tensor.C

/*
 *  Methods of class Tensor
 *
 *   (see file tensor.h for documentation)
 *
 */

/*
 *   Copyright (c) 2003-2004 Eric Gourgoulhon & Jerome Novak
 *
 *   Copyright (c) 1999-2001 Philippe Grandclement (for preceding class Tenseur)
 *
 *   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 tensor_C[] = "$Header: /cvsroot/Lorene/C++/Source/Tensor/tensor.C,v 1.39 2007/12/21 16:07:08 j_novak Exp $" ;

/*
 * $Id: tensor.C,v 1.39 2007/12/21 16:07:08 j_novak Exp $
 * $Log: tensor.C,v $
 * Revision 1.39  2007/12/21 16:07:08  j_novak
 * Methods to filter Tensor, Vector and Sym_tensor objects.
 *
 * Revision 1.38  2005/10/25 08:56:38  p_grandclement
 * addition of std_spectral_base in the case of odd functions near the origin
 *
 * Revision 1.37  2005/05/18 11:45:44  j_novak
 * Added del_deriv() calls at the end of inc/dec_dzpuis.
 *
 * Revision 1.36  2004/07/08 12:21:53  j_novak
 * Replaced tensor::annule_extern_c2 with tensor::annule_extern_cn for a
 * more general transition.
 *
 * Revision 1.35  2004/06/17 06:55:07  e_gourgoulhon
 * Added method annule_extern_c2.
 *
 * Revision 1.34  2004/03/04 09:47:51  e_gourgoulhon
 * Method annule_domain(int, int): added call to virtual function
 *  del_deriv() at the end !
 *
 * Revision 1.33  2004/02/27 21:14:27  e_gourgoulhon
 * Modif of method derive_con to create proper type of the result.
 *
 * Revision 1.32  2004/02/19 22:10:14  e_gourgoulhon
 * Added argument "comment" in method spectral_display.
 *
 * Revision 1.31  2004/02/05 15:03:47  e_gourgoulhon
 * Corrected bug in method derive_con().
 *
 * Revision 1.30  2004/01/27 13:05:11  j_novak
 * Removed the method Tensor::mult_r_ced()
 *
 * Revision 1.29  2004/01/19 16:32:13  e_gourgoulhon
 * Added operator()(int, int, int, int) and set(int, int, int, int)
 * for direct access to components of valence 4 tensors.
 *
 * Revision 1.28  2004/01/04 20:55:23  e_gourgoulhon
 * Method spectral_display(): added printing of type of class (through typeid).
 *
 * Revision 1.27  2003/12/30 23:09:47  e_gourgoulhon
 * Change in methods derive_cov() and divergence() to take into account
 *  the change of name: Metric::get_connect() --> Metric::connect().
 *
 * Revision 1.26  2003/12/27 15:01:50  e_gourgoulhon
 * Method derive_con(): the position of the derivation index has
 * been changed from the first one to the last one.
 *
 * Revision 1.25  2003/11/03 22:34:41  e_gourgoulhon
 * Method dec_dzpuis: changed the name of argument dec --> decrem
 * (in order not to shadow some globally defined dec).
 *
 * Revision 1.24  2003/10/29 11:02:54  e_gourgoulhon
 * Functions dec_dzpuis and inc_dzpuis have now an integer argument to
 * specify by which amount dzpuis is to be increased.
 * Accordingly methods dec2_dzpuis and inc2_dzpuis have been suppressed
 *
 * Revision 1.23  2003/10/27 10:49:48  e_gourgoulhon
 * Slightly modified operator<<.
 *
 * Revision 1.22  2003/10/19 19:57:00  e_gourgoulhon
 * -- Added new method spectral_display
 * -- slightly rearranged the operator<<
 *
 * Revision 1.21  2003/10/16 15:27:46  e_gourgoulhon
 * Name of method annule(int ) changed to annule_domain(int ).
 *
 * Revision 1.20  2003/10/16 14:21:36  j_novak
 * The calculation of the divergence of a Tensor is now possible.
 *
 * Revision 1.19  2003/10/13 13:52:40  j_novak
 * Better managment of derived quantities.
 *
 * Revision 1.18  2003/10/11 16:47:10  e_gourgoulhon
 * Suppressed the call to Ibtl::set_etat_qcq() after the construction
 * of the Itbl's, thanks to the new property of the Itbl class.
 *
 * Revision 1.17  2003/10/11 14:48:40  e_gourgoulhon
 * Line 344: suppressed assert(resu == -1)
 *           and added a break command to quit the loop.
 *
 * Revision 1.16  2003/10/08 14:24:09  j_novak
 * replaced mult_r_zec with mult_r_ced
 *
 * Revision 1.15  2003/10/07 15:25:38  e_gourgoulhon
 * Added call to del_derive_met in del_deriv().
 *
 * Revision 1.14  2003/10/07 09:10:00  j_novak
 * Use of ::contract instead of up()
 *
 * Revision 1.13  2003/10/06 20:51:43  e_gourgoulhon
 * In methods set: changed name "indices" to "idx" to avoid shadowing
 *  of class member.
 *
 * Revision 1.12  2003/10/06 16:17:31  j_novak
 * Calculation of contravariant derivative and Ricci scalar.
 *
 * Revision 1.11  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 1.10  2003/10/05 21:11:22  e_gourgoulhon
 * - Added method std_spectral_base().
 * - Removed method change_triad() from this file.
 *
 * Revision 1.9  2003/10/03 15:09:38  j_novak
 * Improved display
 *
 * Revision 1.8  2003/10/03 11:21:48  j_novak
 * More methods for the class Metric
 *
 * Revision 1.7  2003/10/01 11:56:31  e_gourgoulhon
 * Corrected error: '=' replaced by '==' in two assert tests.
 *
 * Revision 1.6  2003/09/30 08:38:23  j_novak
 * added a header typeinfo
 *
 * Revision 1.5  2003/09/29 12:52:57  j_novak
 * Methods for changing the triad are implemented.
 *
 * Revision 1.4  2003/09/26 14:33:53  j_novak
 * Arithmetic functions for the class Tensor
 *
 * 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  2003/09/23 08:52:17  e_gourgoulhon
 * new version
 *
 * Revision 1.1  2003/09/22 12:52:51  e_gourgoulhon
 * First version: not ready yet !
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Tensor/tensor.C,v 1.39 2007/12/21 16:07:08 j_novak Exp $
 *
 */

