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* Definition of Lorene class Cmp
*
*/
/*
* Copyright (c) 1999-2000 Jean-Alain Marck
* Copyright (c) 1999-2002 Eric Gourgoulhon
* Copyright (c) 1999-2001 Philippe Grandclement
* Copyright (c) 2000-2002 Jerome Novak
* Copyright (c) 2000-2001 Keisuke Taniguchi
*
* 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 __CMP_H_
#define __CMP_H_
/*
* $Id: cmp.h,v 1.23 2016/09/19 15:26:22 j_novak Exp $
* $Log: cmp.h,v $
* Revision 1.23 2016/09/19 15:26:22 j_novak
* Correction of several bugs preventing the shared library compilation.
*
* Revision 1.22 2014/10/13 08:52:33 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.21 2014/10/06 15:09:39 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.20 2012/08/12 17:35:36 p_cerda
* Magnetstar: adding new member to class Cmp
*
* Revision 1.19 2010/02/02 13:34:12 e_gourgoulhon
* Marked DEPRECATED (in the documentation).
*
* Revision 1.18 2005/08/30 08:35:10 p_grandclement
* Addition of the Tau version of the vectorial Poisson equation for the Tensors
*
* Revision 1.17 2005/08/02 06:09:58 m_saijo
* Modified comment lines (div_r, multi_r, mult_rsint, div_rsint)
*
* Revision 1.16 2004/12/29 16:20:20 k_taniguchi
* Addition of the function poisson_ylm.
*
* Revision 1.15 2004/11/30 20:38:10 k_taniguchi
* Addition of the function poisson_falloff.
*
* Revision 1.14 2004/10/11 15:08:59 j_novak
* The radial manipulation functions take Scalar as arguments, instead of Cmp.
* Added a conversion operator from Scalar to Cmp.
* The Cmp radial manipulation function make conversion to Scalar, call to the
* Map_radial version with a Scalar argument and back.
*
* Revision 1.13 2004/03/31 11:21:02 f_limousin
* Method Cmp::poisson_neumann_interne has been implemented to solve
* the continuity equation for strange stars.
*
* Revision 1.12 2004/03/22 13:12:40 j_novak
* Modification of comments to use doxygen instead of doc++
*
* Revision 1.11 2004/03/01 09:54:58 j_novak
* Suppression of the Cmp version of avance_dalembert (now only with Scalar's)
*
* Revision 1.10 2003/11/06 14:43:37 e_gourgoulhon
* Gave a name to const arguments in certain method prototypes (e.g.
* constructors) to correct a bug of DOC++.
*
* Revision 1.9 2003/09/24 20:52:37 e_gourgoulhon
* Added constructor by conversion of a Scalar.
*
* Revision 1.8 2003/08/26 09:46:10 j_novak
* Added the method multipole_spectrum
*
* Revision 1.7 2003/06/20 14:16:10 f_limousin
* Add the function compare().
*
* Revision 1.6 2003/06/20 09:27:09 j_novak
* Modif commentaires.
*
* Revision 1.5 2002/09/13 09:17:31 j_novak
* Modif. commentaires
*
* Revision 1.4 2002/06/17 14:05:16 j_novak
* friend functions are now also declared outside the class definition
*
* Revision 1.3 2002/05/17 12:08:46 e_gourgoulhon
* Corrected error in the comment about dzpuis: multiplied --> divided
*
* Revision 1.2 2002/01/03 15:30:27 j_novak
* Some comments modified.
*
* Revision 1.1.1.1 2001/11/20 15:19:27 e_gourgoulhon
* LORENE
*
* Revision 2.101 2001/10/29 15:36:03 novak
* Ajout de Cmp::div_r()
*
* Revision 2.100 2001/10/16 10:03:57 novak
* *** empty log message ***
*
* Revision 2.99 2001/08/31 14:52:10 novak
* Back to 2.97 version 2.98 was useless
*
* Revision 2.97 2001/07/19 14:01:39 novak
* new arguments for Cmp::avance_dalembert
*
* Revision 2.96 2001/05/29 16:09:40 eric
* Modif commentaires (mise en conformite Doc++ 3.4.7).
*
* Revision 2.95 2001/05/26 15:07:20 eric
* Ajout de operator% : multiplication de deux Cmp avec desaliasage
*
* Revision 2.94 2001/05/25 09:30:07 phil
* ajout de filtre_phi
*
* Revision 2.93 2001/03/30 13:36:22 phil
* ajout de raccord_externe
*
* Revision 2.92 2001/03/26 08:11:50 eric
* Modif commentaires.
*
* Revision 2.91 2001/03/22 10:25:19 phil
* modification prototypage de raccord_zec.C
*
* Revision 2.90 2001/02/12 18:08:10 phil
* ajout de Cmp::fixe_decroissance
*
* Revision 2.89 2000/12/13 14:50:05 phil
* changement nom variable dzpuis dans raccord_c1_zec
*
* Revision 2.88 2000/12/13 14:35:53 phil
* *** empty log message ***
*
* Revision 2.87 2000/12/13 14:26:42 phil
* *** empty log message ***
*
* Revision 2.86 2000/12/13 14:25:26 phil
* vire commentaires des raccords (provisioire)
*
* Revision 2.85 2000/12/13 14:19:49 phil
* modif commentaires
*
* Revision 2.84 2000/12/13 14:08:36 phil
* ajout procedure raccord_c1_zec
*
* Revision 2.83 2000/12/04 16:48:47 novak
* *** empty log message ***
*
* Revision 2.82 2000/12/04 15:06:15 novak
* *** empty log message ***
*
* Revision 2.81 2000/11/15 13:24:28 phil
* modification de asymptot
*
* Revision 2.80 2000/11/15 13:19:13 phil
* *** empty log message ***
*
* Revision 2.79 2000/11/15 13:17:01 phil
* *** empty log message ***
*
* Revision 2.78 2000/11/15 13:15:45 phil
* gestion affichage dans asymptot
*
* Revision 2.77 2000/10/20 09:43:30 phil
* changement commentaires
*
* Revision 2.76 2000/10/19 14:07:06 novak
* Ajout de la fonction membre avance_dalembert (experimentale)
*
* Revision 2.75 2000/10/19 09:20:36 phil
* *** empty log message ***
*
* Revision 2.74 2000/10/19 09:13:45 phil
* ajout des fonctions :
* filtre(int)
* set_val_inf(double)
* set_val_hor(double,int)
*
* Revision 2.73 2000/10/05 14:18:14 eric
* La fonction check_poisson est rebaptisee test_poisson.
