tensor_calculus_ext.C

/*
 *  Function external to class Tensor for tensor calculus
 *
 *
 */
 
/*
 *   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
 *
 */
 
 
 
 
/*
 * $Id: tensor_calculus_ext.C,v 1.15 2016/12/05 16:18:17 j_novak Exp $
 * $Log: tensor_calculus_ext.C,v $
 * Revision 1.15  2016/12/05 16:18:17  j_novak
 * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
 *
 * Revision 1.14  2014/10/13 08:53:44  j_novak
 * Lorene classes and functions now belong to the namespace Lorene.
 *
 * Revision 1.13  2014/10/06 15:13:20  j_novak
 * Modified #include directives to use c++ syntax.
 *
 * Revision 1.12  2008/12/05 08:44:02  j_novak
 * New flag to control the "verbosity" of maxabs.
 *
 * Revision 1.11  2004/05/13 21:32:29  e_gourgoulhon
 * Added functions central_value, max_all_domains,
 *  min_all_domains and maxabs_all_domains.
 *
 * Revision 1.10  2004/02/27 21:15:34  e_gourgoulhon
 * Suppressed function contract_desal (since function contract has now
 * the boolean argument "desaliasing").
 *
 * Revision 1.9  2004/02/19 22:11:00  e_gourgoulhon
 * Added argument "comment" in functions max, min, etc...
 *
 * Revision 1.8  2004/02/18 18:51:04  e_gourgoulhon
 * Tensorial product moved from file tensor_calculus.C, since
 * it is not a method of class Tensor.
 *
 * Revision 1.7  2004/02/18 15:56:23  e_gourgoulhon
 * -- Added function contract for double contraction.
 * -- Efficiency improved in functions contract: better handling of variable
 *    "work"(work is now a reference on the relevant component of the result).
 *
 * Revision 1.6  2004/01/23 08:00:16  e_gourgoulhon
 * Minor modifs. in output of methods min, max, maxabs, diffrel to
 * better handle the display in the scalar case.
 *
 * Revision 1.5  2004/01/15 10:59:53  f_limousin
 * Added method contract_desal for the contraction of two tensors with desaliasing
 *
 * Revision 1.4  2004/01/14 11:38:32  f_limousin
 * Added method contract for one tensor
 *
 * Revision 1.3  2003/11/05 15:29:36  e_gourgoulhon
 *  Added declaration of externa functions max, min, maxabs,
 * diffrel and diffrelmax.
 *
 * Revision 1.2  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 1.1  2003/10/06 15:13:38  e_gourgoulhon
 * Tensor contraction.
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Tensor/tensor_calculus_ext.C,v 1.15 2016/12/05 16:18:17 j_novak Exp $
 *
 */
 
// Headers C
#include <cstdlib>
#include <cassert>
#include <cmath>
 
// Headers Lorene
#include "tensor.h"
 
 
 
                //-----------------------//
                //   Tensorial product   //
                //-----------------------//
 
 
namespace Lorene {
Tensor operator*(const Tensor& t1, const Tensor& t2) {
   
    assert (t1.mp == t2.mp) ;
    
    int val_res = t1.valence + t2.valence ;
     
    Itbl tipe (val_res) ;
  
    for (int i=0 ; i<t1.valence ; i++)
    tipe.set(i) = t1.type_indice(i) ;
    for (int i=0 ; i<t2.valence ; i++)
    tipe.set(i+t1.valence) = t2.type_indice(i) ;
    
    
    if ( (t1.valence != 0) && (t2.valence != 0) ) {
    assert ( *(t1.get_triad()) == *(t2.get_triad()) ) ;
    }
    
    const Base_vect* triad_res ; 
    if (t1.valence != 0) {
    triad_res = t1.get_triad() ; 
    }
    else{
    triad_res = t2.get_triad() ; 
    }
    
    Tensor res(*t1.mp, val_res, tipe, triad_res) ;
    
    Itbl jeux_indice_t1 (t1.valence) ;
    Itbl jeux_indice_t2 (t2.valence) ;
        
    for (int i=0 ; i<res.n_comp ; i++) {
    Itbl jeux_indice_res(res.indices(i)) ;
    for (int j=0 ; j<t1.valence ; j++)
        jeux_indice_t1.set(j) = jeux_indice_res(j) ;
    for (int j=0 ; j<t2.valence ; j++)
        jeux_indice_t2.set(j) = jeux_indice_res(j+t1.valence) ;
    
    res.set(jeux_indice_res) = t1(jeux_indice_t1)*t2(jeux_indice_t2) ;
    }
    
    return res ;
}
 
 
 
