domain_shell.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 "utilities.hpp"
#include "spheric.hpp"
#include "point.hpp"
#include "val_domain.hpp"
namespace Kadath {
// Standard constructor
Domain_shell::Domain_shell (int num, int ttype, double rint, double rext, const Point& cr, const Dim_array& nbr) : Domain(num, ttype, nbr),
                             alpha((rext-rint)/2.), beta((rext+rint)/2.), center(cr) {
    
     assert (nbr.get_ndim()==3) ;
     assert (cr.get_ndim()==3) ;    // Affectation de type_point :
     do_coloc() ;
 
}
 
 
// Constructor by copy
Domain_shell::Domain_shell (const Domain_shell& so) : Domain(so), alpha(so.alpha), 
                        beta(so.beta), center(so.center){}
 
 
 
Domain_shell::Domain_shell (int num, FILE* fd) : Domain(num, fd), center(fd) {
    fread_be (&alpha, sizeof(double), 1, fd) ;
    fread_be (&beta, sizeof(double), 1, fd) ;
    do_coloc() ;
}
 
// Destructor
Domain_shell::~Domain_shell() {}
 
void Domain_shell::save (FILE* fd) const {
    nbr_points.save(fd) ;
    nbr_coefs.save(fd) ;
    fwrite_be (&ndim, sizeof(int), 1, fd) ;
    fwrite_be (&type_base, sizeof(int), 1, fd) ;    
    center.save(fd) ;
    fwrite_be (&alpha, sizeof(double), 1, fd) ; 
    fwrite_be (&beta, sizeof(double), 1, fd) ;
}
 
ostream& Domain_shell::print (ostream& o) const {
  o << "Shell" << endl ;
  o <<  beta-alpha << " < r < " << beta+alpha << endl ;
  o << "Center  = " << center << endl ;
  o << "Nbr pts = " << nbr_points << endl ;
  o << endl ;
  return o ;
}
 
 
 
Val_domain Domain_shell::der_normal (const Val_domain& so, int bound) const {
 
    Val_domain res (so.der_var(1)) ;
    switch (bound) {
        case OUTER_BC :
            res /= alpha ;
            break ;
        case INNER_BC :
            res /= alpha ;
            break ;
        default:
            cerr << "Unknown boundary case in Domain_shell::der_normal" << endl ;
            abort() ;
        }
return res ;
}
 
// Computes the Cartesian coordinates
void Domain_shell::do_absol () const  {
    for (int i=0 ; i<3 ; i++)
       assert (coloc[i] != 0x0) ;
    for (int i=0 ; i<3 ; i++)
       assert (absol[i] == 0x0) ;
    for (int i=0 ; i<3 ; i++) {
       absol[i] = new Val_domain(this) ;
       absol[i]->allocate_conf() ;
       }
    Index index (nbr_points) ;
 
    do  {
        absol[0]->set(index) = (alpha* ((*coloc[0])(index(0))) +beta)*
         sin((*coloc[1])(index(1)))*cos((*coloc[2])(index(2))) + center(1) ;
        absol[1]->set(index) = (alpha* ((*coloc[0])(index(0))) +beta) *
         sin((*coloc[1])(index(1)))*sin((*coloc[2])(index(2))) + center(2) ;
        absol[2]->set(index) = (alpha* ((*coloc[0])(index(0))) + beta) * cos((*coloc[1])(index(1))) + center(3) ;
            }
    while (index.inc())  ;
}
 
// Computes the radius
void Domain_shell::do_radius () const  {
    for (int i=0 ; i<3 ; i++)
       assert (coloc[i] != 0x0) ;
    assert (radius == 0x0) ;
    radius = new Val_domain(this) ;
    radius->allocate_conf() ;
    Index index (nbr_points) ;
    do 
        radius->set(index) = alpha* ((*coloc[0])(index(0))) + beta ;
    while (index.inc())  ;
}
 