*
* Revision 2.72 2000/10/05 13:56:52 eric
* *** empty log message ***
*
* Revision 2.71 2000/10/05 13:52:25 eric
* Ajout de la fonction check_poisson.
*
* Revision 2.70 2000/09/13 12:21:44 eric
* Modif commentaires.
*
* Revision 2.69 2000/09/13 12:11:48 eric
* Ajout de la fonction allocate_all().
*
* Revision 2.68 2000/09/07 15:26:40 keisuke
* Add a new argument Cmp& uu in Cmp::poisson_regular.
*
* Revision 2.67 2000/09/04 09:11:06 keisuke
* Suppress Cmp::poisson_regular (version without parameter).
*
* Revision 2.66 2000/08/31 13:04:30 eric
* Ajout des fonctions mult_rsint et div_rsint.
*
* Revision 2.65 2000/08/29 13:51:36 keisuke
* *** empty log message ***
*
* Revision 2.64 2000/08/29 13:46:14 keisuke
* Add the polar and azimuthal derivatives of the diverging potential
* in Cmp::poisson_regular.
* Modify the argumants of Cmp::poisson_regular.
*
* Revision 2.63 2000/08/28 15:48:22 keisuke
* Modif Cmp::poisson_regular
*
* Revision 2.62 2000/08/28 15:43:11 keisuke
* Modif Cmp::poisson_regular
*
* Revision 2.61 2000/08/04 12:09:58 eric
* Ajout de l'operator()(int l) et de la fonction set(int l) pour
* l'acces aux Tbl individuels.
*
* Revision 2.60 2000/08/04 09:18:05 keisuke
* Transformation Cmp::poisson_regular_param en Cmp::poisson_regular
*
* Revision 2.59 2000/08/03 14:01:29 keisuke
* Modif Cmp::poisson_regular et ajout de Cmp::poisson_regular_param
*
* Revision 2.58 2000/07/29 12:50:01 keisuke
* Modif Cmp::poisson_regular
*
* Revision 2.57 2000/07/20 13:33:50 keisuke
* Modif Cmp::poisson_regular
*
* Revision 2.56 2000/07/20 10:25:09 keisuke
* Modif Cmp::poisson_regular
*
* Revision 2.55 2000/07/19 15:50:23 keisuke
* Ajout de Cmp::poisson_regular
*
* Revision 2.54 2000/05/22 14:38:32 phil
* ajout de dec_dzpuis et inc_dzpuis
*
* Revision 2.53 2000/04/27 15:18:57 phil
* *** empty log message ***
*
* Revision 2.52 2000/03/28 17:44:41 phil
* Cmp::raccord() -> Cmp::raccord(int)
*
* Revision 2.51 2000/03/28 17:31:31 phil
* *** empty log message ***
*
* Revision 2.50 2000/03/28 17:25:35 phil
* ajout de Cmp::raccord()
*
* Revision 2.49 2000/03/25 12:52:45 eric
* Ajout de la fonction asymptot(int ).
*
* Revision 2.48 2000/03/20 13:33:31 phil
* commentaires
*
* Revision 2.47 2000/03/17 17:32:54 phil
* *** empty log message ***
*
* Revision 2.46 2000/03/17 17:07:14 phil
* *** empty log message ***
*
* Revision 2.45 2000/03/17 16:56:00 phil
* ajout de poisson_dirichlet et de son amie poisson_neumann
*
* Revision 2.44 2000/03/06 10:55:44 eric
* Ajout des methodes import_symy et import_asymy.
*
* Revision 2.43 2000/02/28 16:29:48 eric
* Ajout des fonctions import_gal, import_align, import_anti.
*
* Revision 2.42 2000/01/28 16:08:55 eric
* Ajout des fonctions dz_nonzero et check_dzpuis.
*
* Revision 2.41 2000/01/07 16:28:15 eric
* Suppression de la fonction membre gradient.
*
* Revision 2.40 1999/12/21 13:03:22 eric
* Changement de prototype de la routine poisson avec Param& : la solution est
* desormais passee en argument (et non plus en valeur de retour)
* pour permettre l'initialisation de methodes de resolution iteratives.
*
* Revision 2.39 1999/12/21 10:06:52 eric
* Il y a desormais deux versions de poisson: une sans Param et une
* avec Param.
*
* Revision 2.38 1999/12/10 16:19:33 eric
* Modif commentaires.
*
* Revision 2.37 1999/12/10 15:59:01 eric
* Modif commentaires fonction set.
*
* Revision 2.36 1999/12/09 10:45:54 eric
* Ajout du calcul d'integrale (membre p_integ et fonctions
* integrale et integrale_domains).
*
* Revision 2.35 1999/12/08 12:38:38 eric
* Ajout de la fonction import.
*
* Revision 2.34 1999/12/07 14:53:13 eric
* Changement ordre des arguments (phi,theta,r) --> (r,theta,phi)
* dans la routine val_point.
*
* Revision 2.33 1999/12/06 16:47:00 eric
* Ajout de la fonction val_point.
*
* Revision 2.32 1999/12/02 17:59:11 phil
* *** empty log message ***
*
* Revision 2.31 1999/12/02 14:28:46 eric
* Reprototypage de la fonction poisson(): const.
* Commentaires.
*
* Revision 2.30 1999/11/30 14:20:54 eric
* Reprototypage des fonctions membres mult_r, mult_r_zec,
* dec2_dzpuis et inc2_dzpuis : Cmp --> void.
