mult_xm1_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 "base_spectral.hpp"
#include "headcpp.hpp"
#include "matrice.hpp"
#include "array.hpp"
 
namespace Kadath {
int mult_xm1_1d_pasprevu (Array<double>&) {
    cout << "mult_xm1_1d not implemented." << endl ;
    abort() ;
} 
 
 
int mult_xm1_1d_cheb (Array<double>& so) {
    assert (so.get_ndim()==1) ;
    int nr = so.get_size(0) ;
    Array<double> res (nr) ;
    
    res.set(0) = -so(0) + 0.5*so(1) ;
    res.set(1) = so(0) - so(1) + 0.5*so(2) ;
    for (int i=2 ; i<nr-1 ; i++)
        res.set(i) = 0.5*so(i-1) - so(i) + 0.5*so(i+1) ;
    res.set(nr-1) = 0.5*so(nr-2) - so(nr-1) ;
 
    so = res ;
    return CHEB ;
}
 
int mult_xm1_1d_leg (Array<double>& so) {
    assert (so.get_ndim()==1) ;
    int nr = so.get_size(0) ;
    Array<double> res (nr) ;
    
    res.set(0) = -so(0) + so(1)/3. ;
    for (int i=1 ; i<nr-1 ; i++)
        res.set(i) = double(i)/double(2*i-1)*so(i-1) - so(i) + double(i+1)/double(2*i+3)*so(i+1) ;
    res.set(nr-1) = double(nr-1)/double(2*nr-3)*so(nr-2) - so(nr-1) ;
    
    so = res ;
    return LEG ;
}
 
int mult_xm1_1d (int base, Array<double>& so) {
    static int (*mult_xm1_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++)
        mult_xm1_1d[i] = mult_xm1_1d_pasprevu ;
 
    mult_xm1_1d[CHEB] = mult_xm1_1d_cheb ;
    mult_xm1_1d[LEG] = mult_xm1_1d_leg ;;
    }
    
        return mult_xm1_1d[base](so) ;
}}