tensor_calculus.C

/*
 *  Methods of class Tensor for tensor calculus
 *
 *
 */

/*
 *   Copyright (c) 2003 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_calculus_C[] = "$Header: /cvsroot/Lorene/C++/Source/Tensor/tensor_calculus.C,v 1.8 2004/02/26 22:49:45 e_gourgoulhon Exp $" ;

/*
 * $Id: tensor_calculus.C,v 1.8 2004/02/26 22:49:45 e_gourgoulhon Exp $
 * $Log: tensor_calculus.C,v $
 * Revision 1.8  2004/02/26 22:49:45  e_gourgoulhon
 * Added methods compute_derive_lie and derive_lie.
 *
 * Revision 1.7  2004/02/18 18:50:07  e_gourgoulhon
 * -- Added new methods trace(...).
 * -- Tensorial product moved to file tensor_calculus_ext.C, since it is not
 *    a method of class Tensor.
 *
 * Revision 1.6  2004/02/18 15:54:23  e_gourgoulhon
 * Efficiency improved in method scontract: better handling of work (it is
 * now considered as a reference on the relevant component of the result).
 *
 * Revision 1.5  2003/12/05 16:38:50  f_limousin
 * Added method operator*
 *
 * Revision 1.4  2003/10/28 21:25:34  e_gourgoulhon
 * Method contract renamed scontract.
 *
 * Revision 1.3  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 1.2  2003/10/06 20:52:22  e_gourgoulhon
 * Added methods up, down and up_down.
 *
 * Revision 1.1  2003/10/06 15:13:38  e_gourgoulhon
 * Tensor contraction.
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Tensor/tensor_calculus.C,v 1.8 2004/02/26 22:49:45 e_gourgoulhon Exp $
 *
 */

// Headers C++
#include "headcpp.h"

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

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


                //------------------//
                //       Trace      //
                //------------------//


Tensor Tensor::trace(int ind_1, int ind_2) const {
    
    // Les verifications :
    assert( (ind_1 >= 0) && (ind_1 < valence) ) ;
    assert( (ind_2 >= 0) && (ind_2 < valence) ) ;
    assert( ind_1 != ind_2 )  ;
    assert( type_indice(ind_1) != type_indice(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 = valence - 2 ;
   
    Itbl tipe(val_res) ;
    
    for (int i=0 ; i<ind_1 ; i++)
        tipe.set(i) = type_indice(i) ;
    for (int i=ind_1 ; i<ind_2-1 ; i++)
        tipe.set(i) = type_indice(i+1) ;
    for (int i = ind_2-1 ; i<val_res ; i++)
        tipe.set(i) = type_indice(i+2) ;
    
    Tensor res(*mp, val_res, tipe, triad) ; 
    
    // Boucle sur les composantes de res :
    
    Itbl jeux_indice_source(valence) ;
    
    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<valence ; 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 += (*cmp[position(jeux_indice_source)]) ;
        }
        
    }
    
    return res ;
}


Tensor Tensor::trace(int ind1, int ind2, const Metric& gam) const {

    // Les verifications :
    assert( (ind1 >= 0) && (ind1 < valence) ) ;
    assert( (ind2 >= 0) && (ind2 < valence) ) ;
    assert( ind1 != ind2 )  ;
 
    if ( type_indice(ind1) != type_indice(ind2) ) {
        cout << "Tensor::trace(int, int, const Metric&) : Warning : \n"
            << "  the two indices for the trace have opposite types,\n"
            << "  hence the metric is useless !\n" ; 

        return trace(ind1, ind2) ;               
    }
    else {
        if ( type_indice(ind1) == COV  ) {
            return contract(gam.con(), 0, 1, *this, ind1, ind2) ; 
        }
        else{
            return contract(gam.cov(), 0, 1, *this, ind1, ind2) ; 
        }
    }
          
}



Scalar Tensor::trace() const {
    
    // Les verifications :
    assert( valence == 2 )  ;
    assert( type_indice(0) != type_indice(1) )  ;
    