*
* Revision 2.29 1999/11/29 13:18:06 eric
* Modif commentaires.
*
* Revision 2.28 1999/11/29 12:56:11 eric
* Introduction des membres p_lap, ind_lap.
* Changement prototype de la fonction laplacien.
*
* Revision 2.27 1999/11/26 14:22:54 eric
* Ajout du membre dzpuis et des fonctions de manipulation associees.
*
* Revision 2.26 1999/11/25 16:27:00 eric
* Reorganisation complete du calcul et stokage des derivees partielles.
*
* Revision 2.25 1999/11/23 16:21:32 eric
* Suppression du membre statique Cmp_Zero.
* Suppression du constructeur par defaut.
*
* Revision 2.24 1999/11/22 16:48:00 phil
* Cmp_Zero est desormais public
*
* Revision 2.23 1999/11/22 16:34:17 eric
* Ajout de l'element global Cmp_Zero.
*
* Revision 2.22 1999/11/22 15:41:42 eric
* Ajout des operateurs set(l,k,j,i) et (l,k,j,i).
* Ajout de la fonction annule(int l).
*
* Revision 2.21 1999/11/15 14:12:28 eric
* Ajout des fonctions mathematiques cos, sin, ..., min, max, norme,...
*
* Revision 2.20 1999/11/12 17:08:10 eric
* Ajout de la partie manquante de l'arithmetique.
*
* Revision 2.19 1999/10/28 09:36:56 eric
* Ajout de la fonction affiche_seuil.
*
* Revision 2.18 1999/10/28 09:01:24 eric
* Constructeur par lecture de fichier.
* Ajout de la fonction annule(int, int).
*
* Revision 2.17 1999/10/27 16:46:23 phil
* ajout de mult_r_zec
*
* Revision 2.16 1999/10/27 15:38:40 eric
* Suppression du membre c.
*
* Revision 2.15 1999/10/27 08:42:40 eric
* Introduction du membre Valeur va.
* Le pointeur Valeur* c est desormais un membre prive constant qui pointe
* sur va.
* Suppression de la fonction nouveau(), ainsi que du constructeur par
* defaut.
*
* Revision 2.14 1999/10/22 08:14:19 eric
* Depoussierage.
* Documentation.
*
* Revision 2.13 1999/10/19 14:40:51 phil
* ajout de inc2_dzpuis()
*
* Revision 2.12 1999/09/16 13:16:47 phil
* ajout de Cmp mult_r()
*
* Revision 2.11 1999/09/15 10:29:44 phil
* ajout de dec2_dzpuis()
*
* Revision 2.10 1999/09/14 17:13:05 phil
* ajout de Cmp operator*(double,const Cmp&)
*
* Revision 2.9 1999/09/14 13:45:27 phil
* suppression de la divergence
*
* Revision 2.8 1999/09/14 12:50:31 phil
* ajout de Cmp deriv(int) et de Cmp divergence()
*
* Revision 2.7 1999/09/07 16:08:04 phil
* ajout de la fonction membre gradient
*
* Revision 2.6 1999/09/06 14:50:27 phil
* ajout du laplacien
*
* Revision 2.5 1999/09/06 14:35:05 phil
* ajout de poisson
*
* Revision 2.4 1999/03/03 11:13:46 hyc
* *** empty log message ***
*
* Revision 2.3 1999/03/03 11:07:27 hyc
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Include/cmp.h,v 1.23 2016/09/19 15:26:22 j_novak Exp $
*
*/
#include <cstdio>
#include "valeur.h"
#include "map.h"
namespace Lorene {
class Param ;
/**
* Component of a tensorial field *** DEPRECATED : use class \c Scalar instead ***. \ingroup (otens)
*/
class Cmp {
// Data :
// -----
private:
const Map* mp ; ///< Reference mapping
/// Logical state (\c ETATNONDEF , \c ETATQCQ or \c ETATZERO ).
int etat ;
/**
* Power of \e r by which the quantity represented by \c this
* must be divided in the external compactified zone in order
* to get the correct physical values
*/
int dzpuis ;
public:
Valeur va ; ///< The numerical value of the \c Cmp
// Derived data :
// ------------
private:
/// Pointer on \f$\partial/\partial r\f$ of \c *this
mutable Cmp* p_dsdr ;
/// Pointer on \f$1/r \partial/\partial \theta\f$ of \c *this
mutable Cmp* p_srdsdt ;
/// Pointer on \f$1/(r\sin\theta) \partial/\partial \phi\f$ of \c *this
mutable Cmp* p_srstdsdp ;
/** Pointer on \f$\partial/\partial x\f$ of \c *this ,
* where \f$x=r\sin\theta \cos\phi\f$
*/
mutable Cmp* p_dsdx ;
/** Pointer on \f$\partial/\partial y\f$ of \c *this ,
* where \f$y=r\sin\theta \sin\phi\f$
*/
mutable Cmp* p_dsdy ;
/** Pointer on \f$\partial/\partial z\f$ of \c *this ,
* where \f$z=r\cos\theta\f$
*/
mutable Cmp* p_dsdz ;
/** Pointer on the Laplacian of \c *this
*/
mutable Cmp* p_lap ;
/** Power of \e r by which the last computed Laplacian has been
* multiplied in the external compactified domain.
*/
mutable int ind_lap ;
/** Pointer on the space integral of \c *this (values in each
* domain)
*/
mutable Tbl* p_integ ;
// Constructors - Destructor
// -------------------------
public:
explicit Cmp(const Map& map) ; ///< Constructor from mapping
explicit Cmp(const Map* p_map) ; ///< Constructor from mapping
Cmp(const Cmp& a) ; ///< Copy constructor
/// Constructor from a file (see \c sauve(FILE*) )
Cmp(const Map&, const Mg3d&, FILE* ) ;
~Cmp() ; ///< Destructor
// Assignment
// -----------
public:
/// Assignment to another \c Cmp defined on the same mapping
void operator=(const Cmp& a) ;
void operator=(const Valeur& a) ; ///< Assignment to a \c Valeur
void operator=(const Mtbl& a) ; ///< Assignment to a \c Mtbl
void operator=(double ) ; ///< Assignment to a \c double
void operator=(int ) ; ///< Assignment to an \c int
/** Assignment to another \c Cmp defined on a different mapping.
