sym_tensor_trans_dirac_bound2.C

/*
 *  Methods to impose the Dirac gauge: divergence-free condition, with interior boundary conditions added
 *
 *    (see file sym_tensor.h for documentation).
 *
 */

/*
 *   Copyright (c) 2006, 2007  Jerome Novak,Nicolas Vasset
 *
 *   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 version 2
 *   as published by the Free Software Foundation.
 *
 *   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 sym_tensor_trans_dirac_C[] = "$Header: /cvsroot/Lorene/C++/Source/Tensor/sym_tensor_trans_dirac_bound2.C,v 1.2 2008/08/20 15:08:06 n_vasset Exp $" ;

/*
 * $Id: sym_tensor_trans_dirac_bound2.C,v 1.2 2008/08/20 15:08:06 n_vasset Exp $
 * $Log: sym_tensor_trans_dirac_bound2.C,v $
 * Revision 1.2  2008/08/20 15:08:06  n_vasset
 * Cleaning up the code...
 *
 * Revision 1.1  2007/05/04 16:45:25  n_vasset
 * First version
 *
 * Revision 1.2  2006/10/24 13:03:19  j_novak
 * New methods for the solution of the tensor wave equation. Perhaps, first
 * operational version...
 *
 * Revision 1.1  2006/09/05 15:38:45  j_novak
 * The fuctions sol_Dirac... are in a separate file, with new parameters to
 * control the boundary conditions.
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Tensor/sym_tensor_trans_dirac_bound2.C,v 1.2 2008/08/20 15:08:06 n_vasset Exp $
 *
 */

// C headers
#include <assert.h>
#include <math.h>

// Lorene headers
#include "nbr_spx.h"
#include "utilitaires.h"
#include "math.h"
#include "param.h"
#include "param_elliptic.h"
#include "metric.h"
#include "tensor.h"
#include "sym_tensor.h"
#include "diff.h"
#include "proto.h"
#include "param.h"


//----------------------------------------------------------------------------------
//
//                               sol_Dirac_A
//
//----------------------------------------------------------------------------------

void Sym_tensor_trans::sol_Dirac_Abound(const Scalar& aaa, Scalar& tilde_mu, Scalar& x_new, Scalar bound_mu, const Param* par_bc) {
  
  const Map_af* mp_aff = dynamic_cast<const Map_af*>(mp) ;
  assert(mp_aff != 0x0) ; //Only affine mapping for the moment
  
  //  WARNING!
  // This will only work if we have at least 2 shells!
  
  
  const Mg3d& mgrid = *mp_aff->get_mg() ;
  assert(mgrid.get_type_r(0) == RARE)  ;
  if (aaa.get_etat() == ETATZERO) {
    tilde_mu = 0 ;
    x_new = 0 ;
    return ;
  }
 
  double dir = 1.;
  double neum = 0.;
 
  // On suppose que le sym_tensor_entré est bien transverse;  
  
  //  assert ( maxabs(contract((*this).derive_cov(mets), 1, 2)) < 0.00000000000001 ) ; 
  

    bound_mu.set_spectral_va().ylm();
 
 
  assert(aaa.get_etat() != ETATNONDEF) ;
  int nz = mgrid.get_nzone() ;
  int nzm1 = nz - 1 ;
  bool ced = (mgrid.get_type_r(nzm1) == UNSURR) ;
  int n_shell = ced ? nz-2 : nzm1 ;
  int nz_bc = nzm1 ;
  if (par_bc != 0x0)
    if (par_bc->get_n_int() > 0) nz_bc = par_bc->get_int() ;
  n_shell = (nz_bc < n_shell ? nz_bc : n_shell) ;
  bool cedbc = (ced && (nz_bc == nzm1)) ; 
#ifndef NDEBUG
  if (!cedbc) {
    assert(par_bc != 0x0) ;
    assert(par_bc->get_n_tbl_mod() >= 3) ;
  }
#endif
  int nt = mgrid.get_nt(0) ;
  int np = mgrid.get_np(0) ;
  
  Scalar source = aaa ;
  Scalar source_coq = aaa ;
  source_coq.annule_domain(0) ;
  if (ced) source_coq.annule_domain(nzm1) ;
  source_coq.mult_r() ;
  source.set_spectral_va().ylm() ;
  source_coq.set_spectral_va().ylm() ;
  Base_val base = source.get_spectral_base() ;
  base.mult_x() ;
  
  tilde_mu.annule_hard() ;
  tilde_mu.set_spectral_base(base) ;
  tilde_mu.set_spectral_va().set_etat_cf_qcq() ;
  tilde_mu.set_spectral_va().c_cf->annule_hard() ;   
  x_new.annule_hard() ;
  x_new.set_spectral_base(base) ;
  x_new.set_spectral_va().set_etat_cf_qcq() ;
  x_new.set_spectral_va().c_cf->annule_hard() ;   
  
  Mtbl_cf sol_part_mu(mgrid, base) ; sol_part_mu.annule_hard() ;
  Mtbl_cf sol_part_x(mgrid, base) ; sol_part_x.annule_hard() ;
  Mtbl_cf sol_hom1_mu(mgrid, base) ; sol_hom1_mu.annule_hard() ;
  Mtbl_cf sol_hom1_x(mgrid, base) ; sol_hom1_x.annule_hard() ;
  Mtbl_cf sol_hom2_mu(mgrid, base) ; sol_hom2_mu.annule_hard() ;
  Mtbl_cf sol_hom2_x(mgrid, base) ; sol_hom2_x.annule_hard() ;
  
  int l_q, m_q, base_r ;
  
  //---------------
  //--  NUCLEUS ---
  //---------------

  // On va annuler toutes les solutions dans le noyau

  { int lz = 0 ;  
  int nr = mgrid.get_nr(lz) ;
  //  double alpha = mp_aff->get_alpha()[lz] ;
  // Matrice ope(2*nr, 2*nr) ;
  //  ope.set_etat_qcq() ;
  
  for (int k=0 ; k<np+1 ; k++) {
    for (int j=0 ; j<nt ; j++) {
      // quantic numbers and spectral bases
      base.give_quant_numbers(lz, k, j, m_q, l_q, base_r) ;
      if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q > 1)) {
    
    
    Tbl sol(2*nr) ;
    sol.set_etat_zero();                
    for (int i=0; i<nr; i++) {
      sol_part_mu.set(lz, k, j, i) = 0 ;
      sol_part_x.set(lz, k, j, i) = 0 ;
    }
    for (int i=0; i<nr; i++) {
      sol_hom2_mu.set(lz, k, j, i) = 0 ;
      sol_hom2_x.set(lz, k, j, i) = 0 ;
        }
      }
    }
  }
  }
  
    //-------------
    // -- Shells --
    //-------------

  for (int lz=1; lz <= n_shell; lz++) {
    int nr = mgrid.get_nr(lz) ;
    assert(mgrid.get_nt(lz) == nt) ;
    assert(mgrid.get_np(lz) == np) ;
    double alpha = mp_aff->get_alpha()[lz] ;
    double ech = mp_aff->get_beta()[lz] / alpha ;
    Matrice ope(2*nr, 2*nr) ;
    ope.set_etat_qcq() ;
    
    for (int k=0 ; k<np+1 ; k++) {
      for (int j=0 ; j<nt ; j++) {
    // quantic numbers and spectral bases
    base.give_quant_numbers(lz, k, j, m_q, l_q, base_r) ;
    if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q > 1)) {
      Diff_xdsdx oxd(base_r, nr) ; const Matrice& mxd = oxd.get_matrice() ;
      Diff_dsdx od(base_r, nr) ; const Matrice& md = od.get_matrice() ;
      Diff_id oid(base_r, nr) ; const Matrice& mid = oid.get_matrice() ;
      
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin,col) = mxd(lin,col) + ech*md(lin,col) 
        + 3*mid(lin,col) ;
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin,col+nr) = (2-l_q*(l_q+1))*mid(lin,col) ;
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+nr,col) = -mid(lin,col) ;
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+nr,col+nr) = mxd(lin,col) + ech*md(lin,col) ;
      
      int ind0 = 0 ;
      int ind1 = nr ;
      for (int col=0; col<2*nr; col++) {
        ope.set(ind0+nr-1, col) = 0 ;
        ope.set(ind1+nr-1, col) = 0 ;
      }
      ope.set(ind0+nr-1, ind0) = 1 ;
      ope.set(ind1+nr-1, ind1) = 1 ;
      
      ope.set_lu() ;
      
      Tbl sec(2*nr) ;
      sec.set_etat_qcq() ;
      for (int lin=0; lin<nr; lin++)
        sec.set(lin) = 0 ;
      for (int lin=0; lin<nr; lin++)
        sec.set(nr+lin) = (*source_coq.get_spectral_va().c_cf)
          (lz, k, j, lin) ;
      sec.set(ind0+nr-1) = 0 ;
      sec.set(ind1+nr-1) = 0 ;
      Tbl sol = ope.inverse(sec) ;
      for (int i=0; i<nr; i++) {
        sol_part_mu.set(lz, k, j, i) = sol(i) ;
        sol_part_x.set(lz, k, j, i) = sol(i+nr) ;
      }
      sec.annule_hard() ;
      sec.set(ind0+nr-1) = 1 ;
      sol = ope.inverse(sec) ;
      for (int i=0; i<nr; i++) {
        sol_hom1_mu.set(lz, k, j, i) = sol(i) ;
        sol_hom1_x.set(lz, k, j, i) = sol(i+nr) ;
      }         
      sec.set(ind0+nr-1) = 0 ;
      sec.set(ind1+nr-1) = 1 ;
      sol = ope.inverse(sec) ;
      for (int i=0; i<nr; i++) {
        sol_hom2_mu.set(lz, k, j, i) = sol(i) ;
        sol_hom2_x.set(lz, k, j, i) = sol(i+nr) ;
      }         
    }
      }
    }
  }
  
  //------------------------------
  // Compactified external domain
  //------------------------------
  if (cedbc) {int lz = nzm1 ;  
  int nr = mgrid.get_nr(lz) ;
  assert(mgrid.get_nt(lz) == nt) ;
  assert(mgrid.get_np(lz) == np) ;
  double alpha = mp_aff->get_alpha()[lz] ;
  Matrice ope(2*nr, 2*nr) ;
  ope.set_etat_qcq() ;
  
  for (int k=0 ; k<np+1 ; k++) {
    for (int j=0 ; j<nt ; j++) {
      // quantic numbers and spectral bases
      base.give_quant_numbers(lz, k, j, m_q, l_q, base_r) ;
      if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q > 1)) {
    Diff_dsdx od(base_r, nr) ; const Matrice& md = od.get_matrice() ;
    Diff_sx os(base_r, nr) ; const Matrice& ms = os.get_matrice() ;
    
    for (int lin=0; lin<nr; lin++) 
      for (int col=0; col<nr; col++) 
        ope.set(lin,col) = - md(lin,col) + 3*ms(lin,col) ;
    for (int lin=0; lin<nr; lin++) 
      for (int col=0; col<nr; col++) 
        ope.set(lin,col+nr) = (2-l_q*(l_q+1))*ms(lin,col) ;
    for (int lin=0; lin<nr; lin++) 
      for (int col=0; col<nr; col++) 
        ope.set(lin+nr,col) = -ms(lin,col) ;
    for (int lin=0; lin<nr; lin++) 
      for (int col=0; col<nr; col++) 
        ope.set(lin+nr,col+nr) = -md(lin,col) ;
    
    ope *= 1./alpha ;
    int ind0 = 0 ;
    int ind1 = nr ;
    for (int col=0; col<2*nr; col++) {
      ope.set(ind0+nr-1, col) = 0 ;
      ope.set(ind1+nr-2, col) = 0 ;
      ope.set(ind1+nr-1, col) = 0 ;
    }
    for (int col=0; col<nr; col++) {
      ope.set(ind0+nr-1, col+ind0) = 1 ;
      ope.set(ind1+nr-1, col+ind1) = 1 ;
    }
    ope.set(ind1+nr-2, ind1+1) = 1 ;
    
    ope.set_lu() ;
    
