scalar.C

/*
 *  Methods of class Scalar
 *
 *   (see file scalar.h for documentation)
 *
 */

/*
 *   Copyright (c) 2003-2004 Eric Gourgoulhon & Jerome Novak
 *
 *   Copyright (c) 1999-2001 Philippe Grandclement (for preceding class Cmp)
 *
 *   This file is part of LORENE.
 *
 *   LORENE 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 2 of the License, or
 *   (at your option) any later version.
 *
 *   LORENE 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 LORENE; if not, write to the Free Software
 *   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 */


 


/*
 * $Id: scalar.C,v 1.42 2021/06/25 12:27:26 j_novak Exp $
 * $Log: scalar.C,v $
 * Revision 1.42  2021/06/25 12:27:26  j_novak
 * Added namespace 'std' to the call of 'isnan' function.
 *
 * Revision 1.41  2016/12/05 16:18:18  j_novak
 * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
 *
 * Revision 1.40  2015/12/18 15:52:52  j_novak
 * New method is_nan() for class Scalar.
 *
 * Revision 1.39  2014/10/13 08:53:45  j_novak
 * Lorene classes and functions now belong to the namespace Lorene.
 *
 * Revision 1.38  2014/10/06 15:16:15  j_novak
 * Modified #include directives to use c++ syntax.
 *
 * Revision 1.37  2013/06/05 15:06:11  j_novak
 * Legendre bases are treated as standard bases, when the multi-grid
 * (Mg3d) is built with BASE_LEG.
 *
 * Revision 1.36  2013/03/27 09:51:42  e_gourgoulhon
 * Restored log
 *
 *
 * revision 1.35
 * date: 2013/01/11 15:44:54;  author: j_novak;  state: Exp;  lines: +15 -4
 * Addition of Legendre bases (part 2).
 *
 * revision 1.34
 * date: 2012/01/17 15:10:12;  author: j_penner;  state: Exp;  lines: +2 -7
 *
 * revision 1.33
 * date: 2012/01/17 10:26:48;  author: j_penner;  state: Exp;  lines: +11 -3
 * added a derivative with respect to the computational coordinate xi
 *
 * Revision 1.32  2011/04/08 12:55:50  e_gourgoulhon
 * Scalar::val_point : division by r^dzpuis to return the actual
 * (i.e. physical) value of the field in the external compactified
 * domain.
 *
 * Revision 1.31  2005/10/25 08:56:39  p_grandclement
 * addition of std_spectral_base in the case of odd functions near the origin
 *
 * Revision 1.30  2005/03/11 13:16:37  j_novak
 * Corrected an error in multipole_spectrum().
 *
 * Revision 1.29  2004/10/11 15:09:04  j_novak
 * The radial manipulation functions take Scalar as arguments, instead of Cmp.
 * Added a conversion operator from Scalar to Cmp.
 * The Cmp radial manipulation function make conversion to Scalar, call to the
 * Map_radial version with a Scalar argument and back.
 *
 * Revision 1.28  2004/08/24 09:14:51  p_grandclement
 * Addition of some new operators, like Poisson in 2d... It now requieres the
 * GSL library to work.
 *
 * Also, the way a variable change is stored by a Param_elliptic is changed and
 * no longer uses Change_var but rather 2 Scalars. The codes using that feature
 * will requiere some modification. (It should concern only the ones about monopoles)
 *
 * Revision 1.27  2004/06/22 08:50:00  p_grandclement
 * Addition of everything needed for using the logarithmic mapping
 *