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param ci [input] \c Cmp to be imported.
*/
void import(const Cmp& ci) ;
/** Assignment to another \c Cmp defined on a different mapping.
* Case where the \c Cmp is symmetric with respect to the plane y=0.
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param ci [input] \c Cmp to be imported.
*/
void import_symy(const Cmp& ci) ;
/** Assignment to another \c Cmp defined on a different mapping.
* Case where the \c Cmp is antisymmetric with respect to the
* plane y=0.
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param ci [input] \c Cmp to be imported.
*/
void import_asymy(const Cmp& ci) ;
/** Assignment to another \c Cmp defined on a different mapping.
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param nzet [input] Number of domains of the destination
* mapping (i.e. \c this->mp ) where the
* importation is performed: the assignment
* is done for the domains whose indices are
* between 0 and \c nzet-1 . In the other
* domains, \c *this is set to zero.
* @param ci [input] \c Cmp to be imported.
*/
void import(int nzet, const Cmp& ci) ;
/** Assignment to another \c Cmp defined on a different mapping.
* Case where the \c Cmp is symmetric with respect to the plane y=0.
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param nzet [input] Number of domains of the destination
* mapping (i.e. \c this->mp ) where the
* importation is performed: the assignment
* is done for the domains whose indices are
* between 0 and \c nzet-1 . In the other
* domains, \c *this is set to zero.
* @param ci [input] \c Cmp to be imported.
*/
void import_symy(int nzet, const Cmp& ci) ;
/** Assignment to another \c Cmp defined on a different mapping.
* Case where the \c Cmp is antisymmetric with respect to the
* plane y=0.
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param nzet [input] Number of domains of the destination
* mapping (i.e. \c this->mp ) where the
* importation is performed: the assignment
* is done for the domains whose indices are
* between 0 and \c nzet-1 . In the other
* domains, \c *this is set to zero.
* @param ci [input] \c Cmp to be imported.
*/
void import_asymy(int nzet, const Cmp& ci) ;
private:
/** Assignment to another \c Cmp defined on a different mapping,
* when the two mappings do not have a particular relative orientation.
*
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param nzet [input] Number of domains of the destination
* mapping (i.e. \c this->mp ) where the
* importation is performed: the assignment
* is done for the domains whose indices are
* between 0 and \c nzet-1 . In the other
* domains, \c *this is set to zero.
* @param ci [input] \c Cmp to be imported.
*/
void import_gal(int nzet, const Cmp& ci) ;
/** Assignment to another \c Cmp defined on a different mapping,
* when the two mappings have aligned Cartesian axis.
*
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param nzet [input] Number of domains of the destination
* mapping (i.e. \c this->mp ) where the
* importation is performed: the assignment
* is done for the domains whose indices are
* between 0 and \c nzet-1 . In the other
* domains, \c *this is set to zero.
* @param ci [input] \c Cmp to be imported.
*/
void import_align(int nzet, const Cmp& ci) ;
/** Assignment to another \c Cmp defined on a different mapping,
* when the two mappings have anti-aligned Cartesian axis (i.e.
* \f$x_1 = - x_2\f$, \f$y_1 = - y_2\f$, \f$z_1 = z_2\f$).
*
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param nzet [input] Number of domains of the destination
* mapping (i.e. \c this->mp ) where the
* importation is performed: the assignment
* is done for the domains whose indices are
* between 0 and \c nzet-1 . In the other
* domains, \c *this is set to zero.
* @param ci [input] \c Cmp to be imported.
*/
void import_anti(int nzet, const Cmp& ci) ;
/** Assignment to another \c Cmp defined on a different mapping,
* when the two mappings have aligned Cartesian axis.
* Case where the \c Cmp is symmetric with respect to the plane y=0.
*
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param nzet [input] Number of domains of the destination
* mapping (i.e. \c this->mp ) where the
* importation is performed: the assignment
* is done for the domains whose indices are
* between 0 and \c nzet-1 . In the other
* domains, \c *this is set to zero.
* @param ci [input] \c Cmp to be imported.
*/
void import_align_symy(int nzet, const Cmp& ci) ;
/** Assignment to another \c Cmp defined on a different mapping,
* when the two mappings have anti-aligned Cartesian axis (i.e.
* \f$x_1 = - x_2\f$, \f$y_1 = - y_2\f$, \f$z_1 = z_2\f$).
* Case where the \c Cmp is symmetric with respect to the plane y=0.
*
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param nzet [input] Number of domains of the destination
* mapping (i.e. \c this->mp ) where the
* importation is performed: the assignment
* is done for the domains whose indices are
* between 0 and \c nzet-1 . In the other
* domains, \c *this is set to zero.
* @param ci [input] \c Cmp to be imported.
*/
void import_anti_symy(int nzet, const Cmp& ci) ;
/** Assignment to another \c Cmp defined on a different mapping,
* when the two mappings have aligned Cartesian axis.
* Case where the \c Cmp is antisymmetric with respect to the
* plane y=0.
*
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param nzet [input] Number of domains of the destination
* mapping (i.e. \c this->mp ) where the
* importation is performed: the assignment
* is done for the domains whose indices are
* between 0 and \c nzet-1 . In the other
* domains, \c *this is set to zero.
* @param ci [input] \c Cmp to be imported.
*/
void import_align_asymy(int nzet, const Cmp& ci) ;
/** Assignment to another \c Cmp defined on a different mapping,
* when the two mappings have anti-aligned Cartesian axis (i.e.
* \f$x_1 = - x_2\f$, \f$y_1 = - y_2\f$, \f$z_1 = z_2\f$).