    Tbl sec(2*nr) ;
    sec.set_etat_qcq() ;
    for (int lin=0; lin<nr; lin++)
      sec.set(lin) = 0 ;
    for (int lin=0; lin<nr; lin++)
      sec.set(nr+lin) = (*source.get_spectral_va().c_cf)
        (lz, k, j, lin) ;
    sec.set(ind0+nr-1) = 0 ;
    sec.set(ind1+nr-2) = 0 ;
    sec.set(ind1+nr-1) = 0 ;
    Tbl sol = ope.inverse(sec) ;
    for (int i=0; i<nr; i++) {
      sol_part_mu.set(lz, k, j, i) = sol(i) ;
      sol_part_x.set(lz, k, j, i) = sol(i+nr) ;
    }
    sec.annule_hard() ;
    sec.set(ind1+nr-2) = 1 ;
    sol = ope.inverse(sec) ;
    for (int i=0; i<nr; i++) {
      sol_hom1_mu.set(lz, k, j, i) = sol(i) ;
      sol_hom1_x.set(lz, k, j, i) = sol(i+nr) ;
    }           
      }
    }
  }
  }
  
  
  // On écrit maintenant le système de raccord
  
  int taille = 2*nz_bc ;
  if (cedbc) taille-- ;
  Mtbl_cf& mmu = *tilde_mu.set_spectral_va().c_cf ;
  Mtbl_cf& mw = *x_new.set_spectral_va().c_cf ;
  
  Tbl sec_membre(taille) ; 
  Matrice systeme(taille, taille) ; 
  int ligne ;  int colonne ;
  Tbl pipo(1) ;
  const Tbl& mub = (cedbc ? pipo : par_bc->get_tbl_mod(2) );
  double c_mu = (cedbc ? 0 : par_bc->get_tbl_mod(0)(0) ) ;
  double d_mu = (cedbc ? 0 : par_bc->get_tbl_mod(0)(1) ) ;
  double c_x = (cedbc ? 0 : par_bc->get_tbl_mod(0)(2) ) ;
  double d_x = (cedbc ? 0 : par_bc->get_tbl_mod(0)(3) ) ;
  Mtbl_cf dhom1_mu = sol_hom1_mu ; 
  Mtbl_cf dhom2_mu = sol_hom2_mu ; 
  Mtbl_cf dpart_mu = sol_part_mu ; 
  Mtbl_cf dhom1_x = sol_hom1_x ; 
  Mtbl_cf dhom2_x = sol_hom2_x ; 
  Mtbl_cf dpart_x = sol_part_x ; 
  
  
  dhom1_mu.dsdx() ;
  dhom2_mu.dsdx() ;
  dpart_mu.dsdx() ;
  dhom1_x.dsdx() ;
  dhom2_x.dsdx() ;
  dpart_x.dsdx() ;
  
  
  // Loop on l and m
  //----------------
  for (int k=0 ; k<np+1 ; k++)
    for (int j=0 ; j<nt ; j++) {
      base.give_quant_numbers(0, k, j, m_q, l_q, base_r) ;
      if ((nullite_plm(j, nt, k, np, base) == 1) && (l_q > 1)) {
    ligne = 0 ;
    colonne = 0 ;
    systeme.annule_hard() ;
    sec_membre.annule_hard() ;
    
    //First shell 
    // Internal boundary condition
    int nr = mgrid.get_nr(1) ;
    
    systeme.set(ligne, colonne) = dir * sol_hom1_mu.val_in_bound_jk(1, j, k) + neum* dhom1_mu.val_in_bound_jk(1,j,k);
    systeme.set(ligne, colonne+1) = dir * sol_hom2_mu.val_in_bound_jk(1, j, k) + neum* dhom2_mu.val_in_bound_jk(1,j,k);
    
    Mtbl_cf *boundmu = bound_mu.get_spectral_va().c_cf;
        double blob = (*boundmu).val_in_bound_jk(1,j,k);
    sec_membre.set(ligne) = - dir* sol_part_mu.val_in_bound_jk(1, j, k) - neum * dpart_mu.val_in_bound_jk(1,j,k) + blob;

  

    ligne++; 
    // Condition at x=1
    systeme.set(ligne, colonne) = 
      sol_hom1_mu.val_out_bound_jk(1, j, k) ;
    systeme.set(ligne, colonne+1) = 
      sol_hom2_mu.val_out_bound_jk(1, j, k) ;
    
    sec_membre.set(ligne) -= sol_part_mu.val_out_bound_jk(1, j, k) ;
    ligne++ ;
    
    systeme.set(ligne, colonne) = 
      sol_hom1_x.val_out_bound_jk(1, j, k) ;
    systeme.set(ligne, colonne+1) = 
      sol_hom2_x.val_out_bound_jk(1, j, k) ;
    
    sec_membre.set(ligne) -= sol_part_x.val_out_bound_jk(1, j, k) ;
    
    colonne += 2 ;

    //shells with nz>2
    for (int zone=2 ; zone<nz_bc ; zone++) {
      nr = mgrid.get_nr(zone) ;
      ligne-- ;
      
      //Condition at x = -1
      systeme.set(ligne, colonne) = 
        - sol_hom1_mu.val_in_bound_jk(zone, j, k) ;
      systeme.set(ligne, colonne+1) = 
        - sol_hom2_mu.val_in_bound_jk(zone, j, k) ;
      
      sec_membre.set(ligne) += sol_part_mu.val_in_bound_jk(zone, j, k) ;
      ligne++ ;
      
      systeme.set(ligne, colonne) = 
        - sol_hom1_x.val_in_bound_jk(zone, j, k) ;
      systeme.set(ligne, colonne+1) = 
        - sol_hom2_x.val_in_bound_jk(zone, j, k) ;
      
      sec_membre.set(ligne) += sol_part_x.val_in_bound_jk(zone, j, k) ;
      ligne++ ;
      
      // Condition at x=1
      systeme.set(ligne, colonne) = 
        sol_hom1_mu.val_out_bound_jk(zone, j, k) ;
      systeme.set(ligne, colonne+1) = 
        sol_hom2_mu.val_out_bound_jk(zone, j, k) ;
      
      sec_membre.set(ligne) -= sol_part_mu.val_out_bound_jk(zone, j, k) ;
      ligne++ ;
      
      systeme.set(ligne, colonne) = 
        sol_hom1_x.val_out_bound_jk(zone, j, k) ;
      systeme.set(ligne, colonne+1) = 
        sol_hom2_x.val_out_bound_jk(zone, j, k) ;
      
      sec_membre.set(ligne) -= sol_part_x.val_out_bound_jk(zone, j, k) ;
      
      colonne += 2 ;
    }
    
    //Last  domain   
    nr = mgrid.get_nr(nz_bc) ;
    double alpha = mp_aff->get_alpha()[nz_bc] ;
    ligne-- ;
    
    //Condition at x = -1
    systeme.set(ligne, colonne) = 
      - sol_hom1_mu.val_in_bound_jk(nz_bc, j, k) ;
    if (!cedbc) systeme.set(ligne, colonne+1) = 
              - sol_hom2_mu.val_in_bound_jk(nz_bc, j, k) ;
    
    sec_membre.set(ligne) += sol_part_mu.val_in_bound_jk(nz_bc, j, k) ;
    ligne++ ;
    
    systeme.set(ligne, colonne) = 
      - sol_hom1_x.val_in_bound_jk(nz_bc, j, k) ;
    if (!cedbc) systeme.set(ligne, colonne+1) = 
              - sol_hom2_x.val_in_bound_jk(nz_bc, j, k) ;
    
    sec_membre.set(ligne) += sol_part_x.val_in_bound_jk(nz_bc, j, k) ;
    ligne++ ;
    
    if (!cedbc) {// Special condition at x=1
      
      systeme.set(ligne, colonne) = 
        c_mu*sol_hom1_mu.val_out_bound_jk(nz_bc, j, k) 
        + d_mu*dhom1_mu.val_out_bound_jk(nz_bc, j, k) / alpha 
        + c_x*sol_hom1_x.val_out_bound_jk(nz_bc, j, k) 
        + d_x*dhom1_x.val_out_bound_jk(nz_bc, j, k) / alpha ;
      systeme.set(ligne, colonne+1) = 
        c_mu*sol_hom2_mu.val_out_bound_jk(nz_bc, j, k) 
        + d_mu*dhom2_mu.val_out_bound_jk(nz_bc, j, k) / alpha
        + c_x*sol_hom2_x.val_out_bound_jk(nz_bc, j, k) 
        + d_x*dhom2_x.val_out_bound_jk(nz_bc, j, k) / alpha ;
      
      sec_membre.set(ligne) -= c_mu*sol_part_mu.val_out_bound_jk(nz_bc, j, k) 
        + d_mu*dpart_mu.val_out_bound_jk(nz_bc, j, k)/alpha
        + c_x*sol_part_mu.val_out_bound_jk(nz_bc, j, k) 
        + d_x*dpart_mu.val_out_bound_jk(nz_bc, j, k)/alpha
        - mub(k, j) ;
    }
    
    
    
    
    // System inversion: Solution of the system giving the coefficients for the homogeneous 
    // solutions
    //-------------------------------------------------------------------
    systeme.set_lu() ;
    Tbl facteur = systeme.inverse(sec_membre) ;
    
       
    int conte = 0 ;
    
    // everything is put to the right place...
    //----------------------------------------
    nr = mgrid.get_nr(0) ; //nucleus
    for (int i=0 ; i<nr ; i++) {
      mmu.set(0, k, j, i) = 0 ;
      mw.set(0, k, j, i) = 0 ;
    }
    nr = mgrid.get_nr(1) ; //first shell
    for (int i=0 ; i<nr ; i++) {
      mmu.set(1, k, j, i) = sol_part_mu(1, k, j, i)
        + facteur(conte)*sol_hom1_mu(1, k, j, i)
        + facteur(conte+1)*sol_hom2_mu(1, k, j, i);
      mw.set(1, k, j, i) = sol_part_x(1, k, j, i)
        + facteur(conte)*sol_hom1_x(1, k, j, i)
        + facteur(conte+1)*sol_hom2_x(1,k,j,i);
    }
    conte+=2 ;
    for (int zone=2 ; zone<=n_shell ; zone++) { //shells
      nr = mgrid.get_nr(zone) ;
      for (int i=0 ; i<nr ; i++) {
        mmu.set(zone, k, j, i) = sol_part_mu(zone, k, j, i)
          + facteur(conte)*sol_hom1_mu(zone, k, j, i) 
          + facteur(conte+1)*sol_hom2_mu(zone, k, j, i) ;
        
        mw.set(zone, k, j, i) = sol_part_x(zone, k, j, i)
          + facteur(conte)*sol_hom1_x(zone, k, j, i) 
          + facteur(conte+1)*sol_hom2_x(zone, k, j, i) ;
      }
      conte+=2 ;
    }
    if (cedbc) {
      nr = mgrid.get_nr(nzm1) ; //compactified external domain
      for (int i=0 ; i<nr ; i++) {
        mmu.set(nzm1, k, j, i) = sol_part_mu(nzm1, k, j, i)
          + facteur(conte)*sol_hom1_mu(nzm1, k, j, i) ;
        
        mw.set(nzm1, k, j, i) = sol_part_x(nzm1, k, j, i)
          + facteur(conte)*sol_hom1_x(nzm1, k, j, i) ;
      }
    }
      } // End of nullite_plm  
    } //End of loop on theta
  
  if (tilde_mu.set_spectral_va().c != 0x0) 
    delete tilde_mu.set_spectral_va().c ;
  tilde_mu.set_spectral_va().c = 0x0 ;
  tilde_mu.set_spectral_va().ylm_i() ;
  
  if (x_new.set_spectral_va().c != 0x0) 
    delete x_new.set_spectral_va().c ;
  x_new.set_spectral_va().c = 0x0 ;
  x_new.set_spectral_va().ylm_i();
  