 * Revision 1.26  2004/06/11 14:29:58  j_novak
 * Scalar::multipole_spectrum() is now a const method.
 *
 * Revision 1.25  2004/03/04 09:51:36  e_gourgoulhon
 * Method dz_nonzero() : treated the case ETATUN.
 *
 * Revision 1.24  2004/02/19 22:11:50  e_gourgoulhon
 * Added argument "comment" in method spectral_display.
 *
 * Revision 1.23  2004/01/12 15:32:25  j_novak
 * Yet another problem with ETATUN
 *
 * Revision 1.22  2003/11/05 15:31:13  e_gourgoulhon
 * Method set_etat_qcq(): del_t() is not invoqued for etat == ETATUN.
 *
 * Revision 1.21  2003/11/03 10:25:27  j_novak
 * Suppressed the call to del_deriv() in set_etat_qcq() method.
 *
 * Revision 1.20  2003/10/28 21:33:13  e_gourgoulhon
 * In operator=(const Scalar& ci) changed the place of va.del_t()
 * in order to correct an error in the case where both this and ci
 * are in the state ETATUN.
 *
 * Revision 1.19  2003/10/28 12:36:10  e_gourgoulhon
 * Corrected operator=(const Scalar& ci) for the case ETATUN: the
 * spectral bases are now copied.
 *
 * Revision 1.18  2003/10/27 14:51:25  e_gourgoulhon
 * Correction of errors in constructor from a Tensor.
 *
 * Revision 1.17  2003/10/22 08:35:30  j_novak
 * Error corrected
 *
 * Revision 1.16  2003/10/19 19:54:37  e_gourgoulhon
 * -- Modified method spectral_display: now calling Valeur::display_coef.
 *
 * Revision 1.15  2003/10/15 16:03:38  j_novak
 * Added the angular Laplace operator for Scalar.
 *
 * Revision 1.14  2003/10/15 10:43:06  e_gourgoulhon
 * Added new members p_dsdt and p_stdsdp.
 *
 * Revision 1.13  2003/10/13 13:52:40  j_novak
 * Better managment of derived quantities.
 *
 * Revision 1.12  2003/10/11 14:42:16  e_gourgoulhon
 * Suppressed unusued argument new_triad in method change_triad.
 *
 * Revision 1.11  2003/10/10 15:57:29  j_novak
 * Added the state one (ETATUN) to the class Scalar
 *
 * Revision 1.10  2003/10/07 08:05:03  j_novak
 * Added an assert for the constructor from a Tensor.
 *
 * Revision 1.9  2003/10/06 16:16:03  j_novak
 * New constructor from a Tensor.
 *
 * Revision 1.8  2003/10/06 13:58:48  j_novak
 * The memory management has been improved.
 * Implementation of the covariant derivative with respect to the exact Tensor
 * type.
 *
 * Revision 1.7  2003/10/05 21:15:42  e_gourgoulhon
 * - Suppressed method std_spectral_base_scal().
 * - Added method std_spectral_base().
 *
 * Revision 1.6  2003/10/01 13:04:44  e_gourgoulhon
 * The method Tensor::get_mp() returns now a reference (and not
 * a pointer) onto a mapping.
 *
 * Revision 1.5  2003/09/29 12:52:58  j_novak
 * Methods for changing the triad are implemented.
 *
 * Revision 1.4  2003/09/24 20:55:27  e_gourgoulhon
 * Added -- constructor by conversion of a Cmp
 *       -- operator=(const Cmp&)
 *
 * Revision 1.3  2003/09/24 15:10:54  j_novak
 * Suppression of the etat flag in class Tensor (still present in Scalar)
 *
 * Revision 1.2  2003/09/24 10:21:07  e_gourgoulhon
 * added more methods
 *
 * Revision 1.1  2003/09/23 08:52:17  e_gourgoulhon
 * new version
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Tensor/Scalar/scalar.C,v 1.42 2021/06/25 12:27:26 j_novak Exp $
 *
 */

