map_et_deriv.C

/*
 * Computations of Cmp partial derivatives for a Map_et mapping
 */
 
/*
 *   Copyright (c) 1999-2003 Eric Gourgoulhon
 *
 *   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
 *
 */
 
 
char map_et_deriv_C[] = "$Header: /cvsroot/Lorene/C++/Source/Map/map_et_deriv.C,v 1.10 2014/10/13 08:53:03 j_novak Exp $" ;
 
/*
 * $Id: map_et_deriv.C,v 1.10 2014/10/13 08:53:03 j_novak Exp $
 * $Log: map_et_deriv.C,v $
 * Revision 1.10  2014/10/13 08:53:03  j_novak
 * Lorene classes and functions now belong to the namespace Lorene.
 *
 * Revision 1.9  2012/01/17 10:33:33  j_penner
 * added a derivative with respect to the computational coordinate xi
 *
 * Revision 1.8  2004/06/22 08:49:58  p_grandclement
 * Addition of everything needed for using the logarithmic mapping
 *
 * Revision 1.7  2004/05/07 13:19:24  j_novak
 * Prevention of warnings
 *
 * Revision 1.6  2004/04/08 17:16:07  f_limousin
 * Add comments
 *
 * Revision 1.5  2004/04/08 16:39:23  f_limousin
 * Add the case dzpuis different of 0 for methods dsdr, srdsdt, srstdsdp
 * for Scalar's.
 *
 * Revision 1.4  2004/01/26 16:16:17  j_novak
 * Methods of gradient for Scalar s. The input can have any dzpuis.
 *
 * Revision 1.3  2003/10/20 19:45:53  e_gourgoulhon
 * check_dzpuis in dsdt and stdsdp.
 *
 * Revision 1.2  2003/10/15 10:37:43  e_gourgoulhon
 * Added new methods dsdt and stdsdp.
 *
 * Revision 1.1.1.1  2001/11/20 15:19:27  e_gourgoulhon
 * LORENE
 *
 * Revision 1.3  2000/02/25  09:01:28  eric
 * Remplacement de ci.get_dzpuis() == 0  par ci.check_dzpuis(0).
 * Suppression de l'affectation des dzpuis Mtbl/Mtnl_cf a la fin car
 *   c'est fait par Cmp::set_dzpuis.
 *
 * Revision 1.2  2000/01/26  13:09:52  eric
 * Reprototypage complet des routines de derivation:
 * le resultat est desormais suppose alloue a l'exterieur de la routine
 * et est passe en argument (Cmp& resu), si bien que le prototypage
 * complet devient:
 *            void DERIV(const Cmp& ci, Cmp& resu) const
 *
 * Revision 1.1  1999/12/17  12:59:29  eric
 * Initial revision
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Map/map_et_deriv.C,v 1.10 2014/10/13 08:53:03 j_novak Exp $
 *
 */
 
 
// Header Lorene
#include "map.h"
#include "cmp.h"
#include "tensor.h"
 
            //-----------------------//
            //        d/d\xi         //
            //-----------------------//
            
            
namespace Lorene {
void Map_et::dsdxi(const Cmp& ci, Cmp& resu) const {
 
    assert (ci.get_etat() != ETATNONDEF) ; 
    assert (ci.get_mp()->get_mg() == mg) ; 
    
    if (ci.get_etat() == ETATZERO) {
    resu.set_etat_zero() ; 
    }
    else {    
    assert( ci.get_etat() == ETATQCQ ) ; 
    assert( ci.check_dzpuis(0) ) ; 
 
    (ci.va).coef() ;    // (ci.va).c_cf is up to date
    
    resu = (ci.va).dsdx() ;     //  dsdx == d/d\xi
    
    (resu.va).base = (ci.va).dsdx().base ;  // same basis as d/dxi
    
    int nz = mg->get_nzone() ; 
    if (mg->get_type_r(nz-1) == UNSURR) {
        resu.set_dzpuis(2) ;        // r^2 d/dr has been computed in the
                        // external domain
    }
 
