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* Definition of Lorene classes Tenseur
* Tenseur_sym
*
*/
/*
* Copyright (c) 1999-2001 Philippe Grandclement
* Copyright (c) 2000-2001 Eric Gourgoulhon
* Copyright (c) 2002 Jerome Novak
*
* 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
*
*/
#ifndef __TENSEUR_H_
#define __TENSEUR_H_
/*
* $Id: tenseur.h,v 1.19 2016/09/19 15:26:22 j_novak Exp $
* $Log: tenseur.h,v $
* Revision 1.19 2016/09/19 15:26:22 j_novak
* Correction of several bugs preventing the shared library compilation.
*
* Revision 1.18 2014/10/13 08:52:37 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.17 2010/02/02 13:34:12 e_gourgoulhon
* Marked DEPRECATED (in the documentation).
*
* Revision 1.16 2005/08/30 08:35:10 p_grandclement
* Addition of the Tau version of the vectorial Poisson equation for the Tensors
*
* Revision 1.15 2004/12/29 16:24:03 k_taniguchi
* Addition of the method for vectorial Poisson equations with a multipole
* falloff condition at the outer boundary.
*
* Revision 1.14 2004/12/22 18:25:12 k_taniguchi
* Change an argument of poisson_vect_falloff
*
* Revision 1.13 2004/11/30 20:43:32 k_taniguchi
* Addition of the method for vectorial Poisson equations with falloff
* condition at the outer boundary.
*
* Revision 1.12 2004/03/22 13:12:43 j_novak
* Modification of comments to use doxygen instead of doc++
*
* Revision 1.11 2003/11/06 12:17:31 r_prix
* fixed mini-bug in documentation: without explicit argument in function-prototype,
* doc++ seemed to merge docu of Tensor::operator=(Cmp&) and operator=(Tenseur&)
*
* Revision 1.10 2003/06/20 14:23:38 f_limousin
* Add the functions compare().
*
* Revision 1.9 2002/10/16 14:36:29 j_novak
* Reorganization of #include instructions of standard C++, in order to
* use experimental version 3 of gcc.
*
* Revision 1.8 2002/09/19 14:12:37 e_gourgoulhon
* Modif documentation for LaTeX compliance.
*
* Revision 1.7 2002/09/10 13:44:17 j_novak
* The method "manipule" of one indice has been removed for Tenseur_sym objects
* (the result cannot be a Tenseur_sym).
* The method "sans_trace" now computes the traceless part of a Tenseur (or
* Tenseur_sym) of valence 2.
*
* Revision 1.6 2002/09/06 14:49:25 j_novak
* Added method lie_derive for Tenseur and Tenseur_sym.
* Corrected various errors for derive_cov and arithmetic.
*
* Revision 1.5 2002/08/14 13:46:14 j_novak
* Derived quantities of a Tenseur can now depend on several Metrique's
*
* Revision 1.4 2002/08/08 15:10:44 j_novak
* The flag "plat" has been added to the class Metrique to show flat metrics.
*
* Revision 1.3 2002/08/07 16:14:11 j_novak
* class Tenseur can now also handle tensor densities, this should be transparent to older codes
*
* Revision 1.2 2002/06/17 14:05:17 j_novak
* friend functions are now also declared outside the class definition
*
* Revision 1.1.1.1 2001/11/20 15:19:27 e_gourgoulhon
* LORENE
*
* Revision 2.46 2001/08/27 10:03:56 eric
* Ajout de l'operator% (produit tensoriel avec desaliasing)
*
* Revision 2.45 2001/06/19 15:38:00 eric
* Modif commentaires: mise en conformite Doc++ 3.4.8.
*
* Revision 2.44 2001/06/18 13:56:07 novak
* Ajout de la fonction abs()
*
* Revision 2.43 2001/05/29 16:10:43 eric
* Modif commentaires (mise en conformite Doc++ 3.4.7).
*
* Revision 2.42 2001/05/26 15:48:17 eric
* *** empty log message ***
*
* Revision 2.41 2001/05/26 15:42:54 eric
* Ajout de la fonction flat_scalar_prod_desal (desaliasage)
*
* Revision 2.40 2000/10/19 10:37:51 phil
* *** empty log message ***
*
* Revision 2.39 2000/10/19 09:47:15 phil
* *** empty log message ***
*
* Revision 2.38 2000/10/19 09:41:48 phil
* ajout de inverse_poisson_vect
*
* Revision 2.37 2000/10/06 12:37:09 keisuke
* Add a vectorial Poisson equation Tenseur::poisson_vect_regu.
*
* Revision 2.36 2000/09/27 08:52:34 eric
* Modif commentaires.
*
* Revision 2.35 2000/09/13 12:21:36 eric
* Modif commentaires.
*
* Revision 2.34 2000/09/13 12:11:26 eric
* Ajout de la fonction allocate_all().
*
* Revision 2.33 2000/05/22 14:39:11 phil
* ajout de inc_dzpuis et dec_dzpuis
*
* Revision 2.32 2000/04/03 15:18:54 phil
* suppression de poisson_vect_dirichlet
*
* Revision 2.31 2000/03/31 13:29:43 phil
* poisson_vect_neumann devient poisson_vect_dirichlet
*
* Revision 2.30 2000/03/30 16:10:46 phil
* *** empty log message ***
*
* Revision 2.29 2000/02/18 10:45:05 eric
* Modif commentaires.
*
* Revision 2.28 2000/02/11 19:11:55 phil
* commentaires
*
* Revision 2.27 2000/02/10 16:26:48 eric
* Modif commentaires.
*
* Revision 2.26 2000/02/10 16:10:49 eric
* Ajout de la fonction change_triad.
*
* Revision 2.25 2000/02/09 19:29:25 eric
* MODIF IMPORTANTE: la triade de decomposition est desormais passee en
* argument des constructeurs.
*
* Revision 2.24 2000/02/09 09:53:56 phil
* ajout de poisson_vect_oohara
* ,
*
* Revision 2.23 2000/02/08 19:04:25 eric
* Les fonctions arithmetiques ne sont plus amies.
