domain_polar_nucleus_ope.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 "polar.hpp"
#include "val_domain.hpp"
#include "array_math.hpp"
namespace Kadath {
int mult_cos_1d (int, Array<double>&) ;
int mult_sin_1d (int, Array<double>&) ;
int div_sin_1d (int, Array<double>&) ;
int div_x_1d (int, Array<double>&) ;
int mult_x_1d (int, Array<double>&) ;
 
Val_domain Domain_polar_nucleus::mult_cos_theta (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
    res.base = so.base ;
    res.cf = new Array<double> (so.base.ope_1d(mult_cos_1d, 1, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_polar_nucleus::mult_sin_theta (const Val_domain& so) const {
 
    so.coef() ;
    Val_domain res(this) ;
 
    res.base= so.base ;
    res.cf = new Array<double> (so.base.ope_1d(mult_sin_1d, 1, *so.cf, res.base)) ;
    res.in_coef = true ;    
    return res ;
}
 
Val_domain Domain_polar_nucleus::div_sin_theta (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base = so.base ;    
    
    res.cf = new Array<double> (so.base.ope_1d(div_sin_1d, 1, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_polar_nucleus::div_x (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base= so.base ;
    
    res.cf = new Array<double> (so.base.ope_1d(div_x_1d, 0, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_polar_nucleus::mult_r (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base= so.base ;
    
    res.cf = new Array<double> (so.base.ope_1d(mult_x_1d, 0, *so.cf, res.base)) ;
    *res.cf *= alpha ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_polar_nucleus::div_r (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base= so.base ;
    
    res.cf = new Array<double> (so.base.ope_1d(div_x_1d, 0, *so.cf, res.base)) ;
    *res.cf /= alpha ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_polar_nucleus::srdr (const Val_domain& so) const {
  return (div_x(so.der_var(1)) / alpha / alpha) ;
}
 
Val_domain Domain_polar_nucleus::laplacian2 (const Val_domain& so, int m) const {
  Val_domain derr (so.der_var(1)/alpha) ;
  Val_domain dert (so.der_var(2)) ;
  Val_domain res (derr.der_var(1)/alpha + div_r(derr + div_r(dert.der_var(2)))) ;
  if (m!=0)
    res -= m * m * div_r(div_r(so.div_sin_theta().div_sin_theta())) ;
  return res ;
}
 
Val_domain Domain_polar_nucleus::laplacian (const Val_domain& so, int m) const {
  Val_domain derr (so.der_var(1)/alpha) ;
  Val_domain dert (so.der_var(2)) ;
  Val_domain res (derr.der_var(1)/alpha + div_r(2*derr + div_r(dert.der_var(2) + dert.mult_cos_theta().div_sin_theta()))) ;
  if (m!=0)
    res -= m * m * div_r(div_r(so.div_sin_theta().div_sin_theta())) ;
  return res ;
}
 
Val_domain Domain_polar_nucleus::der_r (const Val_domain& so) const {
  return (so.der_var(1)/alpha) ;
}
 
Val_domain Domain_polar_nucleus::dt (const Val_domain& so) const {
  return (so.der_var(2)) ;
}
 
double Domain_polar_nucleus::integrale (const Val_domain& so) const {
  double res = 0 ;
  Val_domain integrant (mult_r(so)) ;
  integrant.get_coef() ;
  Array<double> cf (integrant.get_coef()) ;
 
  int baset = (*integrant.get_base().bases_1d[1]) (0) ;
  switch (baset) {
    case COS_ODD :
    break ;
    case SIN_EVEN :
    break ;
    case COS_EVEN : {
    // Only m=0 :
    double facttheta = M_PI ;
    int baser = (*integrant.get_base().bases_1d[0]) (0) ;
    switch (baser) {
          case CHEB_EVEN : {
            for (int i=0 ; i<nbr_coefs(0) ; i++)
            res += -facttheta / (4*i*i-1)*cf(i,0) ;
            break ;
            }
          case CHEB_ODD : {
            for (int i=0 ; i<nbr_coefs(0)-1 ; i++) 
            res += (i%2==0) ? facttheta / double (2*i+2) *cf(i,0) : -facttheta/double (2*i) *cf(i,0) ;
            break ;
          }
          case LEG_EVEN : {
           res += facttheta*cf(0,0) ;
           break ;
          }
          case LEG_ODD : {
              double pm1 = 1 ;
              double pp1 = -0.5 ;
              for (int i=0 ; i<nbr_coefs(0)-1 ; i++) {
                  res += facttheta * (pm1 - pp1) / double(4*i+3) ;
                  pm1 = pp1 ;
                  pp1 *= -double(2*i+3)/double(2*i+4) ;
              }
              break ;
          }
          default :
          cerr << "Case not yet implemented in Domain_polar_nucleus::integrale" << endl ;
          abort() ;
    }
    break ;
    }
    case SIN_ODD : {
      for (int j=0 ; j<nbr_coefs(1) ; j++) {
        double facttheta = 2./double(2*j+1) ;
        int baser = (*integrant.get_base().bases_1d[0]) (0) ;
      switch (baser) {
          case CHEB_EVEN : {
            for (int i=0 ; i<nbr_coefs(0) ; i++) {
            res += -facttheta / double(4*i*i-1) * cf(i,j) ;
            }
            break ;
            }
          case CHEB_ODD : {
            res += facttheta/2. * cf(0,j);
            int signe = -1 ;
            for (int i=1 ; i<nbr_coefs(0)-1 ; i++) {
            res += facttheta *(-1. + signe * double(2*i+1))/((2*i+1)*(2*i+1)-1) * cf(i,j) ;
            signe *= -1 ;
            }
            break ;
          }   
          case LEG_EVEN : {
           res += facttheta*cf(0,j) ;
           break ;
          }
          case LEG_ODD : {
              double pm1 = 1 ;
              double pp1 = -0.5 ;
              for (int i=0 ; i<nbr_coefs(0)-1 ; i++) {
                  res += facttheta * (pm1 - pp1) / double(4*i+3)*cf(i,j) ;
                  pm1 = pp1 ;
                  pp1 *= -double(2*i+3)/double(2*i+4) ;
              }
              break ;
          }
          default :
          cerr << "Case not yet implemented in Domain_polar_nucleus::integrale" << endl ;
          abort() ;
          }
 
    }
    break ;
    }
    default : 
      cerr << "Case not yet implemented in Domain_polar_nucleus::integrale" << endl ;
      abort() ;
  }
  // Phi contribution :
  //res *= 2*M_PI*alpha ;  
  res *= alpha ;
  return res ;
}
 
double Domain_polar_nucleus::integ_volume (const Val_domain& so) const {
  return integrale(so) ;
}
 
}