// Headers C
#include <stdlib.h>
#include <assert.h>
#include <math.h>

// Headers Lorene
#include "metric.h"
#include "utilitaires.h"

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

// Standard constructor 
// --------------------
Tensor::Tensor(const Map& map, int val, const Itbl& tipe, 
         const Base_vect& triad_i) 
        : mp(&map), valence(val), triad(&triad_i), type_indice(tipe), 
           n_comp(int(pow(3., val))){
        
    // Des verifs :
    assert (valence >= 0) ;
    assert (tipe.get_ndim() == 1) ;
    assert (valence == tipe.get_dim(0)) ;
    for (int i=0 ; i<valence ; i++)
    assert ((tipe(i) == COV) || (tipe(i) == CON)) ;
    
    cmp = new Scalar*[n_comp] ;

    for (int i=0 ; i<n_comp ; i++)
    cmp[i] = new Scalar(map) ;

    set_der_0x0() ;
    
}

// Standard constructor with the triad passed as a pointer
// -------------------------------------------------------
Tensor::Tensor(const Map& map, int val, const Itbl& tipe, 
         const Base_vect* triad_i) 
        : mp(&map), valence(val), triad(triad_i), type_indice(tipe), 
           n_comp(int(pow(3., val))){
        
    // Des verifs :
    assert (valence >= 0) ;
    assert (tipe.get_ndim() == 1) ;
    assert (valence == tipe.get_dim(0)) ;
    for (int i=0 ; i<valence ; i++)
    assert ((tipe(i) == COV) || (tipe(i) == CON)) ;
    
    cmp = new Scalar*[n_comp] ;

    for (int i=0 ; i<n_comp ; i++)
    cmp[i] = new Scalar(map) ;

    set_der_0x0() ;