    Scalar res(*mp) ; 
    res.set_etat_zero() ; 
    
    for (int i=1; i<=3; i++) {
        res += operator()(i,i) ;    
    }
    
    return res ;
}


Scalar Tensor::trace(const Metric& gam) const {
    
    assert( valence == 2 )  ;
    
    if ( type_indice(0) != type_indice(1) ) {
        cout << "Tensor::trace(const Metric&) : Warning : \n"
            << "  the two indices have opposite types,\n"
            << "  hence the metric is useless to get the trace !\n" ; 

        return trace() ;               
    }
    else {
        if ( type_indice(0) == COV  ) {
            return contract(gam.con(), 0, 1, *this, 0, 1) ; 
        }
        else{
            return contract(gam.cov(), 0, 1, *this, 0, 1) ; 
        }
    }
          
}


                //----------------------//
                //  Index manipulation  //
                //----------------------//


Tensor Tensor::up(int place, const Metric& met) const {
    
    assert (valence != 0) ;     // Aucun interet pour un scalaire...
    assert ((place >=0) && (place < valence)) ;
    
    
    Tensor auxi = ::contract(met.con(), 1, *this, place) ;
    
    // On doit remettre les indices a la bonne place ...
    
    Itbl tipe(valence) ;

    for (int i=0 ; i<valence ; i++)
        tipe.set(i) = type_indice(i) ;
    tipe.set(place) = CON ;
    
    Tensor res(*mp, valence, tipe, triad) ;
    
    Itbl place_auxi(valence) ;
    
    for (int i=0 ; i<res.n_comp ; i++) {
    
        Itbl place_res(res.indices(i)) ;
    
        place_auxi.set(0) = place_res(place) ;
        for (int j=1 ; j<place+1 ; j++)
            place_auxi.set(j) = place_res(j-1)  ;
        place_res.set(place) = place_auxi(0) ;
    
        for (int j=place+1 ; j<valence ; j++)
            place_auxi.set(j) = place_res(j);   
    
        res.set(place_res) = auxi(place_auxi) ;
    }
    
    return res ;

} 


Tensor Tensor::down(int place, const Metric& met) const {
    
    assert (valence != 0) ;     // Aucun interet pour un scalaire...
    assert ((place >=0) && (place < valence)) ;
    
    Tensor auxi = ::contract(met.cov(), 1, *this, place) ;
    
    // On doit remettre les indices a la bonne place ...
    
    Itbl tipe(valence) ;

    for (int i=0 ; i<valence ; i++)
        tipe.set(i) = type_indice(i) ;
    tipe.set(place) = COV ;
    
    Tensor res(*mp, valence, tipe, triad) ;
    
    Itbl place_auxi(valence) ;
    
    for (int i=0 ; i<res.n_comp ; i++) {
    
        Itbl place_res(res.indices(i)) ;
    
        place_auxi.set(0) = place_res(place) ;
        for (int j=1 ; j<place+1 ; j++)
            place_auxi.set(j) = place_res(j-1)  ;
        place_res.set(place) = place_auxi(0) ;
    
        for (int j=place+1 ; j<valence ; j++)
            place_auxi.set(j) = place_res(j);   
    
        res.set(place_res) = auxi(place_auxi) ;
    }
    
    return res ;

} 



Tensor Tensor::up_down(const Metric& met) const  {
    
    Tensor* auxi ;
    Tensor* auxi_old = new Tensor(*this) ;
    
    for (int i=0 ; i<valence ; i++) {

        if (type_indice(i) == COV) {
            auxi = new Tensor( auxi_old->up(i, met) ) ;
        }
        else{
            auxi = new Tensor( auxi_old->down(i, met) ) ;
        }
        
        delete auxi_old ;
        auxi_old = new Tensor(*auxi) ;
        delete auxi ;

    }
    
    Tensor result(*auxi_old) ;
    delete auxi_old ;

    return result ;
}


                //-----------------------//
                //     Lie derivative    //
                //-----------------------//

// Protected method
//-----------------

void Tensor::compute_derive_lie(const Vector& vv, Tensor& resu) const {


    // Protections
    // -----------
    if (valence > 0) {
        assert(vv.get_triad() == triad) ; 
        assert(resu.get_triad() == triad) ; 
    }


