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/*
* Copyright (c) 2004 Jerome Novak
*
* 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 val_dern_1d_C[] = "$Header: /cvsroot/Lorene/C++/Source/Non_class_members/Operators/val_dern_1d.C,v 1.2 2014/10/13 08:53:27 j_novak Exp $" ;
/*
* $Id: val_dern_1d.C,v 1.2 2014/10/13 08:53:27 j_novak Exp $
* $Log: val_dern_1d.C,v $
* Revision 1.2 2014/10/13 08:53:27 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.1 2004/02/17 09:21:39 j_novak
* New functions for calculating values of the derivatives of a function
* using its Chebyshev coefficients.
*
*
* $Header: /cvsroot/Lorene/C++/Source/Non_class_members/Operators/val_dern_1d.C,v 1.2 2014/10/13 08:53:27 j_novak Exp $
*
*/
#include "type_parite.h"
#include "tbl.h"
/*
* Functions computing value of f^(n) at boundaries of the interval [-1, 1],
* using the Chebyshev expansion of f. Note: n=0 works too.
*
* Input : 1-dimensional Tbl containing the Chebyshev coefficients of f.
* int base : base of spectral expansion.
*
* Output : double : the value of the n-th derivative of f at x=+/- 1.
*
*/
namespace Lorene {
double val1_dern_1d(int n, const Tbl& tb, int base_r)
{
//This function should be OK for any radial base
assert ( (base_r == R_CHEB) || (base_r == R_CHEBI) || (base_r == R_CHEBP) ||
(base_r == R_CHEBU) ) ;
assert (n>=0) ;
assert (tb.get_ndim() == 1) ;
int nr = tb.get_dim(0) ;
double resu = 0. ;
int n_ini = ( (base_r == R_CHEBP) || (base_r == R_CHEBI) ) ? n / 2 : n ;
double *tbi = &tb.t[n_ini] ;
for (int i=n_ini; i<nr; i++) {
double fact = 1. ;
int ii = i ;
if (base_r == R_CHEBP) ii *= 2 ;
if (base_r == R_CHEBI) ii = 2*i + 1 ;
for (int j=0; j<n; j++)
fact *= double(ii*ii - j*j)/double(2*j + 1) ;
resu += fact * (*tbi) ;
tbi++ ;
}
return resu ;
}
double valm1_dern_1d(int n, const Tbl& tb, int base_r)
{
//This function should be OK for any radial base
assert ( (base_r == R_CHEB) || (base_r == R_CHEBI) || (base_r == R_CHEBP) ||
(base_r == R_CHEBU) ) ;
assert (n>=0) ;
assert (tb.get_ndim() == 1) ;
int nr = tb.get_dim(0) ;
double resu = 0. ;
double parite, fac ;
int n_ini ;
switch (base_r) {
case R_CHEBP:
n_ini = n / 2 ;
parite = 1 ;
fac = (n%2 == 0 ? 1 : -1) ;
break ;
case R_CHEBI:
n_ini = n / 2 ;
fac = (n%2 == 0 ? -1 : 1) ;
parite = 1 ;
break ;
default:
n_ini = n ;
parite = -1 ;
fac = 1 ;
break ;
}
double *tbi = &tb.t[n_ini] ;
for (int i=n_ini; i<nr; i++) {
double fact = fac ;
int ii = i ;
if (base_r == R_CHEBP) ii *= 2 ;
if (base_r == R_CHEBI) ii = 2*i + 1 ;
for (int j=0; j<n; j++)
fact *= double(ii*ii - j*j)/double(2*j + 1) ;
resu += fact * (*tbi) ;
fac *= parite ;
tbi++ ;
}
return resu ;
}
}
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