// Computes the Cartesian coordinates
void Domain_shell::do_cart () const  {
    for (int i=0 ; i<3 ; i++)
       assert (coloc[i] != 0x0) ;
    for (int i=0 ; i<3 ; i++)
       assert (cart[i] == 0x0) ;
    for (int i=0 ; i<3 ; i++) {
       cart[i] = new Val_domain(this) ;
       cart[i]->allocate_conf() ;
       }
    Index index (nbr_points) ;
 
    do  {
        cart[0]->set(index) = (alpha* ((*coloc[0])(index(0))) +beta)*
         sin((*coloc[1])(index(1)))*cos((*coloc[2])(index(2))) + center(1) ;
        cart[1]->set(index) = (alpha* ((*coloc[0])(index(0))) +beta) *
         sin((*coloc[1])(index(1)))*sin((*coloc[2])(index(2))) + center(2) ;
        cart[2]->set(index) = (alpha* ((*coloc[0])(index(0))) + beta) * cos((*coloc[1])(index(1))) + center(3) ;
            }
    while (index.inc())  ;
}
 
// Computes the Cartesian coordinates
void Domain_shell::do_cart_surr () const  {
    for (int i=0 ; i<3 ; i++)
       assert (coloc[i] != 0x0) ;
    for (int i=0 ; i<3 ; i++)
       assert (cart_surr[i] == 0x0) ;
    for (int i=0 ; i<3 ; i++) {
       cart_surr[i] = new Val_domain(this) ;
       cart_surr[i]->allocate_conf() ;
       }
    Index index (nbr_points) ;
 
    do  {
        cart_surr[0]->set(index) = sin((*coloc[1])(index(1)))*cos((*coloc[2])(index(2))) ;
        cart_surr[1]->set(index) = sin((*coloc[1])(index(1)))*sin((*coloc[2])(index(2))) ;
        cart_surr[2]->set(index) =  cos((*coloc[1])(index(1))) ;
            }
    while (index.inc())  ;
}
 
// Check if a point is inside this domain
bool Domain_shell::is_in (const Point& xx, double prec) const {
 
    assert (xx.get_ndim()==3) ;
    
    double x_loc = xx(1) - center(1) ;
    double y_loc = xx(2) - center(2) ;
    double z_loc = xx(3) - center(3) ;
    double air_loc = sqrt (x_loc*x_loc + y_loc*y_loc + z_loc*z_loc) ;
 
    bool res = ((air_loc / (alpha+beta) - 1  <= prec) && (air_loc/ (beta-alpha) - 1 >= -prec)) ? true : false ;
    return res ;
}
 
//Computes the numerical coordinates, as a function of the absolute ones.
const Point Domain_shell::absol_to_num(const Point& abs) const {
 
    assert (is_in(abs)) ;
    Point num(3) ;
    
    double x_loc = abs(1) - center(1) ;
    double y_loc = abs(2) - center(2) ;
    double z_loc = abs(3) - center(3) ;
    double air = sqrt(x_loc*x_loc+y_loc*y_loc+z_loc*z_loc) ;
    num.set(1) = (air-beta)/alpha ;
    double rho = sqrt(x_loc*x_loc+y_loc*y_loc) ;
    
    if (rho==0) {
        // On the axis ?
        num.set(2) = (z_loc>=0) ? 0 : M_PI ;
        num.set(3) = 0 ;
    }
    else {
        num.set(2) = atan(rho/z_loc) ;
        num.set(3) = atan2 (y_loc, x_loc) ;
        }   
    
    if (num(2) <0)
        num.set(2) = M_PI + num(2) ;
 
    return num ;
}
 
// Convert absolute coordinates to numerical ones
const Point Domain_shell::absol_to_num_bound(const Point& abs, int bound) const {
 
    assert ((bound==OUTER_BC) || (bound==INNER_BC)) ;
    assert (is_in(abs, 1e-3)) ;
    Point num(3) ;
    
    double x_loc = abs(1) - center(1) ;
    double y_loc = abs(2) - center(2) ;
    double z_loc = abs(3) - center(3) ;
    
    switch (bound) {
      case INNER_BC:
        num.set(1) = -1 ;
        break ;
      case OUTER_BC:
        num.set(1) = 1 ;
        break ;
      default:
          cerr << "unknown boundary in Domain_shell::absol_to_num" << endl ;
          abort() ;
    }
    