* Ajout de nouvelles fonctions arithmetiques.
*
* Revision 2.22 2000/02/01 15:40:19 eric
* Ajout de la fonction sqrt
*
* Revision 2.21 2000/02/01 14:13:56 eric
* Modif commentaires.
* Ajout de la fonction amie flat_scalar_prod.
*
* Revision 2.20 2000/01/21 12:48:55 phil
* changement prototypage de Tenseur::poisson_vect
*
* Revision 2.19 2000/01/20 16:02:20 eric
* Ajout des operator=(double ) et operator=(int ).
*
* Revision 2.18 2000/01/20 14:52:08 phil
* *** empty log message ***
*
* Revision 2.17 2000/01/20 14:50:56 phil
* *** empty log message ***
*
* Revision 2.16 2000/01/20 14:39:31 phil
* *** empty log message ***
*
* Revision 2.15 2000/01/20 13:10:56 phil
* Ajout de Tenseur::poisson_vect (double)
*
* Revision 2.14 2000/01/20 11:20:17 phil
* changement prototypage
*
* Revision 2.13 2000/01/20 10:31:30 phil
* ajout de xksk
*
* Revision 2.12 2000/01/14 14:17:47 eric
* Modif commentaires.
*
* Revision 2.11 2000/01/14 14:04:07 eric
* Ajout de la fonction annule.
* classe Tenseur: constructeurs pour les classes derivees et fonctions
* de gestion memoire (del_t(), ...) declarees protected et non plus
* private.
*
* Revision 2.10 2000/01/13 14:15:30 eric
* Modif commentaires.
*
* Revision 2.9 2000/01/13 14:10:18 eric
* Ajout du constructeur par copie d'un Cmp (pour un scalaire)
* ainsi que l'affectation a un Cmp.
*
* Revision 2.8 2000/01/13 13:45:56 eric
* Ajout du membre p_gradient_spher et des fonctions fait_gradient_spher(),
* gradient_spher() pour le calcul du gradient d'un scalaire en
* coordonnees spheriques sur la triade spherique associee.
*
* Revision 2.7 2000/01/12 13:17:49 eric
* Les operator::(...) renvoie desormais une reference const sur le c[...]
* correspondant et non plus un Cmp copie de c[...].
* (ceci grace a Map::cmp_zero()).
*
* Revision 2.6 2000/01/11 11:13:16 eric
* Changement de nom pour la base vectorielle : base --> triad
*
* Revision 2.5 2000/01/10 17:22:26 eric
* Modif des #include
*
* Revision 2.4 2000/01/10 15:14:58 eric
* Ajout du membre base (base vectorielle sur laquelle sont definies
* les composantes).
*
* Revision 2.3 1999/12/09 12:39:39 phil
* changement prototypage des derivees
*
* Revision 2.2 1999/12/07 15:24:17 phil
* ajout include
*
* Revision 2.1 1999/12/03 09:37:11 phil
* *** empty log message ***
*
* Revision 2.0 1999/12/02 17:15:32 phil
* *** empty log message ***
*
* Revision 1.1 1999/12/02 17:13:29 phil
* Initial revision
*
*
* $Header: /cvsroot/Lorene/C++/Include/tenseur.h,v 1.19 2016/09/19 15:26:22 j_novak Exp $
*
*/
#define COV -1
#define CON +1
#define N_MET_MAX 5
// Headers Lorene
#include "cmp.h"
#include "itbl.h"
#include "base_vect.h"
namespace Lorene {
class Metrique ;
class Tenseur_sym ;
//---------------------------------//
// class Tenseur //
//---------------------------------//
/**
* Tensor handling *** DEPRECATED : use class \c Tensor instead ***. \ingroup (otens)
*
* This class is intended to store the components of a tensorial field in
* a specific basis. \a Tensor \a densities can also be stored. A tensor
* density \f$\tau^{i_1\ldots i_p}_{j_1\ldots j_q}\f$ is defined by:
* \f$ \tau^{i_1\ldots i_p}_{j_1\ldots j_q} = \gamma^{\frac{n}{2}}
* T^{i_1\ldots i_p}_{j_1\ldots j_q}\f$ where \e T is a \e q -covariant
* \e p -contravariant tensor and \f$\gamma\f$ is the determinant of the
* used 3-metric. \e n is called the weight of the tensor density.
*
* All this is \b 3D meaning that the indices go from 0 to 2. Moreover,
* the components are described in orthonormal bases.
*
* When first constructed, the memory for each component is not allocated.
*
*/
class Tenseur {
// Data :
// -----
protected:
const Map* const mp ; ///< Reference mapping
int valence ; ///< Valence
/** Vectorial basis (triad) with respect to which the tensor
* components are defined.
*/
const Base_vect* triad ;
/** Array of size \c valence contening the type of each index,
* \c COV for a covariant one and \c CON for a contravariant one.
*
*/
Itbl type_indice ;
int n_comp ; ///< Number of components, depending on the symmetry.
int etat ; ///< Logical state \c ETATZERO , \c ETATQCQ or \c ETATNONDEF
Cmp** c ; ///< The components.
double poids ; ///< For tensor densities: the weight
/// For tensor densities: the metric defining the conformal factor
const Metrique* metric ;
// Derived data :
// ------------
protected:
/** Array of pointers on the \c Metrique 's used to calculate
* derivatives members. If no such member has been calculated
* the pointer is set to zero. The array has the size
* \c N_MET_MAX abd the i-th corresponds to the i-th ones
* in \c p_derive_cov and p_derive_con.
*
*/
const Metrique** met_depend ;
/** Pointer on the gradient of \c *this .
* It is set to zero if it has not been calculated yet.
*
*/
mutable Tenseur* p_gradient ;
/** Pointer on the gradient of \c *this in a spherical orthonormal
* basis (scalar field only).
* It is set to zero if it has not been calculated yet.
*
*/
mutable Tenseur* p_gradient_spher ;
/** Array of pointers on the covariant derivatives of \c *this
* with respect to the corresponding metric in \c *met_depend .
* It is set to zero if it has not been calculated yet, or
* for a scalar field.