* Case where the \c Cmp is antisymmetric with respect to the
* plane y=0.
*
* This assignment is performed point to point by means of the
* spectral expansion of the original \c Cmp .
* @param nzet [input] Number of domains of the destination
* mapping (i.e. \c this->mp ) where the
* importation is performed: the assignment
* is done for the domains whose indices are
* between 0 and \c nzet-1 . In the other
* domains, \c *this is set to zero.
* @param ci [input] \c Cmp to be imported.
*/
void import_anti_asymy(int nzet, const Cmp& ci) ;
// Access to individual elements
// -----------------------------
public:
/** Read/write of the value in a given domain.
* NB: to gain in efficiency, the method \c del_deriv() (to delete
* the derived members) is not called by this function. It must
* thus be invoqued by the user.
*
* @param l [input] domain index
* @return Tbl containing the value of the field in domain \c l .
*/
Tbl& set(int l) {
assert(etat == ETATQCQ) ;
return va.set(l) ;
};
/** Read-only of the value in a given domain.
* @param l [input] domain index
* @return Tbl containing the value of the field in domain \c l .
*/
const Tbl& operator()(int l) const {
assert(etat == ETATQCQ) ;
return va(l) ;
};
/** Read/write of a particular element.
* NB: to gain in efficiency, the method \c del_deriv() (to delete
* the derived members) is not called by this function. It must
* thus be invoqued by the user.
*
* @param l [input] domain index
* @param k [input] \f$\phi\f$ index
* @param j [input] \f$\theta\f$ index
* @param i [input] \e r (\f$\xi\f$) index
*/
double& set(int l, int k, int j, int i) {
assert(etat == ETATQCQ) ;
return va.set(l, k, j, i) ;
};
/** Read-only of a particular element.
* @param l [input] domain index
* @param k [input] \f$\phi\f$ index
* @param j [input] \f$\theta\f$ index
* @param i [input] \e r (\f$\xi\f$) index
*/
double operator()(int l, int k, int j, int i) const {
assert(etat != ETATNONDEF) ;
if (etat == ETATZERO) {
double zero = 0. ;
return zero ;
}
else{
return va(l, k, j, i) ;
}
};
/** Computes the value of the field represented by \c *this at an
* arbitrary point \f$(r, \theta, \phi)\f$, by means of the spectral
* expansion.
* @param r [input] value of the coordinate \e r
* @param theta [input] value of the coordinate \f$\theta\f$
* @param phi [input] value of the coordinate \f$\phi\f$
* @return value at the point \f$(r, \theta, \phi)\f$
* of the field represented by \c *this .
*/
double val_point(double r, double theta, double phi) const ;
// Memory management
// -----------------
private:
void del_t() ; ///< Logical destructor
void del_deriv() ; ///< Logical destructor of the derivatives
void set_der_0x0() ; ///< Sets the pointers for derivatives to 0x0
public:
/**
* Sets the logical state to \c ETATNONDEF (undefined).
* Calls the logical destructor of the \c Valeur \c va and
* deallocates the memory occupied by all the derivatives.
*/
void set_etat_nondef() ;
/**
* Sets the logical state to \c ETATZERO (zero).
* Calls the logical destructor of the \c Valeur \c va and
* deallocates the memory occupied by all the derivatives.
*/
void set_etat_zero() ;
/**
* Sets the logical state to \c ETATQCQ (ordinary state).
* If the state is already \c ETATQCQ , this function does nothing.
* Otherwise, it calls the logical destructor of the \c Valeur \c va and
* deallocates the memory occupied by all the derivatives.
*/
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 Cmp ->
* \c Valeur -> \c Mtbl -> \c Tbl .
*/
void allocate_all() ;
/**
* Sets the \c Cmp to zero in a hard way.
* 1/ Sets the logical state to \c ETATQCQ , i.e. to an ordinary state.
* 2/ Fills the \c Valeur \c va with zeros.
* NB: this function must be used for debugging purposes only.
* For other operations, the functions \c set_etat_zero()
* or \c annule(int, int) must be perferred.
*/
void annule_hard() ;
/**
* Sets the \c Cmp to zero in a given domain.
* @param l [input] Index of the domain in which the \c Cmp
* will be set (logically) to zero.
*/
void annule(int l) ;
/**
* Sets the \c Cmp to zero in several domains.
* @param l_min [input] The \c Cmp 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,va.mg->get_nzone()-1) is equivalent to
* \c set_etat_zero() .
*/
void annule(int l_min, int l_max) ;
/**
* Sets the \c n lasts coefficients in \e r to 0 in the external domain.
*/
void filtre (int n) ;
/**
* Sets the \c n lasts coefficients in \f$\Phi\f$ to 0 in the
* domain \c zone .
*/
void filtre_phi (int n, int zone) ;
/**
* Sets the value of the \c Cmp to \c val at infinity. This is usefull
* for dealing with undefined values. The external domain must be
* compactified.
*/
void set_val_inf (double val) ;
/**
* Sets the value of the \c Cmp to \c val on the inner boudary of the
* shell number \c zone .This is usefull
* for dealing with undefined values.
*/
void set_val_hor (double val, int zone) ;
/**
* Substracts all the components behaving like \f$r^{-n}\f$ in the external
* domain, with \e n strictly lower than \c puis , so that \c *this
* decreases at least like \f$r^{\tt puis} \f$ at infinity.
*/
void fixe_decroissance (int puis) ;
/**
* Gives the spectrum in terms of multipolar modes \e l .
* @return a \c Tbl of size (nzone, lmax), where lmax is the
* maximal multipolar momentum over all domains. The \e l -th
* element contains the L1 norm of the \e l -th multipole
* (i.e. a sum over all \e m of the norms (coefficient space)
* of the component of a given \f$Y_l^m\f$.