    }
    
}
 
void Map_et::dsdxi(const Scalar& uu, Scalar& resu) const {
 
  assert (uu.get_etat() != ETATNONDEF) ; 
  assert (uu.get_mp().get_mg() == mg) ; 
    
  if (uu.get_etat() == ETATZERO) {
    resu.set_etat_zero() ; 
  }
  else {   
    assert( uu.get_etat() == ETATQCQ ) ; 
 
    const Valeur& uuva = uu.get_spectral_va() ; 
 
    uuva.coef() ;    // (uu.va).c_cf is up to date
    
    int nz = mg->get_nzone() ; 
    int nzm1 = nz - 1 ;
 
    if ( uu.get_dzpuis() == 0 ) {
      resu = uuva.dsdx() ;     //  dsdxi = d/d\xi
    
      if (mg->get_type_r(nzm1) == UNSURR) {
    resu.set_dzpuis(2) ;    // r^2 d/dr has been computed in the
                            // external domain
      } 
    }
    else {
      assert(mg->get_type_r(nzm1) == UNSURR) ;
 
      int dzp = uu.get_dzpuis() ;
      
      resu = uuva.dsdx() ;
      resu.annule_domain(nzm1) ;  // zero in the CED
      
      // Special treatment in the CED
      Valeur tmp_ced = uuva.dsdx() ;
      Base_val sauve_base( tmp_ced.get_base() ) ; 
      tmp_ced = tmp_ced ;
      tmp_ced.set_base(sauve_base) ;   // The above operation does not 
                                       //change the basis
      tmp_ced = tmp_ced.mult_x() ;  // xi, Id, (xi-1)
      tmp_ced = tmp_ced / xsr ; // xi/R, 1/R, (xi-1)/U
   
      tmp_ced.annule(0, nz-2) ; // only non zero in the CED
      tmp_ced.set(nzm1) -= dzp * uuva(nzm1) ;
      
      // Recombination shells + CED : 
      resu.set_spectral_va() += tmp_ced ;
      
      resu.set_dzpuis(dzp+1) ;         
    
    }
 
    resu.set_spectral_base( uuva.dsdx().get_base() ) ; // same basis as d/dxi
 
  }
 
}
 
            //---------------------//
            //        d/dr         //
            //---------------------//
            
            
void Map_et::dsdr(const Cmp& ci, Cmp& resu) const {
 
    assert (ci.get_etat() != ETATNONDEF) ; 
    assert (ci.get_mp()->get_mg() == mg) ; 
    
    if (ci.get_etat() == ETATZERO) {
    resu.set_etat_zero() ; 
    }
    else {    
    assert( ci.get_etat() == ETATQCQ ) ; 
    assert( ci.check_dzpuis(0) ) ; 
 
    (ci.va).coef() ;    // (ci.va).c_cf is up to date
    
    resu = (ci.va).dsdx() * dxdr ;     //  dxi/dR, - dxi/dU (ZEC)
    
    (resu.va).base = (ci.va).dsdx().base ;  // same basis as d/dxi
    
    int nz = mg->get_nzone() ; 
    if (mg->get_type_r(nz-1) == UNSURR) {
        resu.set_dzpuis(2) ;        // r^2 d/dr has been computed in the
                        // external domain
    }
 
    }
    
}
 
void Map_et::dsdr(const Scalar& uu, Scalar& resu) const {
 
  assert (uu.get_etat() != ETATNONDEF) ; 
  assert (uu.get_mp().get_mg() == mg) ; 
    
  if (uu.get_etat() == ETATZERO) {
    resu.set_etat_zero() ; 
  }
  else {   
    assert( uu.get_etat() == ETATQCQ ) ; 
 
    const Valeur& uuva = uu.get_spectral_va() ; 
 
    uuva.coef() ;    // (uu.va).c_cf is up to date
    
    int nz = mg->get_nzone() ; 
    int nzm1 = nz - 1 ;
 
    if ( uu.get_dzpuis() == 0 ) {
      resu = uuva.dsdx() * dxdr ;     //  dxdr = dxi/dR, - dxi/dU (ZEC)
    
      if (mg->get_type_r(nzm1) == UNSURR) {
    resu.set_dzpuis(2) ;    // r^2 d/dr has been computed in the
                            // external domain
      } 
    }
    else {
      assert(mg->get_type_r(nzm1) == UNSURR) ;
 