// headers C
#include <cassert>
#include <cstdlib>
#include <cmath>

// headers Lorene
#include "tensor.h"
#include "type_parite.h"
#include "utilitaires.h"
#include "proto.h"
#include "cmp.h"


            //---------------//
            // Constructors  //
            //---------------//


namespace Lorene {
Scalar::Scalar(const Map& mpi) : Tensor(mpi), etat(ETATNONDEF), dzpuis(0), 
                 va(mpi.get_mg()) {

    cmp[0] = this ; 
    set_der_0x0() ;

}


// Constructor from a Tensor
// -------------------------
Scalar::Scalar(const Tensor& ti) : Tensor(*(ti.mp)), etat(ti.cmp[0]->etat), 
                   dzpuis(ti.cmp[0]->dzpuis), va(ti.cmp[0]->va) {

  assert(ti.valence == 0) ;

  cmp[0] = this ; 
  set_der_0x0() ;

}


// Copy constructor
// ----------------
Scalar::Scalar(const Scalar& sci)  : Tensor(*(sci.mp)), etat(sci.etat), 
                     dzpuis(sci.dzpuis), va(sci.va) {
    
  cmp[0] = this ; 
  set_der_0x0() ;   // On ne recopie pas les derivees

}

// Conversion from a Cmp
//----------------------
Scalar::Scalar(const Cmp& ci) : Tensor(*(ci.get_mp())),
                                etat(ci.get_etat()),
                                dzpuis(ci.get_dzpuis()),
                                va(ci.va) {
    cmp[0] = this ;
    set_der_0x0() ; 
}
    
// From file
// ---------
Scalar::Scalar(const Map& mpi, const Mg3d& mgi, FILE* fd) : Tensor(mpi), 
        va(mgi, fd) {

    assert( mpi.get_mg() == &mgi ) ; 

    fread_be(&etat, sizeof(int), 1, fd) ;           // L'etat
    fread_be(&dzpuis, sizeof(int), 1, fd) ;     // dzpuis

    cmp[0] = this ; 

    set_der_0x0() ; // Les derivees sont initialisees a zero

}

            //--------------//
            // Destructor  //
            //--------------//

// Destructeur
Scalar::~Scalar() {
    del_t() ;
    cmp[0] = 0x0 ; //cmp[0] was set to 'this' before (now 0x0 to break a 
                   // in loop in ~Tensor!)
           
}

            //-----------------------//
            // Memory management     //
            //-----------------------//

// Destructeur logique
void Scalar::del_t() {

    va.del_t() ;
    va.set_etat_nondef() ;
    Scalar::del_deriv() ;

}

void Scalar::del_deriv() const{
    if (p_dsdr != 0x0) delete p_dsdr ;
    if (p_srdsdt != 0x0) delete p_srdsdt ;
    if (p_srstdsdp != 0x0) delete p_srstdsdp ; 
    if (p_dsdt != 0x0) delete p_dsdt ;
    if (p_stdsdp != 0x0) delete p_stdsdp ;
    if (p_dsdx != 0x0) delete p_dsdx ; 
    if (p_dsdy != 0x0) delete p_dsdy ;
    if (p_dsdz != 0x0) delete p_dsdz ;
    if (p_lap != 0x0) delete p_lap ; 
    if (p_lapang != 0x0) delete p_lapang ; 
    if (p_integ != 0x0) delete p_integ ;
    if (p_dsdradial != 0x0) delete p_dsdradial ;
    if (p_dsdrho != 0x0) delete p_dsdrho ;
    set_der_0x0() ;

    Tensor::del_deriv() ;
}

void Scalar::set_der_0x0() const {
    p_dsdr = 0x0 ;
    p_srdsdt = 0x0 ;
    p_srstdsdp = 0x0 ;
    p_dsdt = 0x0 ;
    p_stdsdp = 0x0 ;
    p_dsdx = 0x0 ;
    p_dsdy = 0x0 ;
    p_dsdz = 0x0 ;
    p_lap = 0x0 ; 
    p_lapang = 0x0 ; 
    ind_lap = - 1 ; 
    p_integ = 0x0 ; 
    p_dsdradial = 0x0 ;
    p_dsdrho = 0x0 ;
}

// ETATZERO
void Scalar::set_etat_zero() {
    if (etat == ETATZERO) return ;
    else {
        del_deriv() ;
        va.set_etat_zero() ;
        etat = ETATZERO ;
    }
}

// ETATUN
void Scalar::set_etat_one() {
    if (etat == ETATUN) return ;
    else {
      del_deriv() ;
      va = 1 ;
      etat = ETATUN ;
    }
}

// ETATNONDEF
void Scalar::set_etat_nondef() {
    if (etat == ETATNONDEF) return ;
    else {
        del_t() ;
        etat = ETATNONDEF ;
    }
}

// ETATQCQ
void Scalar::set_etat_qcq() {

    if (etat == ETATQCQ) return ;
    else {
        if (etat != ETATUN) del_t() ;
        etat = ETATQCQ ;
    }
}


// Allocates everything
// --------------------
void Scalar::allocate_all() {
    
    set_etat_qcq() ; 
    va.set_etat_c_qcq() ;       // allocation in configuration space
    Mtbl* mt = va.c ; 
    mt->set_etat_qcq() ;
    for (int l=0; l<mt->get_nzone(); l++) {
        mt->t[l]->set_etat_qcq() ; 
    }
    
