[nr-1] ;
xo[nr-2] = som1 - (2*nr-3)*(2*nr-3)*som2 ;
for (int i = nr-3 ; i >= 0 ; i-- ) {
som1 += cx1[i] * tb[i+1] ;
som2 += cx2[i] * tb[i+1] ;
xo[i] = som1 - cx3[i] * som2 ;
} // Fin de la boucle su r
}
//--------------
// cas R_LEG ---
//--------------
void _d2sdx2_1d_r_leg(int nr, double* tb, double *xo)
{
// Variables statiques
static double* cx1 = 0x0 ;
static double* cx2 = 0x0 ;
static double* cx3 = 0x0 ;
static int nr_pre = 0 ;
// Test sur np pour initialisation eventuelle
if (nr > nr_pre) {
nr_pre = nr ;
if (cx1 != 0x0) delete [] cx1 ;
if (cx2 != 0x0) delete [] cx2 ;
if (cx3 != 0x0) delete [] cx3 ;
cx1 = new double [nr] ;
cx2 = new double [nr] ;
cx3 = new double [nr] ;
for (int i=0 ; i<nr ; i++) {
cx1[i] = (i+2)*(i+3) ;
cx2[i] = i*(i+1) ;
cx3[i] = double(i) + 0.5 ;
}
}
double som1, som2 ;
xo[nr-1] = 0 ;
som1 = (nr-1)* nr * tb[nr-1] ;
som2 = tb[nr-1] ;
if (nr > 2)
xo[nr-3] = (double(nr) - 2.5) * (som1 - (nr-3)*(nr-2)*som2) ;
for (int i = nr-5 ; i >= 0 ; i -= 2 ) {
som1 += cx1[i] * tb[i+2] ;
som2 += tb[i+2] ;
xo[i] = cx3[i]*(som1 - cx2[i] * som2) ;
} // Fin de la premiere boucle sur r
if (nr > 1) xo[nr-2] = 0 ;
if (nr > 3) {
som1 = (nr-2)*(nr-1) * tb[nr-2] ;
som2 = tb[nr-2] ;
xo[nr-4] = (double(nr) - 3.5) * (som1 - (nr-4)*(nr-3)*som2) ;
}
for (int i = nr-6 ; i >= 0 ; i -= 2 ) {
som1 += cx1[i] * tb[i+2] ;
som2 += tb[i+2] ;
xo[i] = cx3[i]*(som1 - cx2[i] * som2) ;
} // Fin de la deuxieme boucle sur r
}
//---------------
// cas R_LEGP ---
//---------------
void _d2sdx2_1d_r_legp(int nr, double* tb, double *xo)
{
// Variables statiques
static double* cx1 = 0x0 ;
static double* cx2 = 0x0 ;
static double* cx3 = 0x0 ;
static int nr_pre = 0 ;
// Test sur np pour initialisation eventuelle
if (nr > nr_pre) {
nr_pre = nr ;
if (cx1 != 0x0) delete [] cx1 ;
if (cx2 != 0x0) delete [] cx2 ;
if (cx3 != 0x0) delete [] cx3 ;
cx1 = new double [nr] ;
cx2 = new double [nr] ;
cx3 = new double [nr] ;
for (int i=0 ; i<nr ; i++) {
cx1[i] = (2*i+2)*(2*i+3) ;
cx2[i] = 2*i*2*(i+1) ;
cx3[i] = double(2*i)+ 0.5 ;
}
}
double som1, som2 ;
xo[nr-1] = 0 ;
som1 = (2*nr-2)*(2*nr-1)* tb[nr-1] ;
som2 = tb[nr-1] ;
if (nr > 1)
xo[nr-2] = (double(2*nr) - 1.5)*(som1 - 2*(nr-2)*(2*nr-1)*som2) ;
for (int i = nr-3 ; i >= 0 ; i-- ) {
som1 += cx1[i] * tb[i+1] ;
som2 += tb[i+1] ;
xo[i] = cx3[i]*(som1 - cx2[i]*som2) ;
} // Fin de la boucle sur r
}
//---------------
// cas R_LEGI --
//---------------
void _d2sdx2_1d_r_legi(int nr, double* tb, double *xo)
{
// Variables statiques
static double* cx1 = 0x0 ;
static double* cx2 = 0x0 ;
static double* cx3 = 0x0 ;
static int nr_pre = 0 ;