}



//----------------------------------------------------------------------------------
//
//                               sol_Dirac_tilde_B
//
//----------------------------------------------------------------------------------

void Sym_tensor_trans::sol_Dirac_BC2(const Scalar& bb, const Scalar& cc, const Scalar& hh, 
                      Scalar& hrr, Scalar& tilde_eta, Scalar& ww, Scalar bound_eta,double dir, double neum, double rhor, Param* par_bc, Param* par_mat) {
  
  const Map_af* mp_aff = dynamic_cast<const Map_af*>(mp) ;
  assert(mp_aff != 0x0) ; //Only affine mapping for the moment
  
  const Mg3d& mgrid = *mp_aff->get_mg() ;
  assert(mgrid.get_type_r(0) == RARE)  ;

  int nz = mgrid.get_nzone() ;
  int nzm1 = nz - 1 ;
  bool ced = (mgrid.get_type_r(nzm1) == UNSURR) ;
  int n_shell = ced ? nz-2 : nzm1 ;
  int nz_bc = nzm1 ;
  if (par_bc != 0x0)
    if (par_bc->get_n_int() > 0)
      nz_bc = par_bc->get_int() ;
  n_shell = (nz_bc < n_shell ? nz_bc : n_shell) ;
  bool cedbc = (ced && (nz_bc == nzm1)) ; 
#ifndef NDEBUG
  if (!cedbc) {
    assert(par_bc != 0x0) ;
    assert(par_bc->get_n_tbl_mod() >= 2) ;
  }
#endif
  int nt = mgrid.get_nt(0) ;
  int np = mgrid.get_np(0) ;
    
  int l_q, m_q, base_r;

  // ON passe en ylm les quantités B et C !!! CRUCIAL !!! 
 
  Scalar bb2 = bb; bb2.set_spectral_va().ylm();
  Scalar cc2 = cc; cc2.set_spectral_va().ylm();
 

  Scalar hh2 = hh; hh2.set_spectral_va().ylm();
 
  Base_val base = hh2.get_spectral_base() ; 
  
  
  Scalar tilde_b(*mp_aff); tilde_b.annule_hard(); tilde_b.std_spectral_base();
  tilde_b.set_spectral_va().ylm();

  // Base_val base = hrr.get_spectral_base();

  //    int m_q, l_q, base_r ;
    for (int lz=0; lz<nz; lz++) {
    int nr = mgrid.get_nr(lz);
        for (int k=0; k<np+1; k++)
        for (int j=0; j<nt; j++) {
            base.give_quant_numbers(lz, k, j, m_q, l_q, base_r) ;
            if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q > 1))
            {
            for (int i=0; i<nr; i++) 
                tilde_b.set_spectral_va().c_cf->set(lz, k, j, i)
        +=  2*(*bb2.get_spectral_va().c_cf)(lz, k, j, i)
          +  (*cc2.get_spectral_va().c_cf)(lz, k, j, i)/ (2* double(l_q +1.));
            }
        }
    }


        if (tilde_b.set_spectral_va().c != 0x0) 
        delete tilde_b.set_spectral_va().c ;
            tilde_b.set_spectral_va().c = 0x0 ;
    tilde_b.set_spectral_va().coef_i();
    

   if ( (tilde_b.get_etat() == ETATZERO) && (hh.get_etat() == ETATZERO) ) {
    hrr = 0 ;
    tilde_eta = 0 ;
    ww = 0 ;
    return ;
  }

  bound_eta.set_spectral_va().ylm();
  Scalar tilde_b2 = tilde_b;
  tilde_b2.set_spectral_va().ylm();

  assert (tilde_b.get_etat() != ETATNONDEF) ;
  assert (hh.get_etat() != ETATNONDEF) ;
  
  Scalar source = tilde_b ;
  Scalar source_coq = tilde_b ;
  source_coq.annule_domain(0) ;
  source_coq.annule_domain(nzm1) ;
  source_coq.mult_r() ;
  source.set_spectral_va().ylm() ;
  source_coq.set_spectral_va().ylm() ;
  bool bnull = (tilde_b.get_etat() == ETATZERO) ;
  
  assert(hh.check_dzpuis(0)) ;
  Scalar hoverr = hh ;
  hoverr.div_r_dzpuis(2) ;
  hoverr.set_spectral_va().ylm() ;
  Scalar dhdr = hh.dsdr() ;
  dhdr.set_spectral_va().ylm() ;
  Scalar h_coq = hh ;
  h_coq.set_spectral_va().ylm() ;
  Scalar dh_coq = hh.dsdr() ;
  dh_coq.mult_r_dzpuis(0) ;
  dh_coq.set_spectral_va().ylm() ;    
  bool hnull = (hh.get_etat() == ETATZERO) ;
    
    int lmax = base.give_lmax(mgrid, 0) + 1;
    

    // Utilisation des params, facultative, permettant uniquement une optimisation....
    
    bool need_calculation = true ;
    if (par_mat != 0x0) {
      bool param_new = false ;
      if ((par_mat->get_n_int_mod() >= 4)
      &&(par_mat->get_n_tbl_mod()>=1)
      &&(par_mat->get_n_matrice_mod()>=1)
      &&(par_mat->get_n_itbl_mod()>=1)) {
    if (par_mat->get_int_mod(0) < nz_bc) param_new = true ;
    if (par_mat->get_int_mod(1) != lmax) param_new = true ;
        if (par_mat->get_int_mod(2) != mgrid.get_type_t() ) param_new = true ;
        if (par_mat->get_int_mod(3) != mgrid.get_type_p() ) param_new = true ;
        if (par_mat->get_itbl_mod(0)(0) != mgrid.get_nr(0)) param_new = true ;
        if (fabs(par_mat->get_tbl_mod(0)(0) - mp_aff->get_alpha()[0]) > 2.e-15)
          param_new = true ; 
        for (int l=1; l<= n_shell; l++) {
          if (par_mat->get_itbl_mod(0)(l) != mgrid.get_nr(l)) param_new = true ;
          if (fabs(par_mat->get_tbl_mod(0)(l) - mp_aff->get_beta()[l] / 
               mp_aff->get_alpha()[l]) > 2.e-15) param_new = true ;
        }
        if (ced) {
        if (par_mat->get_itbl_mod(0)(nzm1) != mgrid.get_nr(nzm1)) param_new = true ;
        if (fabs(par_mat->get_tbl_mod(0)(nzm1) - mp_aff->get_alpha()[nzm1]) > 2.e-15)
          param_new = true ; 
        }
      }
      else{
    param_new = true ;
      }
      if (param_new) {
    par_mat->clean_all() ;
    par_mat->add_int_mod(*(new int(nz_bc)), 0) ;
    par_mat->add_int_mod(*(new int(lmax)), 1) ;
    par_mat->add_int_mod(*(new int(mgrid.get_type_t())), 2) ;
    par_mat->add_int_mod(*(new int(mgrid.get_type_p())), 3) ;
    Itbl* pnr = new Itbl(nz) ;
    pnr->set_etat_qcq() ;
    par_mat->add_itbl_mod(*pnr) ;
    for (int l=0; l<nz; l++)
      pnr->set(l) = mgrid.get_nr(l) ;
    Tbl* palpha = new Tbl(nz) ;
    palpha->set_etat_qcq() ;
    par_mat->add_tbl_mod(*palpha) ;
    palpha->set(0) = mp_aff->get_alpha()[0] ;
    for (int l=1; l<nzm1; l++)
      palpha->set(l) = mp_aff->get_beta()[l] / mp_aff->get_alpha()[l] ;
    palpha->set(nzm1) = mp_aff->get_alpha()[nzm1] ;
      }
      else need_calculation = false ;
    }

    hrr.set_etat_qcq() ;
    hrr.set_spectral_base(base) ;
    hrr.set_spectral_va().set_etat_cf_qcq() ;
    hrr.set_spectral_va().c_cf->annule_hard() ;   
    tilde_eta.annule_hard() ;
    tilde_eta.set_spectral_base(base) ;
    tilde_eta.set_spectral_va().set_etat_cf_qcq() ;
    tilde_eta.set_spectral_va().c_cf->annule_hard() ;   
    ww.annule_hard() ;
    ww.set_spectral_base(base) ;
    ww.set_spectral_va().set_etat_cf_qcq() ;
    ww.set_spectral_va().c_cf->annule_hard() ;   

    sol_Dirac_l01(hh2, hrr, tilde_eta, par_mat) ;
    tilde_eta.annule_l(0,0, true) ;
    
    Mtbl_cf sol_part_hrr(mgrid, base) ; sol_part_hrr.annule_hard() ;
    Mtbl_cf sol_part_eta(mgrid, base) ; sol_part_eta.annule_hard() ;
    Mtbl_cf sol_part_w(mgrid, base) ; sol_part_w.annule_hard() ;
    Mtbl_cf sol_hom1_hrr(mgrid, base) ; sol_hom1_hrr.annule_hard() ;
    Mtbl_cf sol_hom1_eta(mgrid, base) ; sol_hom1_eta.annule_hard() ;
    Mtbl_cf sol_hom1_w(mgrid, base) ; sol_hom1_w.annule_hard() ;
    Mtbl_cf sol_hom2_hrr(mgrid, base) ; sol_hom2_hrr.annule_hard() ;
    Mtbl_cf sol_hom2_eta(mgrid, base) ; sol_hom2_eta.annule_hard() ;
    Mtbl_cf sol_hom2_w(mgrid, base) ; sol_hom2_w.annule_hard() ;
    Mtbl_cf sol_hom3_hrr(mgrid, base) ; sol_hom3_hrr.annule_hard() ;
    Mtbl_cf sol_hom3_eta(mgrid, base) ; sol_hom3_eta.annule_hard() ;
    Mtbl_cf sol_hom3_w(mgrid, base) ; sol_hom3_w.annule_hard() ;
    
    Itbl mat_done(lmax) ;
    
    
    //   Calcul des solutions homogenes et particulieres... 
    