}




// Standard constructor when all the indices are of the same type
// --------------------------------------------------------------
Tensor::Tensor(const Map& map, int val, int tipe, const Base_vect& triad_i) 
        : mp(&map), valence(val), triad(&triad_i), type_indice(val), 
                  n_comp(int(pow(3., val))){
    
    // Des verifs :
    assert (valence >= 0) ;
    assert ((tipe == COV) || (tipe == CON)) ;

    type_indice = tipe ;
    
    cmp = new Scalar*[n_comp] ;

    for (int i=0 ; i<n_comp ; i++)
    cmp[i] = new Scalar(map) ;

    set_der_0x0() ;
}   
    
// Copy constructor
// ----------------
Tensor::Tensor (const Tensor& source) : 
    mp(source.mp), valence(source.valence), triad(source.triad), 
    type_indice(source.type_indice) {
  
    n_comp = int(pow(3., valence)) ;
        
    cmp = new Scalar*[n_comp] ;
    for (int i=0 ; i<n_comp ; i++) {

        // the following writing takes into account the case where
        // source belongs to a derived class of Tensor with a different
        // storage of components :

    int place_source = source.position(indices(i)) ;
    cmp[i] = new Scalar(*source.cmp[place_source]) ;
    }

    set_der_0x0() ;

}   


// Constructor from a file
// -----------------------
Tensor::Tensor(const Map& mapping, const Base_vect& triad_i, FILE* fd)
         : mp(&mapping), triad(&triad_i), type_indice(fd){
   
    fread_be(&valence, sizeof(int), 1, fd) ;

    if (valence != 0) {
        Base_vect* triad_fich = Base_vect::bvect_from_file(fd) ; 
        assert( *triad_fich == *triad) ; 
        delete triad_fich ; 
    }
    else{
        triad = 0x0 ; 
    }
    
    fread_be(&n_comp, sizeof(int), 1, fd) ;
    
    cmp = new Scalar*[n_comp] ;
    for (int i=0 ; i<n_comp ; i++)
      cmp[i] = new Scalar(*mp, *(mp->get_mg()), fd) ;

    set_der_0x0() ;
}


//  Constructor for a scalar field: to be used by the derived
//  class {\tt Scalar}
//-----------------------------------------------------------
Tensor::Tensor(const Map& map) : mp(&map), valence(0), triad(0x0),
        type_indice(0), n_comp(1) {
        
  cmp = new Scalar*[n_comp] ; 
  cmp[0] = 0x0 ; 
  
  set_der_0x0() ;
}


// Constructor used by the derived classes
// ---------------------------------------
Tensor::Tensor (const Map& map, int val, const Itbl& tipe, int compo, 
        const Base_vect& triad_i) :
     mp(&map), valence(val), triad(&triad_i), type_indice(tipe), n_comp(compo)
{
     
    // Des verifs :
    assert (valence >= 0) ;
    assert (tipe.get_ndim() == 1) ;
    assert (n_comp > 0) ;   
    assert (valence == tipe.get_dim(0)) ;
    for (int i=0 ; i<valence ; i++)
    assert ((tipe(i) == COV) || (tipe(i) == CON)) ;
    
    cmp = new Scalar*[n_comp] ;

    for (int i=0 ; i<n_comp ; i++)
    cmp[i] = new Scalar(map) ;

    set_der_0x0() ;
  
}

// Constructor used by the derived classes when all the indices are of 
// the same type.
// -------------------------------------------------------------------
Tensor::Tensor (const Map& map, int val, int tipe, int compo, 
        const Base_vect& triad_i) :
     mp(&map), valence(val), triad(&triad_i), type_indice(val), n_comp(compo)
{

    // Des verifs :
    assert (valence >= 0) ;
    assert (n_comp >= 0) ;
    assert ((tipe == COV) || (tipe == CON)) ;

    type_indice = tipe ;
    
    cmp = new Scalar*[n_comp] ;

    for (int i=0 ; i<n_comp ; i++)
      cmp[i] = new Scalar(map) ;

    set_der_0x0() ;