} 



// ZERO hard
void Scalar::annule_hard() {

    va.annule_hard() ;
    del_deriv() ; 
    etat = ETATQCQ ;
}


// Sets the Scalar to zero in several domains
// ---------------------------------------

void Scalar::annule(int l_min, int l_max) {
    
    // Cas particulier: annulation globale : 
    if ( (l_min == 0) && (l_max == va.mg->get_nzone()-1) ) {
      set_etat_zero() ;
      return ; 
    }
    
    assert( etat != ETATNONDEF ) ; 
    
    if ( etat == ETATZERO ) {
        return ;        // rien n'a faire si c'est deja zero
    }
    else {
        assert( (etat == ETATQCQ) || (etat == ETATUN) ) ;   // sinon...

        etat = ETATQCQ ;
        va.annule(l_min, l_max) ;   // Annule la Valeur
    
        // Annulation des membres derives
        if (p_dsdr != 0x0) p_dsdr->annule(l_min, l_max) ;
        if (p_srdsdt != 0x0) p_srdsdt->annule(l_min, l_max) ;
        if (p_srstdsdp != 0x0) p_srstdsdp->annule(l_min, l_max) ;
        if (p_dsdt != 0x0) p_dsdt->annule(l_min, l_max) ;
        if (p_stdsdp != 0x0) p_stdsdp->annule(l_min, l_max) ;
        if (p_dsdx != 0x0) p_dsdx->annule(l_min, l_max) ;
        if (p_dsdy != 0x0) p_dsdy->annule(l_min, l_max) ;
        if (p_dsdz != 0x0) p_dsdz->annule(l_min, l_max) ;
        if (p_lap != 0x0) p_lap->annule(l_min, l_max) ;
        if (p_lapang != 0x0) p_lapang->annule(l_min, l_max) ;
        if (p_integ != 0x0) delete p_integ ;
        if (p_dsdradial != 0x0) p_dsdradial->annule(l_min, l_max) ;
    }
    
}


            //------------//
            // Assignment //
            //------------//


// From tensor
// -----------

void Scalar::operator=(const Tensor& uu) {

    assert(uu.valence == 0) ; 
    
    operator=(*(uu.cmp[0])) ; 

}

// From Scalar
// ----------
void Scalar::operator=(const Scalar& ci) {
    

    assert(&ci != this) ;    // pour eviter l'auto-affectation
    
    // Les elements fixes
    assert( mp == ci.mp ) ;
    
    dzpuis = ci.dzpuis ; 
    
    // La valeur eventuelle
    switch(ci.etat) {
    case ETATNONDEF: {
        set_etat_nondef() ; 
        break ;         // valeur par defaut
    }
    
    case ETATZERO: {
        set_etat_zero() ;
        break ;
    }
    
    case ETATUN: {
        set_etat_one() ;
        va.set_base( ci.va.get_base() )  ;   
        break ;
    }
    
    case ETATQCQ: {
        // Menage general de la Valeur, mais pas des quantites derivees !
        va.del_t() ;
        
        set_etat_qcq() ; // set_etat_qcq n'appelle pas del_deriv()
        va = ci.va ;

        // On detruit les quantites derivees (seulement lorsque tout est fini !)
        del_deriv() ; 

        break ;
    }
    
    default: {
        cout << "Unkwown state in Scalar::operator=(const Scalar&) !" 
         << endl ;
        abort() ;
        break ;
    }
    }

}
    
// From Cmp
// --------
void Scalar::operator=(const Cmp& ci) {
    

    // Menage general de la Valeur, mais pas des quantites derivees !
    va.del_t() ;
    
    // Les elements fixes
    assert( mp == ci.get_mp() ) ;
    
    dzpuis = ci.get_dzpuis() ; 
    
    // La valeur eventuelle
    switch(ci.get_etat()) {
    
    case ETATNONDEF: {
        set_etat_nondef() ; 
        break ;         // valeur par defaut
    }
    
    case ETATZERO: {
        set_etat_zero() ;
        break ;
    }
    
    case ETATQCQ: {
        set_etat_qcq() ;
        va = ci.va ;

        // On detruit les quantites derivees (seulement lorsque tout est fini !)
        del_deriv() ; 

        break ;
    }
    
    default: {
        cout << "Unkwown state in Scalar::operator=(const Cmp&) !" 
         << endl ;
        abort() ;
        break ;
    }
    }

