domain_compact_symphi.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_symphi.hpp"
#include "array_math.hpp"
#include "val_domain.hpp"
namespace Kadath {
// Standard constructor
Domain_compact_symphi::Domain_compact_symphi (int num, int ttype, double r, const Point& cr, const Dim_array& nbr) : Domain(num, ttype, nbr), alpha(-0.5/r), 
                                center(cr) {
    
     assert (nbr.get_ndim()==3) ;
     assert (cr.get_ndim()==3) ;
     do_coloc() ;
 
}
 
// Copy constructor
Domain_compact_symphi::Domain_compact_symphi (const Domain_compact_symphi& so) : Domain(so), alpha(so.alpha), center(so.center){}
 
 
Domain_compact_symphi::Domain_compact_symphi (int num, FILE* fd) : Domain(num, fd), center(fd) {
    fread_be (&alpha, sizeof(double), 1, fd) ;
    do_coloc() ;
}
 
// Destructor
Domain_compact_symphi::~Domain_compact_symphi() {}
 
ostream& Domain_compact_symphi::print (ostream& o) const {
  o << "Compactified domain sym phi" << endl ;
  o << "Rmin    = " << -0.5/alpha << endl ;
  o << "Center  = " << center << endl ;
  o << "Nbr pts = " << nbr_points << endl ;
  o << endl ;
  return o ;
}
 
void Domain_compact_symphi::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) ;
}
 
 
Val_domain Domain_compact_symphi::der_normal (const Val_domain& so, int bound) const {
 
    Val_domain res (so.der_var(1)) ;
    switch (bound) {
        case INNER_BC :
            res = res.mult_xm1() ;
            res = res.mult_xm1() ;
            res *= -alpha ;
            break ;
        case OUTER_BC :
            res = res.mult_xm1() ;
            res = res.mult_xm1() ;
            res *= -alpha ;
            break ;
        default:
            cerr << "Unknown boundary case in Domain_compact_symphi::der_normal" << endl ;
            abort() ;
        }
return res ;
}
 
double Domain_compact_symphi::integ (const Val_domain& so, int bound) const {
    double res = 0 ;
 
    if (bound!=OUTER_BC) {
      cerr << "Domain_compact_symphi::integ only defined for r=infty yet..." << endl ;
      abort() ;
    }
 
    int baset = (*so.base.bases_1d[1]) (0) ;
    if (baset != COS_EVEN) {
        // Odd function
        return res ;
    }
    else {
    
        Val_domain auxi (so.div_xm1()) ;
        auxi = auxi.div_xm1() ;
        auxi /= alpha * alpha ;
        auxi.coef() ;
 
        //Loop on theta :
        Index pos (get_nbr_coefs()) ;
        pos.set(2) = 0 ;
        for (int j=0 ; j<nbr_coefs(1) ; j++) {
            pos.set(1) = j ;
            double fact_tet = 2./double(1-4*j*j) ;
            // Loop on r :
            for (int i=0 ; i<nbr_coefs(0) ; i++) {
                pos.set(0) = i ;
                res += fact_tet*(*auxi.cf)(pos) ;
            }
        }
        return res*2*M_PI ;
    }
}
 
// Computes the Cartesian coordinates
void Domain_compact_symphi::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) = (1./alpha/ ((*coloc[0])(index(0))-1)) *
            sin((*coloc[1])(index(1)))*cos((*coloc[2])(index(2))) + center(1) ;
        absol[1]->set(index) = (1./alpha/ ((*coloc[0])(index(0))-1)) *
            sin((*coloc[1])(index(1)))*sin((*coloc[2])(index(2))) + center(2) ;
        absol[2]->set(index) = (1./alpha/ ((*coloc[0])(index(0))-1)) * cos((*coloc[1])(index(1))) +
                     center(3) ;
            }
    while (index.inc())  ;  
}
 
// Computes the radius
void Domain_compact_symphi::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) = 1./alpha/ ((*coloc[0])(index(0))-1) ;
    while (index.inc())  ;
}
 