    
    //---------------
    //--  NUCLEUS ---
    //---------------
    {int lz = 0 ;  
    int nr = mgrid.get_nr(lz) ;
    double alpha = mp_aff->get_alpha()[lz] ;
    Matrice ope(3*nr, 3*nr) ;
    int ind2 = 2*nr ;
    if (need_calculation && (par_mat != 0x0)) mat_done.annule_hard() ;
    
    for (int k=0 ; k<np+1 ; k++) {
    for (int j=0 ; j<nt ; j++) {
      // quantic numbers and spectral bases
      base.give_quant_numbers(lz, k, j, m_q, l_q, base_r) ;
      if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q > 1)) {
        if (need_calculation) {
          ope.set_etat_qcq() ;
          Diff_dsdx od(base_r, nr) ; const Matrice& md = od.get_matrice() ;
          Diff_sx os(base_r, nr) ; const Matrice& ms = os.get_matrice() ;
          
          for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin,col) = md(lin,col) + 3*ms(lin,col) ;
          for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin,col+nr) = -l_q*(l_q+1)*ms(lin,col) ;
          for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin,col+2*nr) = 0 ;
          for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+nr,col) = -0.5*ms(lin,col) ;
          for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+nr,col+nr) = md(lin,col) + 3*ms(lin,col) ;
          for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+nr,col+2*nr) = (2. - l_q*(l_q+1))*ms(lin,col) ;
          for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+2*nr,col) = -0.5*md(lin,col)/double(l_q+1) 
            - 0.5*double(l_q+4)/double(l_q+1)*ms(lin,col) ;
          for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+2*nr,col+nr) = -2*ms(lin,col) ;
          for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+2*nr,col+2*nr) =  (l_q+2)*md(lin,col) 
            + l_q*(l_q+2)*ms(lin,col) ;
          
          ope *= 1./alpha ;
          for (int col=0; col<3*nr; col++) 
        if (l_q>2) ope.set(ind2+nr-2, col) = 0 ;
          for (int col=0; col<3*nr; col++) {
        ope.set(nr-1, col) = 0 ;
        ope.set(2*nr-1, col) = 0 ;
        ope.set(3*nr-1, col) = 0 ;
          }
          int pari = 1 ;
          if (base_r == R_CHEBP) {
        for (int col=0; col<nr; col++) {
          ope.set(nr-1, col) = pari ;
          ope.set(2*nr-1, col+nr) = pari ;
          ope.set(3*nr-1, col+2*nr) = pari ;
          pari = - pari ;
        }
          }
          else { //In the odd case, the last coefficient must be zero!
        ope.set(nr-1, nr-1) = 1 ;
        ope.set(2*nr-1, 2*nr-1) = 1 ;
        ope.set(3*nr-1, 3*nr-1) = 1 ;
          }         
          if (l_q>2) 
        ope.set(ind2+nr-2, ind2) = 1 ;
          
            ope.set_lu() ;
            if ((par_mat != 0x0) && (mat_done(l_q) == 0)) {
              Matrice* pope = new Matrice(ope) ;
              par_mat->add_matrice_mod(*pope, lz*lmax + l_q) ;
              mat_done.set(l_q) = 1 ;
            }
        } //End of case when a calculation is needed
        
        const Matrice& oper = (par_mat == 0x0 ? ope : 
                       par_mat->get_matrice_mod(lz*lmax + l_q) ) ;
        Tbl sec(3*nr) ;
        sec.set_etat_qcq() ;
        if (hnull) {
          for (int lin=0; lin<2*nr; lin++)
            sec.set(lin) = 0 ;
          for (int lin=0; lin<nr; lin++)
            sec.set(2*nr+lin) = (*source.get_spectral_va().c_cf)
              (lz, k, j, lin) ;
        }
        else {
          for (int lin=0; lin<nr; lin++)
            sec.set(lin) = (*hoverr.get_spectral_va().c_cf)(lz, k, j, lin) ;
          for (int lin=0; lin<nr; lin++)
            sec.set(lin+nr) = -0.5*(*hoverr.get_spectral_va().c_cf)
              (lz, k, j, lin) ;
          if (bnull) {
            for (int lin=0; lin<nr; lin++)
              sec.set(2*nr+lin) = -0.5/double(l_q+1)*(
                                  (*dhdr.get_spectral_va().c_cf)(lz, k, j, lin)
                                  + (l_q+2)*(*hoverr.get_spectral_va().c_cf)(lz, k, j, lin) ) ;
          }
          else {
            for (int lin=0; lin<nr; lin++)
              sec.set(2*nr+lin) = -0.5/double(l_q+1)*(
                                  (*dhdr.get_spectral_va().c_cf)(lz, k, j, lin)
                                  + (l_q+2)*(*hoverr.get_spectral_va().c_cf)(lz, k, j, lin) )
            + (*source.get_spectral_va().c_cf)(lz, k, j, lin) ;
          }         
        }
        if (l_q>2) sec.set(ind2+nr-2) = 0 ;
        sec.set(3*nr-1) = 0 ;
        Tbl sol = oper.inverse(sec) ;
        for (int i=0; i<nr; i++) {
          sol_part_hrr.set(lz, k, j, i) = sol(i) ;
          sol_part_eta.set(lz, k, j, i) = sol(i+nr) ;
          sol_part_w.set(lz, k, j, i) = sol(i+2*nr) ;
        }
        sec.annule_hard() ;
        if (l_q>2) {
          sec.set(ind2+nr-2) = 1 ;
          sol = oper.inverse(sec) ;
        }
        else { //Homogeneous solution put in by hand in the case l=2
          sol.annule_hard() ;
          sol.set(0) = 4 ;
          sol.set(nr) = 2 ;
          sol.set(2*nr) = 1 ;
        }
        for (int i=0; i<nr; i++) {
          sol_hom3_hrr.set(lz, k, j, i) = sol(i) ;
          sol_hom3_eta.set(lz, k, j, i) = sol(i+nr) ;
          sol_hom3_w.set(lz, k, j, i) = sol(i+2*nr) ;
        }
      }
    }
    }
    }
    
    
    //-------------
    // -- Shells --
    //-------------
    
    for (int lz=1; lz<= n_shell; lz++) {
      if (need_calculation && (par_mat != 0x0)) mat_done.annule_hard() ;
      int nr = mgrid.get_nr(lz) ;
      int ind0 = 0 ;
      int ind1 = nr ;
      int ind2 = 2*nr ;
      double alpha = mp_aff->get_alpha()[lz] ;
      double ech = mp_aff->get_beta()[lz] / alpha ;
      Matrice ope(3*nr, 3*nr) ;
      
      for (int k=0 ; k<np+1 ; k++) {
    for (int j=0 ; j<nt ; j++) {
      // quantic numbers and spectral bases
      base.give_quant_numbers(lz, k, j, m_q, l_q, base_r) ;
      if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q > 1)) {
            if (need_calculation) {
              ope.set_etat_qcq() ;
              Diff_xdsdx oxd(base_r, nr) ; const Matrice& mxd = oxd.get_matrice() ;
              Diff_dsdx od(base_r, nr) ; const Matrice& md = od.get_matrice() ;
              Diff_id oid(base_r, nr) ; const Matrice& mid = oid.get_matrice() ;
              
              for (int lin=0; lin<nr; lin++) 
            for (int col=0; col<nr; col++) 
              ope.set(lin,col) = mxd(lin,col) + ech*md(lin,col) 
                + 3*mid(lin,col) ;
              for (int lin=0; lin<nr; lin++) 
            for (int col=0; col<nr; col++) 
              ope.set(lin,col+nr) = -l_q*(l_q+1)*mid(lin,col) ;
              for (int lin=0; lin<nr; lin++) 
            for (int col=0; col<nr; col++) 
              ope.set(lin,col+2*nr) = 0 ;
              for (int lin=0; lin<nr; lin++) 
            for (int col=0; col<nr; col++) 
              ope.set(lin+nr,col) = -0.5*mid(lin,col) ;
              for (int lin=0; lin<nr; lin++) 
            for (int col=0; col<nr; col++) 
              ope.set(lin+nr,col+nr) = mxd(lin,col) + ech*md(lin,col) 
                + 3*mid(lin,col) ;
              for (int lin=0; lin<nr; lin++) 
            for (int col=0; col<nr; col++) 
              ope.set(lin+nr,col+2*nr) = (2. - l_q*(l_q+1))*mid(lin,col) ;
              for (int lin=0; lin<nr; lin++) 
            for (int col=0; col<nr; col++) 
              ope.set(lin+2*nr,col) = 
                -0.5/double(l_q+1)*(mxd(lin,col) + ech*md(lin,col)
                        + double(l_q+4)*mid(lin,col)) ;
              for (int lin=0; lin<nr; lin++) 
            for (int col=0; col<nr; col++) 
              ope.set(lin+2*nr,col+nr) = -2*mid(lin,col) ;
              for (int lin=0; lin<nr; lin++) 
            for (int col=0; col<nr; col++) 
              ope.set(lin+2*nr,col+2*nr) =  
                double(l_q+2)*(mxd(lin,col) + ech*md(lin,col) 
                       + l_q*mid(lin,col)) ;
              for (int col=0; col<3*nr; col++) {
            ope.set(ind0+nr-1, col) = 0 ;
            ope.set(ind1+nr-1, col) = 0 ;
            ope.set(ind2+nr-1, col) = 0 ;
              }
              ope.set(ind0+nr-1, ind0) = 1 ;
              ope.set(ind1+nr-1, ind1) = 1 ;
              ope.set(ind2+nr-1, ind2) = 1 ;
              
              ope.set_lu() ;
            if ((par_mat != 0x0) && (mat_done(l_q) == 0)) {
              Matrice* pope = new Matrice(ope) ;
              par_mat->add_matrice_mod(*pope, lz*lmax + l_q) ;
              mat_done.set(l_q) = 1 ;
            }
            } //End of case when a calculation is needed
            const Matrice& oper = (par_mat == 0x0 ? ope : 
                       par_mat->get_matrice_mod(lz*lmax + l_q) ) ;
            Tbl sec(3*nr) ;
            sec.set_etat_qcq() ;
            if (hnull) {
              for (int lin=0; lin<2*nr; lin++)
            sec.set(lin) = 0 ;
              for (int lin=0; lin<nr; lin++)
            sec.set(2*nr+lin) = (*source_coq.get_spectral_va().c_cf)
              (lz, k, j, lin) ;
            }
            else {
              for (int lin=0; lin<nr; lin++)
            sec.set(lin) = (*h_coq.get_spectral_va().c_cf)(lz, k, j, lin) ;
              for (int lin=0; lin<nr; lin++)
            sec.set(lin+nr) = -0.5*(*h_coq.get_spectral_va().c_cf)
              (lz, k, j, lin) ;
              if (bnull) {
            for (int lin=0; lin<nr; lin++)
              sec.set(2*nr+lin) = -0.5/double(l_q+1)*(
                                  (*dh_coq.get_spectral_va().c_cf)(lz, k, j, lin)
                                  + (l_q+2)*(*h_coq.get_spectral_va().c_cf)(lz, k, j, lin) ) ;
              }
              else {
            for (int lin=0; lin<nr; lin++)
              sec.set(2*nr+lin) = -0.5/double(l_q+1)*(
                                  (*dh_coq.get_spectral_va().c_cf)(lz, k, j, lin)
                                  + (l_q+2)*(*h_coq.get_spectral_va().c_cf)(lz, k, j, lin) )
                + (*source_coq.get_spectral_va().c_cf)(lz, k, j, lin) ;
              }
            }
            sec.set(ind0+nr-1) = 0 ;
            sec.set(ind1+nr-1) = 0 ;
            sec.set(ind2+nr-1) = 0 ;
            Tbl sol = oper.inverse(sec) ;
            for (int i=0; i<nr; i++) {
              sol_part_hrr.set(lz, k, j, i) = sol(i) ;
              sol_part_eta.set(lz, k, j, i) = sol(i+nr) ;
              sol_part_w.set(lz, k, j, i) = sol(i+2*nr) ;
            }
            sec.annule_hard() ;
            sec.set(ind0+nr-1) = 1 ;
            sol = oper.inverse(sec) ;
            for (int i=0; i<nr; i++) {
              sol_hom1_hrr.set(lz, k, j, i) = sol(i) ;
              sol_hom1_eta.set(lz, k, j, i) = sol(i+nr) ;
              sol_hom1_w.set(lz, k, j, i) = sol(i+2*nr) ;
            }           
            sec.set(ind0+nr-1) = 0 ;
            sec.set(ind1+nr-1) = 1 ;
            sol = oper.inverse(sec) ;
            for (int i=0; i<nr; i++) {
              sol_hom2_hrr.set(lz, k, j, i) = sol(i) ;
              sol_hom2_eta.set(lz, k, j, i) = sol(i+nr) ;
              sol_hom2_w.set(lz, k, j, i) = sol(i+2*nr) ;
            }           
            sec.set(ind1+nr-1) = 0 ;
            sec.set(ind2+nr-1) = 1 ;
            sol = oper.inverse(sec) ;
            for (int i=0; i<nr; i++) {
              sol_hom3_hrr.set(lz, k, j, i) = sol(i) ;
              sol_hom3_eta.set(lz, k, j, i) = sol(i+nr) ;
              sol_hom3_w.set(lz, k, j, i) = sol(i+2*nr) ;
            }   
      }
    }
      }
    }
    