    double rho = sqrt(x_loc*x_loc+y_loc*y_loc) ;
    
    if (rho==0) {
        // Sur l'axe
        num.set(2) = (z_loc>=0) ? 0 : M_PI ;
        num.set(3) = 0 ;
    }
    else {
        num.set(2) = atan(rho/z_loc) ;
        num.set(3) = atan2 (y_loc, x_loc) ;
        }   
    
    if (num(2) <0)
        num.set(2) = M_PI + num(2) ;
    
    return num ;
}
double coloc_leg (int, int) ;
void Domain_shell::do_coloc () {
 
    switch (type_base) {
        case CHEB_TYPE:
            nbr_coefs = nbr_points ;
            nbr_coefs.set(2) += 2 ;
            del_deriv() ;
            for (int i=0 ; i<ndim ; i++)
                coloc[i] = new Array<double> (nbr_points(i)) ;
            for (int i=0 ; i<nbr_points(0) ; i++)
                coloc[0]->set(i) = -cos(M_PI*i/(nbr_points(0)-1)) ;
            for (int j=0 ; j<nbr_points(1) ; j++)
                coloc[1]->set(j) = M_PI/2.*j/(nbr_points(1)-1) ;
            for (int k=0 ; k<nbr_points(2) ; k++)
                coloc[2]->set(k) = M_PI*2.*k/nbr_points(2) ;
            break ;
        case LEG_TYPE:
            nbr_coefs = nbr_points ;
            nbr_coefs.set(2) += 2 ;
            del_deriv() ;
            for (int i=0 ; i<ndim ; i++) 
                coloc[i] = new Array<double> (nbr_points(i)) ;
            for (int i=0 ; i<nbr_points(0) ; i++)
                coloc[0]->set(i) = coloc_leg(i, nbr_points(0)) ;
            for (int j=0 ; j<nbr_points(1) ; j++)
                coloc[1]->set(j) = M_PI/2.*j/(nbr_points(1)-1) ;
            for (int k=0 ; k<nbr_points(2) ; k++)
                coloc[2]->set(k) = M_PI*2.*k/nbr_points(2) ;
            break ;
        default :
            cerr << "Unknown type of basis in Domain_shell::do_coloc" << endl ;
            abort() ;
    }
}
 
// standard base for a symetric function in z, using Chebyshev
void Domain_shell::set_cheb_base(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == CHEB_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? COS_EVEN : SIN_ODD ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = CHEB ;
         }
    }   
}
 
void Domain_shell::set_cheb_base_with_m(Base_spectral& base, int mquant) const  {
 
    int m ;
 
    assert (type_base == CHEB_TYPE) ;
 
    base.allocate(nbr_coefs) ;
    
    if (mquant%2==0) {
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? COS_EVEN : SIN_ODD ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = CHEB ;
         }
    }
    }
    else   {
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? SIN_ODD : COS_EVEN ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = CHEB ;
         }
    }
    }
}
 
void Domain_shell::set_cheb_r_base(Base_spectral& base) const  {
  set_cheb_base(base) ;
}
 
void Domain_shell::set_legendre_r_base(Base_spectral& base) const  {
  set_legendre_base(base) ;
}
  
// standard base for a anti-symetric function in z, using Chebyshev
void Domain_shell::set_anti_cheb_base(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == CHEB_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? COS_ODD : SIN_EVEN ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = CHEB ;
         }
    }   
}
 
void Domain_shell::set_cheb_base_r_spher(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == CHEB_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? COS_EVEN : SIN_ODD ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = CHEB ;
         }
    }   
}
 
void Domain_shell::set_cheb_base_t_spher(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == CHEB_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? SIN_EVEN : COS_ODD ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = CHEB ;
         }
    }   
}
 
void Domain_shell::set_cheb_base_p_spher(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == CHEB_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? SIN_ODD : COS_EVEN ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = CHEB ;
         }
    }   
}
void Domain_shell::set_cheb_base_r_mtz(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == CHEB_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? COS_EVEN : SIN_ODD ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = CHEB ;
         }
    }   
}
 
void Domain_shell::set_cheb_base_t_mtz(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == CHEB_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? SIN_ODD : COS_EVEN ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = CHEB ;
         }
    }   
}
 
void Domain_shell::set_cheb_base_p_mtz(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == CHEB_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? SIN_EVEN: COS_ODD ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = CHEB ;
         }
    }   
}
 
