LORENE
scalar.h
1 /*
2  * Definition of Lorene class Scalar
3  *
4  */
5 
6 /*
7  * Copyright (c) 2003-2004 Eric Gourgoulhon & Jerome Novak
8  *
9  * Copyright (c) 1999-2000 Jean-Alain Marck (for previous class Cmp)
10  * Copyright (c) 1999-2002 Eric Gourgoulhon (for previous class Cmp)
11  * Copyright (c) 1999-2001 Philippe Grandclement (for previous class Cmp)
12  * Copyright (c) 2000-2002 Jerome Novak (for previous class Cmp)
13  * Copyright (c) 2000-2001 Keisuke Taniguchi (for previous class Cmp)
14  *
15  * This file is part of LORENE.
16  *
17  * LORENE is free software; you can redistribute it and/or modify
18  * it under the terms of the GNU General Public License as published by
19  * the Free Software Foundation; either version 2 of the License, or
20  * (at your option) any later version.
21  *
22  * LORENE is distributed in the hope that it will be useful,
23  * but WITHOUT ANY WARRANTY; without even the implied warranty of
24  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
25  * GNU General Public License for more details.
26  *
27  * You should have received a copy of the GNU General Public License
28  * along with LORENE; if not, write to the Free Software
29  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
30  *
31  */
32 
33 
34 #ifndef __SCALAR_H_
35 #define __SCALAR_H_
36 
37 
38 /*
39  * $Id: scalar.h,v 1.94 2015/12/18 15:52:51 j_novak Exp $
40  * $Log: scalar.h,v $
41  * Revision 1.94 2015/12/18 15:52:51 j_novak
42  * New method is_nan() for class Scalar.
43  *
44  * Revision 1.93 2015/09/10 13:28:05 j_novak
45  * New methods for the class Hot_Eos
46  *
47  * Revision 1.92 2014/10/13 08:52:36 j_novak
48  * Lorene classes and functions now belong to the namespace Lorene.
49  *
50  * Revision 1.91 2013/06/05 15:06:10 j_novak
51  * Legendre bases are treated as standard bases, when the multi-grid
52  * (Mg3d) is built with BASE_LEG.
53  *
54  * Revision 1.90 2013/01/11 15:44:54 j_novak
55  * Addition of Legendre bases (part 2).
56  *
57  * Revision 1.89 2012/12/19 13:59:56 j_penner
58  * added a few lines to the documentation for scalar_match_tau function
59  *
60  * Revision 1.88 2012/01/17 15:05:46 j_penner
61  * *** empty log message ***
62  *
63  * Revision 1.87 2012/01/17 10:16:27 j_penner
64  * functions added: sarra_filter_r, sarra_filter_r_all_domains, Heaviside
65  *
66  * Revision 1.86 2011/04/08 13:13:09 e_gourgoulhon
67  * Changed the comment of function val_point to indicate specifically the
68  * division by r^dzpuis in the compactified external domain.
69  *
70  * Revision 1.85 2008/09/29 13:23:51 j_novak
71  * Implementation of the angular mapping associated with an affine
72  * mapping. Things must be improved to take into account the domain index.
73  *
74  * Revision 1.84 2008/09/22 19:08:01 j_novak
75  * New methods to deal with boundary conditions
76  *
77  * Revision 1.83 2008/05/24 15:05:22 j_novak
78  * New method Scalar::match_tau to match the output of an explicit time-marching scheme with the tau method.
79  *
80  * Revision 1.82 2007/12/21 16:06:16 j_novak
81  * Methods to filter Tensor, Vector and Sym_tensor objects.
82  *
83  * Revision 1.81 2007/10/31 10:33:11 j_novak
84  * Added exponential filters to smooth Gibbs-type phenomena.
85  *
86  * Revision 1.80 2007/06/21 19:56:36 k_taniguchi
87  * Introduction of another filtre_r.