*
*/
Tenseur** p_derive_cov ;
/** Array of pointers on the contravariant derivatives of \c *this
* with respect to the corresponding metric in \c *met_depend .
* It is set to zero if it has not been calculated yet.
*
*/
Tenseur** p_derive_con ;
/** Array of pointers on the scalar squares of \c *this
* with respect to the corresponding metric in \c *met_depend .
* It is set to zero if it has not been calculated yet.
*
*/
Tenseur** p_carre_scal ;
// Constructors - Destructor :
// -------------------------
protected:
/// Returns false for a tensor density without a defined metric
bool verif() const ;
/** Builds the arrays \c met_depend , \c p_derive_cov ,
* \c p_derive_con and \c p_carre_scal and fills them with
* null pointers.
*
*/
void new_der_met() ;
public:
explicit Tenseur (const Map& map, const Metrique* met = 0x0,
double weight = 0) ; ///< Constructor for a scalar field.
/// Constructor for a scalar field and from a \c Cmp .
explicit Tenseur (const Cmp& cmp, const Metrique* met = 0x0,
double weight = 0) ;
/** Standard constructor.
*
* @param map the mapping
* @param val valence of the tensor
* @param tipe 1-D \c Itbl of size \c valence containing the type
* of each index, \c COV for a covariant one
* and \c CON for a contravariant one, with the
* following storage convention:
* \li \c tipe(0) : type of the first index
* \li \c tipe(1) : type of the second index
* \li and so on...
* @param triad_i vectorial basis (triad) with respect to which
* the tensor components are defined
* @param met for tensor densities only: a pointer on the metric
* defining the conformal factor
* @param weight for tensor densities: the weight
*/
Tenseur (const Map& map, int val, const Itbl& tipe,
const Base_vect& triad_i, const Metrique* met = 0x0,
double weight = 0) ;
/** Standard constructor with the triad passed as a pointer.
*
* @param map the mapping
* @param val valence of the tensor
* @param tipe 1-D \c Itbl of size \c valence containing the type
* of each index, \c COV for a covariant one
* and \c CON for a contravariant one, with the
* following storage convention:
* \li \c tipe(0) : type of the first index
* \li \c tipe(1) : type of the second index
* \li and so on...
* @param triad_i pointer on the vectorial basis (triad) with respect
* to which the tensor components are defined
* (can be set to 0x0 for a scalar field)
* @param met for tensor densities only: a pointer on the metric
* defining the conformal factor
* @param weight for tensor densities: the weight
*/
Tenseur (const Map& map, int val, const Itbl& tipe,
const Base_vect* triad_i, const Metrique* met = 0x0,
double weight = 0) ;
/** Standard constructor when all the indices are of
* the same type.
*
* @param map the mapping
* @param val valence of the tensor
* @param tipe the type of the indices.
* @param triad_i vectorial basis (triad) with respect to which
* the tensor components are defined.
* @param met for tensor densities only: a pointer on the metric
* defining the conformal factor
* @param weight for tensor densities: the weight
*/
Tenseur (const Map& map, int val, int tipe, const
Base_vect& triad_i, const Metrique* met = 0x0,
double weight = 0) ;
Tenseur (const Tenseur&) ; ///< Copy constructor
/// Constructor from a symmetric tensor.
explicit Tenseur (const Tenseur_sym&) ;
/** Constructor from a file (see \c sauve(FILE*) ).
*
* @param map the mapping
* @param triad_i vectorial basis (triad) with respect to which
* the tensor components are defined. It will
* be checked that it coincides with the basis
* saved in the file.
* @param fich file which has been created by
* the function \c sauve(FILE*) .
* @param met for tensor densities only: a pointer on the metric
* defining the conformal factor
*/
Tenseur (const Map& map, const Base_vect& triad_i, FILE* fich,
const Metrique* met = 0x0) ;
/** Constructor from a file for a scalar field
* (see \c sauve(FILE*) ).
*
* @param map the mapping
* @param fich file which has been created by
* the function \c sauve(FILE*) .
* @param met for tensor densities only: a pointer on the metric
* defining the conformal factor
*/
Tenseur (const Map& map, FILE* fich, const Metrique* met = 0x0) ;
protected:
/**
* Constructor used by the derived classes.
*
* @param map the mapping
* @param val valence of the tensor
* @param tipe 1-D \c Itbl of size \c valence containing the type
* of each index, \c COV for a covariant one
* and \c CON for a contravariant one, with the
* following storage convention:
* \li \c tipe(0) : type of the first index
* \li \c tipe(1) : type of the second index
* \li and so on...
* @param n_comp the number of components.
* @param triad_i vectorial basis (triad) with respect to which
* the tensor components are defined
* @param met for tensor densities only: a pointer on the metric
* defining the conformal factor
* @param weight for tensor densities: the weight
*/
Tenseur (const Map& map, int val, const Itbl& tipe, int n_comp,
const Base_vect& triad_i, const Metrique* met = 0x0,
double weight = 0) ;
/**
* Constructor used by the derived classes when all the indices are of
* the same type.
*
* @param map the mapping
* @param val valence of the tensor
* @param tipe the type of the indices.
* @param n_comp the number of components.
* @param triad_i vectorial basis (triad) with respect to which
* the tensor components are defined
* @param met for tensor densities only: a pointer on the metric
* defining the conformal factor
* @param weight for tensor densities: the weight
*/
Tenseur (const Map&, int val, int tipe, int n_comp,
const Base_vect& triad_i, const Metrique* met = 0x0,
double weight = 0) ;
public:
virtual ~Tenseur() ; ///< Destructor
// Memory management
// -----------------
protected:
void del_t() ; ///< Logical destructor
/**
* Logical destructor of the derivatives depending on the i-th
* element of \c *met_depend .
*/
void del_derive_met(int i) const ;
/**
* Logical destructor of all the derivatives.
*/
void del_derive() const ;
/**
* Sets the pointers of the derivatives depending on the i-th
* element of \c *met_depend to zero (as well as that i-th
* element).
*/
void set_der_met_0x0(int i) const ;
/**
* Sets the pointers of all the derivatives
* to zero.