    //------------------------------
    // Compactified external domain
    //------------------------------
    if (cedbc) {int lz = nzm1 ;  
    if (need_calculation && (par_mat != 0x0)) mat_done.annule_hard() ;
    int nr = mgrid.get_nr(lz) ;
    int ind0 = 0 ;
    int ind1 = nr ;
    int ind2 = 2*nr ;
    double alpha = mp_aff->get_alpha()[lz] ;
    Matrice ope(3*nr, 3*nr) ;
    
    for (int k=0 ; k<np+1 ; k++) {
      for (int j=0 ; j<nt ; j++) {
    // quantic numbers and spectral bases
    base.give_quant_numbers(lz, k, j, m_q, l_q, base_r) ;
    if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q > 1)) {
      if (need_calculation) {
        ope.set_etat_qcq() ;
        Diff_dsdx od(base_r, nr) ; const Matrice& md = od.get_matrice() ;
        Diff_sx os(base_r, nr) ; const Matrice& ms = os.get_matrice() ;
        
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin,col) = - md(lin,col) + 3*ms(lin,col) ;
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin,col+nr) = -l_q*(l_q+1)*ms(lin,col) ;
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin,col+2*nr) = 0 ;
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin+nr,col) = -0.5*ms(lin,col) ;
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin+nr,col+nr) = -md(lin,col) + 3*ms(lin,col) ;
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin+nr,col+2*nr) = (2. - l_q*(l_q+1))*ms(lin,col) ;
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin+2*nr,col) =  0.5*md(lin,col)/double(l_q+1) 
          - 0.5*double(l_q+4)/double(l_q+1)*ms(lin,col) ;
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin+2*nr,col+nr) = -2*ms(lin,col) ;
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin+2*nr,col+2*nr) =  -(l_q+2)*md(lin,col) 
          + l_q*(l_q+2)*ms(lin,col) ;
        ope *= 1./alpha ;
        for (int col=0; col<3*nr; col++) {
          ope.set(ind0+nr-2, col) = 0 ;
          ope.set(ind0+nr-1, col) = 0 ;
          ope.set(ind1+nr-2, col) = 0 ;
          ope.set(ind1+nr-1, col) = 0 ;
          ope.set(ind2+nr-1, col) = 0 ;
        }
        for (int col=0; col<nr; col++) {
          ope.set(ind0+nr-1, col+ind0) = 1 ;
          ope.set(ind1+nr-1, col+ind1) = 1 ;
          ope.set(ind2+nr-1, col+ind2) = 1 ;
        }
        ope.set(ind0+nr-2, ind0+1) = 1 ;
        ope.set(ind1+nr-2, ind1+2) = 1 ;
        
        ope.set_lu() ;
        if ((par_mat != 0x0) && (mat_done(l_q) == 0)) {
          Matrice* pope = new Matrice(ope) ;
          par_mat->add_matrice_mod(*pope, lz*lmax + l_q) ;
          mat_done.set(l_q) = 1 ;
        }
      } //End of case when a calculation is needed
      const Matrice& oper = (par_mat == 0x0 ? ope : 
                 par_mat->get_matrice_mod(lz*lmax + l_q) ) ;
      
      Tbl sec(3*nr) ;
      sec.set_etat_qcq() ;
      if (hnull) {
        for (int lin=0; lin<2*nr; lin++)
          sec.set(lin) = 0 ;
        for (int lin=0; lin<nr; lin++)
            sec.set(2*nr+lin) = (*source.get_spectral_va().c_cf)
              (lz, k, j, lin) ;
        }
      else {
        for (int lin=0; lin<nr; lin++)
          sec.set(lin) = (*hoverr.get_spectral_va().c_cf)(lz, k, j, lin) ;
        for (int lin=0; lin<nr; lin++)
          sec.set(lin+nr) = -0.5*(*hoverr.get_spectral_va().c_cf)
        (lz, k, j, lin) ;
        if (bnull) {
          for (int lin=0; lin<nr; lin++)
        sec.set(2*nr+lin) = -0.5/double(l_q+1)*(
                            (*dhdr.get_spectral_va().c_cf)(lz, k, j, lin)
                            + (l_q+2)*(*hoverr.get_spectral_va().c_cf)(lz, k, j, lin) ) ;
        }
        else {
          for (int lin=0; lin<nr; lin++)
        sec.set(2*nr+lin) = -0.5/double(l_q+1)*(
                            (*dhdr.get_spectral_va().c_cf)(lz, k, j, lin)
                            + (l_q+2)*(*hoverr.get_spectral_va().c_cf)(lz, k, j, lin) )
          + (*source.get_spectral_va().c_cf)(lz, k, j, lin) ;
        }
      }
      sec.set(ind0+nr-2) = 0 ;
      sec.set(ind0+nr-1) = 0 ;
      sec.set(ind1+nr-1) = 0 ;
      sec.set(ind1+nr-2) = 0 ;
      sec.set(ind2+nr-1) = 0 ;
      Tbl sol = oper.inverse(sec) ;
      for (int i=0; i<nr; i++) {
        sol_part_hrr.set(lz, k, j, i) = sol(i) ;
        sol_part_eta.set(lz, k, j, i) = sol(i+nr) ;
        sol_part_w.set(lz, k, j, i) = sol(i+2*nr) ;
      }
      sec.annule_hard() ;
      sec.set(ind0+nr-2) = 1 ;
      sol = oper.inverse(sec) ;
      for (int i=0; i<nr; i++) {
        sol_hom1_hrr.set(lz, k, j, i) = sol(i) ;
        sol_hom1_eta.set(lz, k, j, i) = sol(i+nr) ;
        sol_hom1_w.set(lz, k, j, i) = sol(i+2*nr) ;
      }         
      sec.set(ind0+nr-2) = 0 ;
      sec.set(ind1+nr-2) = 1 ;
      sol = oper.inverse(sec) ;
      for (int i=0; i<nr; i++) {
        sol_hom2_hrr.set(lz, k, j, i) = sol(i) ;
        sol_hom2_eta.set(lz, k, j, i) = sol(i+nr) ;
        sol_hom2_w.set(lz, k, j, i) = sol(i+2*nr) ;
      }
    }
      }
    }
    }
    
    // Matching system...
    
    
    
    int taille = 3*nz_bc ; // Un de moins que dans la version complete R3
    if (cedbc) taille-- ;
    Mtbl_cf& mhrr = *hrr.set_spectral_va().c_cf ;
    Mtbl_cf& meta = *tilde_eta.set_spectral_va().c_cf ;
    Mtbl_cf& mw = *ww.set_spectral_va().c_cf ;
      Tbl sec_membre(taille) ; 
    Matrice systeme(taille, taille) ; 
    int ligne ;  int colonne ;
    Tbl pipo(1) ;
    const Tbl& hrrb = (cedbc ? pipo : par_bc->get_tbl_mod(1) );
    double chrr = (cedbc ? 0 : par_bc->get_tbl_mod()(4) ) ;
    double dhrr = (cedbc ? 0 : par_bc->get_tbl_mod()(5) ) ;
    double ceta = (cedbc ? 0 : par_bc->get_tbl_mod()(6) ) ;
    double deta = (cedbc ? 0 : par_bc->get_tbl_mod()(7) ) ;
    double cw = (cedbc ? 0 : par_bc->get_tbl_mod()(8) ) ;
    double dw = (cedbc ? 0 : par_bc->get_tbl_mod()(9) ) ;
    Mtbl_cf dhom1_hrr = sol_hom1_hrr ; 
    Mtbl_cf dhom2_hrr = sol_hom2_hrr ; 
    Mtbl_cf dhom3_hrr = sol_hom3_hrr ; 
    Mtbl_cf dpart_hrr = sol_part_hrr ; 
    Mtbl_cf dhom1_eta = sol_hom1_eta ; 
    Mtbl_cf dhom2_eta = sol_hom2_eta ; 
    Mtbl_cf dhom3_eta = sol_hom3_eta ; 
    Mtbl_cf dpart_eta = sol_part_eta ; 
    Mtbl_cf dhom1_w = sol_hom1_w ; 
    Mtbl_cf dhom2_w = sol_hom2_w ; 
    Mtbl_cf dhom3_w = sol_hom3_w ; 
    Mtbl_cf dpart_w = sol_part_w ; 


    dhom1_hrr.dsdx() ; dhom1_eta.dsdx() ; dhom1_w.dsdx() ;
    dhom2_hrr.dsdx() ; dhom2_eta.dsdx() ; dhom2_w.dsdx() ;
    dhom3_hrr.dsdx() ; dhom3_eta.dsdx() ; dhom3_w.dsdx() ;
    dpart_hrr.dsdx() ; dpart_eta.dsdx() ; dpart_w.dsdx() ;
    
    Mtbl_cf d2hom1_hrr = dhom1_hrr ; 
    Mtbl_cf d2hom2_hrr = dhom2_hrr ;
    Mtbl_cf d2hom3_hrr = dhom3_hrr; 
    Mtbl_cf d2part_hrr = dpart_hrr ; 
    d2hom1_hrr.dsdx(); d2hom2_hrr.dsdx(); d2hom3_hrr.dsdx(); d2part_hrr.dsdx();
 


    // Loop on l and m//
    
    for (int k=0 ; k<np+1 ; k++)
      for (int j=0 ; j<nt ; j++) {
    base.give_quant_numbers(0, k, j, m_q, l_q, base_r) ;
    if ((nullite_plm(j, nt, k, np, base) == 1) && (l_q > 1)) {
      ligne = 0 ;
      colonne = 0 ;
      systeme.annule_hard() ;
      sec_membre.annule_hard() ;
      
      //First shell
      //Condition at x=-1;
      int nr = mgrid.get_nr(1);
         double alpha2 = mp_aff->get_alpha()[1] ; 
      // A compatibility condition is set in order to be coherent with second order potentials definition

    const Coord& rr = (*mp_aff).r ;
        Scalar rrr(*mp_aff); rrr = rr;

      systeme.set(ligne, colonne)= (dhom1_w.val_in_bound_jk(1,j,k))/alpha2 + (0.5/rhor)*(double(l_q*(l_q+1)))*sol_hom1_w.val_in_bound_jk(1,j,k) - (1./rhor)*sol_hom1_eta.val_in_bound_jk(1,j,k) - (0.25/rhor)*sol_hom1_hrr.val_in_bound_jk(1,j,k);

      systeme.set(ligne, colonne+1)= (dhom2_w.val_in_bound_jk(1,j,k))/alpha2 +(0.5/rhor)*(double(l_q*(l_q+1)))*sol_hom2_w.val_in_bound_jk(1,j,k) - (1./rhor)*sol_hom2_eta.val_in_bound_jk(1,j,k) - (0.25/rhor)*sol_hom2_hrr.val_in_bound_jk(1,j,k);
  
      systeme.set(ligne, colonne+2)= (dhom3_w.val_in_bound_jk(1,j,k))/alpha2 +(0.5/rhor)*(double(l_q*(l_q+1)))*sol_hom3_w.val_in_bound_jk(1,j,k) - (1./rhor)*sol_hom3_eta.val_in_bound_jk(1,j,k) - (0.25/rhor)*sol_hom3_hrr.val_in_bound_jk(1,j,k) ;
  
      sec_membre.set(ligne)= - (dpart_w.val_in_bound_jk(1,j,k)/alpha2 +(0.5/rhor)*(double(l_q*(l_q+1)))*sol_part_w.val_in_bound_jk(1,j,k) - (1./rhor)*sol_part_eta.val_in_bound_jk(1,j,k) - (0.25/rhor)*sol_part_hrr.val_in_bound_jk(1,j,k));