}

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


Tensor::~Tensor () {
    
    Tensor::del_deriv() ;

    for (int i=0 ; i<n_comp ; i++) {
      if (cmp[i] != 0x0)
    delete cmp[i] ;
    }
    delete [] cmp ;
}



void Tensor::del_deriv() const {

  for (int i=0; i<N_MET_MAX; i++) 
    del_derive_met(i) ;

  set_der_0x0() ;

}

void Tensor::set_der_0x0() const {

  for (int i=0; i<N_MET_MAX; i++) 
    set_der_met_0x0(i) ;

}

void Tensor::del_derive_met(int j) const {

  assert( (j>=0) && (j<N_MET_MAX) ) ;

  if (met_depend[j] != 0x0) {
    for (int i=0 ; i<N_TENSOR_DEPEND ; i++)
      if (met_depend[j]->tensor_depend[i] == this)
        met_depend[j]->tensor_depend[i] = 0x0 ;
    if (p_derive_cov[j] != 0x0)
      delete p_derive_cov[j] ;
    if (p_derive_con[j] != 0x0)
      delete p_derive_con[j] ;
    if (p_divergence[j] != 0x0)
      delete p_divergence[j] ;

    set_der_met_0x0(j) ;
  }
}

void Tensor::set_der_met_0x0(int i) const {

  assert( (i>=0) && (i<N_MET_MAX) ) ;
  met_depend[i] = 0x0 ;
  p_derive_cov[i] = 0x0 ;
  p_derive_con[i] = 0x0 ;
  p_divergence[i] = 0x0 ;

}

int Tensor::get_place_met(const Metric& metre) const {
  int resu = -1 ;
  for (int i=0; i<N_MET_MAX; i++) 
    if (met_depend[i] == &metre) {
        resu = i ;
        break ; 
    }
  return resu ;
}

void Tensor::set_dependance (const Metric& met) const {
    
  int nmet = 0 ;
  bool deja = false ;
  for (int i=0; i<N_MET_MAX; i++) {
    if (met_depend[i] == &met) deja = true ;
    if ((!deja) && (met_depend[i] != 0x0)) nmet++ ;
  }
  if (nmet == N_MET_MAX) {
    cout << "Too many metrics in Tensor::set_dependances" << endl ;
    abort() ;
  }
  if (!deja) { 
    int conte = 0 ;
    while ((conte < N_TENSOR_DEPEND) && (met.tensor_depend[conte] != 0x0))
      conte ++ ;
    
    if (conte == N_TENSOR_DEPEND) {
      cout << "Too many dependancies in Tensor::set_dependances " << endl ;
      abort() ;
    }
    else {
      met.tensor_depend[conte] = this ;
      met_depend[nmet] = &met ;
    }
  }
}

void Tensor::set_etat_qcq() { 
    
    del_deriv() ;
    for (int i=0 ; i<n_comp ; i++) {
      cmp[i]->set_etat_qcq() ; 
    }
}

void Tensor::set_etat_nondef() { 
    
    del_deriv() ;
    for (int i=0 ; i<n_comp ; i++) {
      cmp[i]->set_etat_nondef() ; 
    }
}

void Tensor::set_etat_zero() { 
    
    del_deriv() ;
    for (int i=0 ; i<n_comp ; i++) {
      cmp[i]->set_etat_zero() ; 
    }
}


// Allocates everything
// --------------------
void Tensor::allocate_all() {
    
  del_deriv() ;
  for (int i=0 ; i<n_comp ; i++) {
    cmp[i]->allocate_all() ; 
  }
    
} 



void Tensor::set_triad(const Base_vect& bi) {
    
    triad = &bi ; 
    
}

int Tensor::position (const Itbl& idx) const {
    
    assert (idx.get_ndim() == 1) ;
    assert (idx.get_dim(0) == valence) ;
    
    for (int i=0 ; i<valence ; i++)
    assert ((idx(i)>=1) && (idx(i)<=3)) ;
    int res = 0 ;
    for (int i=0 ; i<valence ; i++)
        res = 3*res+(idx(i)-1) ;
    
    return res;
}

Itbl Tensor::indices (int place) const {
    
    assert ((place >= 0) && (place < n_comp)) ;