*/
void set_der_0x0() const ;
// Mutators / assignment
// ---------------------
public:
/**
* Sets the logical state to \c ETATNONDEF (undefined state).
* The components are not allocated.
*/
void set_etat_nondef() ;
/**
* Sets the logical state to \c ETATZERO (zero state).
* The components are not allocated.
*/
void set_etat_zero() ;
/**
* Sets the logical state to \c ETATQCQ (ordinary state).
* The components are now allocated and set to \c ETATNONDEF .
*/
void set_etat_qcq() ;
/**
* Sets the logical state to \c ETATQCQ (ordinary state)
* and performs the memory allocation of all the
* elements, down to the \c double arrays of the \c Tbl s.
* This function performs in fact recursive calls to
* \c set_etat_qcq()
* on each element of the chain \c Tenseur -> \c Cmp ->
* \c Valeur -> \c Mtbl -> \c Tbl .
*/
void allocate_all() ;
/** Sets a new vectorial basis (triad) of decomposition and modifies
* the components accordingly.
*/
void change_triad(const Base_vect& new_triad) ;
/** Assigns a new vectorial basis (triad) of decomposition.
* NB: this function modifies only the member \c triad and
* leave unchanged the components (member \c c ). In order to
* change them coherently with the new basis, the function
* \c change_triad(const Base_vect\&) must be called instead.
*/
void set_triad(const Base_vect& new_triad) ;
void set_poids(double weight) ; ///<Sets the weight for a tensor density
/// Sets the pointer on the metric for a tensor density
void set_metric(const Metrique& met) ;
/// Assignment to another \c Tenseur
virtual void operator=(const Tenseur& tens) ;
/// Assignment to a \c Cmp (scalar field only)
void operator=(const Cmp& field) ;
/// Assignment to a \c double (scalar field only, except for zero)
void operator=(double ) ;
/// Assignment to a \c int (scalar field only, except for zero)
void operator=(int ) ;
/// Read/write for a scalar (see also \c operator=(const \c Cmp\&) ).
Cmp& set () ;
Cmp& set (int) ; ///< Read/write for a vector.
Cmp& set (int, int) ; ///< Read/write for a tensor of valence 2.
Cmp& set (int, int, int) ; ///< Read/write for a tensor of valence 3.
Cmp& set (const Itbl&) ; ///< Read/write in the general case.
/**
* Sets the \c Tenseur to zero in a given domain.
* @param l [input] Index of the domain in which the \c Tenseur
* will be set (logically) to zero.
*/
void annule(int l) ;
/**
* Sets the \c Tenseur to zero in several domains.
* @param l_min [input] The \c Tenseur will be set (logically)
* to zero
* in the domains whose indices are in the range
* \c [l_min,l_max] .
* @param l_max [input] see the comments for \c l_min .
*
* Note that \c annule(0,nz-1), where \c nz is the total number
* of domains, is equivalent to \c set_etat_zero() .
*/
void annule(int l_min, int l_max) ;
/**
* Set the standard spectal basis of decomposition for each component.
* To be used only with \c valence strictly lower than 3.
*
*/
void set_std_base() ;
void dec_dzpuis() ; ///< dzpuis -= 1 ;
void inc_dzpuis() ; ///< dzpuis += 1 ;
void dec2_dzpuis() ; ///< dzpuis -= 2 ;
void inc2_dzpuis() ; ///< dzpuis += 2 ;
void mult_r_zec() ; ///< Multiplication by \e r in the external zone.
/**
* Compute \f$\Delta + \lambda \nabla\nabla\f$ of \c *this , \c *this
* being of valence 1.
*/
Tenseur inverse_poisson_vect (double lambda) const ;
// Accessors
// ---------
public:
/**
* Returns the position in the \c Cmp 1-D array \c c of a
* component given by its indices.
*
* @return position in the \c Cmp 1-D array \c c
* corresponding to the indices given in \c idx . \c idx
* must be a 1-D \c Itbl of size \c valence ,
* each element of which must be 0, 1 or 2,
* corresponding to spatial indices 1, 2 or 3 respectively.
*/
virtual int donne_place (const Itbl& idx) const ;
/**
* Returns the indices of a component given by its position in the
* \c Cmp 1-D array \c c .
*
* @return 1-D array of integers (\c Itbl ) of
* size \c valence giving the value of each index
* for the component located at the position \c place
* in the \c Cmp 1-D array \c c .
* Each element of this \c Itbl is 0, 1 or 2, which
* corresponds to spatial indices 1, 2 or 3 respectively.
* If \c (*this) is a scalar the function returns an undefined
* \c Itbl .
*/
virtual Itbl donne_indices (int place) const ;
/// Returns pointer on the mapping.
const Map* get_mp() const {return mp ;} ;
/** Returns the vectorial basis (triad) on which the components
* are defined.
*/
const Base_vect* get_triad() const {return triad;} ;
/// Returns the logical state.
int get_etat() const {return etat ;} ;
///Returns the valence.
int get_valence() const {return valence ; } ;
///Returns the number of components.
int get_n_comp() const {return n_comp ;} ;
/**
* Returns the type of the index number \c i . \c i must be
* strictly lower than \c valence and obey the following
* convention:
* \li \c i = 0 : first index
* \li \c i = 1 : second index
* \li and so on...
*
* @return COV for a covariant index, CON for a
* contravariant one.
*/
int get_type_indice (int i) const {return type_indice(i) ;};
/**
* Returns the types of all the indices.
*
* @return 1-D \c Itbl of size \c valence containing the type
* of each index, \c COV for a covariant one and \c CON
* for a contravariant one.
*/
Itbl get_type_indice () const {return type_indice ; } ;
///Returns the weight
double get_poids() const {return poids ; } ;
/**
* Returns a pointer on the metric defining the conformal factor
* for tensor densities. Otherwise (case of a pure tensor), it
* returns 0x0.
*/
const Metrique* get_metric() const {return metric ; } ;
const Cmp& operator()() const ; ///< Read only for a scalar.
const Cmp& operator()(int) const ; ///< Read only for a vector.
const Cmp& operator()(int, int) const ; ///< Read only for a tensor of valence 2.
const Cmp& operator()(int, int, int) const ; ///< Read only for a tensor of valence 3.
const Cmp& operator()(const Itbl&) const ; ///< Read only in the general case.
