div_x_1d.cpp

/*
    Copyright 2017 Philippe Grandclement
 
    This file is part of Kadath.
 
    Kadath 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 3 of the License, or
    (at your option) any later version.
 
    Kadath 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 Kadath.  If not, see <http://www.gnu.org/licenses/>.
*/
 
#include "headcpp.hpp"
#include "base_spectral.hpp"
#include "matrice.hpp"
#include "array.hpp"
namespace Kadath {
int div_x_1d_pasprevu (Array<double>&) {
    cout << "div_x_1d not implemented." << endl ;
    abort() ;
} 
 
 
int div_x_1d_cheb_even (Array<double>& so) {
    assert (so.get_ndim()==1) ;
    int nr = so.get_size(0) ;
    Array<double> res (nr) ;
 
    int sgn = 1 ;
    res.set(nr-1) = 0 ;
    double somme = 2*sgn*so(nr-1) ;
    res.set(nr-2) = somme ;
    for (int i=nr-3 ; i>=0 ; i--) {
        sgn *= -1 ;
        somme += 2*sgn*so(i+1) ;
        res.set(i) = somme ;
    }
    for (int i=0 ; i<nr ; i+=2)
        res.set(i) *= -1 ;
 
    so = res ;
    return CHEB_ODD ;
}
 
int div_x_1d_cheb_odd (Array<double>& so) {
    assert (so.get_ndim()==1) ;
    int nr = so.get_size(0) ;
    Array<double> res (nr) ;
 
    int sgn = 1 ;
    res.set(nr-1) = 0 ;
    double somme = 2*sgn*so(nr-2) ;
    res.set(nr-2) = somme ;
    for (int i=nr-3 ; i>=0 ; i--) {
        sgn *= -1 ;
        somme += 2*sgn*so(i) ;
        res.set(i) = somme ;
    }
    for (int i=0 ; i<nr ; i+=2)
        res.set(i) *= -1 ;
    res.set(0) *= 0.5 ; 
 
    so = res ;
    return CHEB_EVEN ;
}
 
int div_x_1d_leg_odd (Array<double>& so) {
    assert (so.get_ndim()==1) ;
    int nr = so.get_size(0) ;
    Array<double> res (nr) ;
    
    double coef ;
    for (int i=0 ; i<nr ; i++) {
            coef =  double(4*i+1)/double(2*i+1) ;
            res.set(i) = coef * so(i) ;
        for (int j=i+1 ; j<nr ; j++) {
            coef *= -double(2*j)/double(2*j+1) ;
            res.set(i) += coef*so(j) ;
        }
    }
    
    so = res ;
    return LEG_EVEN ;
}
 
int div_x_1d_leg_even (Array<double>& so) {
    assert (so.get_ndim()==1) ;
    int nr = so.get_size(0) ;
    Array<double> res (nr) ;
    res = 0 ;
    
    double coef ;
    for (int i=0 ; i<nr-1 ; i++) {
            coef =  double(4*i+3)/double(2*i+2) ;
            res.set(i) = coef * so(i+1) ;
        for (int j=i+2 ; j<nr ; j++) {
            coef *= -double(2*j-1)/double(2*j) ;
            res.set(i) += coef*so(j) ;
        }
    }
    
    so = res ;
    return LEG_ODD ;
}
 
int div_x_1d (int base, Array<double>& so) {
    static int (*div_x_1d[NBR_MAX_BASE])(Array<double>&) ;
    static bool premier_appel = true ;
    
    // Premier appel
    if (premier_appel) {
    premier_appel = false ;
 
    for (int i=0; i<NBR_MAX_BASE; i++)
        div_x_1d[i] = div_x_1d_pasprevu ;
 
    div_x_1d[CHEB_EVEN] = div_x_1d_cheb_even ;
    div_x_1d[CHEB_ODD] = div_x_1d_cheb_odd ;
    div_x_1d[LEG_EVEN] = div_x_1d_leg_even ;
    div_x_1d[LEG_ODD] = div_x_1d_leg_odd ;
    }
    
        return div_x_1d[base](so) ;
}}