 
                //------------------//
                //   Contraction    //
                //------------------//
 
// Contraction on one index
// ------------------------
Tensor contract(const Tensor& t1, int ind1, const Tensor& t2, int ind2,
                bool desaliasing) {
    
    int val1 = t1.get_valence() ; 
    int val2 = t2.get_valence() ; 
 
    // Verifs :
    assert((ind1>=0) && (ind1<val1)) ;
    assert((ind2>=0) && (ind2<val2)) ;
    assert(t1.get_mp() == t2.get_mp()) ;
    
    // Contraction possible ?
    if ( (val1 != 0) && (val2 != 0) ) {
        assert ( *(t1.get_triad()) == *(t2.get_triad()) ) ;
    }
    assert (t1.get_index_type(ind1) != t2.get_index_type(ind2)) ;
    
    int val_res = val1 + val2 - 2;
    
    Itbl tipe(val_res) ;
 
    for (int i=0 ; i<ind1 ; i++)
        tipe.set(i) = t1.get_index_type(i) ;
    for (int i=ind1 ; i<val1-1 ; i++)
        tipe.set(i) = t1.get_index_type(i+1) ;
    for (int i=val1-1 ; i<val1+ind2-1 ; i++)
        tipe.set(i) = t2.get_index_type(i-val1+1) ;
    for (int i = val1+ind2-1 ; i<val_res ; i++)
        tipe.set(i) = t2.get_index_type(i-val1+2) ;
    
    const Base_vect* triad_res = (val_res == 0) ? 0x0 : t1.get_triad() ; 
 
    Tensor res(t1.get_mp(), val_res, tipe, triad_res) ;
    
    // Boucle sur les composantes de res :
    
    Itbl jeux_indice_t1(val1) ;
    Itbl jeux_indice_t2(val2) ;
    
    for (int i=0 ; i<res.get_n_comp() ; i++) {
    
        Itbl jeux_indice_res(res.indices(i)) ;
        
        for (int j=0 ; j<ind1 ; j++)
            jeux_indice_t1.set(j) = jeux_indice_res(j) ;
            
        for (int j=ind1+1 ; j<val1 ; j++)
            jeux_indice_t1.set(j) = jeux_indice_res(j-1) ;
 
        for (int j=0 ; j<ind2 ; j++)
            jeux_indice_t2.set(j) = jeux_indice_res(val1+j-1) ;
 
        for (int j=ind2+1 ; j<val2 ; j++)
            jeux_indice_t2.set(j) = jeux_indice_res(val1+j-2) ;
    
        Scalar& work = res.set(jeux_indice_res) ;
        work.set_etat_zero() ;
 
        for (int j=1 ; j<=3 ; j++) {
            jeux_indice_t1.set(ind1) = j ;
            jeux_indice_t2.set(ind2) = j ;
            if (desaliasing) {
                work += t1(jeux_indice_t1) % t2(jeux_indice_t2) ;
            }
            else {
                work += t1(jeux_indice_t1) * t2(jeux_indice_t2) ;
            }
        }
        
    }
    
    return res ;
}
 
 
 
// Contraction on two indices
// --------------------------
Tensor contract(const Tensor& t1, int i1, int j1, 
                const Tensor& t2, int i2, int j2,
                bool desaliasing) {
    
    int val1 = t1.get_valence() ; 
    int val2 = t2.get_valence() ; 
 
    // Verifs :
    assert( val1 >= 2 ) ; 
    assert( val2 >= 2 ) ; 
    assert( (0<=i1) && (i1<j1) && (j1<val1) ) ;
    assert( (0<=i2) && (i2<j2) && (j2<val2) ) ;
    assert( t1.get_mp() == t2.get_mp() ) ;
    
    // Contraction possible ?
    assert( *(t1.get_triad()) == *(t2.get_triad()) ) ;
    assert( t1.get_index_type(i1) != t2.get_index_type(i2) ) ;
    assert( t1.get_index_type(j1) != t2.get_index_type(j2) ) ;
    
    int val_res = val1 + val2 - 4 ;
    