// Outputs
// -------
public:
void sauve(FILE *) const ; ///< Save in a file
friend ostream& operator<<(ostream& , const Tenseur & ) ;
// Computation of derived members
// ------------------------------
protected:
/**
* Calculates, if needed, the gradient of \c *this .
* The result is in \c *p_gradient
*/
virtual void fait_gradient () const ;
/**
* Calculates, if needed, the gradient of \c *this in a
* spherical orthonormal basis (scalar field only).
* The result is in \c *p_gradient_spher
*/
void fait_gradient_spher () const ;
/**
* Calculates, if needed, the covariant derivative of \c *this ,
* with respect to \c met .
* The result is in \c *p_derive_cov[i]
*/
virtual void fait_derive_cov (const Metrique& met, int i) const ;
/**
* Calculates, if needed, the contravariant derivative of \c *this ,
* with respect to \c met .
* The result is in \c *p_derive_con[i]
*/
virtual void fait_derive_con (const Metrique&, int i) const ;
/**
* Calculates, if needed, the scalar square of \c *this ,
* with respect to \c met .
* The result is in \c *p_carre_scal[i]
*/
void fait_carre_scal (const Metrique&, int i) const ;
/**
* To be used to describe the fact that the derivatives members have
* been calculated with \c met .
*
* First it sets a null element of \c met_depend to
* \c \&met and puts \c this in
* the list of the dependancies of \c met .
*
*/
void set_dependance (const Metrique& met) const ;
/**
* Returns the position of the pointer on \c metre in
* the array \c met_depend .
*
*/
int get_place_met(const Metrique& metre) const ;
// Differential operators
// ----------------------
public:
/// Returns the gradient of \c *this (Cartesian coordinates)
const Tenseur& gradient() const ;
/** Returns the gradient of \c *this (Spherical coordinates)
* (scalar field only).
*/
const Tenseur& gradient_spher() const ;
/**
* Returns the covariant derivative of \c *this , with respect to
* \c met .
*/
const Tenseur& derive_cov (const Metrique& met) const ;
/**
* Returns the contravariant derivative of \c *this , with respect to
* \c met .
*/
const Tenseur& derive_con (const Metrique&) const ;
/**
* Returns the scalar square of \c *this , with respect to
* \c met .
*/
const Tenseur& carre_scal (const Metrique&) const ;
// Resolution d'EDP :
/**
* Solves the vectorial Poisson equation :
* \f$\Delta N^i +\lambda \nabla^i \nabla_k N^k = S^i\f$.
* with \f$\lambda \not= 1\f$.
*
* \c *this must be given with \c dzpuis = 4.
*
* It uses the Shibata scheme, where \f$N^i\f$ is given by :
* \f[
* N^i = \frac{1}{2}\frac{\lambda+2}{\lambda+1}W^i-\frac{1}{2}
* \frac{\lambda}{\lambda+1}\left(\nabla^i\chi+\nabla^iW^kx_k\right)
* \f]
* with \f$\Delta W^i = S^i\f$ and \f$\Delta \chi = -x_kS^k\f$.
*
* @param lambda [input] \f$\lambda\f$.
* @param par [input/output] see Map::donne_para_poisson_vect.
* @param shift [input] solution \f$N^i\f$ at the previous step.
* Zero if nothing is known.
* @param shift [output] solution at this step.
* @param vect [input/output] the same thing than for \c shift but for
* \f$W^i\f$.
* @param scal [input/output] the same thing than for \c shift but for
* \f$\chi\f$.
*/
void poisson_vect(double lambda, Param& par, Tenseur& shift, Tenseur& vect
, Tenseur& scal) const ;
/*
* Same as poisson_vect with a Tau method
**/
void poisson_vect_tau(double lambda, Param& par, Tenseur& shift, Tenseur& vect
, Tenseur& scal) const ;
void poisson_vect_falloff(double lambda, Param& par, Tenseur& shift,
Tenseur& vect, Tenseur& scal, int* k_falloff) const ;
void poisson_vect_ylm(double lambda, Param& para, Tenseur& shift,
Tenseur& vecteur, Tenseur& scalaire, int nylm,
double* intvec) const ;
/**
* Solves the vectorial Poisson equation \f$\Delta N^i +\lambda \nabla^i
* \nabla_k N^k = S^i\f$.
* with \f$\lambda \not= 1\f$.
*
* \c *this must be given with \c dzpuis = 4.
*
* It uses the Shibata scheme, where \f$N^i\f$ is given by :
* \f[
* N^i = \frac{1}{2}\frac{\lambda+2}{\lambda+1}W^i-\frac{1}{2}
* \frac{\lambda}{\lambda+1}\left(\nabla^i\chi+\nabla^iW^kx_k\right)
* \f]
* with \f$\Delta W^i = S^i\f$ and \f$\Delta \chi = -x_kS^k\f$.
*
* This version is to be used only with an affine mapping.
*
* @param lambda [input] \f$\lambda\f$.
* @param vect [input] \f$W^i\f$ at the previous step.
* Zero if nothing is known.
* @param vect [output] \f$W^i\f$ at this step.
* @param scal [input/output] the same thing than for \c shift but for
* \f$\chi\f$.
*
* @return the solution \f$N^i\f$.
*/
Tenseur poisson_vect(double lambda, Tenseur& vect , Tenseur& scal ) const ;
/*
* Same as poisson_vect with a Tau method
**/
Tenseur poisson_vect_tau(double lambda, Tenseur& vect , Tenseur& scal ) const ;
Tenseur poisson_vect_falloff(double lambda, Tenseur& vect ,
Tenseur& scal, int* k_falloff ) const ;
Tenseur poisson_vect_ylm(double lambda, Tenseur& vecteur,
Tenseur& scalaire, int nylm, double* intvec) const ;
/**
* Solves the vectorial Poisson equation \f$\Delta N^i +\lambda \nabla^i
* \nabla_k N^k = S^i\f$.