}
    




// From Valeur
// -----------
void Scalar::operator=(const Valeur& vi) {

    // Traitement de l'auto-affectation :
    if (&vi == &va) {
        return ; 
    }

    // Protection
    assert(vi.get_etat() != ETATNONDEF) ;
    
    // Menage general de la Valeur, mais pas des quantites derivees !
    va.del_t() ;

    
    // La valeure eventuelle
    switch(vi.get_etat()) {

    case ETATZERO: {
        set_etat_zero() ;
        break ;
    }

    case ETATQCQ: {
        set_etat_qcq() ;
        va = vi ;
        
        // On detruit les quantites derivees (seulement lorsque tout est fini !)
        del_deriv() ; 

        break ;
    }
    
    default: {
        cout << "Unkwown state in Scalar::operator=(const Valeur&) !" << endl ;
        abort() ;
        break ;
    }
    }

}

// From Mtbl
// ---------
void Scalar::operator=(const Mtbl& mi) {
    
    // Protection
    assert(mi.get_etat() != ETATNONDEF) ;

    assert(&mi != va.c) ;  // pour eviter l'auto-affectation

   
    // Menage general de la Valeur, mais pas des quantites derivees !
    va.del_t() ;

    // La valeure eventuelle
    switch(mi.get_etat()) {
    case ETATZERO: {
        set_etat_zero() ;
        break ;
    }
    
    case ETATQCQ: {
        set_etat_qcq() ;
        va = mi ;

        // On detruit les quantites derivees (seulement lorsque tout est fini !)
        del_deriv() ; 

        break ;
     }
    
    default: {
        cout << "Unkwown state in Scalar::operator=(const Mtbl&) !" << endl ;
        abort() ;
        break ;
    }
    }


}

// From double
// -----------
void Scalar::operator=(double x) {
    
  if (x == double(0)) {
    set_etat_zero() ;
  }
  else {
    if (x == double(1)) {
      set_etat_one() ;
    }
    else {
      set_etat_qcq() ;
      del_deriv() ;
    va = x ;
    }
  }
  
  dzpuis = 0 ; 
}

// From int
// --------
void Scalar::operator=(int n) {
    
  if (n == 0) {
    set_etat_zero() ;
  }
  else {
    if (n == 1) {
      set_etat_one() ;
    }
    else {
      set_etat_qcq() ;
      del_deriv() ;
      va = n ;
    }
  } 
  dzpuis = 0 ; 
  
}

// Conversion to a Cmp
//----------------------
Scalar::operator Cmp() const {

  Cmp resu(mp) ;
  resu = va ;
  resu.set_dzpuis(dzpuis) ;
  return resu ;

}
            //------------//
            // Sauvegarde //
            //------------//

void Scalar::sauve(FILE* fd) const {

    va.sauve(fd) ;      // la valeur (en premier pour la construction
                //   lors de la lecture du fichier)

    fwrite_be(&etat, sizeof(int), 1, fd) ;          // l'etat
    fwrite_be(&dzpuis, sizeof(int), 1, fd) ;        // dzpuis

}
    
            //------------//
            // Impression //
            //------------//

// Operator <<
// -----------
ostream& operator<<(ostream& ost, const Scalar& ci) {

    switch(ci.etat) {
    case ETATNONDEF: {
        ost << "*** UNDEFINED STATE *** " << endl ;
        break ;
    }
    
    case ETATZERO: {
        ost << "*** identically ZERO ***" << endl ; 
        break ; 
    }
    
    case ETATUN: {
        ost << "*** identically ONE ***" << endl ; 
        break ; 
    }
    
    case ETATQCQ: {
        ost << "*** dzpuis = " << ci.get_dzpuis() << endl ; 
        ost << ci.va << endl ; 
        break ;
    }
    
    default: {
        cout << "operator<<(ostream&, const Scalar&) : unknown state !" 
         << endl ;
        abort() ;
        break ; 
    }
    }
    