  Mtbl_cf *Bbb = bb2.get_spectral_va().c_cf; 
  
    sec_membre.set(ligne) += (*Bbb).val_in_bound_jk(1,j,k);


  ligne++ ;

      // A Robyn-type boundary condition is imposed on eta
      
      systeme.set(ligne, colonne) = 
        dir*sol_hom1_hrr.val_in_bound_jk(1, j, k) + neum*dhom1_hrr.val_in_bound_jk(1,j,k)/alpha2;
      systeme.set(ligne, colonne+1) = 
        dir*sol_hom2_hrr.val_in_bound_jk(1, j, k) +neum*dhom2_hrr.val_in_bound_jk(1,j,k)/alpha2;
      systeme.set(ligne, colonne+2) = 
        + dir*sol_hom3_hrr.val_in_bound_jk(1, j, k) + neum*dhom3_hrr.val_in_bound_jk(1,j,k)/alpha2;
      
      
      double blob =  (*(bound_eta.get_spectral_va().c_cf)).val_in_bound_jk(1, j, k);
      sec_membre.set(ligne) += - sol_part_hrr.val_in_bound_jk(1, j, k) - neum*dpart_hrr.val_in_bound_jk(1,j,k)/alpha2 +  blob ;
      
      ligne++ ;
      
      
      //Conditions at x=1;  

      systeme.set(ligne, colonne) = 
        sol_hom1_hrr.val_out_bound_jk(1, j, k) ;
      systeme.set(ligne, colonne+1) = 
        sol_hom2_hrr.val_out_bound_jk(1, j, k) ;
      systeme.set(ligne, colonne+2) = 
        sol_hom3_hrr.val_out_bound_jk(1, j, k) ;
      
      sec_membre.set(ligne) -= sol_part_hrr.val_out_bound_jk(1, j, k) ;
      ligne++ ;
      
      systeme.set(ligne, colonne) = 
        sol_hom1_eta.val_out_bound_jk(1, j, k) ;
      systeme.set(ligne, colonne+1) = 
        sol_hom2_eta.val_out_bound_jk(1, j, k) ;
      systeme.set(ligne, colonne+2) = 
        sol_hom3_eta.val_out_bound_jk(1, j, k) ;
      
      sec_membre.set(ligne) -= sol_part_eta.val_out_bound_jk(1, j, k) ;
      ligne++ ;
      
      systeme.set(ligne, colonne) = 
        sol_hom1_w.val_out_bound_jk(1, j, k) ;
      systeme.set(ligne, colonne+1) = 
        sol_hom2_w.val_out_bound_jk(1, j, k) ;
      systeme.set(ligne, colonne+2) = 
        sol_hom3_w.val_out_bound_jk(1, j, k) ;
      
      sec_membre.set(ligne) -= sol_part_w.val_out_bound_jk(1, j, k) ;
      
      colonne += 3 ;

      //shells
      for (int zone=2 ; zone<nz_bc ; zone++) {
        nr = mgrid.get_nr(zone) ;
        ligne -= 2 ;
        
        //Condition at x = -1
        systeme.set(ligne, colonne) = 
          - sol_hom1_hrr.val_in_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+1) = 
          - sol_hom2_hrr.val_in_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+2) = 
          - sol_hom3_hrr.val_in_bound_jk(zone, j, k) ;
        
        sec_membre.set(ligne) += sol_part_hrr.val_in_bound_jk(zone, j, k) ;
        ligne++ ;
        
        systeme.set(ligne, colonne) = 
          - sol_hom1_eta.val_in_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+1) = 
          - sol_hom2_eta.val_in_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+2) = 
          - sol_hom3_eta.val_in_bound_jk(zone, j, k) ;
        
        sec_membre.set(ligne) += sol_part_eta.val_in_bound_jk(zone, j, k) ;
        ligne++ ;
        
        systeme.set(ligne, colonne) = 
          - sol_hom1_w.val_in_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+1) = 
          - sol_hom2_w.val_in_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+2) = 
          - sol_hom3_w.val_in_bound_jk(zone, j, k) ;
        
        sec_membre.set(ligne) += sol_part_w.val_in_bound_jk(zone, j, k) ;
        ligne++ ;
        
        // Condition at x=1
        systeme.set(ligne, colonne) = 
          sol_hom1_hrr.val_out_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+1) = 
          sol_hom2_hrr.val_out_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+2) = 
          sol_hom3_hrr.val_out_bound_jk(zone, j, k) ;
        
        sec_membre.set(ligne) -= sol_part_hrr.val_out_bound_jk(zone, j, k) ;
        ligne++ ;
        
        systeme.set(ligne, colonne) = 
          sol_hom1_eta.val_out_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+1) = 
          sol_hom2_eta.val_out_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+2) = 
          sol_hom3_eta.val_out_bound_jk(zone, j, k) ;
        
        sec_membre.set(ligne) -= sol_part_eta.val_out_bound_jk(zone, j, k) ;
        ligne++ ;
        
        systeme.set(ligne, colonne) = 
          sol_hom1_w.val_out_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+1) = 
          sol_hom2_w.val_out_bound_jk(zone, j, k) ;
        systeme.set(ligne, colonne+2) = 
          sol_hom3_w.val_out_bound_jk(zone, j, k) ;
        
        sec_membre.set(ligne) -= sol_part_w.val_out_bound_jk(zone, j, k) ;
        
        colonne += 3 ;
      }
      
      //Last domain
      nr = mgrid.get_nr(nz_bc) ;
      double alpha = mp_aff->get_alpha()[nz_bc] ;
      ligne -= 2 ;
      
      //Condition at x = -1
      systeme.set(ligne, colonne) = 
        - sol_hom1_hrr.val_in_bound_jk(nz_bc, j, k) ;
      systeme.set(ligne, colonne+1) = 
        - sol_hom2_hrr.val_in_bound_jk(nz_bc, j, k) ;
      if (!cedbc) systeme.set(ligne, colonne+2) = 
            - sol_hom3_hrr.val_in_bound_jk(nz_bc, j, k) ;
      
      sec_membre.set(ligne) += sol_part_hrr.val_in_bound_jk(nz_bc, j, k) ;
      ligne++ ;
      
      systeme.set(ligne, colonne) = 
        - sol_hom1_eta.val_in_bound_jk(nz_bc, j, k) ;
      systeme.set(ligne, colonne+1) = 
        - sol_hom2_eta.val_in_bound_jk(nz_bc, j, k) ;
      if (!cedbc) systeme.set(ligne, colonne+2) = 
            - sol_hom3_eta.val_in_bound_jk(nz_bc, j, k) ;
      
      sec_membre.set(ligne) += sol_part_eta.val_in_bound_jk(nz_bc, j, k) ;
      ligne++ ;
      
      systeme.set(ligne, colonne) = 
        - sol_hom1_w.val_in_bound_jk(nz_bc, j, k) ;
      systeme.set(ligne, colonne+1) = 
        - sol_hom2_w.val_in_bound_jk(nz_bc, j, k) ;
      if (!cedbc) systeme.set(ligne, colonne+2) = 
            - sol_hom3_w.val_in_bound_jk(nz_bc, j, k) ;
      
      sec_membre.set(ligne) += sol_part_w.val_in_bound_jk(nz_bc, j, k) ;
      ligne++ ;
      
      if (!cedbc) {//Special condition at x=1
        systeme.set(ligne, colonne) = 
          chrr*sol_hom1_hrr.val_out_bound_jk(nz_bc, j, k) 
          + dhrr*dhom1_hrr.val_out_bound_jk(nz_bc, j, k) / alpha 
          + ceta*sol_hom1_eta.val_out_bound_jk(nz_bc, j, k) 
          + deta*dhom1_eta.val_out_bound_jk(nz_bc, j, k) / alpha 
          + cw*sol_hom1_w.val_out_bound_jk(nz_bc, j, k) 
            + dw*dhom1_w.val_out_bound_jk(nz_bc, j, k) / alpha ;
        systeme.set(ligne, colonne+1) = 
          chrr*sol_hom2_hrr.val_out_bound_jk(nz_bc, j, k) 
          + dhrr*dhom2_hrr.val_out_bound_jk(nz_bc, j, k) / alpha 
          + ceta*sol_hom2_eta.val_out_bound_jk(nz_bc, j, k) 
          + deta*dhom2_eta.val_out_bound_jk(nz_bc, j, k) / alpha 
          + cw*sol_hom2_w.val_out_bound_jk(nz_bc, j, k) 
          + dw*dhom2_w.val_out_bound_jk(nz_bc, j, k) / alpha ;
        systeme.set(ligne, colonne+2) = 
          chrr*sol_hom3_hrr.val_out_bound_jk(nz_bc, j, k) 
          + dhrr*dhom3_hrr.val_out_bound_jk(nz_bc, j, k) / alpha 
          + ceta*sol_hom3_eta.val_out_bound_jk(nz_bc, j, k) 
          + deta*dhom3_eta.val_out_bound_jk(nz_bc, j, k) / alpha 
          + cw*sol_hom3_w.val_out_bound_jk(nz_bc, j, k) 
          + dw*dhom3_w.val_out_bound_jk(nz_bc, j, k) / alpha ;
        
        sec_membre.set(ligne) -= chrr*sol_part_hrr.val_out_bound_jk(nz_bc, j, k) 
          + dhrr*dpart_hrr.val_out_bound_jk(nz_bc, j, k)/alpha 
          + ceta*sol_part_eta.val_out_bound_jk(nz_bc, j, k) 
          + deta*dpart_eta.val_out_bound_jk(nz_bc, j, k)/alpha 
          + cw*sol_part_w.val_out_bound_jk(nz_bc, j, k) 
          + dw*dpart_w.val_out_bound_jk(nz_bc, j, k)/alpha 
          - hrrb(k, j)  ;
      }
      

       
      
      
        //System inversion:  Solution of the system giving the coefficients for the homogeneous 
        // solutions
        //-------------------------------------------------------------------

      systeme.set_lu() ;
        Tbl facteur = systeme.inverse(sec_membre) ;
        int conte = 0 ;
           