    Itbl tipe(val_res) ;
 
    for (int i=0 ; i<i1 ; i++) 
        tipe.set(i) = t1.get_index_type(i) ;
 
    for (int i=i1 ; i<j1-1 ; i++) 
        tipe.set(i) = t1.get_index_type(i+1) ;
 
    for (int i=j1-1 ; i<val1-2 ; i++) 
        tipe.set(i) = t1.get_index_type(i+2) ;
 
    for (int i=val1-2 ; i<val1-2+i2 ; i++)
        tipe.set(i) = t2.get_index_type(i-val1+2) ;
        
    for (int i=val1-2+i2 ; i<val1+j2-3 ; i++)
        tipe.set(i) = t2.get_index_type(i-val1+3) ;
    
    for (int i=val1+j2-3 ; i<val_res ; i++) 
        tipe.set(i) = t2.get_index_type(i-val1+4) ;
    
    const Base_vect* triad_res = (val_res == 0) ? 0x0 : t1.get_triad() ; 
 
    Tensor res(t1.get_mp(), val_res, tipe, triad_res) ;
    
    // Boucle sur les composantes de res :
    
    Itbl jeux_indice_t1(val1) ;
    Itbl jeux_indice_t2(val2) ;
    
    for (int ic=0 ; ic<res.get_n_comp() ; ic++) {
    
        Itbl jeux_indice_res(res.indices(ic)) ;
        
        for (int k=0 ; k<i1 ; k++)
            jeux_indice_t1.set(k) = jeux_indice_res(k) ;
            
        for (int k=i1+1 ; k<j1 ; k++)
            jeux_indice_t1.set(k) = jeux_indice_res(k-1) ;
 
        for (int k=j1+1 ; k<val1 ; k++)
            jeux_indice_t1.set(k) = jeux_indice_res(k-2) ;
 
        for (int k=0 ; k<i2 ; k++)
            jeux_indice_t2.set(k) = jeux_indice_res(val1+k-2) ;
 
        for (int k=i2+1 ; k<j2 ; k++)
            jeux_indice_t2.set(k) = jeux_indice_res(val1+k-3) ;
    
        for (int k=j2+1 ; k<val2 ; k++)
            jeux_indice_t2.set(k) = jeux_indice_res(val1+k-4) ;
    
        Scalar& work = res.set(jeux_indice_res) ;
        work.set_etat_zero() ;
 
        for (int i=1 ; i<=3 ; i++) {
 
            jeux_indice_t1.set(i1) = i ; 
            jeux_indice_t2.set(i2) = i ; 
            
            for (int j=1 ; j<=3 ; j++) {
 
                jeux_indice_t1.set(j1) = j ;
                jeux_indice_t2.set(j2) = j ;
            
                if (desaliasing) {
                    work += t1(jeux_indice_t1) % t2(jeux_indice_t2) ;
                }
                else {
                    work += t1(jeux_indice_t1) * t2(jeux_indice_t2) ;
                }
            }
        }
        
    }
    
    return res ;
}
 
 
 
 
Tensor contract(const Tensor& source, int ind_1, int ind_2) {
    
    int val = source.get_valence() ;   
 
    // Les verifications :
    assert ((ind_1 >= 0) && (ind_1 < val)) ;
    assert ((ind_2 >= 0) && (ind_2 < val)) ;
    assert (ind_1 != ind_2) ;
    assert (source.get_index_type(ind_1) != source.get_index_type(ind_2)) ;
 
    // On veut ind_1 < ind_2 :
    if (ind_1 > ind_2) {
        int auxi = ind_2 ;
        ind_2 = ind_1 ;
        ind_1 = auxi ;
    }
    
    // On construit le resultat :
    int val_res = val - 2 ;
   
    Itbl tipe(val_res) ;
    
    for (int i=0 ; i<ind_1 ; i++)
        tipe.set(i) = source.get_index_type(i) ;
    for (int i=ind_1 ; i<ind_2-1 ; i++)
        tipe.set(i) = source.get_index_type(i+1) ;
    for (int i = ind_2-1 ; i<val_res ; i++)
        tipe.set(i) = source.get_index_type(i+2) ;
    
    Tensor res(source.get_mp(), val_res, tipe, source.get_triad()) ; 
    
    // Boucle sur les composantes de res :
    