*/
Tbl multipole_spectrum () ;
// Extraction of information
// -------------------------
public:
/// Returns the logical state
int get_etat() const {return etat;} ;
/// Returns the mapping
const Map* get_mp() const {return mp;};
/// Returns \c dzpuis
int get_dzpuis() const {return dzpuis;} ;
/** Returns \c true if the last domain is compactified and
* \c *this is not zero in this domain
*/
bool dz_nonzero() const ;
/** Returns \c false if the last domain is compactified
* and \c *this is not zero in this domain and \c dzpuis
* is not equal to \c dzi , otherwise return true.
*/
bool check_dzpuis(int dzi) const ;
// Outputs
// -------
public:
void sauve(FILE *) const ; ///< Save in a file
/** Prints only the values greater than a given threshold.
* @param ostr [input] Output stream used for the printing
* @param type [input] Type of display : 0 = prints only the
* coefficients, 1 = prints only the values in configuration
* space, 2 = prints both
* @param precision [input] Number of printed digits (default: 4)
* @param threshold [input] Value above which an array element is printed
* (default: 1.e-7)
*/
void affiche_seuil(ostream& ostr, int type = 0, int precision = 4,
double threshold = 1.e-7) const ;
/// Display
friend ostream& operator<<(ostream& , const Cmp & ) ;
// Member arithmetics
// ------------------
public:
void operator+=(const Cmp &) ; ///< += Cmp
void operator-=(const Cmp &) ; ///< -= Cmp
void operator*=(const Cmp &) ; ///< *= Cmp
// Manipulation of spectral bases
// ------------------------------
/** Sets the spectral bases of the \c Valeur \c va to the standard ones
* for a scalar
*/
void std_base_scal() ;
// Differential operators and others
// ---------------------------------
public:
/** Returns \f$\partial / \partial r\f$ of \c *this .
* Note that in the external compactified domain (ZEC), it returns
* instead \f$r^2 \partial/ \partial r\f$.
*/
const Cmp& dsdr() const ;
/** Returns \f$1/r \partial / \partial \theta\f$ of \c *this .
* Note that in the external compactified domain (ZEC), it returns
* instead \f$r \partial/ \partial \theta\f$.
*/
const Cmp& srdsdt() const ;
/** Returns \f$1/(r\sin\theta) \partial / \partial \phi\f$ of \c *this .
* Note that in the external compactified domain (ZEC), it returns
* instead \f$r/\sin\theta \partial/ \partial \phi\f$.
*/
const Cmp& srstdsdp() const ;
/** Returns \f$\partial/\partial x\f$ of \c *this ,
* where \f$x=r\sin\theta \cos\phi\f$.
* Note that in the external compactified domain (ZEC), it returns
* instead \f$r^2 \partial/ \partial x\f$.
*/
const Cmp& dsdx() const ;
/** Returns \f$\partial/\partial y\f$ of \c *this ,
* where \f$y=r\sin\theta \sin\phi\f$.
* Note that in the external compactified domain (ZEC), it returns
* instead \f$r^2 \partial/ \partial y\f$.
*/
const Cmp& dsdy() const ;
/** Returns \f$\partial/\partial z\f$ of \c *this ,
* where \f$z=r\cos\theta\f$.
* Note that in the external compactified domain (ZEC), it returns
* instead \f$r^2 \partial/ \partial z\f$.
*/
const Cmp& dsdz() const ;
/** Returns \f$\partial/\partial x_i\f$ of \c *this ,
* where \f$x_i = (x, y, z)\f$.
* Note that in the external compactified domain (ZEC), it returns
* instead \f$r^2 \partial/ \partial x_i\f$.
* @param i [input] i=0 for \e x , i=1 for \e y , i=2 for \e z .
*/
const Cmp& deriv(int i) const ;
/** Returns the Laplacian of \c *this
* @param zec_mult_r [input] Determines the quantity computed in
* the external compactified domain (ZEC)
* (\e u in the field represented by \c *this ) : \\
* zec_mult_r = 0 : \f$\Delta u\f$ \\
* zec_mult_r = 2 : \f$r^2 \, \Delta u\f$ \\
* zec_mult_r = 4 (default) : \f$r^4 \, \Delta u\f$
*/
const Cmp& laplacien(int zec_mult_r = 4) const ;
/// Division by \e r everywhere.
void div_r() ;
/// Multiplication by \e r everywhere.
void mult_r() ;
/** Multiplication by \e r in the external compactified domain (ZEC)
*/
void mult_r_zec() ;
/// Multiplication by \f$r\sin\theta\f$
void mult_rsint() ;
/// Multiplication by \f\cos\theta\f$
void mult_cost() ;
/// Division by \f$r\sin\theta\f$
void div_rsint() ;
/** Decreases by 1 the value of \c dzpuis and changes accordingly
* the values of the \c Cmp in the external compactified domain (ZEC).
*/
void dec_dzpuis() ;
/** Increases by the value of \c dzpuis and changes accordingly
* the values of the \c Cmp in the external compactified domain (ZEC).
*/
void inc_dzpuis() ;
/** Decreases by 2 the value of \c dzpuis and changes accordingly
* the values of the \c Cmp in the external compactified domain (ZEC).
*/
void dec2_dzpuis() ;
/** Increases by 2 the value of \c dzpuis and changes accordingly
* the values of the \c Cmp in the external compactified domain (ZEC).
*/
void inc2_dzpuis() ;
void set_dzpuis(int ) ; ///< Set a value to \c dzpuis
/** Computes the integral over all space of \c *this .
* The computed quantity is (\e u being the field represented by
* \c *this )
* \f$\int u \, r^2 \sin\theta \, dr\, d\theta \, d\phi\f$.
* Note that in the external compactified domain (ZEC), \c dzpuis
* must be 4 for the computation to take place.
*/
double integrale() const ;
/** Computes the integral in each domain of \c *this .
* The computed quantity is (\e u being the field represented by
* \c *this )
* \f$\int u \, r^2 \sin\theta \, dr\, d\theta \, d\phi\f$
* in each domain. The result is returned a \c Tbl on the
* various domains.
* Note that in the external compactified domain (ZEC), \c dzpuis
* must be 4 for the computation to take place.