    // Termine
    return ost ;
}

// spectral_display
//-----------------

void Scalar::spectral_display(const char* comment, 
            double thres, int precis, ostream& ost) const {


    if (comment != 0x0) {
        ost << comment << " : " << endl ; 
    }
    
    // Cas particuliers
    //-----------------

    if (etat == ETATNONDEF) {
        ost << "*** UNDEFINED ***" << endl << endl ; 
        return ;
    }

    if (etat == ETATZERO) {
        ost << "*** identically ZERO ***" << endl ; 
        return ;
    }

    if (etat == ETATUN) {
        ost << "*** identically ONE ***" << endl ; 
        return ;
    }

    // Cas general : on affiche la Valeur
    //------------
       
    if (dzpuis != 0) {
        ost << "*** dzpuis = " << dzpuis << endl ; 
    }
    va.display_coef(thres, precis, ost) ;

}



    
            //------------------------------------//
            //  Spectral bases of the Valeur va   //
            //------------------------------------//
            
void Scalar::std_spectral_base() {
      
    va.std_base_scal() ;  
                   
}    

            
void Scalar::std_spectral_base_odd() {
      
    va.std_base_scal_odd() ;  
                   
}    

void Scalar::set_spectral_base(const Base_val& bi) {

    va.set_base(bi) ; 

}    


            //--------------------------//
            //  dzpuis manipulations    //
            //--------------------------//
            
void Scalar::set_dzpuis(int dzi) {
    
    dzpuis = dzi ;
    
}

bool Scalar::dz_nonzero() const {
    
    assert(etat != ETATNONDEF) ; 
    
    const Mg3d* mg = mp->get_mg() ;
    
    int nzm1 = mg->get_nzone() - 1; 
    if (mg->get_type_r(nzm1) != UNSURR) {
        return false ; 
    } 
    
    if (etat == ETATZERO) {
        return false ; 
    }
    
    if (etat == ETATUN) {
        return true ; 
    }
    
    assert( etat == ETATQCQ ) ;
    
    if (va.etat == ETATZERO) {
        return false ; 
    }

    assert(va.etat == ETATQCQ) ; 
    
    if (va.c != 0x0) {
    if ( (va.c)->get_etat() == ETATZERO ) {
        return false ; 
    }
    
    assert( (va.c)->get_etat() == ETATQCQ ) ; 
    if ( (va.c)->t[nzm1]->get_etat() == ETATZERO ) {
        return false ; 
    }
    else {
        assert( (va.c)->t[nzm1]->get_etat() == ETATQCQ ) ; 
        return true ; 
    }
    }
    else{
    assert(va.c_cf != 0x0) ; 
    if ( (va.c_cf)->get_etat() == ETATZERO ) {
        return false ; 
    }
    assert( (va.c_cf)->get_etat() == ETATQCQ ) ; 
    if ( (va.c_cf)->t[nzm1]->get_etat() == ETATZERO ) {
        return false ; 
    }
    else {
        assert( (va.c_cf)->t[nzm1]->get_etat() == ETATQCQ ) ; 
        return true ; 
    }
    
    } 
    
}

bool Scalar::check_dzpuis(int dzi) const {
    
    if (dz_nonzero()) {     // the check must be done
        return (dzpuis == dzi) ; 
    }
    else{
        return true ; 
    }
    
}



        //---------------------------------------//
        //      Value at an arbitrary point      //
        //---------------------------------------//

double Scalar::val_point(double r, double theta, double phi) const {


    assert(etat != ETATNONDEF) ; 
    
    if (etat == ETATZERO) {
        return double(0) ; 
    }
    
    if (etat == ETATUN) {
        return double(1) ; 
    }
    
    assert(etat == ETATQCQ) ; 
    
    // 1/ Search for the domain and the grid coordinates (xi,theta',phi')
    //    which corresponds to the point (r,theta,phi)
    
    int l ; 
    double xi ; 
    mp->val_lx(r, theta, phi, l,  xi) ;     // call of val_lx with default 
                        // accuracy parameters
    // 2/ Call to the Valeur version
    if (l == mp->get_mg()->get_nzone() - 1){  // in the last domain, one must take into account dzpuis
      switch (dzpuis) {
      case 0:
    {
      return va.val_point(l, xi, theta, phi);
      break;
    }
      case 1:
    {
      return va.val_point(l, xi, theta, phi)/r ; 
      break;
    }
      case 2:
    {
      return va.val_point(l, xi, theta, phi)/(r*r) ; 
      break;
    }
      case 3:
    {
      return va.val_point(l, xi, theta, phi)/(r*r*r) ; 
      break;
    }
      case 4:
    {
      return va.val_point(l, xi, theta, phi)/(r*r*r*r) ; 
      break;
    }
      default:
    {
      cout << "scalar::val_point unexpected value of dzpuis !" << endl;
      abort();
    }
      }
    }
    else{
      return va.val_point(l, xi, theta, phi);
    }
}
 