    Itbl jeux_indice_source(val) ;
    
    for (int i=0 ; i<res.get_n_comp() ; i++) {
 
        Itbl jeux_indice_res(res.indices(i)) ;
        
        for (int j=0 ; j<ind_1 ; j++)
            jeux_indice_source.set(j) = jeux_indice_res(j) ;
        for (int j=ind_1+1 ; j<ind_2 ; j++)
            jeux_indice_source.set(j) = jeux_indice_res(j-1) ;
        for (int j=ind_2+1 ; j<val ; j++)
            jeux_indice_source.set(j) = jeux_indice_res(j-2) ;
        
        Scalar& work = res.set(jeux_indice_res) ;
        work.set_etat_zero() ;
 
        for (int j=1 ; j<=3 ; j++) {
            jeux_indice_source.set(ind_1) = j ;
            jeux_indice_source.set(ind_2) = j ;
            work += source(jeux_indice_source) ;
        }
        
    }
    
    return res ;
}
 
 
 
 
                //------------------//
                //     diffrel      //
                //------------------//
 
 
Tbl diffrel(const Tensor& aa, const Tensor& bb, const char* comment,
            ostream& ost) {
 
        if (comment != 0x0) ost << comment << " : " << endl ; 
 
    int val = aa.get_valence() ; 
 
    assert(bb.get_valence() == val) ; 
    
    int n_comp_a = aa.get_n_comp() ; 
    int n_comp_b = bb.get_n_comp() ; 
    
    const Tensor* tmax ; 
    int n_comp_max ; 
    if (n_comp_a >= n_comp_b) {
        n_comp_max = n_comp_a ; 
        tmax = &aa ; 
    }
    else {
        n_comp_max = n_comp_b ; 
        tmax = &bb ; 
    }
    
    int nz = aa.get_mp().get_mg()->get_nzone() ; 
    Tbl resu(n_comp_max, nz) ; 
    resu.set_etat_qcq() ; 
 
    Itbl idx(val) ; 
    
    for (int ic=0; ic<n_comp_max; ic++) {
        idx = tmax->indices(ic) ; 
        Tbl diff = diffrel( aa(idx), bb(idx) ) ; 
        
        if (n_comp_max > 1) ost << "   Comp." ; 
        for (int j=0 ; j<val ; j++) {
            ost << " " << idx(j) ;
        }
        if (n_comp_max > 1) ost << " : " ; 
                else ost << "   " ;
        for (int l=0; l<nz; l++) {
            ost << "  " << diff(l) ;
            resu.set(ic, l) = diff(l) ; 
        }
        ost << "\n" ; 
        
    }
    
    return resu ; 
}
 
 
                //--------------------//
                //     diffrelmax     //
                //--------------------//
 
 
Tbl diffrelmax(const Tensor& aa, const Tensor& bb, const char* comment,
               ostream& ost) {
 
        if (comment != 0x0) ost << comment << " : " << endl ; 
 
    int val = aa.get_valence() ; 
 
    assert(bb.get_valence() == val) ; 
    
    int n_comp_a = aa.get_n_comp() ; 
    int n_comp_b = bb.get_n_comp() ; 
    
    const Tensor* tmax ; 
    int n_comp_max ; 
    if (n_comp_a >= n_comp_b) {
        n_comp_max = n_comp_a ; 
        tmax = &aa ; 
    }
    else {
        n_comp_max = n_comp_b ; 
        tmax = &bb ; 
    }
    
    int nz = aa.get_mp().get_mg()->get_nzone() ; 
    Tbl resu(n_comp_max, nz) ; 
    resu.set_etat_qcq() ; 
 
    Itbl idx(val) ; 
    
    for (int ic=0; ic<n_comp_max; ic++) {
        idx = tmax->indices(ic) ; 
        Tbl diff = diffrelmax( aa(idx), bb(idx) ) ; 
        
        if (n_comp_max > 1) ost << "   Comp." ; 
        for (int j=0 ; j<val ; j++) {
            ost << " " << idx(j) ;
        }
        if (n_comp_max > 1) ost << " : " ; 
                else ost << "   " ;
        for (int l=0; l<nz; l++) {
            ost << "  " << diff(l) ;
            resu.set(ic, l) = diff(l) ; 
        }
        ost << "\n" ; 
        
    }
    
    return resu ; 
}
 
 
 
                //----------------//
                //     max    //
                //----------------//
 
 
Tbl max(const Tensor& aa, const char* comment, ostream& ost) {
 
        if (comment != 0x0) ost << comment << " : " << endl ; 
 
    int val = aa.get_valence() ; 
 
    int n_comp = aa.get_n_comp() ; 
    
    int nz = aa.get_mp().get_mg()->get_nzone() ; 
    Tbl resu(n_comp, nz) ; 
    resu.set_etat_qcq() ; 
 