* with \f$\lambda \not= 1\f$.
*
* \c *this must be given with \c dzpuis = 3 or 4 and be continuous.
*
* It uses the Oohara scheme, where \f$N^i\f$ is given by
* \f[
* \Delta N^i = S^i-\lambda \nabla^i \chi
* \f]
* with \f$\chi\f$ solution of :
* \f[
* \Delta \chi = \frac{1}{\lambda+1}\nabla_k S^k
* \f]
*
* @param lambda [input] \f$\lambda\f$.
* @param par [input/output] see Map::donne_para_poisson_vect.
* @param shift [input] solution \f$N^i\f$ at the previous step.
* Zero if nothing is known.
* @param shift [output] solution at this step.
* @param scal [input/output] the same thing than for \c shift but for
* \f$\chi\f$.
*/
void poisson_vect_oohara(double lambda, Param& par, Tenseur& shift,
Tenseur& scal) const ;
/*
* Same as poisson_vect_oohara with a Tau method
**/
void poisson_vect_oohara_tau(double lambda, Param& par, Tenseur& shift,
Tenseur& scal) const ;
/**
* Solves the vectorial Poisson equation \f$\Delta N^i +\lambda \nabla^i
* \nabla_k N^k = S^i\f$.
* with \f$\lambda \not= 1\f$.
*
* \c *this must be given with \c dzpuis = 3 or 4 and be continuous.
*
* This version is to be used only with an affine mapping.
*
* It uses the Oohara scheme, where \f$N^i\f$ is given by :
* \f[
* \Delta N^i = S^i-\lambda \nabla^i \chi
* \f]
*
* with \f$\chi\f$ solution of :
* \f[
* \Delta \chi = \frac{1}{\lambda+1}\nabla_k S^k
* \f]
*
* This version is to be used only with an affine mapping.
*
* @param lambda [input] \f$\lambda\f$.
* @param scal [input]\f$\chi\f$ at the previous step.
* Zero if nothing is known.
* @param scal [output] \f$\chi\f$ at this step.
* @return the solution \f$N^i\f$.
*/
Tenseur poisson_vect_oohara(double lambda, Tenseur& scal) const ;
/*
* Same as poisson_vect_oohara with a Tau method
**/
Tenseur poisson_vect_oohara_tau(double lambda, Tenseur& scal) const ;
/**
* Solves the vectorial Poisson equation :
* \f$\Delta N^i +\lambda \nabla^i \nabla_k N^k = S^i\f$.
* with \f$\lambda \not= 1\f$ by regularizing the source term.
*
* \c *this must be given with \c dzpuis = 4.
*
* It uses the Shibata scheme, where \f$N^i\f$ is given by :
* \f[
* N^i = \frac{1}{2}\frac{\lambda+2}{\lambda+1}W^i-\frac{1}{2}
* \frac{\lambda}{\lambda+1}\left(\nabla^i\chi+\nabla^iW^kx_k\right)
* \f]
* with \f$\Delta W^i = S^i\f$ and \f$\Delta \chi = -x_kS^k\f$.
*
* @param k_div [input] regularization degree.
* @param nzet [input] number of domains covering a star.
* @param unsgam1 [input] \f$1/(\gamma - 1)\f$.
* @param lambda [input] \f$\lambda\f$.
* @param par [input/output] see Map::donne_para_poisson_vect.
* @param shift [input] solution \f$N^i\f$ at the previous step.
* Zero if nothing is known.
* @param shift [output] solution at this step.
* @param vect [input/output] the same thing than for \c shift but for
* \f$W^i\f$.
* @param scal [input/output] the same thing than for \c shift but for
* \f$\chi\f$.
*/
void poisson_vect_regu(int k_div, int nzet, double unsgam1,
double lambda, Param& par, Tenseur& shift,
Tenseur& vect, Tenseur& scal) const ;
// Friend classes
// ---------------
friend class Tenseur_sym ;
friend class Metrique ;
// Mathematical operators
// ----------------------
friend Tenseur operator* (const Tenseur&, const Tenseur&) ;
friend Tenseur operator% (const Tenseur&, const Tenseur&) ;
friend Tenseur contract(const Tenseur&, int id1, int id2) ;
friend Tenseur contract(const Tenseur&, int id1, const Tenseur&,
int id2) ;
friend Tenseur contract_desal(const Tenseur&, int id1, const Tenseur&,
int id2) ;
friend Tenseur flat_scalar_prod(const Tenseur& t1, const Tenseur& t2) ;
friend Tenseur flat_scalar_prod_desal(const Tenseur& t1,
const Tenseur& t2) ;
friend Tenseur manipule(const Tenseur&, const Metrique&, int idx) ;
friend Tenseur manipule(const Tenseur&, const Metrique&) ;
friend Tenseur skxk (const Tenseur&) ;
friend Tenseur lie_derive(const Tenseur& , const Tenseur& ,
const Metrique* ) ;
};
/**
* \defgroup tens_cal Tenseur calculus
* \ingroup (otens)
*
*@{
*/
/// Tensorial product.
Tenseur operator*(const Tenseur&, const Tenseur&) ;
/// Tensorial product with desaliasing.
Tenseur operator%(const Tenseur&, const Tenseur&) ;
/**
* Self contraction of two indices of a \c Tenseur .
*
* The two indices must be of different type, i.e. covariant and
* contravariant, or contravariant and covariant.
*
* @param id1 [input] number of the first index for the contraction;
* \c id1 must be strictly lower than the
* valence of the tensor and obeys the following
* convention:
* \li \c id1 = 0 : first index
* \li \c id1 = 1 : second index
* \li and so on...
* @param id2 [input] number of the second index for the contraction;
* \c id2 must be strictly lower than the
* valence of the tensor and obeys the following
* convention:
* \li \c id2 = 0 : first index
* \li \c id2 = 1 : second index
* \li and so on...
*
*/
Tenseur contract(const Tenseur&, int id1, int id2) ;
/**
* Contraction of two \c Tenseur .
*
* The two indices must be of different type, i.e. covariant and
* contravariant, or contravariant and covariant.