       
        // everything is put to the right place, 
        //---------------------------------------
        nr = mgrid.get_nr(0) ; //nucleus
        for (int i=0 ; i<nr ; i++) {
          mhrr.set(0, k, j, i) = 0 ;
          meta.set(0, k, j, i) = 0 ;
          mw.set(0, k, j, i) = 0 ;
        }
        for (int zone=1 ; zone<=n_shell ; zone++) { //shells
          nr = mgrid.get_nr(zone) ;
          for (int i=0 ; i<nr ; i++) {
            mhrr.set(zone, k, j, i) = sol_part_hrr(zone, k, j, i)
              + facteur(conte)*sol_hom1_hrr(zone, k, j, i) 
              + facteur(conte+1)*sol_hom2_hrr(zone, k, j, i) 
              + facteur(conte+2)*sol_hom3_hrr(zone, k, j, i) ;
            
            meta.set(zone, k, j, i) = sol_part_eta(zone, k, j, i)
              + facteur(conte)*sol_hom1_eta(zone, k, j, i) 
              + facteur(conte+1)*sol_hom2_eta(zone, k, j, i) 
              + facteur(conte+2)*sol_hom3_eta(zone, k, j, i) ;
            
            mw.set(zone, k, j, i) = sol_part_w(zone, k, j, i)
              + facteur(conte)*sol_hom1_w(zone, k, j, i) 
              + facteur(conte+1)*sol_hom2_w(zone, k, j, i) 
              + facteur(conte+2)*sol_hom3_w(zone, k, j, i) ;            
          }
          conte+=3 ;
        }
        if (cedbc) {
          nr = mgrid.get_nr(nzm1) ; //compactified external domain
          for (int i=0 ; i<nr ; i++) {
            mhrr.set(nzm1, k, j, i) = sol_part_hrr(nzm1, k, j, i)
              + facteur(conte)*sol_hom1_hrr(nzm1, k, j, i) 
              + facteur(conte+1)*sol_hom2_hrr(nzm1, k, j, i) ;
            
            meta.set(nzm1, k, j, i) = sol_part_eta(nzm1, k, j, i)
              + facteur(conte)*sol_hom1_eta(nzm1, k, j, i) 
              + facteur(conte+1)*sol_hom2_eta(nzm1, k, j, i) ; 
            
            mw.set(nzm1, k, j, i) = sol_part_w(nzm1, k, j, i)
              + facteur(conte)*sol_hom1_w(nzm1, k, j, i) 
              + facteur(conte+1)*sol_hom2_w(nzm1, k, j, i) ;
          }
        }
    } // End of nullite_plm  
      } //End of loop on theta
    
     
    if (hrr.set_spectral_va().c != 0x0) 
      delete hrr.set_spectral_va().c;
    hrr.set_spectral_va().c = 0x0 ;
    hrr.set_spectral_va().ylm_i() ;
    
    if (tilde_eta.set_spectral_va().c != 0x0) 
      delete tilde_eta.set_spectral_va().c ;
    tilde_eta.set_spectral_va().c = 0x0 ;
    tilde_eta.set_spectral_va().ylm_i() ;
    
    if (ww.set_spectral_va().c != 0x0) 
      delete ww.set_spectral_va().c ;
    ww.set_spectral_va().c = 0x0 ;
    ww.set_spectral_va().ylm_i() ;
    
    

// // On doit resoudre séparément les cas l=0 et l=1; notamment dansces cas le systeme electrique se resout a deux equations
// // au lieu de 3.

    
}

void Sym_tensor_trans::sol_Dirac_l01_2(const Scalar& hh, Scalar& hrr, Scalar& tilde_eta, 
                       Param* par_mat) {
  
  
  
  // void Sym_tensor_trans::sol_Dirac_tilde_B2(const Scalar& tilde_b, const Scalar& hh, 
  //                      Scalar& hrr, Scalar& tilde_eta, Scalar& ww, Scalar bound_eta,double dir, double neum, double rhor, Param* par_bc, Param* par_mat) {
  
  
  const Map_af* mp_aff = dynamic_cast<const Map_af*>(mp) ;
  assert(mp_aff != 0x0) ; //Only affine mapping for the moment
  
  const Mg3d& mgrid = *mp_aff->get_mg() ;
  int nz = mgrid.get_nzone() ;
  assert(mgrid.get_type_r(0) == RARE)  ;
  assert(mgrid.get_type_r(nz-1) == UNSURR) ;
  
  if (hh.get_etat() == ETATZERO) {
    hrr.annule_hard() ;
    tilde_eta.annule_hard() ;
    return ;
  }
  
  int nt = mgrid.get_nt(0) ;
  int np = mgrid.get_np(0) ;
  
  Scalar source = hh ;
  source.div_r_dzpuis(2) ;
  Scalar source_coq = hh ;
  source.set_spectral_va().ylm() ;
  source_coq.set_spectral_va().ylm() ;
  Base_val base = source.get_spectral_base() ;
  base.mult_x() ;
  int lmax = base.give_lmax(mgrid, 0) + 1;
  
  assert (hrr.get_spectral_base() == base) ;
  assert (tilde_eta.get_spectral_base() == base) ;
  assert (hrr.get_spectral_va().c_cf != 0x0) ;
  assert (tilde_eta.get_spectral_va().c_cf != 0x0) ;
  
  Mtbl_cf sol_part_hrr(mgrid, base) ; sol_part_hrr.annule_hard() ;
  Mtbl_cf sol_part_eta(mgrid, base) ; sol_part_eta.annule_hard() ;
  Mtbl_cf sol_hom1_hrr(mgrid, base) ; sol_hom1_hrr.annule_hard() ;
  Mtbl_cf sol_hom1_eta(mgrid, base) ; sol_hom1_eta.annule_hard() ;
  Mtbl_cf sol_hom2_hrr(mgrid, base) ; sol_hom2_hrr.annule_hard() ;
  Mtbl_cf sol_hom2_eta(mgrid, base) ; sol_hom2_eta.annule_hard() ;
  
  bool need_calculation = true ;
  if (par_mat != 0x0)
    if (par_mat->get_n_matrice_mod() > 0) 
      if (&par_mat->get_matrice_mod(0) != 0x0) need_calculation = false ;
  
  int l_q, m_q, base_r ;
  Itbl mat_done(lmax) ;
  
  //---------------
  //--  NUCLEUS ---
  //---------------
  {int lz = 0 ;  
  int nr = mgrid.get_nr(lz) ;
  double alpha = mp_aff->get_alpha()[lz] ;
  Matrice ope(2*nr, 2*nr) ;
  if (need_calculation && (par_mat != 0x0)) mat_done.annule_hard() ;
  
  for (int k=0 ; k<np+1 ; k++) {
    for (int j=0 ; j<nt ; j++) {
      // quantic numbers and spectral bases
      base.give_quant_numbers(lz, k, j, m_q, l_q, base_r) ;
      if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q < 2)) {
    if (need_calculation) {
      ope.set_etat_qcq() ;
      Diff_dsdx od(base_r, nr) ; const Matrice& md = od.get_matrice() ;
      Diff_sx os(base_r, nr) ; const Matrice& ms = os.get_matrice() ;
      
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin,col) = md(lin,col) + 3*ms(lin,col) ;
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin,col+nr) = -l_q*(l_q+1)*ms(lin,col) ;
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+nr,col) = -0.5*ms(lin,col) ;
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+nr,col+nr) = md(lin,col) + 3*ms(lin, col);
      
      ope *= 1./alpha ;
      for (int col=0; col<2*nr; col++) {
        ope.set(nr-1, col) = 0 ;
        ope.set(2*nr-1, col) = 0 ;
      }
      int pari = 1 ;
      if (base_r == R_CHEBP) {
        for (int col=0; col<nr; col++) {
          ope.set(nr-1, col) = pari ;
          ope.set(2*nr-1, col+nr) = pari ;
          pari = - pari ;
        }
      }
      else { //In the odd case, the last coefficient must be zero!
        ope.set(nr-1, nr-1) = 1 ;
        ope.set(2*nr-1, 2*nr-1) = 1 ;
      }
      
      ope.set_lu() ;
      if ((par_mat != 0x0) && (mat_done(l_q) == 0)) {
        Matrice* pope = new Matrice(ope) ;
        par_mat->add_matrice_mod(*pope, lz*lmax + l_q) ;
        mat_done.set(l_q) = 1 ;
      }
    } //End of case when a calculation is needed
    
    const Matrice& oper = (par_mat == 0x0 ? ope : 
                   par_mat->get_matrice_mod(lz*lmax + l_q) ) ;
    Tbl sec(2*nr) ;
    sec.set_etat_qcq() ;
    for (int lin=0; lin<nr; lin++)
      sec.set(lin) = (*source.get_spectral_va().c_cf)(lz, k, j, lin) ;
    for (int lin=0; lin<nr; lin++)
      sec.set(nr+lin) = -0.5*(*source.get_spectral_va().c_cf)
        (lz, k, j, lin) ;
    sec.set(nr-1) = 0 ;
    if (base_r == R_CHEBP) {
      double h0 = 0 ; //In the l=0 case:  3*hrr(r=0) = h(r=0) 
      int pari = 1 ;
      for (int col=0; col<nr; col++) {
        h0 += pari*
          (*source_coq.get_spectral_va().c_cf)(lz, k, j, col) ;
        pari = - pari ;
      }
      sec.set(nr-1) = h0 / 3. ;
    }
    sec.set(2*nr-1) = 0 ;
    Tbl sol = oper.inverse(sec) ;
    for (int i=0; i<nr; i++) {
      sol_part_hrr.set(lz, k, j, i) = sol(i) ;
      sol_part_eta.set(lz, k, j, i) = sol(i+nr) ;
        }
    sec.annule_hard() ;
      }
    }
  }
  }
  
  //-------------
  // -- Shells --
  //-------------
  
  for (int lz=1; lz<nz-1; lz++) {
    if (need_calculation && (par_mat != 0x0)) mat_done.annule_hard() ;
    int nr = mgrid.get_nr(lz) ;
    int ind0 = 0 ;
    int ind1 = nr ;
    assert(mgrid.get_nt(lz) == nt) ;
    assert(mgrid.get_np(lz) == np) ;
    double alpha = mp_aff->get_alpha()[lz] ;
    double ech = mp_aff->get_beta()[lz] / alpha ;
    Matrice ope(2*nr, 2*nr) ;
    
    for (int k=0 ; k<np+1 ; k++) {
      for (int j=0 ; j<nt ; j++) {
    // quantic numbers and spectral bases
    base.give_quant_numbers(lz, k, j, m_q, l_q, base_r) ;
    if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q < 2)) {
      if (need_calculation) {
        ope.set_etat_qcq() ;
        Diff_xdsdx oxd(base_r, nr) ; const Matrice& mxd = oxd.get_matrice() ;
        Diff_dsdx od(base_r, nr) ; const Matrice& md = od.get_matrice() ;
        Diff_id oid(base_r, nr) ; const Matrice& mid = oid.get_matrice() ;
        