        //---------------------------------//
        //      Multipolar spectrum        //
        //---------------------------------//

Tbl Scalar::multipole_spectrum() const {

  assert (etat != ETATNONDEF) ;

  const Mg3d* mg = mp->get_mg() ;
  int nzone = mg->get_nzone() ;
  int lmax = 0 ;
  
  for (int lz=0; lz<nzone; lz++) 
    lmax = (lmax < 2*mg->get_nt(lz) - 1 ? 2*mg->get_nt(lz) - 1 : lmax) ;

  Tbl resu(nzone, lmax) ;
  if (etat == ETATZERO) {
    resu.set_etat_zero() ;
    return resu ;
  }

  assert((etat == ETATQCQ) || (etat == ETATUN));

  Valeur va_copy = va ;

  va_copy.coef() ;
  va_copy.ylm() ;
  resu.annule_hard() ;
  const Base_val& base = va_copy.c_cf->base ;
  int m_quant, l_quant, base_r ;
  for (int lz=0; lz<nzone; lz++) 
    for (int k=0 ; k<mg->get_np(lz) ; k++) 
      for (int j=0 ; j<mg->get_nt(lz) ; j++) {
    if (nullite_plm(j, mg->get_nt(lz), k, mg->get_np(lz), base) == 1) 
      {
        // quantic numbers and spectral bases
        donne_lm(nzone, lz, j, k, base, m_quant, l_quant, base_r) ;
        for (int i=0; i<mg->get_nr(lz); i++) resu.set(lz, l_quant) 
                     += fabs((*va_copy.c_cf)(lz, k, j, i)) ; 
      }
      }

  return resu ;
}

void Scalar::change_triad(const Base_vect& ) {

  cout << "WARNING: Scalar::change_triad : "<< endl ;
  cout << "This method does nothing ... " << endl ;

}

        //---------------------------------//
                //         Check for NaNs          //
        //---------------------------------//

  bool Scalar::is_nan(bool verb) const {

    bool resu = false ;
    if (etat == ETATQCQ) {
      bool phys = false ;
      bool coef = false ;
      if (va.c != 0x0)
    phys = true ;
      if (va.c_cf != 0x0)
    coef = true ;
      int nz = mp->get_mg()->get_nzone() ;
      for (int lz=0; lz<nz; lz++) {
    bool domain_p = false ;
    bool domain_c = false ;
    if (phys) domain_p = (va.c->get_etat() == ETATQCQ) ;
    if (coef) domain_c = (va.c_cf->get_etat() == ETATQCQ) ;
    if (domain_p) {
      int np = mp->get_mg()->get_np(lz) ;
      int nt = mp->get_mg()->get_nt(lz) ;
      int nr = mp->get_mg()->get_nr(lz) ;
      for (int k=0; k<np; k++) {
        for (int j=0; j<nt; j++) {
          for (int i=0; i<nr; i++) {
        if (std::isnan( (*va.c)(lz, k, j, i) ) ) {
          resu = true ;
          if (verb) {
            cout << "NaN found at physical grid point domain = " << lz
             << ", i= " << i << ", j= " << j << ", k= " << k << endl ;
          }
        } 
          } // i loop 
        } // j loop
      } // k loop
    }
    if (domain_c) {
      int np = mp->get_mg()->get_np(lz) + 2 ;
      int nt = mp->get_mg()->get_nt(lz) ;
      int nr = mp->get_mg()->get_nr(lz) ;
      for (int k=0; k<np; k++) {
        for (int j=0; j<nt; j++) {
          for (int i=0; i<nr; i++) {
        if (std::isnan( (*va.c_cf)(lz, k, j, i) ) ) {
          resu = true ;
          if (verb) {
            cout << "NaN found at coefficient, domain = " << lz
             << ", i= " << i << ", j= " << j << ", k= " << k << endl ;
          }
        } 
          } // i loop 
        } // j loop
      } // k loop
    }
      } // lz loop
    } // etat condition

    return resu ;

  }

  
}