// standard base for a symetric function in z, using Legendre
void Domain_shell::set_legendre_base(Base_spectral& base) const {
 
    int m ;
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    base.def = true ;    
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? COS_EVEN : SIN_ODD ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = LEG ;
         }
    }
}
 
// standard base for a anti-symetric function in z, using Legendre
void Domain_shell::set_anti_legendre_base(Base_spectral& base) const {
 
    int m ;
    assert (type_base == LEG_TYPE) ;
 
    base.allocate(nbr_coefs) ;
    
    base.def = true ;    
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? COS_ODD : SIN_EVEN ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = LEG ;
         }
    }
}
 
void Domain_shell::set_legendre_base_r_spher(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == LEG_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? COS_EVEN : SIN_ODD ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = LEG ;
         }
    }   
}
 
void Domain_shell::set_legendre_base_t_spher(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == LEG_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? SIN_EVEN : COS_ODD ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = LEG ;
         }
    }   
}
 
void Domain_shell::set_legendre_base_p_spher(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == LEG_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? SIN_ODD : COS_EVEN ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = LEG ;
         }
    }   
}
 
void Domain_shell::set_legendre_base_r_mtz(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == LEG_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? COS_EVEN : SIN_ODD ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = LEG ;
         }
    }   
}
 
void Domain_shell::set_legendre_base_t_mtz(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == LEG_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? SIN_ODD : COS_EVEN ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = LEG ;
         }
    }   
}
 
void Domain_shell::set_legendre_base_p_mtz(Base_spectral& base) const  {
 
    int m ;
 
    assert (type_base == LEG_TYPE) ;
 
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    base.bases_1d[2]->set(0) = COSSIN ;
    
    Index index (base.bases_1d[0]->get_dimensions()) ;
    
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
            m = (k%2==0) ? k/2 : (k-1)/2 ;
        base.bases_1d[1]->set(k) = (m%2==0) ? SIN_EVEN : COS_ODD ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            index.set(0) = j ; index.set(1) = k ;
            base.bases_1d[0]->set(index) = LEG ;
         }
    }   
}
 
// Computes the derivatives with respect to XYZ as a function of the numerical ones.
void Domain_shell::do_der_abs_from_der_var(const Val_domain *const *const der_var, Val_domain **const der_abs) const {
 
    // d/dx :
    Val_domain sintdr (der_var[0]->mult_sin_theta()/alpha) ;    
    Val_domain dtsr (*der_var[1]/get_radius()) ;
    dtsr.set_base() = der_var[1]->get_base() ;
    Val_domain dpsr (*der_var[2]/get_radius()) ;    
    dpsr.set_base() = der_var[2]->get_base() ;
    Val_domain costdtsr (dtsr.mult_cos_theta()) ;
 
    Val_domain dpsrssint (dpsr.div_sin_theta()) ;
    der_abs[0] = new Val_domain ((sintdr+costdtsr).mult_cos_phi() - dpsrssint.mult_sin_phi()) ;
 
    // d/dy :
    der_abs[1] = new Val_domain ((sintdr+costdtsr).mult_sin_phi() + dpsrssint.mult_cos_phi()) ;
    // d/dz :
    der_abs[2] = new Val_domain (der_var[0]->mult_cos_theta()/alpha - dtsr.mult_sin_theta()) ;
}
 
// Rules for the multiplication of two basis.
Base_spectral Domain_shell::mult (const Base_spectral& a, const Base_spectral& b) const {
 
    assert (a.ndim==3) ;
    assert (b.ndim==3) ;
    
    Base_spectral res(3) ;
    bool res_def = true ;
 
    if (!a.def)
        res_def=false ;
    if (!b.def)
        res_def=false ;
        
    if (res_def) {
 
    // Base in phi :
    res.bases_1d[2] = new Array<int> (a.bases_1d[2]->get_dimensions()) ;
    switch ((*a.bases_1d[2])(0)) {
        case COSSIN:
            switch ((*b.bases_1d[2])(0)) {
                case COSSIN:
                    res.bases_1d[2]->set(0) = COSSIN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        default:
            res_def = false ;
            break ;
    }
 