*/
const Tbl& integrale_domains() const ;
/** Asymptotic expansion at r = infinity.
*
* Determines the coefficients \f$a_k(\theta, \phi)\f$ of the expansion
* \f[
* \sum_{k=0}^n {a_k(\theta, \phi) \over r^k}
* \f]
* of \c *this when \f$r \rightarrow \infty\f$.
*
* @param n order of the expansion
* @param flag : output
* @return Array of n+1 \c Valeur s on \c mg->angu
* describing the coefficients \f$a_k(\theta, \phi)\f$.
* This array is allocated by the routine.
*
*/
Valeur** asymptot(int n, const int flag = 0) const ;
// PDE resolution
// --------------
public:
/** Solves the scalar Poisson equation with \c *this as a source.
* The source \f$\sigma\f$ of the equation \f$\Delta u = \sigma\f$ is
* represented by the \c Cmp \c *this .
* Note that \c dzpuis must be equal to 2, 3 or 4, i.e. that the
* quantity stored in \c *this is in fact \f$r^2 \sigma\f$ or
* \f$r^4 \sigma\f$ in the external compactified domain.
* The solution \e u with the boundary condition \e u =0 at spatial
* infinity is the returned \c Cmp .
*/
Cmp poisson() const ;
/** Same as Poisson with a Tau method
*/
Cmp poisson_tau() const ;
Cmp poisson_falloff(int k_falloff) const ;
Cmp poisson_ylm(int nylm, double* intvec) const ;
/** Solves the scalar Poisson equation with \c *this as a source
* (version with parameters to control the resolution).
* The source \f$\sigma\f$ of the equation \f$\Delta u = \sigma\f$ is
* represented by the \c Cmp \c *this .
* Note that \c dzpuis must be equal to 2 or 4, i.e. that the
* quantity stored in \c *this is in fact \f$r^2 \sigma\f$ or
* \f$r^4 \sigma\f$ in the external compactified domain.
* @param par [input/output] possible parameters
* @param uu [input/output] solution \e u with the boundary condition
* \e u =0 at spatial infinity.
*/
void poisson(Param& par, Cmp& uu) const ;
/** Same as Poisson with a Tau method
*/
void poisson_tau(Param& par, Cmp& uu) const ;
void poisson_falloff(Param& par, Cmp& uu, int k_falloff) const ;
void poisson_ylm(Param& par, Cmp& uu, int nylm, double* intvec) const ;
/**
* Is identicall to \c Cmp::poisson() . The regularity condition at the
* origin is replace by a boundary condition of the Dirichlet type.
*
* @param limite [input] : angular function. The boundary condition is
* given by \c limite[num] .
* @param num [input] : index of the boudary at which the condition is to
* be fullfilled.
*
* More precisely we impose the solution is equal to \c limite[num] at the
* boundary between the domains \c num and \c num+1 (the latter one being
* a shell).
*
*/
Cmp poisson_dirichlet (const Valeur& limite, int num) const ;
/**
* Idem as \c Cmp::poisson_dirichlet , the boundary condition being on
* the radial derivative of the solution.
*/
Cmp poisson_neumann (const Valeur&, int) const ;
/**
* Idem as \c Cmp::poisson_neumann , the boundary condition is on
* the radial derivative of the solution. But in this method, the
* poisson equation is solved in the shell only. We have so to
* impose a boundary condition on the surface of the star.
* This is used for example to solve the continuity equation
* for the fluid in the star.
*/
Cmp poisson_neumann_interne (const Valeur&, Param& par, Cmp& resu) const ;
Cmp poisson_frontiere_double (const Valeur&, const Valeur&, int) const ;
/** Solves the scalar Poisson equation with \c *this as a source
* (version with parameters to control the resolution).
* The source \f$\sigma\f$ of the equation \f$\Delta u = \sigma\f$ is
* represented by the \c Cmp \c *this .
* The regularized source
* \f$\sigma_{\rm regu} = \sigma - \sigma_{\rm div}\f$
* is constructed and solved.
* Note that \c dzpuis must be equal to 2 or 4, i.e. that the
* quantity stored in \c *this is in fact \f$r^2 \sigma\f$ or
* \f$r^4 \sigma\f$ in the external compactified domain.
* @param k_div [input] regularization degree of the procedure
* @param nzet [input] number of domains covering the star
* @param unsgam1 [input] parameter \f$1/(\gamma-1)\f$ where \f$\gamma\f$
* denotes the adiabatic index
* @param par [input/output] possible parameters
@param uu [input/output] solution
* @param uu_regu [output] solution of the regular part of
* the source.
* @param uu_div [output] solution of the diverging part of
* the source.
* @param duu_div [output] derivative of the diverging potential.
* @param source_regu [output] regularized source
* @param source_div [output] diverging part of the source
*/
void poisson_regular(int k_div, int nzet, double unsgam1, Param& par,
Cmp& uu, Cmp& uu_regu, Cmp& uu_div,
Tenseur& duu_div,
Cmp& source_regu, Cmp& source_div) const ;
/** Checks if a Poisson equation with \c *this as a source
* has been correctly solved.
*
* @param uu [input] Solution \e u of the Poisson equation
* \f$\Delta u = \sigma\f$, \f$\sigma\f$ being
* represented by the \c Cmp \c *this .
*
* @param ostr [input/output] Output stream used for displaying
* \c err .
*
* @param detail [input] \li if \c true displays \c err(0,*) ,
* \c err(1,*) and \c err(2,*)
* \li if \c false (default), displays only
* the relative error \c err(0,*).
*
* @return 2-D \c Tbl \c err decribing the errors in each
* domain:
* \li \c err(0,l) : Relative error in domain no. \c l ,
* defined as the maximum value of
* \f$|\Delta u - \sigma|\f$ in that domain divided by \e m ,
* where \e m is the maximum value of \f$|\sigma|\f$
* over all domains if \c dzpuis = 0} or \f$\sigma\f$ is
* zero in the external compactified domain (ECD). If
* \c dzpuis != 0} and \f$\sigma\f$ does not vanish in the
* ECD, the value of \e m used in the
* non-compactified domains is the maximum value over
* these domains, whereas the value of \e m used in the
* external compactified domain is the maximum value
* on that particular domain.