    Itbl res(valence) ;
            
    for (int i=valence-1 ; i>=0 ; i--) {
        res.set(i) = div(place, 3).rem ;
        place = int((place-res(i))/3) ;
        res.set(i)++ ; 
    }
    return res ;
}

void Tensor::operator=(const Tensor& t) {
    
    assert (valence == t.valence) ;

    triad = t.triad ; 

    for (int i=0 ; i<valence ; i++)
      assert(t.type_indice(i) == type_indice(i)) ;
    
    for (int i=0 ; i<n_comp ; i++) {
      int place_t = t.position(indices(i)) ;
      *cmp[i] = *t.cmp[place_t] ;
    }

    del_deriv() ;

}

void Tensor::operator+=(const Tensor& t) {
    
    assert (valence == t.valence) ;
    assert (triad == t.triad) ; 
    for (int i=0 ; i<valence ; i++)
      assert(t.type_indice(i) == type_indice(i)) ;
    
    for (int i=0 ; i<n_comp ; i++) {
      int place_t = t.position(indices(i)) ;
      *cmp[i] += *t.cmp[place_t] ;
    }

    del_deriv() ;

}

void Tensor::operator-=(const Tensor& t) {
    
    assert (valence == t.valence) ;
    assert (triad == t.triad) ; 
    for (int i=0 ; i<valence ; i++)
      assert(t.type_indice(i) == type_indice(i)) ;
    
    for (int i=0 ; i<n_comp ; i++) {
      int place_t = t.position(indices(i)) ;
      *cmp[i] -= *t.cmp[place_t] ;
    }

    del_deriv() ;

}



// Affectation d'un tenseur d'ordre 2 :
Scalar& Tensor::set(int ind1, int ind2) {
    
    assert (valence == 2) ;
    
    Itbl ind (valence) ;
    ind.set(0) = ind1 ;
    ind.set(1) = ind2 ;
    
    int place = position(ind) ;
    
    del_deriv() ;
    return *cmp[place] ;
}

// Affectation d'un tenseur d'ordre 3 :
Scalar& Tensor::set(int ind1, int ind2, int ind3) {
    
    assert (valence == 3) ;
    
    Itbl idx(valence) ;
    idx.set(0) = ind1 ;
    idx.set(1) = ind2 ;
    idx.set(2) = ind3 ;
    int place = position(idx) ;
    del_deriv() ;
 
    return *cmp[place] ;
}


// Affectation d'un tenseur d'ordre 4 :
Scalar& Tensor::set(int ind1, int ind2, int ind3, int ind4) {
    
    assert (valence == 4) ;
    
    Itbl idx(valence) ;
    idx.set(0) = ind1 ;
    idx.set(1) = ind2 ;
    idx.set(2) = ind3 ;
    idx.set(3) = ind4 ;
    int place = position(idx) ;
    del_deriv() ;
 
    return *cmp[place] ;
}


// Affectation cas general
Scalar& Tensor::set(const Itbl& idx) {
    
    assert (idx.get_ndim() == 1) ;
    assert (idx.get_dim(0) == valence) ;
        
    int place = position(idx) ;
    
    del_deriv() ;
    return *cmp[place] ;
}

// Annulation dans des domaines
void Tensor::annule_domain(int l) {
    
    annule(l, l) ;     
}

void Tensor::annule(int l_min, int l_max) {
    
    // Cas particulier: annulation globale : 
    if ( (l_min == 0) && (l_max == mp->get_mg()->get_nzone()-1) ) {
      set_etat_zero() ;
      return ; 
    }
    
    // Annulation des composantes:
    for (int i=0 ; i<n_comp ; i++) {
      cmp[i]->annule(l_min, l_max) ; 
    }
    
    // The derived members are no longer up to date:
    del_deriv() ;
    