    // Flat metric
    // -----------
        
    const Metric_flat* fmet ;
    
    if (valence == 0) {
        fmet = &(mp->flat_met_spher()) ; 
    }
    else {
        assert( triad != 0x0 ) ; 

        const Base_vect_spher* bvs = 
            dynamic_cast<const Base_vect_spher*>(triad) ; 
        if (bvs != 0x0) {
            fmet = &(mp->flat_met_spher()) ; 
        }
        else {
            const Base_vect_cart* bvc = 
                dynamic_cast<const Base_vect_cart*>(triad) ; 
            if (bvc != 0x0) {
                fmet = &(mp->flat_met_cart()) ; 
            }
            else {
                cerr << "Tensor::compute_derive_lie : unknown triad type !\n" ; 
                abort() ; 
            }
        }
    }

    // Determination of the dzpuis parameter of the input  --> dz_in
    // ---------------------------------------------------
    int dz_in = 0 ;
    for (int ic=0; ic<n_comp; ic++) {
        int dzp = cmp[ic]->get_dzpuis() ; 
        assert(dzp >= 0) ; 
        if (dzp > dz_in) dz_in = dzp ; 
    }

#ifndef NDEBUG
    // Check : do all components have the same dzpuis ?
    for (int ic=0; ic<n_comp; ic++) {
        if ( !(cmp[ic]->check_dzpuis(dz_in)) ) {
            cout << "######## WARNING #######\n" ; 
            cout << " Tensor::compute_derive_lie: the tensor components \n"
            << "    do not have all the same dzpuis ! : \n" 
            << "    ic, dzpuis(ic), dz_in : " << ic << "  " 
            <<  cmp[ic]->get_dzpuis() << "  " << dz_in << endl ; 
        } 
    }
#endif
        
    
    // Initialisation to nabla_V T 
    // ---------------------------
    
    resu = contract(vv, 0, derive_cov(*fmet), valence) ;
    

    // Addition of the terms with derivatives of V  (only if valence > 0)
    // -------------------------------------------
    
    if (valence > 0) {
    
        const Tensor& dv = vv.derive_cov(*fmet) ;  // gradient of V
    
        Itbl ind1(valence) ; // working Itbl to store the indices of resu
        Itbl ind0(valence) ; // working Itbl to store the indices of this
        Scalar tmp(*mp) ;   // working scalar
    
        // loop on all the components of the output tensor:

        int ncomp_resu = resu.get_n_comp() ; 
        
        for (int ic=0; ic<ncomp_resu; ic++) {
    
            // indices corresponding to the component no. ic in the output tensor
            ind1 = resu.indices(ic) ; 
    
            tmp = 0 ; 
        
            // Loop on the number of indices of this 
            for (int id=0; id<valence; id++) {
            
                ind0 = ind1 ;
                
                switch( type_indice(id) ) {
                
                    case CON : {
                        for (int k=1; k<=3; k++) {
                            ind0.set(id) = k ; 
                            tmp -= operator()(ind0) * dv(ind1(id), k) ;
                        }
                        break ; 
                    }
                
                    case COV : {
                        for (int k=1; k<=3; k++) {
                            ind0.set(id) = k ; 
                            tmp += operator()(ind0) * dv(k, ind1(id)) ;
                        }
                        break ; 
                    }
                
                    default : {
                        cerr << 
                        "Tensor::compute_derive_lie: unexpected type of index !\n" ;
                        abort() ; 
                        break ; 
                    }
                
                }   // end of switch on index type 
                
            }   // end of loop on the number of indices of uu               


            if (dz_in > 0) tmp.dec_dzpuis() ; // to get the same dzpuis as
                                              // nabla_V T

            resu.set(ind1) += tmp ;    // Addition to the nabla_V T term
        
        
        }   // end of loop on all the components of the output tensor
        
    }   // end of case valence > 0 
    
}
 

// Public interface
//-----------------

Tensor Tensor::derive_lie(const Vector& vv) const {

    Tensor resu(*mp, valence, type_indice, triad) ; 
    
    compute_derive_lie(vv, resu) ;
    
    return resu ; 
    
}










 

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