* \li \c err(1,l) : Maximum value of the absolute error
* \f$|\Delta u - \sigma|\f$ in domain no. \c l
* \li \c err(2,l) : Maximum value of \f$|\sigma|\f$ in domain
* no. \c l
*/
Tbl test_poisson(const Cmp& uu, ostream& ostr,
bool detail = false) const ;
/**
* Performs the \f$C^n\f$ matching of the nucleus with respect to the
* first shell.
*/
void raccord(int n) ;
/**
* Performs the \f$C^1\f$ matching of the external domain with respect to
* the last shell using function like \f$\frac{1}{r^i}\f$ with
* \f${\tt puis} \leq i \leq {\tt puis+nbre}\f$ for each spherical harmonics
* with \f$l \leq {\tt lmax}\f$.
*/
void raccord_c1_zec (int puis, int nbre, int lmax) ;
/**
* Matching of the external domain with the outermost shell
*/
void raccord_externe (int puis, int nbre, int lmax) ;
};
ostream& operator<<(ostream& , const Cmp & ) ;
/**
* \defgroup cmp_m Cmp Mathematics
* \ingroup (otens)
* @{
*/
Cmp operator+(const Cmp& ) ; ///< + Cmp
Cmp operator-(const Cmp& ) ; ///< \c - Cmp
Cmp operator+(const Cmp&, const Cmp &) ; ///< Cmp + Cmp
Cmp operator+(const Cmp&, double ) ; ///< Cmp + double
Cmp operator+(double, const Cmp& ) ; ///< double + Cmp
Cmp operator+(const Cmp&, int ) ; ///< Cmp + int
Cmp operator+(int, const Cmp& ) ; ///< int + Cmp
Cmp operator-(const Cmp &, const Cmp &) ; ///< Cmp - Cmp
Cmp operator-(const Cmp&, double ) ; ///< Cmp - double
Cmp operator-(double, const Cmp& ) ; ///< double - Cmp
Cmp operator-(const Cmp&, int ) ; ///< Cmp - int
Cmp operator-(int, const Cmp& ) ; ///< int - Cmp
Cmp operator*(const Cmp &, const Cmp &) ; ///< Cmp * Cmp
Cmp operator%(const Cmp &, const Cmp &) ; ///< Cmp * Cmp with desaliasing
Cmp operator*(const Cmp&, double ) ; ///< Cmp * double
Cmp operator*(double, const Cmp &) ; ///< double * Cmp
Cmp operator*(const Cmp&, int ) ; ///< Cmp * int
Cmp operator*(int, const Cmp& ) ; ///< int * Cmp
Cmp operator/(const Cmp &, const Cmp &) ; ///< Cmp / Cmp
Cmp operator/(const Cmp&, double ) ; ///< Cmp / double
Cmp operator/(double, const Cmp &) ; ///< double / Cmp
Cmp operator/(const Cmp&, int ) ; ///< Cmp / int
Cmp operator/(int, const Cmp &) ; ///< int / Cmp
Cmp sin(const Cmp& ) ; ///< Sine
Cmp cos(const Cmp& ) ; ///< Cosine
Cmp tan(const Cmp& ) ; ///< Tangent
Cmp asin(const Cmp& ) ; ///< Arcsine
Cmp acos(const Cmp& ) ; ///< Arccosine
Cmp atan(const Cmp& ) ; ///< Arctangent
Cmp exp(const Cmp& ) ; ///< Exponential
Cmp log(const Cmp& ) ; ///< Neperian logarithm
Cmp log10(const Cmp& ) ; ///< Basis 10 logarithm
Cmp sqrt(const Cmp& ) ; ///< Square root
Cmp racine_cubique (const Cmp& ) ; ///< Cube root
Cmp pow(const Cmp& , int ) ; ///< Power \f${\tt Cmp} ^{\tt int}\f$
Cmp pow(const Cmp& , double ) ; ///< Power \f${\tt Cmp} ^{\tt double}\f$
Cmp abs(const Cmp& ) ; ///< Absolute value
/**
* Maximum values of a \c Cmp in each domain.
* @return 1-D \c Tbl of size the number of domains, the elements of which
* are the set of the maximum values in each domain.
*/
Tbl max(const Cmp& ) ;
/**
* Minimum values of a \c Cmp in each domain.
* @return 1-D \c Tbl of size the number of domains, the elements of which
* are the set of the minimum values in each domain.
*/
Tbl min(const Cmp& ) ;
/**
* Sums of the absolute values of all the values of the \c Cmp
* in each domain.
* @return 1-D \c Tbl of size the number of domains, the elements of which
* are the set of the sums of the absolute values in each domain.
*/
Tbl norme(const Cmp& ) ;
/**
* Relative difference between two \c Cmp (norme version).
* @return 1-D \c Tbl of size the number of domains, the elements of which
* are \c norme[a(l)-b(l)]/norme[b(l)] if \c b(l)!=0 and
* \c norme[a(l)-b(l)] if \c b(l)=0 , where \c a(l) and
* \c b(l) denote symbolically the values of \c a and \c b
* in domain no. \c l .
*/
Tbl diffrel(const Cmp& a, const Cmp& b) ;
/**
* Relative difference between two \c Cmp (max version).
* @return 1-D \c Tbl of size the number of domains, the elements of which
* are \c max[abs(a(l)-b(l))]/max[abs(b(l))] if \c b(l)!=0 and
* \c max[abs(a(l)-b(l))] if \c b(l)=0 , where \c a(l) and
* \c b(l) denote symbolically the values of \c a and \c b
* in domain no. \c l .
*/
Tbl diffrelmax(const Cmp& a, const Cmp& b) ;
/** @}*/
}
#endif
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