}


void Tensor::annule_extern_cn(int lrac, int deg) {

    // Not applicable in the nucleus nor the CED:
    assert( mp->get_mg()->get_type_r(lrac) == FIN ) ; 

    int nz = mp->get_mg()->get_nzone() ;
#ifndef NDEBUG
    if ((2*deg+1) >= mp->get_mg()->get_nr(lrac)) 
      cout << "Tensor::annule_extern_cn : \n" 
       << "WARNING!! \n"
       << "The number of coefficients in r is too low \n"
       << "to do a clean matching..." << endl ;
#endif
    // Boundary of domain lrac
    double r_min = mp->val_r(lrac, -1., 0., 0.)  ; 
    double r_max = mp->val_r(lrac, 1., 0., 0.)  ; 

    //Definition of binomial coefficients array
    Itbl binom(deg+1, deg+1) ;
    binom.annule_hard() ;
    binom.set(0,0) = 1 ;
    for (int n=1; n<=deg; n++) {
      binom.set(n,0) = 1 ;
      for (int k=1; k<=n; k++) 
    binom.set(n,k) = binom(n-1, k) + binom(n-1, k-1) ;
    }
    
    // Coefficient of the second polynomial factor
    Tbl coef(deg+1) ;
    coef.set_etat_qcq() ;
    coef.set(deg) = 1 ;
    int sg = -1 ;
    for (int i=deg-1; i>=0; i--) {
      
      coef.set(i) = double(r_max*(i+1)*coef(i+1) 
               + sg*binom(deg,i)*(2*deg+1)*pow(r_min,deg-i))
    / double(deg+i+1) ;
      sg *= -1 ;
    }
    
    // Normalization to have 1 at r_min
    double aa = coef(deg) ;
    for (int i = deg-1; i>=0; i--) 
      aa = r_min*aa + coef(i) ;
    aa *= pow(r_min - r_max, deg+1) ;
    aa = 1/aa ;

    Mtbl mr = mp->r ;
    Tbl rr = mr(lrac) ;
    
    Tbl poly(rr) ;
    poly = coef(deg) ;
    for (int i=deg-1; i>=0; i--)
      poly = rr*poly + coef(i) ;
    poly *= aa*pow((rr-r_max), deg+1) ;
    
    Scalar rac(*mp) ; 
    rac.allocate_all() ; 
    for (int l=0; l<lrac; l++) rac.set_domain(l) = 1 ; 
    rac.set_domain(lrac) = poly ; 
    rac.annule(lrac+1,nz-1) ; 
    rac.std_spectral_base() ;
    
    for (int ic=0; ic<n_comp; ic++) *(cmp[ic]) *= rac ; 

    del_deriv() ;    
}



const Scalar& Tensor::operator()(int indice1, int indice2) const {
    
    assert(valence == 2) ;
    
    Itbl idx(2) ;       
    idx.set(0) = indice1 ;
    idx.set(1) = indice2 ;
    return *cmp[position(idx)] ;

}

const Scalar& Tensor::operator()(int indice1, int indice2, int indice3) const {
    
    assert(valence == 3) ;
    
    Itbl idx(3) ;       
    idx.set(0) = indice1 ;
    idx.set(1) = indice2 ;
    idx.set(2) = indice3 ;
    return *cmp[position(idx)] ;
}


const Scalar& Tensor::operator()(int indice1, int indice2, int indice3,
                                 int indice4) const {
    
    assert(valence == 4) ;
    
    Itbl idx(4) ;       
    idx.set(0) = indice1 ;
    idx.set(1) = indice2 ;
    idx.set(2) = indice3 ;
    idx.set(3) = indice4 ;
    return *cmp[position(idx)] ;
}



const Scalar& Tensor::operator()(const Itbl& ind) const {
    
    assert (ind.get_ndim() == 1) ;
    assert (ind.get_dim(0) == valence) ;
    return *cmp[position(ind)] ;
    