    // Bases in theta :
    // On check l'alternance :
    Index index_1 (a.bases_1d[1]->get_dimensions()) ;
    res.bases_1d[1] = new Array<int> (a.bases_1d[1]->get_dimensions()) ;
    do {
    switch ((*a.bases_1d[1])(index_1)) {
        case COS_EVEN:
            switch ((*b.bases_1d[1])(index_1)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? COS_EVEN : SIN_ODD ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? COS_ODD : SIN_EVEN ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? SIN_EVEN : COS_ODD ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? SIN_ODD : COS_EVEN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case COS_ODD:
            switch ((*b.bases_1d[1])(index_1)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? COS_ODD : SIN_EVEN ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? COS_EVEN : SIN_ODD ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? SIN_ODD : COS_EVEN ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? SIN_EVEN : COS_ODD ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case SIN_EVEN:
            switch ((*b.bases_1d[1])(index_1)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? SIN_EVEN : COS_ODD ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? SIN_ODD : COS_EVEN ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? COS_EVEN : SIN_ODD ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? COS_ODD : SIN_EVEN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case SIN_ODD:
            switch ((*b.bases_1d[1])(index_1)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? SIN_ODD : COS_EVEN ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? SIN_EVEN : COS_ODD ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? COS_ODD : SIN_EVEN ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) = (index_1(0)%4<2) ? COS_EVEN : SIN_ODD ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        default:
            res_def = false ;
            break ;
        }
    }
    while (index_1.inc()) ;
 
 
    // Base in r :
    Index index_0 (a.bases_1d[0]->get_dimensions()) ;
    res.bases_1d[0] = new Array<int> (a.bases_1d[0]->get_dimensions()) ;
    do {
    switch ((*a.bases_1d[0])(index_0)) {
        case CHEB:
            switch ((*b.bases_1d[0])(index_0)) {
                case CHEB:
                    res.bases_1d[0]->set(index_0) = CHEB ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case LEG:
            switch ((*b.bases_1d[0])(index_0)) {
                case LEG:
                    res.bases_1d[0]->set(index_0) = LEG ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        default:
            res_def = false ;
            break ;
        }
    }
    while (index_0.inc()) ;
    }
        
    if (!res_def) 
        for (int dim=0 ; dim<a.ndim ; dim++)
            if (res.bases_1d[dim]!= 0x0) {
                delete res.bases_1d[dim] ;
                res.bases_1d[dim] = 0x0 ;
                }
    res.def = res_def ;
    return res ;
}
 
int Domain_shell::give_place_var (char* p) const {
    int res = -1 ;
    if (strcmp(p,"R ")==0)
    res = 0 ;
    if (strcmp(p,"T ")==0)
    res = 1 ;
    if (strcmp(p,"P ")==0)
    res = 2 ;
    return res ;
}
 
double Domain_shell::integ(const Val_domain& so, int bound) const
{
   Val_domain rrso (mult_r(mult_r(mult_sin_theta(so)))) ;
    
    double res = 0 ;
    if (!so.check_if_zero())
    {
 
      int baset = (*rrso.get_base().bases_1d[1]) (0) ;
      Index pcf (nbr_coefs) ;
    switch (baset) {
      case COS_ODD :
    break ;
    case SIN_EVEN :
      break ;
    case COS_EVEN : {
    res += M_PI*val_boundary(bound, rrso, pcf) ;
    break ;
    }
    case SIN_ODD : {
      for (int j=0 ; j<nbr_coefs(1) ; j++) {
        pcf.set(1) = j ;
        res += 2./(2*double(j)+1) * val_boundary(bound, rrso, pcf) ;
      }
      break ;
    }
    
    default : 
      cerr << "Case not yet implemented in Domain_shell::integ" << endl ;
      abort() ;
  }
    res *= 2*M_PI ;
    }
    return res ;
}
}