      int dzp = uu.get_dzpuis() ;
      
      resu = uuva.dsdx() * dxdr ;
      resu.annule_domain(nzm1) ;  // zero in the CED
      
      // Special treatment in the CED
      Valeur tmp_ced = uuva.dsdx() ;
      Base_val sauve_base( tmp_ced.get_base() ) ; 
      tmp_ced = tmp_ced * dxdr ;
      tmp_ced.set_base(sauve_base) ;   // The above operation does not 
                                       //change the basis
      tmp_ced = tmp_ced.mult_x() ;  // xi, Id, (xi-1)
      tmp_ced = tmp_ced / xsr ; // xi/R, 1/R, (xi-1)/U
   
      tmp_ced.annule(0, nz-2) ; // only non zero in the CED
      tmp_ced.set(nzm1) -= dzp * uuva(nzm1) ;
      
      // Recombination shells + CED : 
      resu.set_spectral_va() += tmp_ced ;
      
      resu.set_dzpuis(dzp+1) ;         
    
    }
 
    resu.set_spectral_base( uuva.dsdx().get_base() ) ; // same basis as d/dxi
 
  }
 
}
 
void Map_et::dsdradial(const Scalar& uu, Scalar& resu) const {
 
  assert (uu.get_etat() != ETATNONDEF) ; 
  assert (uu.get_mp().get_mg() == mg) ; 
    
  if (uu.get_etat() == ETATZERO) {
    resu.set_etat_zero() ; 
  }
  else {   
    assert( uu.get_etat() == ETATQCQ ) ; 
 
    const Valeur& uuva = uu.get_spectral_va() ; 
 
    uuva.coef() ;    // (uu.va).c_cf is up to date
    
    int nz = mg->get_nzone() ; 
    int nzm1 = nz - 1 ;
 
    if ( uu.get_dzpuis() == 0 ) {
      resu = uuva.dsdx() * dxdr ;     //  dxdr = dxi/dR, - dxi/dU (ZEC)
    
      if (mg->get_type_r(nzm1) == UNSURR) {
    resu.set_dzpuis(2) ;    // r^2 d/dr has been computed in the
                            // external domain
      } 
    }
    else {
      assert(mg->get_type_r(nzm1) == UNSURR) ;
 
      int dzp = uu.get_dzpuis() ;
      
      resu = uuva.dsdx() * dxdr ;
      resu.annule_domain(nzm1) ;  // zero in the CED
      
      // Special treatment in the CED
      Valeur tmp_ced = uuva.dsdx() ;
      Base_val sauve_base( tmp_ced.get_base() ) ; 
      tmp_ced = tmp_ced * dxdr ;
      tmp_ced.set_base(sauve_base) ;   // The above operation does not 
                                       //change the basis
      tmp_ced = tmp_ced.mult_x() ;  // xi, Id, (xi-1)
      tmp_ced = tmp_ced / xsr ; // xi/R, 1/R, (xi-1)/U
   
      tmp_ced.annule(0, nz-2) ; // only non zero in the CED
      tmp_ced.set(nzm1) -= dzp * uuva(nzm1) ;
      
      // Recombination shells + CED : 
      resu.set_spectral_va() += tmp_ced ;
      
      resu.set_dzpuis(dzp+1) ;         
    
    }
 
    resu.set_spectral_base( uuva.dsdx().get_base() ) ; // same basis as d/dxi
 
  }
 
}
 
            //------------------------//
            //      1/r d/dtheta      //
            //------------------------//
 
void Map_et::srdsdt(const Cmp& ci, Cmp& resu) const {
 
    assert (ci.get_etat() != ETATNONDEF) ; 
    assert (ci.get_mp()->get_mg() == mg) ; 
    
    if (ci.get_etat() == ETATZERO) {
    resu.set_etat_zero() ; 
    }
    else {
 
    assert( ci.get_etat() == ETATQCQ ) ; 
    assert( ci.check_dzpuis(0) ) ; 
 