}


// Gestion de la CED :
void Tensor::dec_dzpuis(int decrem) {
    
  for (int i=0 ; i<n_comp ; i++)
    cmp[i]->dec_dzpuis(decrem) ;

  del_deriv() ;
}

void Tensor::inc_dzpuis(int inc) {

    for (int i=0 ; i<n_comp ; i++)
      cmp[i]->inc_dzpuis(inc) ;

    del_deriv() ;
}


// Le cout :
ostream& operator<<(ostream& flux, const Tensor &source ) {

    flux << '\n' ;
    flux << "Lorene class : " << typeid(source).name() 
        << "           Valence : " << source.valence << '\n' ;

    if (source.get_triad() != 0x0) {
        flux << "Vectorial basis (triad) on which the components are defined :" 
         << '\n' ; 
        flux << *(source.get_triad()) << '\n' ;
    }
    
    if (source.valence != 0) {
        flux <<    "Type of the indices : " ;
        for (int i=0 ; i<source.valence ; i++) {
            flux << "index " << i << " : " ;
            if (source.type_indice(i) == CON)
                flux << " contravariant." << '\n' ;
            else
                flux << " covariant." << '\n' ;
            if ( i < source.valence-1 ) flux << "                      " ;
        }
        flux << '\n' ; 
    }
    
    for (int i=0 ; i<source.n_comp ; i++) {

        if (source.valence == 0) {
            flux << 
            "===================== Scalar field ========================= \n" ;
        }
        else { 
            flux << "================ Component " ;
            Itbl num_indices = source.indices(i) ;
            for (int j=0 ; j<source.valence ; j++) {
                flux << " " << num_indices(j) ;
            }
            flux << " ================ \n" ; 
        }
        flux << '\n' ; 
      
        flux << *source.cmp[i] << '\n' ;
    }
    
    return flux ;
}


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

    if (comment != 0x0) {
        ost << comment << " : " << endl ; 
    }
    
    ost << "Lorene class : " << typeid(*this).name() 
        << "           Valence : " << valence << '\n' ;

    for (int ic=0; ic<n_comp; ic++) {
    
        if (valence == 0) {
        ost << 
        "===================== Scalar field ========================= \n" ;
    }
    else { 
            ost << "================ Component " ;
        Itbl num_indices = indices(ic) ;
        for (int j=0 ; j<valence ; j++) {
            ost << " " << num_indices(j) ;
            }
            ost << " ================ \n" ; 
    }
    ost << '\n' ; 
        
    cmp[ic]->spectral_display(0x0, thres, precis, ost) ; 
    ost << '\n' ;           
    }
}


void Tensor::sauve(FILE* fd) const {
    
    type_indice.sauve(fd) ; // type des composantes
    fwrite_be(&valence, sizeof(int), 1, fd) ;    // la valence
    
    if (valence != 0) {
        triad->sauve(fd) ;      // Vectorial basis
    }
    
    fwrite_be(&n_comp, sizeof(int), 1, fd) ; // nbre composantes
    for (int i=0 ; i<n_comp ; i++)
      cmp[i]->sauve(fd) ;

}





// Sets the standard spectal bases of decomposition for each component

void Tensor::std_spectral_base() {

    switch (valence) {

        case 0 : {
            cmp[0]->std_spectral_base() ; 
            break ; 
        }   
        
        case 1 : {
            cout << 
            "Tensor::std_spectral_base: should not be called on a Tensor"
            << " of valence 1 but on a Vector !" << endl ;  
            abort() ; 
            break ; 
        }
    
        case 2 : {
        
            Base_val** bases = 0x0 ; 
            if( triad->identify() == (mp->get_bvect_cart()).identify() ) {
                bases = mp->get_mg()->std_base_vect_cart() ;
            }
            else {
                assert( triad->identify() == (mp->get_bvect_spher()).identify()) ;
                bases = mp->get_mg()->std_base_vect_spher() ;
            }

            Itbl ind(2) ;
            for (int i=0 ; i<n_comp ; i++) {   
                ind = indices(i) ;
                cmp[i]->set_spectral_base( (*bases[ind(0)-1]) * 
                     (*bases[ind(1)-1]) ) ;
            }
        
            for (int i=0 ; i<3 ; i++) {
                delete bases[i] ;
            }
            delete [] bases ;
            break ; 