*
* @param id1 [input] number of the index of contraction for
* the first \c Tenseur ;
* \c id1 must be strictly lower than the
* valence of the tensor and obeys the following
* convention:
* \li \c id1 = 0 : first index
* \li \c id1 = 1 : second index
* \li and so on...
* @param id2 [input] number of index of contraction for the second one;
* \c id2 must be strictly lower than the
* valence of the tensor and obeys the following
* convention:
* \li \c id2 = 0 : first index
* \li \c id2 = 1 : second index
* \li and so on...
*/
Tenseur contract(const Tenseur&, int id1, const Tenseur&, int id2) ;
/**
* Scalar product of two \c Tenseur when the metric is
* \f$\delta_{ij}\f$: performs the contraction of the
* last index of \c t1 with the first one of \c t2 , irrespective
* of the type of these indices.
*/
Tenseur flat_scalar_prod(const Tenseur& t1, const Tenseur& t2) ;
/**
* Same as \c flat_scalar_prod but with desaliasing.
*/
Tenseur flat_scalar_prod_desal(const Tenseur& t1, const Tenseur& t2) ;
/**
* Raise or lower the index \c idx depending on its type, using the
* given \c Metrique .
*/
Tenseur manipule(const Tenseur&, const Metrique&, int idx) ;
/**
* Raise or lower all the indices, depending on their type, using the given
* \c Metrique .
*/
Tenseur manipule(const Tenseur&, const Metrique&) ;
/**
* Contraction of the last index of (*this) with \f$x^k\f$ or \f$x_k\f$, depending
* on the type of \e S .
*
* The calculation is performed to avoid singularities in the external
* zone. This is done only for a flat metric.
*/
Tenseur skxk (const Tenseur&) ;
/**
* Lie Derivative of \c t with respect to \c x . If no other argument
* is given, it uses partial derivatives with respect to cartesian coordinates
* to calculate the result (this is the default). Otherwise, it uses the
* covariant derivative associated to the metric given as last argument.
*/
Tenseur lie_derive (const Tenseur& t, const Tenseur& x, const Metrique* = 0x0);
/**
* Computes the traceless part of a \c Tenseur of valence 2.
*
* @param tens [input] the \c Tenseur of valence 2
* @param metre [input] the metric used to raise or lower the indices
*
* @return The traceless part of the input \c Tenseur
*/
Tenseur sans_trace(const Tenseur& tens, const Metrique& metre) ;
/** @} */
/**
* \defgroup tens_ma Tenseur mathematics
* \ingroup (otens)
*
* @{
*/
Tenseur operator+(const Tenseur& ) ; ///< + Tenseur
Tenseur operator-(const Tenseur& ) ; ///< \c - Tenseur
Tenseur operator+(const Tenseur&, const Tenseur &) ; ///< Tenseur + Tenseur
/// Tenseur + double (the \c Tenseur must be a scalar)
Tenseur operator+(const Tenseur&, double ) ;
/// double + Tenseur (the \c Tenseur must be a scalar)
Tenseur operator+(double, const Tenseur& ) ;
/// Tenseur + int (the \c Tenseur must be a scalar)
Tenseur operator+(const Tenseur&, int ) ;
/// int + Tenseur (the \c Tenseur must be a scalar)
Tenseur operator+(int, const Tenseur& ) ;
Tenseur operator-(const Tenseur &, const Tenseur &) ; ///< Tenseur - Tenseur
/// Tenseur - double (the \c Tenseur must be a scalar)
Tenseur operator-(const Tenseur&, double ) ;
/// double - Tenseur (the \c Tenseur must be a scalar)
Tenseur operator-(double, const Tenseur& ) ;
/// Tenseur - int (the \c Tenseur must be a scalar)
Tenseur operator-(const Tenseur&, int ) ;
/// int - Tenseur (the \c Tenseur must be a scalar)
Tenseur operator-(int, const Tenseur& ) ;
/// Tenseur * double
Tenseur operator*(const Tenseur&, double ) ;
/// double * Tenseur
Tenseur operator*(double, const Tenseur& ) ;
/// Tenseur * int
Tenseur operator*(const Tenseur&, int ) ;
/// int * Tenseur
Tenseur operator*(int, const Tenseur& ) ;
/// Tenseur / Tenseur (\c b must be a scalar)
Tenseur operator/(const Tenseur& a, const Tenseur& b) ;
Tenseur operator/(const Tenseur&, double ) ; ///< Tenseur / double
/// double / Tenseur (the \c Tenseur must be a scalar)
Tenseur operator/(double, const Tenseur &) ;
Tenseur operator/(const Tenseur&, int ) ; ///< Tenseur / int
/// int / Tenseur (the \c Tenseur must be a scalar)
Tenseur operator/(int, const Tenseur &) ;
Tenseur exp(const Tenseur& ) ; ///< Exponential (for a scalar only)
Tenseur log(const Tenseur& ) ; ///< Neperian logarithm (for a scalar only)
Tenseur sqrt(const Tenseur& ) ; ///< Square root (for a scalar only)
Tenseur abs(const Tenseur& ) ; ///< Absolute value (for a scalar only)
Tenseur pow(const Tenseur&, int ) ; ///< Power (for a scalar only)
Tenseur pow(const Tenseur&, double ) ; ///< Power (for a scalar only)
/** @} */
//---------------------------------//
// class Tenseur_sym //
//---------------------------------//
/**
* Class intended to describe tensors with a symmetry on the two last indices *** DEPRECATED : use class \c Tensor_sym instead ***.
* The storage and the calculations are different and quicker than with an
* usual \c Tenseur . \ingroup (otens)
*
* The valence must be >1.
*/
class Tenseur_sym : public Tenseur {
// Constructors - Destructor :
// -------------------------
public:
/** Standard constructor.
*
* @param map the mapping
* @param val valence of the tensor; must be greater or equal to 2.
* @param tipe 1-D \c Itbl of size \c valence containing the type
* of each index, \c COV for a covariant one
* and \c CON for a contravariant one, with the
* following storage convention:
* \li \c tipe(0) : type of the first index
* \li \c tipe(1) : type of the second index
* \li and so on...