// Computes the Cartesian coordinates
void Domain_compact_symphi::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) = (1./alpha/ ((*coloc[0])(index(0))-1)) *
            sin((*coloc[1])(index(1)))*cos((*coloc[2])(index(2))) + center(1) ;
        cart[1]->set(index) = (1./alpha/ ((*coloc[0])(index(0))-1)) *
            sin((*coloc[1])(index(1)))*sin((*coloc[2])(index(2))) + center(2) ;
        cart[2]->set(index) = (1./alpha/ ((*coloc[0])(index(0))-1)) * cos((*coloc[1])(index(1))) +
                     center(3) ;
            }
    while (index.inc())  ;  
 
    switch (type_base) {
        case CHEB_TYPE:
            set_cheb_base_forx_cart(cart[0]->set_base()) ;
            set_cheb_base_fory_cart(cart[1]->set_base()) ;
            set_cheb_base_forz_cart(cart[2]->set_base()) ;
            break ;
        case LEG_TYPE:
            set_legendre_base_forx_cart(cart[0]->set_base()) ;
            set_legendre_base_fory_cart(cart[1]->set_base()) ;
            set_legendre_base_forz_cart(cart[2]->set_base()) ;
            break ; 
        default :
            cerr << "Unknown type of basis in Domain_compact_symphi::do_cart" << endl ;
            abort() ;
    }
}
 
// Computes the Cartesian coordinates ovzr radius
void Domain_compact_symphi::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())  ;  
 
    switch (type_base) {
        case CHEB_TYPE:
            set_cheb_base_forx_cart(cart_surr[0]->set_base()) ;
            set_cheb_base_fory_cart(cart_surr[1]->set_base()) ;
            set_cheb_base_forz_cart(cart_surr[2]->set_base()) ;
            break ;
        case LEG_TYPE:
            set_legendre_base_forx_cart(cart_surr[0]->set_base()) ;
            set_legendre_base_fory_cart(cart_surr[1]->set_base()) ;
            set_legendre_base_forz_cart(cart_surr[2]->set_base()) ;
            break ; 
        default :
            cerr << "Unknown type of basis in Domain_compact_symphi::do_cart_surr" << endl ;
            abort() ;
    }
}
 
// Is inside ?
bool Domain_compact_symphi::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 >= -0.5/alpha-prec) ? true : false ;
    return res ;
}
 
// Converts the absolute coordinates to the numerical ones.
const Point Domain_compact_symphi::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) = 1. + 1./air/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_compact_symphi::absol_to_num_bound(const Point& abs, int bound) const {
 
    assert (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) ;
    num.set(1) = -1 ;
    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_compact_symphi::do_coloc () {
 
    switch (type_base) {
        case CHEB_TYPE:
            nbr_coefs = nbr_points ;
            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)-1)  ;
            break ;
        case LEG_TYPE:
            nbr_coefs = nbr_points ;
            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)-1)  ;
            break ;
        default :
            cerr << "Unknown type of basis in Domain_compact_symphi::do_coloc" << endl ;
            abort() ;
    }
}
 
 
// Base for a function symetric in z, using Chebyshev
void Domain_compact_symphi::set_cheb_base(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = COS_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_cheb_base_r_spher(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = SIN_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_cheb_base_t_spher(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = SIN_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_cheb_base_p_spher(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = COS_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_cheb_base_x_cart(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = SIN_ODD ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_cheb_base_y_cart(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = COS_ODD ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_cheb_base_z_cart(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = SIN_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_cheb_base_forx_cart(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = COS_ODD ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_cheb_base_fory_cart(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = SIN_ODD ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_cheb_base_forz_cart(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = COS_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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 ;
         }
    }
}
 
// Base for a function symetric in z, using Legendre
void Domain_compact_symphi::set_legendre_base(Base_spectral& base) const {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = COS_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_legendre_base_r_spher(Base_spectral& base) const {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = SIN_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_legendre_base_t_spher(Base_spectral& base) const {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = SIN_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_legendre_base_p_spher(Base_spectral& base) const {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = COS_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_legendre_base_x_cart(Base_spectral& base) const {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = SIN_ODD ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_legendre_base_y_cart(Base_spectral& base) const {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = COS_ODD ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_legendre_base_z_cart(Base_spectral& base) const {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = SIN_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_legendre_base_forx_cart(Base_spectral& base) const {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = COS_ODD ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_legendre_base_fory_cart(Base_spectral& base) const {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = SIN_ODD ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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_compact_symphi::set_legendre_base_forz_cart(Base_spectral& base) const {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    base.bases_1d[2]->set(0) = COS_EVEN ;
    for (int k=0 ; k<nbr_coefs(2) ; k++) {
        base.bases_1d[1]->set(k) = 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 ;
         }
    }
}
 