    Itbl idx(val) ; 
    
    for (int ic=0; ic<n_comp; ic++) {
 
        idx = aa.indices(ic) ; 
        Tbl diff = max( aa(idx) ) ; 
        
        if (val > 0) ost << "   Comp." ; 
        for (int j=0 ; j<val ; j++) {
            ost << " " << idx(j) ;
        }
        if (val > 0) ost << " : " ; 
                else ost << "   " ;
        for (int l=0; l<nz; l++) {
            ost << "  " << diff(l) ;
            resu.set(ic, l) = diff(l) ; 
        }
        ost << "\n" ; 
        
    }
    
    return resu ; 
}
 
 
 
                //----------------//
                //     min    //
                //----------------//
 
 
Tbl min(const Tensor& aa, const char* comment, ostream& ost) {
 
        if (comment != 0x0) ost << comment << " : " << endl ; 
 
    int val = aa.get_valence() ; 
 
    int n_comp = aa.get_n_comp() ; 
    
    int nz = aa.get_mp().get_mg()->get_nzone() ; 
    Tbl resu(n_comp, nz) ; 
    resu.set_etat_qcq() ; 
 
    Itbl idx(val) ; 
    
    for (int ic=0; ic<n_comp; ic++) {
 
        idx = aa.indices(ic) ; 
        Tbl diff = min( aa(idx) ) ; 
        
        if (val > 0) ost << "   Comp." ; 
        for (int j=0 ; j<val ; j++) {
            ost << " " << idx(j) ;
        }
        if (val > 0) ost << " : " ; 
                else ost << "   " ;
        for (int l=0; l<nz; l++) {
            ost << "  " << diff(l) ;
            resu.set(ic, l) = diff(l) ; 
        }
        ost << "\n" ; 
        
    }
    
    return resu ; 
}
 
 
                //--------------------//
                //     maxabs         //
                //--------------------//
 
 
Tbl maxabs(const Tensor& aa, const char* comment, ostream& ost, bool verb) {
 
        if (comment != 0x0) ost << comment << " : " << endl ; 
 
    int val = aa.get_valence() ; 
 
    int n_comp = aa.get_n_comp() ; 
    
    int nz = aa.get_mp().get_mg()->get_nzone() ; 
    Tbl resu(n_comp, nz) ; 
    resu.set_etat_qcq() ; 
 
    Itbl idx(val) ; 
    
    for (int ic=0; ic<n_comp; ic++) {
 
        idx = aa.indices(ic) ; 
        Tbl diff = max( abs( aa(idx) ) ) ; 
        
        if (verb) {
        if (val > 0) ost << "   Comp." ; 
        for (int j=0 ; j<val ; j++) {
            ost << " " << idx(j) ;
                }
        if (val > 0 ) ost << " : " ; 
                else ost << "   " ; 
        }
        for (int l=0; l<nz; l++) {
        if (verb) ost << "  " << diff(l) ;
        resu.set(ic, l) = diff(l) ; 
        }
        if (verb) ost << "\n" ; 
        
    }
    
    return resu ; 
}
 
 
        //-------------------//
        //  Central value    //
        //-------------------//
 
Tbl central_value(const Tensor& aa, const char* comment, ostream& ost) {
 
    if (comment != 0x0) ost << comment << " : " << endl ; 
 
    int val = aa.get_valence() ; 
    int n_comp = aa.get_n_comp() ; 
    
    Tbl resu(n_comp) ; 
    resu.set_etat_qcq() ; 
 
    Itbl idx(val) ; 
    
    for (int ic=0; ic<n_comp; ic++) {
 
        idx = aa.indices(ic) ;
        double aa_c = aa(idx).val_grid_point(0,0,0,0) ; 
        resu.set(ic) = aa_c ; 
        
        if ( comment != 0x0 ) {
            if ( val > 0 ) ost << "   Comp." ; 
                for (int j=0 ; j<val ; j++) {
                    ost << " " << idx(j) ;
            }
            if (val > 0 ) ost << " : " ; 
                else ost << "   " ; 
            ost << aa_c << endl ; 
        }
        
    }
    
    return resu ; 
}
    
 
        //-------------------//
        //  max_all_domains  //
        //-------------------//
 