* @param triad_i vectorial basis (triad) with respect to which
* the tensor components are defined
*/
Tenseur_sym (const Map& map, int val, const Itbl& tipe,
const Base_vect& triad_i, const Metrique* met = 0x0,
double weight = 0) ;
/** Standard constructor when all the indices are of the same type.
*
* @param map the mapping
* @param val valence of the tensor; must be greater or equal to 2.
* @param tipe the type of the indices.
* @param triad_i vectorial basis (triad) with respect to which
* the tensor components are defined
*
*/
Tenseur_sym (const Map& map, int val, int tipe,
const Base_vect& triad_i, const Metrique* met = 0x0,
double weight = 0) ;
Tenseur_sym (const Tenseur_sym&) ; ///< Copy constructor
/** Constructor from a \c Tenseur .
* The symmetry is assumed to be true but not checked.
*/
explicit Tenseur_sym (const Tenseur&) ;
/** Constructor from a file (see \c sauve(FILE*) ).
*
* @param map the mapping
* @param triad_i vectorial basis (triad) with respect to which
* the tensor components are defined. It will
* be checked that it coincides with the basis
* saved in the file.
* @param fich file which has been created by
* the function \c sauve(FILE*) .
*/
Tenseur_sym (const Map& map, const Base_vect& triad_i, FILE* fich,
const Metrique* met = 0x0) ;
virtual ~Tenseur_sym() ; ///< Destructor
// Mutators / assignment
// ---------------------
public:
/**
* Assignment from a \c Tenseur .
*
* The symmetry is assumed but not checked.
*/
virtual void operator= (const Tenseur&) ;
// Accessors
// ---------
public:
/**
* Returns the position in the \c Cmp 1-D array \c c of a
* component given by its indices.
*
* @return position in the \c Cmp 1-D array \c c
* corresponding to the indices given in \c idx . \c idx
* must be a 1-D \c Itbl of size \c valence ,
* each element of which must be 0, 1 or 2,
* corresponding to spatial indices 1, 2 or 3 respectively.
*/
virtual int donne_place (const Itbl& idx) const ;
/**
* Returns the indices of a component given by its position in the
* \c Cmp 1-D array \c c .
*
* @return 1-D array of integers (\c Itbl ) of
* size \c valence giving the value of each index
* for the component located at the position \c place
* in the \c Cmp 1-D array \c c .
* Each element of this \c Itbl is 0, 1 or 2, which
* corresponds to spatial indices 1, 2 or 3 respectively.
*/
virtual Itbl donne_indices (int place) const ;
// Computation of derived members
// ------------------------------
protected:
/**
* Calculates, if needed, the gradient of \c *this .
* The result is in \c *p_gradient
*/
virtual void fait_gradient () const ;
/**
* Calculates, if needed, the covariant derivative of \c *this , with
* respect to \c met .
* The result is in \c *p_derive_cov[i]
*/
virtual void fait_derive_cov (const Metrique& met, int i) const ;
/**
* Calculates, if needed, the contravariant derivative of \c *this ,
* with respect to \c met .
* The result is in \c *p_derive_con[i]
*/
virtual void fait_derive_con (const Metrique&, int i) const ;
// Mathematical operators
// ----------------------
friend Tenseur_sym operator* (const Tenseur&, const Tenseur_sym&) ;
friend Tenseur_sym manipule(const Tenseur_sym&, const Metrique&) ;
friend Tenseur lie_derive (const Tenseur& , const Tenseur& ,
const Metrique* );
} ;
/**
* \defgroup tsym_cal Tenseur_sym calculus
* \ingroup (otens)
*
* @{
*/
/// Tensorial product.
Tenseur_sym operator* (const Tenseur&, const Tenseur_sym&) ;
/**
* Raise or lower all the indices, depending on their type, using the given
* \c Metrique .
*/
Tenseur_sym manipule(const Tenseur_sym&, const Metrique&) ;
/**
* Lie Derivative of \c t with respect to \c x . If no other
* argument is given, it uses partial derivatives with respect to
* cartesian coordinates to calculate the result (this is the
* default). Otherwise, it uses the covariant derivative associated
* to the metric given as last argument.
*/
Tenseur_sym lie_derive (const Tenseur_sym& t, const Tenseur& x,
const Metrique* = 0x0);
/**
* Computes the traceless part of a \c Tenseur_sym of valence 2.
*
* @param tens [input] the \c Tenseur_sym of valence 2
* @param metre [input] the metric used to raise or lower the indices
*
* @return The traceless part of the input \c Tenseur_sym
*/
Tenseur_sym sans_trace(const Tenseur_sym& tens, const Metrique& metre) ;
/** @} */
/**
* \defgroup tsym_mat Tenseur_sym mathematics
* \ingroup (otens)
*
* @{
*/
Tenseur_sym operator+(const Tenseur_sym& ) ; ///< + Tenseur_sym
Tenseur_sym operator-(const Tenseur_sym& ) ; ///< \c - Tenseur_sym
/// Tenseur_sym + Tenseur_sym
Tenseur_sym operator+(const Tenseur_sym&, const Tenseur_sym &) ;
/// Tenseur_sym - Tenseur_sym
Tenseur_sym operator-(const Tenseur_sym &, const Tenseur_sym &) ;
/// Tenseur_sym * double
Tenseur_sym operator*(const Tenseur_sym&, double ) ;
/// double * Tenseur_sym
Tenseur_sym operator*(double, const Tenseur_sym& ) ;
/// Tenseur_sym * int
Tenseur_sym operator*(const Tenseur_sym&, int ) ;
/// int * Tenseur_sym
Tenseur_sym operator*(int, const Tenseur_sym& ) ;
/// Tenseur_sym / Tenseur (\c b must be a scalar)
Tenseur_sym operator/(const Tenseur_sym& a, const Tenseur& b) ;
Tenseur_sym operator/(const Tenseur_sym&, double ) ; ///< Tenseur_sym / double
Tenseur_sym operator/(const Tenseur_sym&, int ) ; ///< Tenseur_sym / int
/** @} */
}
#endif
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