    (ci.va).coef() ;    // (ci.va).c_cf is up to date
 
    // Computation of 1/R df/dtheta'   ---> srdfdt
    // ----------------------------
    Valeur srdfdt = ci.va ; 
    
    srdfdt = srdfdt.dsdt() ;    // d/dtheta'
    srdfdt = srdfdt.sx() ;      // 1/xi, Id, 1/(xi-1)
    
    Base_val sauve_base( srdfdt.base ) ; 
    
    srdfdt = srdfdt * xsr ; // xi/R, 1/R, (xi-1)/U
    
    srdfdt.base = sauve_base ;   // The above operation does not change the basis
 
    // Computation of 1/(dR/dx) 1/R dR/dtheta' df/dx   ----> adfdx
    // ----------------------------------------------
 
    Valeur adfdx = ci.va ; 
 
    adfdx = adfdx.dsdx()  ;     // df/dx 
            
    sauve_base = adfdx.base ; 
    adfdx = adfdx * dxdr * srdrdt ;  // 1/(dR/dx) 1/R dR/dtheta' df/dx
    adfdx.base = sauve_base ; 
 
    // Final result 
    // ------------
 
    resu = srdfdt - adfdx ;
 
    int nz = mg->get_nzone() ; 
    if (mg->get_type_r(nz-1) == UNSURR) {
        resu.set_dzpuis(2) ;        // r d/dtheta has been computed in
                        // the external domain
    }
 
    }
    
}
 
void Map_et::srdsdt(const Scalar& uu, Scalar& resu) const {
 
  assert (uu.get_etat() != ETATNONDEF) ; 
  assert (uu.get_mp().get_mg() == mg) ; 
    
  if (uu.get_etat() == ETATZERO) {
    resu.set_etat_zero() ; 
  }
  else {
 
    assert( uu.get_etat() == ETATQCQ ) ; 
 
    const Valeur& uuva = uu.get_spectral_va() ;
    uuva.coef() ;   // (uu.va).c_cf is up to date
 
    int nz = mg->get_nzone() ; 
    int nzm1 = nz - 1 ;
  
    // Computation of 1/R df/dtheta'   ---> srdfdt
    // ----------------------------
    Valeur srdfdt = uuva ; 
    
    srdfdt = srdfdt.dsdt() ;    // d/dtheta'
   
    srdfdt = srdfdt.sx() ;      // 1/xi, Id, 1/(xi-1)
        
    Base_val sauve_base( srdfdt.base ) ; 
    
    srdfdt = srdfdt * xsr ; // xi/R, 1/R, (xi-1)/U
    
    srdfdt.base = sauve_base ;   // The above operation does not change the basis
    // Computation of 1/(dR/dx) 1/R dR/dtheta' df/dx   ----> adfdx
    // ----------------------------------------------
 
    Valeur adfdx = uuva ; 
 
    adfdx = adfdx.dsdx()  ;     // df/dx 
            
    sauve_base = adfdx.base ; 
    adfdx = adfdx * dxdr * srdrdt ;  // 1/(dR/dx) 1/R dR/dtheta' df/dx
    adfdx.base = sauve_base ; 
 
    if (uu.get_dzpuis() == 0) {
 
      // Final result 
      // ------------
 
      resu = srdfdt - adfdx ;
 
      //s int nz = mg->get_nzone() ; 
      if (mg->get_type_r(nz-1) == UNSURR) {
    resu.set_dzpuis(2) ;        // r^2 (1/r d/dtheta) has been computed in
    // the external domain
      }
    
    }
 
    else {
      assert(mg->get_type_r(nzm1) == UNSURR) ;
          
      int dzp = uu.get_dzpuis() ;
 
      Valeur tmp = srdfdt - adfdx ;
      tmp.annule(nzm1) ; 
     
      // Special treatment in the CED
      //-----------------------------
 
      Valeur tmp_ced = - adfdx ;
  
      tmp_ced.annule(0, nz-2) ; // only non zero in the CED
 
      tmp_ced = tmp_ced.mult_x() ;  // xi, Id, (xi-1)
      //s Base_val sauve_base( tmp_ced.get_base() ) ; 
      tmp_ced = tmp_ced / xsr ; // xi/R, 1/R, (xi-1)/U
        
      tmp_ced = tmp_ced + uuva.dsdt() ;
      tmp_ced.annule(0, nz-2) ; // only non zero in the CED
                 