// Test sur np pour initialisation eventuelle
if (nr > nr_pre) {
nr_pre = nr ;
if (cx1 != 0x0) delete [] cx1 ;
if (cx2 != 0x0) delete [] cx2 ;
if (cx3 != 0x0) delete [] cx3 ;
cx1 = new double [nr] ;
cx2 = new double [nr] ;
cx3 = new double [nr] ;
for (int i=0 ; i<nr ; i++) {
cx1[i] = (2*i+3)*(2*i+4) ;
cx2[i] = (2*i+1)*(2*i+2) ;
cx3[i] = double(2*i) + 1.5 ;
}
}
// pt. sur le tableau de double resultat
double som1, som2 ;
xo[nr-1] = 0 ;
som1 = (2*nr-1)*(2*nr) * tb[nr-1] ;
som2 = tb[nr-1] ;
if (nr > 1)
xo[nr-2] = (double(nr) - 1.5)*(som1 - (2*nr-3)*(2*nr-2)*som2) ;
for (int i = nr-3 ; i >= 0 ; i-- ) {
som1 += cx1[i] * tb[i+1] ;
som2 += tb[i+1] ;
xo[i] = cx3[i]*(som1 - cx2[i] * som2) ;
} // Fin de la boucle sur r
}
// ---------------------
// La routine a appeler
//----------------------
void d2sdx2_1d(int nr, double** tb, int base_r)
{
// Routines de derivation
static void (*d2sdx2_1d[MAX_BASE])(int, double*, double *) ;
static int nap = 0 ;
// Premier appel
if (nap==0) {
nap = 1 ;
for (int i=0 ; i<MAX_BASE ; i++) {
d2sdx2_1d[i] = _d2sdx2_1d_pas_prevu ;
}
// Les routines existantes
d2sdx2_1d[R_CHEB >> TRA_R] = _d2sdx2_1d_r_cheb ;
d2sdx2_1d[R_CHEBU >> TRA_R] = _d2sdx2_1d_r_chebu ;
d2sdx2_1d[R_CHEBP >> TRA_R] = _d2sdx2_1d_r_chebp ;
d2sdx2_1d[R_CHEBI >> TRA_R] = _d2sdx2_1d_r_chebi ;
d2sdx2_1d[R_LEG >> TRA_R] = _d2sdx2_1d_r_leg ;
d2sdx2_1d[R_LEGP >> TRA_R] = _d2sdx2_1d_r_legp ;
d2sdx2_1d[R_LEGI >> TRA_R] = _d2sdx2_1d_r_legi ;
d2sdx2_1d[R_JACO02 >> TRA_R] = _d2sdx2_1d_r_jaco02 ;
}
double *result = new double[nr] ;
d2sdx2_1d[base_r](nr, *tb, result) ;
delete [] (*tb) ;
(*tb) = result ;
}
}
R_LEGP
#define R_LEGP
base de Legendre paire (rare) seulement
Definition type_parite.h:184
MAX_BASE
#define MAX_BASE
Nombre max. de bases differentes.
Definition type_parite.h:144
R_CHEBU
#define R_CHEBU
base de Chebychev ordinaire (fin), dev. en 1/r
Definition type_parite.h:180
R_JACO02
#define R_JACO02
base de Jacobi(0,2) ordinaire (finjac)
Definition type_parite.h:188
R_LEGI
#define R_LEGI
base de Legendre impaire (rare) seulement
Definition type_parite.h:186
R_CHEBI
#define R_CHEBI
base de Cheb. impaire (rare) seulement
Definition type_parite.h:170
R_LEG
#define R_LEG
base de Legendre ordinaire (fin)
Definition type_parite.h:182
TRA_R
#define TRA_R
Translation en R, used for a bitwise shift (in hex).
Definition type_parite.h:158
R_CHEB
#define R_CHEB
base de Chebychev ordinaire (fin)
Definition type_parite.h:166
R_CHEBP
#define R_CHEBP
base de Cheb. paire (rare) seulement
Definition type_parite.h:168
Lorene
Lorene prototypes.
Definition app_hor.h:64