// sets the value at infinity
void Domain_compact_symphi::set_val_inf (Val_domain& so, double x) const {
 
    assert (so.get_domain() == this) ;
 
    so.coef_i() ;
    so.set_in_conf() ;
    Index inf (nbr_points) ;
    inf.set(0) = nbr_points(0)-1 ;
    do 
        so.set(inf) = x ;
    while (inf.inc1(1)) ;
}
 
// Computes the derivatives with respect to XYZ as function of the numerical ones.
void Domain_compact_symphi::do_der_abs_from_der_var(const Val_domain *const *const der_var, Val_domain **const der_abs) const {
 
    // d/dx :
    Val_domain dr (-der_var[0]->mult_xm1()) ;
    Val_domain sintdr (dr.mult_sin_theta()) ;
    Val_domain costdt (der_var[1]->mult_cos_theta()) ;
 
    Val_domain dpssint (der_var[2]->div_sin_theta()) ;
    
    Val_domain auxi_x ((sintdr+costdt).mult_cos_phi() - dpssint.mult_sin_phi()) ;
    der_abs[0] = new Val_domain (alpha*auxi_x.mult_xm1()) ;
 
    // d/dy :
    Val_domain auxi_y ((sintdr+costdt).mult_sin_phi() + dpssint.mult_cos_phi()) ;
    der_abs[1] = new Val_domain (alpha*auxi_y.mult_xm1()) ;
    // d/dz :
    Val_domain auxi_z (dr.mult_cos_theta() - der_var[1]->mult_sin_theta()) ;
    der_abs[2] = new Val_domain (alpha*auxi_z.mult_xm1()) ;
 
}
 
// Rules for basis multiplication
Base_spectral Domain_compact_symphi::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 COS_EVEN:
            switch ((*b.bases_1d[2])(0)) {
                case COS_EVEN:
                    res.bases_1d[2]->set(0) = COS_EVEN ;
                    break ;
                case COS_ODD:
                    res.bases_1d[2]->set(0) = COS_ODD ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[2]->set(0) = SIN_EVEN ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[2]->set(0) = SIN_ODD ;
                    break ;
                
                default:
                    res_def = false ;
                    break ;
                }
            break ;
 
        
        case COS_ODD:
            switch ((*b.bases_1d[2])(0)) {
                case COS_EVEN:
                    res.bases_1d[2]->set(0) = COS_ODD ;
                    break ;
                case COS_ODD:
                    res.bases_1d[2]->set(0) = COS_EVEN ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[2]->set(0) = SIN_ODD ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[2]->set(0) = SIN_EVEN ;
                    break ;
                
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case SIN_ODD:
            switch ((*b.bases_1d[2])(0)) {
                case COS_EVEN:
                    res.bases_1d[2]->set(0) = SIN_ODD ;
                    break ;
                case COS_ODD:
                    res.bases_1d[2]->set(0) = SIN_EVEN ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[2]->set(0) = COS_ODD ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[2]->set(0) = COS_EVEN ;
                    break ;
                
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case SIN_EVEN:
            switch ((*b.bases_1d[2])(0)) {
                case COS_EVEN:
                    res.bases_1d[2]->set(0) = SIN_EVEN ;
                    break ;
                case COS_ODD:
                    res.bases_1d[2]->set(0) = SIN_ODD ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[2]->set(0) = COS_EVEN ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[2]->set(0) = COS_ODD ;
                    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) = COS_EVEN ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) = COS_ODD ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) = SIN_EVEN ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) = SIN_ODD ;
                    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) = COS_ODD ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) = COS_EVEN ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) = SIN_ODD ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) = 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) = SIN_ODD ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) = SIN_EVEN ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) = COS_ODD ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) = COS_EVEN ;
                    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) = SIN_EVEN ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) = SIN_ODD ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) = COS_EVEN ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) = COS_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_compact_symphi::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 ;
}}