      // Recombination shells + CED : 
      resu = tmp + tmp_ced ;
                
      resu.set_dzpuis(dzp+1) ;         
    }
            
  }
 
}
 
 
            //------------------------------------//
            //       1/(r sin(theta))  d/dphi     //
            //------------------------------------//
 
void Map_et::srstdsdp(const Cmp& ci, Cmp& resu) const {
 
    assert (ci.get_etat() != ETATNONDEF) ; 
    assert (ci.get_mp()->get_mg() == mg) ; 
 
    if (ci.get_etat() == ETATZERO) {
    resu.set_etat_zero() ; 
    }
    else {
 
    assert( ci.get_etat() == ETATQCQ) ; 
    assert( ci.check_dzpuis(0) ) ; 
 
    (ci.va).coef() ;    // (ci.va).c_cf is up to date
 
    // Computation of 1/(R sin(theta')) df/dphi'   ---> srstdfdp
    // -----------------------------------------
 
    Valeur srstdfdp = ci.va ; 
    
    srstdfdp = srstdfdp.dsdp() ;    // d/dphi
    srstdfdp = srstdfdp.ssint() ;   // 1/sin(theta)
    srstdfdp = srstdfdp.sx() ;  // 1/xi, Id, 1/(xi-1)
    
    Base_val sauve_base( srstdfdp.base ) ; 
    
    srstdfdp = srstdfdp * xsr ; // xi/R, 1/R, (xi-1)/U
    
    srstdfdp.base = sauve_base ;   // The above operation does not change the basis
 
    // Computation of 1/(dR/dx) 1/(R sin(theta') dR/dphi' df/dx   --> bdfdx
    // --------------------------------------------------------
    Valeur bdfdx = ci.va ; 
 
    bdfdx = bdfdx.dsdx()  ;     // df/dx 
            
    sauve_base = bdfdx.base ; 
    bdfdx = bdfdx * dxdr * srstdrdp  ;  
    bdfdx.base = sauve_base ; 
 
    // Final result 
    // ------------
 
    resu = srstdfdp - bdfdx ;
 
    int nz = mg->get_nzone() ; 
    if (mg->get_type_r(nz-1) == UNSURR) {
        resu.set_dzpuis(2) ;        // r/sin(theta) d/dphi has been 
                        // computed in the external domain
    }
 
    }
    
}
 
void Map_et::srstdsdp(const Scalar& uu, Scalar& resu) const {
 
  assert (uu.get_etat() != ETATNONDEF) ; 
  assert (uu.get_mp().get_mg() == mg) ; 
    
  if (uu.get_etat() == ETATZERO) {
    resu.set_etat_zero() ; 
  }
  else {
 
    assert( uu.get_etat() == ETATQCQ ) ; 
 
    const Valeur& uuva = uu.get_spectral_va() ;
    uuva.coef() ;    // (uu.va).c_cf is up to date
 
    int nz = mg->get_nzone() ; 
    int nzm1 = nz - 1 ;
 
    // Computation of 1/(R sin(theta')) df/dphi'   ---> srstdfdp
    // -----------------------------------------
    
    Valeur srstdfdp = uuva ; 
    
    srstdfdp = srstdfdp.dsdp() ;    // d/dphi
    srstdfdp = srstdfdp.ssint() ;   // 1/sin(theta)
    srstdfdp = srstdfdp.sx() ;  // 1/xi, Id, 1/(xi-1)
    
    Base_val sauve_base( srstdfdp.base ) ; 
    
    srstdfdp = srstdfdp * xsr ; // xi/R, 1/R, (xi-1)/U
    
    srstdfdp.base = sauve_base ;   // The above operation does not change the basis
    
    // Computation of 1/(dR/dx) 1/(R sin(theta') dR/dphi' df/dx   --> bdfdx
    // --------------------------------------------------------
    Valeur bdfdx = uuva ; 
 
    bdfdx = bdfdx.dsdx()  ;     // df/dx 
    
    sauve_base = bdfdx.base ; 
    bdfdx = bdfdx * dxdr * srstdrdp  ;  
    bdfdx.base = sauve_base ; 
 
 
    if (uu.get_dzpuis() == 0) {
 
    //Final result
 
    resu = srstdfdp - bdfdx ;
 
      
      if (mg->get_type_r(nz-1) == UNSURR) {
    resu.set_dzpuis(2) ;        // r d/dtheta has been computed in
    // the external domain
      }
    }
 
    else {
      assert(mg->get_type_r(nzm1) == UNSURR) ;
          
      int dzp = uu.get_dzpuis() ;
 