Tbl max_all_domains(const Tensor& aa, int l_excluded, const char* comment, 
        ostream& ost) {
 
    if (comment != 0x0) ost << comment << " : " << endl ; 
 
    Tbl max_dom = max(aa) ; 
    
    int val = aa.get_valence() ; 
    int n_comp = aa.get_n_comp() ; 
    int nz = aa.get_mp().get_mg()->get_nzone() ; 
    
    Tbl resu(n_comp) ; 
    resu.set_etat_qcq() ; 
 
    Itbl idx(val) ; 
    
    for (int ic=0; ic<n_comp; ic++) {
 
        double x0 ; 
        if (l_excluded != 0) x0 = max_dom(ic, 0) ;
        else x0 = max_dom(ic, 1) ; 
        for (int l=0; l<nz; l++) {
            if (l == l_excluded) continue ; 
            double x = max_dom(ic,l) ; 
            if (x > x0) x0 = x ; 
        }
        
        resu.set(ic) = x0 ; 
        
        if ( comment != 0x0 ) {
            if ( val > 0 ) ost << "   Comp." ; 
                idx = aa.indices(ic) ;
                for (int j=0 ; j<val ; j++) {
                    ost << " " << idx(j) ;
            }
            if (val > 0 ) ost << " : " ; 
                else ost << "   " ; 
            ost << x0 << endl ; 
        }
        
    }
    
    return resu ; 
        
}
 
        //-------------------//
        //  min_all_domains  //
        //-------------------//
 
Tbl min_all_domains(const Tensor& aa, int l_excluded, const char* comment, 
        ostream& ost) {
 
    if (comment != 0x0) ost << comment << " : " << endl ; 
 
    Tbl min_dom = min(aa) ; 
    
    int val = aa.get_valence() ; 
    int n_comp = aa.get_n_comp() ; 
    int nz = aa.get_mp().get_mg()->get_nzone() ; 
    
    Tbl resu(n_comp) ; 
    resu.set_etat_qcq() ; 
 
    Itbl idx(val) ; 
    
    for (int ic=0; ic<n_comp; ic++) {
 
        double x0 ; 
        if (l_excluded != 0) x0 = min_dom(ic, 0) ;
        else x0 = min_dom(ic, 1) ; 
        for (int l=0; l<nz; l++) {
            if (l == l_excluded) continue ; 
            double x = min_dom(ic,l) ; 
            if (x < x0) x0 = x ; 
        }
        
        resu.set(ic) = x0 ; 
        
        if ( comment != 0x0 ) {
            if ( val > 0 ) ost << "   Comp." ; 
                idx = aa.indices(ic) ;
                for (int j=0 ; j<val ; j++) {
                    ost << " " << idx(j) ;
            }
            if (val > 0 ) ost << " : " ; 
                else ost << "   " ; 
            ost << x0 << endl ; 
        }
        
    }
    
    return resu ; 
        
}
 
 
        //----------------------//
        //  maxabs_all_domains  //
        //----------------------//
 
Tbl maxabs_all_domains(const Tensor& aa, int l_excluded, const char* comment, 
        ostream& ost, bool verb) {
 
    if (comment != 0x0) ost << comment << " : " << endl ; 
 
    Tbl maxabs_dom = maxabs(aa, 0x0, ost, verb) ; 
    
    int val = aa.get_valence() ; 
    int n_comp = aa.get_n_comp() ; 
    int nz = aa.get_mp().get_mg()->get_nzone() ; 
    
    Tbl resu(n_comp) ; 
    resu.set_etat_qcq() ; 
 
    Itbl idx(val) ; 
    
    for (int ic=0; ic<n_comp; ic++) {
 
        double x0 ; 
        if (l_excluded != 0) x0 = maxabs_dom(ic, 0) ;
        else x0 = maxabs_dom(ic, 1) ; 
        for (int l=0; l<nz; l++) {
            if (l == l_excluded) continue ; 
            double x = maxabs_dom(ic,l) ; 
            if (x > x0) x0 = x ; 
        }
        
        resu.set(ic) = x0 ; 
        
        if ( comment != 0x0 ) {
            if ( val > 0 ) ost << "   Comp." ; 
                idx = aa.indices(ic) ;
                for (int j=0 ; j<val ; j++) {
                    ost << " " << idx(j) ;
            }
            if (val > 0 ) ost << " : " ; 
                else ost << "   " ; 
            ost << x0 << endl ; 
        }
        
    }
    
    return resu ; 
        
}
 
 
 
}