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin,col) = mxd(lin,col) + ech*md(lin,col) 
          + 3*mid(lin,col) ;
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin,col+nr) = -l_q*(l_q+1)*mid(lin,col) ;
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin+nr,col) = -0.5*mid(lin,col) ;
        for (int lin=0; lin<nr; lin++) 
          for (int col=0; col<nr; col++) 
        ope.set(lin+nr,col+nr) = mxd(lin,col) + ech*md(lin,col) 
          + 3*mid(lin, col) ;
        
        for (int col=0; col<2*nr; col++) {
          ope.set(ind0+nr-1, col) = 0 ;
          ope.set(ind1+nr-1, col) = 0 ;
        }
        ope.set(ind0+nr-1, ind0) = 1 ;
        ope.set(ind1+nr-1, ind1) = 1 ;
        
        ope.set_lu() ;
        if ((par_mat != 0x0) && (mat_done(l_q) == 0)) {
          Matrice* pope = new Matrice(ope) ;
          par_mat->add_matrice_mod(*pope, lz*lmax + l_q) ;
            mat_done.set(l_q) = 1 ;
        }
      } //End of case when a calculation is needed
      const Matrice& oper = (par_mat == 0x0 ? ope : 
                 par_mat->get_matrice_mod(lz*lmax + l_q) ) ;
      Tbl sec(2*nr) ;
      sec.set_etat_qcq() ;
      for (int lin=0; lin<nr; lin++)
        sec.set(lin) = (*source_coq.get_spectral_va().c_cf)
          (lz, k, j, lin) ; 
      for (int lin=0; lin<nr; lin++)
        sec.set(nr+lin) = -0.5*(*source_coq.get_spectral_va().c_cf)
          (lz, k, j, lin) ;
      sec.set(ind0+nr-1) = 0 ;
      sec.set(ind1+nr-1) = 0 ;
      Tbl sol = oper.inverse(sec) ;
      
      for (int i=0; i<nr; i++) {
        sol_part_hrr.set(lz, k, j, i) = sol(i) ;
        sol_part_eta.set(lz, k, j, i) = sol(i+nr) ;
      }
      sec.annule_hard() ;
      sec.set(ind0+nr-1) = 1 ;
      sol = oper.inverse(sec) ;
      for (int i=0; i<nr; i++) {
        sol_hom1_hrr.set(lz, k, j, i) = sol(i) ;
        sol_hom1_eta.set(lz, k, j, i) = sol(i+nr) ;
      }         
      sec.set(ind0+nr-1) = 0 ;
      sec.set(ind1+nr-1) = 1 ;
      sol = oper.inverse(sec) ;
      for (int i=0; i<nr; i++) {
        sol_hom2_hrr.set(lz, k, j, i) = sol(i) ;
        sol_hom2_eta.set(lz, k, j, i) = sol(i+nr) ;
      }         
    }
      }
    }
  }
  
  //------------------------------
  // Compactified external domain
  //------------------------------
  {int lz = nz-1 ;  
  if (need_calculation && (par_mat != 0x0)) mat_done.annule_hard() ;
  int nr = mgrid.get_nr(lz) ;
  int ind0 = 0 ;
  int ind1 = nr ;
  assert(mgrid.get_nt(lz) == nt) ;
  assert(mgrid.get_np(lz) == np) ;
  double alpha = mp_aff->get_alpha()[lz] ;
  Matrice ope(2*nr, 2*nr) ;
  
  for (int k=0 ; k<np+1 ; k++) {
    for (int j=0 ; j<nt ; j++) {
      // quantic numbers and spectral bases
      base.give_quant_numbers(lz, k, j, m_q, l_q, base_r) ;
      if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q < 2)) {
    if (need_calculation) {
      ope.set_etat_qcq() ;
      Diff_dsdx od(base_r, nr) ; const Matrice& md = od.get_matrice() ;
      Diff_sx os(base_r, nr) ; const Matrice& ms = os.get_matrice() ;
      
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin,col) = - md(lin,col) + 3*ms(lin,col) ;
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin,col+nr) = -l_q*(l_q+1)*ms(lin,col) ;
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+nr,col) = -0.5*ms(lin,col) ;
      for (int lin=0; lin<nr; lin++) 
        for (int col=0; col<nr; col++) 
          ope.set(lin+nr,col+nr) = -md(lin,col) + 3*ms(lin, col) ;
      
      ope *= 1./alpha ;
      for (int col=0; col<2*nr; col++) {
        ope.set(ind0+nr-2, col) = 0 ;
        ope.set(ind0+nr-1, col) = 0 ;
        ope.set(ind1+nr-2, col) = 0 ;
        ope.set(ind1+nr-1, col) = 0 ;
      }
      for (int col=0; col<nr; col++) {
        ope.set(ind0+nr-1, col+ind0) = 1 ;
        ope.set(ind1+nr-1, col+ind1) = 1 ;
      }
      ope.set(ind0+nr-2, ind0+1) = 1 ;
      ope.set(ind1+nr-2, ind1+1) = 1 ;
      
      ope.set_lu() ;
      if ((par_mat != 0x0) && (mat_done(l_q) == 0)) {
        Matrice* pope = new Matrice(ope) ;
        par_mat->add_matrice_mod(*pope, lz*lmax + l_q) ;
        mat_done.set(l_q) = 1 ;
      }
    } //End of case when a calculation is needed
    const Matrice& oper = (par_mat == 0x0 ? ope : 
                   par_mat->get_matrice_mod(lz*lmax + l_q) ) ;
    Tbl sec(2*nr) ;
    sec.set_etat_qcq() ;
    for (int lin=0; lin<nr; lin++)
      sec.set(lin) = (*source.get_spectral_va().c_cf)
        (lz, k, j, lin) ;
    for (int lin=0; lin<nr; lin++)
      sec.set(nr+lin) = -0.5*(*source.get_spectral_va().c_cf)
        (lz, k, j, lin) ;
    sec.set(ind0+nr-2) = 0 ;
    sec.set(ind0+nr-1) = 0 ;
    sec.set(ind1+nr-2) = 0 ;
    sec.set(ind1+nr-1) = 0 ;
    Tbl sol = oper.inverse(sec) ;
    for (int i=0; i<nr; i++) {
      sol_part_hrr.set(lz, k, j, i) = sol(i) ;
      sol_part_eta.set(lz, k, j, i) = sol(i+nr) ;
    }
    sec.annule_hard() ;
    sec.set(ind0+nr-2) = 1 ;
    sol = oper.inverse(sec) ;
    for (int i=0; i<nr; i++) {
      sol_hom1_hrr.set(lz, k, j, i) = sol(i) ;
      sol_hom1_eta.set(lz, k, j, i) = sol(i+nr) ;
    }
    sec.set(ind0+nr-2) = 0 ;
    sec.set(ind1+nr-2) = 1 ;
    sol = oper.inverse(sec) ;
    for (int i=0; i<nr; i++) {
      sol_hom2_hrr.set(lz, k, j, i) = sol(i) ;
      sol_hom2_eta.set(lz, k, j, i) = sol(i+nr) ;
    }
      }
    }
  }
  }
  
  int taille = 2*(nz-1) ;
  Mtbl_cf& mhrr = *hrr.set_spectral_va().c_cf ;
  Mtbl_cf& meta = *tilde_eta.set_spectral_va().c_cf ;
  
  Tbl sec_membre(taille) ; 
  Matrice systeme(taille, taille) ; 
  int ligne ;  int colonne ;
  
  // Loop on l and m
  //----------------
  for (int k=0 ; k<np+1 ; k++)
    for (int j=0 ; j<nt ; j++) {
      base.give_quant_numbers(0, k, j, m_q, l_q, base_r) ;
      if ((nullite_plm(j, nt, k, np, base) == 1) && (l_q < 2)) {
    ligne = 0 ;
    colonne = 0 ;
    systeme.annule_hard() ;
    sec_membre.annule_hard() ;
    
    //Nucleus 
    int nr = mgrid.get_nr(0) ;
    
    sec_membre.set(ligne) = -sol_part_hrr.val_out_bound_jk(0, j, k) ;
    ligne++ ;
    
    sec_membre.set(ligne) = -sol_part_eta.val_out_bound_jk(0, j, k) ;
    
    //shells
    for (int zone=1 ; zone<nz-1 ; zone++) {
      nr = mgrid.get_nr(zone) ;
      ligne-- ;
      
      //Condition at x = -1
      systeme.set(ligne, colonne) = 
        - sol_hom1_hrr.val_in_bound_jk(zone, j, k) ;
      systeme.set(ligne, colonne+1) = 
        - sol_hom2_hrr.val_in_bound_jk(zone, j, k) ;
      
      sec_membre.set(ligne) += sol_part_hrr.val_in_bound_jk(zone, j, k) ;
      ligne++ ;
      
      systeme.set(ligne, colonne) = 
        - sol_hom1_eta.val_in_bound_jk(zone, j, k) ;
      systeme.set(ligne, colonne+1) = 
        - sol_hom2_eta.val_in_bound_jk(zone, j, k) ;
      
      sec_membre.set(ligne) += sol_part_eta.val_in_bound_jk(zone, j, k) ;
      ligne++ ;
      
      // Condition at x=1
      systeme.set(ligne, colonne) = 
        sol_hom1_hrr.val_out_bound_jk(zone, j, k) ;
      systeme.set(ligne, colonne+1) = 
        sol_hom2_hrr.val_out_bound_jk(zone, j, k) ;
      
      sec_membre.set(ligne) -= sol_part_hrr.val_out_bound_jk(zone, j, k) ;
      ligne++ ;
      
      systeme.set(ligne, colonne) = 
        sol_hom1_eta.val_out_bound_jk(zone, j, k) ;
      systeme.set(ligne, colonne+1) = 
        sol_hom2_eta.val_out_bound_jk(zone, j, k) ;
      
      sec_membre.set(ligne) -= sol_part_eta.val_out_bound_jk(zone, j, k) ;
      
      colonne += 2 ;
    }
    
    //Compactified external domain
    nr = mgrid.get_nr(nz-1) ;
    
    ligne-- ;
    
    systeme.set(ligne, colonne) = 
      - sol_hom1_hrr.val_in_bound_jk(nz-1, j, k) ;
    systeme.set(ligne, colonne+1) = 
      - sol_hom2_hrr.val_in_bound_jk(nz-1, j, k) ;
    
    sec_membre.set(ligne) += sol_part_hrr.val_in_bound_jk(nz-1, j, k) ;
    ligne++ ;
    
    systeme.set(ligne, colonne) = 
      - sol_hom1_eta.val_in_bound_jk(nz-1, j, k) ;
    systeme.set(ligne, colonne+1) = 
      - sol_hom2_eta.val_in_bound_jk(nz-1, j, k) ;
    
    sec_membre.set(ligne) += sol_part_eta.val_in_bound_jk(nz-1, j, k) ;
    
    // Solution of the system giving the coefficients for the homogeneous 
    // solutions
    //-------------------------------------------------------------------
    systeme.set_lu() ;
    Tbl facteur = systeme.inverse(sec_membre) ;
    int conte = 0 ;
    
    // everything is put to the right place...
    //----------------------------------------
    nr = mgrid.get_nr(0) ; //nucleus
    for (int i=0 ; i<nr ; i++) {
      mhrr.set(0, k, j, i) = sol_part_hrr(0, k, j, i) ;
      meta.set(0, k, j, i) = sol_part_eta(0, k, j, i) ;
    }
    for (int zone=1 ; zone<nz-1 ; zone++) { //shells
      nr = mgrid.get_nr(zone) ;
      for (int i=0 ; i<nr ; i++) {
        mhrr.set(zone, k, j, i) = sol_part_hrr(zone, k, j, i)
          + facteur(conte)*sol_hom1_hrr(zone, k, j, i) 
          + facteur(conte+1)*sol_hom2_hrr(zone, k, j, i) ;
        
        meta.set(zone, k, j, i) = sol_part_eta(zone, k, j, i)
          + facteur(conte)*sol_hom1_eta(zone, k, j, i) 
          + facteur(conte+1)*sol_hom2_eta(zone, k, j, i) ;
      }
            conte+=2 ;
    }
    nr = mgrid.get_nr(nz-1) ; //compactified external domain
    for (int i=0 ; i<nr ; i++) {
      mhrr.set(nz-1, k, j, i) = sol_part_hrr(nz-1, k, j, i)
        + facteur(conte)*sol_hom1_hrr(nz-1, k, j, i) 
        + facteur(conte+1)*sol_hom2_hrr(nz-1, k, j, i) ;
      
      meta.set(nz-1, k, j, i) = sol_part_eta(nz-1, k, j, i)
        + facteur(conte)*sol_hom1_eta(nz-1, k, j, i) 
        + facteur(conte+1)*sol_hom2_eta(nz-1, k, j, i) ;
    }
    
      } // End of nullite_plm  
    } //End of loop on theta
}

---