        }
        
       
        default : {

            cout << "Tensor::std_spectral_base: the case valence = " << valence
            << " is not treated yet !" << endl ;
            abort() ;
            break ;
        }
    }
}

// Sets the standard spectal bases of decomposition for each component (odd in the nucleus)

void Tensor::std_spectral_base_odd() {

    switch (valence) {

        case 0 : {
            cmp[0]->std_spectral_base_odd() ; 
            break ; 
        }   
        
        default : {

            cout << "Tensor::std_spectral_base_odd: the case valence = " << valence
            << " is not treated yet !" << endl ;
            abort() ;
            break ;
        }
    }
}


const Tensor& Tensor::derive_cov(const Metric& metre) const {
  
  set_dependance(metre) ;
  int j = get_place_met(metre) ;
  assert ((j>=0) && (j<N_MET_MAX)) ;
  if (p_derive_cov[j] == 0x0) {
    p_derive_cov[j] = metre.connect().p_derive_cov(*this) ;
  }
  return *p_derive_cov[j] ;
}


const Tensor& Tensor::derive_con(const Metric& metre) const {
  
    set_dependance(metre) ;
    int j = get_place_met(metre) ;
    assert ((j>=0) && (j<N_MET_MAX)) ;
    if (p_derive_con[j] == 0x0) {
    
    if (valence == 0) {
        p_derive_con[j] = 
            new Vector( contract(derive_cov(metre), 0, metre.con(), 0) ) ;
    }
    else {
        const Tensor_sym* tsym = dynamic_cast<const Tensor_sym*>(this) ; 

        if (tsym != 0x0) { // symmetric case, preserved by derive_con
            const Tensor& dercov = derive_cov(metre) ; 
            Itbl type_ind = dercov.get_index_type() ;
            type_ind.set(valence) = CON ; 
            p_derive_con[j] = new Tensor_sym(*mp, valence+1, type_ind, *triad,
                                       tsym->sym_index1(), tsym->sym_index2()) ; 
 
            *(p_derive_con[j]) = contract(dercov, valence, metre.con(), 0) ;
                        // valence is the number of the last index of derive_cov 
                        //  (the "derivation" index)
        }
        else {  // general case, no symmetry
        
            p_derive_con[j] =  new Tensor( contract(derive_cov(metre), valence,
                                                    metre.con(), 0) ) ;
                    // valence is the number of the last index of derive_cov 
                    //  (the "derivation" index)
        }
        
    }

    }
  
    return *p_derive_con[j] ;

}

const Tensor& Tensor::divergence(const Metric& metre) const {
  
  set_dependance(metre) ;
  int j = get_place_met(metre) ;
  assert ((j>=0) && (j<N_MET_MAX)) ;
  if (p_divergence[j] == 0x0) {
    p_divergence[j] = metre.connect().p_divergence(*this) ;
  }
  return *p_divergence[j] ;
}

void Tensor::exponential_filter_r(int lzmin, int lzmax, int p, 
              double alpha) {
    if( triad->identify() == (mp->get_bvect_cart()).identify() ) 
    for (int i=0; i<n_comp; i++)
        cmp[i]->exponential_filter_r(lzmin, lzmax, p, alpha) ;
    else {
    cout << "Tensor::exponential_filter_r : " << endl ;
    cout << "Only Cartesian triad is implemented!" << endl ;
    cout << "Exiting..." << endl ;
    abort() ;
    }
}

void Tensor::exponential_filter_ylm(int lzmin, int lzmax, int p, 
              double alpha) {
    if( triad->identify() == (mp->get_bvect_cart()).identify() ) 
    for (int i=0; i<n_comp; i++)
        cmp[i]->exponential_filter_ylm(lzmin, lzmax, p, alpha) ;
    else {
    cout << "Tensor::exponential_filter_ylm : " << endl ;
    cout << "Only Cartesian triad is implemented!" << endl ;
    cout << "Exiting..." << endl ;
    abort() ;
    }
}

---