      Valeur tmp = srstdfdp - bdfdx ;
      tmp.annule(nzm1) ; 
 
      // Special treatment in the CED
 
      Valeur tmp_ced = - bdfdx ;
      tmp_ced.annule(0, nz-2) ; // only non zero in the CED
 
      tmp_ced = tmp_ced.mult_x() ;  // xi, Id, (xi-1)
      //s Base_val sauve_base( tmp_ced.get_base() ) ; 
      tmp_ced = tmp_ced / xsr ; // xi/R, 1/R, (xi-1)/U
      
      tmp_ced = tmp_ced + uuva.dsdp().ssint() ;
      tmp_ced.annule(0, nz-2) ; // only non zero in the CED
 
      // Recombination shells + CED : 
      resu = tmp + tmp_ced ;
      
      resu.set_dzpuis(dzp+1) ;         
    }
  }    
}
 
            //------------------------//
            //        d/dtheta        //
            //------------------------//
 
void Map_et::dsdt(const Scalar& ci, Scalar& resu) const {
 
    assert (ci.get_etat() != ETATNONDEF) ; 
    assert (ci.get_mp().get_mg() == mg) ; 
    
    if (ci.get_etat() == ETATZERO) {
        resu.set_etat_zero() ; 
    }
    else {
 
    //  The relations are true for all dzpuis
    //  assert( ci.check_dzpuis(0) ) ; 
        assert( ci.get_etat() == ETATQCQ ) ; 
 
 
        // Computation of df/dtheta'   ---> dfdt
        // ----------------------------
 
        const Valeur& dfdt = ci.get_spectral_va().dsdt() ;
    
 
        // Computation of 1/(dR/dxi) dR/dtheta' df/dx   ----> adfdx
        // -------------------------------------------
 
        Valeur adfdx = ci.get_spectral_va().dsdx() ;    // df/dx
 
        Base_val sauve_base = adfdx.get_base() ; 
     
        adfdx = adfdx * dxdr * drdt ;  // df/dx / (dR/dx) * dR/dtheta' 
    
        adfdx.set_base( sauve_base ) ; 
 
        // Final result 
        // ------------
 
        resu = dfdt - adfdx ;
 
    }
    
}
 
            //---------------------------------//
            //        1/sin(theta) d/dphi      //
            //---------------------------------//
 
void Map_et::stdsdp(const Scalar& ci, Scalar& resu) const {
 
    assert (ci.get_etat() != ETATNONDEF) ; 
    assert (ci.get_mp().get_mg() == mg) ; 
    
    if (ci.get_etat() == ETATZERO) {
        resu.set_etat_zero() ; 
    }
    else {
 
    assert( ci.get_etat() == ETATQCQ ) ; 
    //  The relations are true for all dzpuis
    //  assert( ci.check_dzpuis(0) ) ; 
 
        // Computation of 1/sin(theta) df/dphi'   ---> stdfdp
        // ----------------------------
        
        const Valeur& stdfdp = ci.get_spectral_va().stdsdp() ;
    
 
        // Computation of 1/(dR/dxi) 1/sin(theta) dR/dphi' df/dx   ----> adfdx
        // -------------------------------------------
 
        Valeur adfdx = ci.get_spectral_va().dsdx() ;    // df/dx
 
        Base_val sauve_base = adfdx.get_base() ;
     
        adfdx = adfdx * dxdr * stdrdp ;  // df/dx / (dR/dx) * 1/sin(th) dR/dphi' 
    
        adfdx.set_base( sauve_base ) ; 
 
        // Final result 
        // ------------
 
        resu = stdfdp - adfdx ;
 
    }
    
}
 
 
 
}