88  *
89  * Revision 1.79 2007/05/06 10:48:08 p_grandclement
90  * Modification of a few operators for the vorton project
91  *
92  * Revision 1.78 2007/01/16 15:05:59 n_vasset
93  * New constructor (taking a Scalar in mono-domain angular grid for
94  * boundary) for function sol_elliptic_boundary
95  *
96  * Revision 1.77 2006/05/26 09:00:09 j_novak
97  * New members for multiplication or division by cos(theta).
98  *
99  * Revision 1.76 2005/11/30 13:48:06 e_gourgoulhon
100  * Replaced M_PI/2 by 1.57... in argument list of sol_elliptic_sin_zec
101  * (in order not to require the definition of M_PI).
102  *
103  * Revision 1.75 2005/11/30 11:09:03 p_grandclement
104  * Changes for the Bin_ns_bh project
105  *
106  * Revision 1.74 2005/11/17 15:29:46 e_gourgoulhon
107  * Added arithmetics with Mtbl.
108  *
109  * Revision 1.73 2005/10/25 08:56:34 p_grandclement
110  * addition of std_spectral_base in the case of odd functions near the origin
111  *
112  * Revision 1.72 2005/09/07 13:10:47 j_novak
113  * Added a filter setting to zero all mulitpoles in a given range.
114  *
115  * Revision 1.71 2005/08/26 14:02:38 p_grandclement
116  * Modification of the elliptic solver that matches with an oscillatory exterior solution
117  * small correction in Poisson tau also...
118  *
119  * Revision 1.70 2005/08/25 12:14:07 p_grandclement
120  * Addition of a new method to solve the scalar Poisson equation, based on a multi-domain Tau-method
121  *
122  * Revision 1.69 2005/06/09 07:56:25 f_limousin
123  * Implement a new function sol_elliptic_boundary() and
124  * Vector::poisson_boundary(...) which solve the vectorial poisson
125  * equation (method 6) with an inner boundary condition.
126  *
127  * Revision 1.68 2005/06/08 12:35:18 j_novak
128  * New method for solving divergence-like ODEs.
129  *
130  * Revision 1.67 2005/05/20 14:42:30 j_novak
131  * Added the method Scalar::get_spectral_base().
132  *
133  * Revision 1.66 2005/04/04 21:28:57 e_gourgoulhon
134  * Added argument lambda to method poisson_angu
135  * to deal with the generalized angular Poisson equation:
136  * Lap_ang u + lambda u = source.
137  *
138  * Revision 1.65 2004/12/14 09:09:39 f_limousin
139  * Modif. comments.
140  *
141  * Revision 1.64 2004/11/23 12:41:53 f_limousin
142  * Intoduce function poisson_dir_neu(...) to solve a scalar poisson
143  * equation with a mixed boundary condition (Dirichlet + Neumann).
144  *
145  * Revision 1.63 2004/10/11 15:09:00 j_novak
146  * The radial manipulation functions take Scalar as arguments, instead of Cmp.
147  * Added a conversion operator from Scalar to Cmp.
148  * The Cmp radial manipulation function make conversion to Scalar, call to the
149  * Map_radial version with a Scalar argument and back.
150  *
151  * Revision 1.62 2004/08/24 09:14:40 p_grandclement
152  * Addition of some new operators, like Poisson in 2d... It now requieres the
153  * GSL library to work.
154  *
155  * Also, the way a variable change is stored by a Param_elliptic is changed and
156  * no longer uses Change_var but rather 2 Scalars. The codes using that feature
157  * will requiere some modification. (It should concern only the ones about monopoles)
158  *
159  * Revision 1.61 2004/07/27 08:24:26 j_novak
160  * Modif. comments
161  *
162  * Revision 1.60 2004/07/26 16:02:21 j_novak
163  * Added a flag to specify whether the primitive should be zero either at r=0
164  * or at r going to infinity.
165  *
166  * Revision 1.59 2004/07/06 13:36:27 j_novak
167  * Added methods for desaliased product (operator |) only in r direction.
168  *
169  * Revision 1.58 2004/06/22 08:49:57 p_grandclement
170  * Addition of everything needed for using the logarithmic mapping
171  *
172  * Revision 1.57 2004/06/14 15:24:23 e_gourgoulhon
173  * Added method primr (radial primitive).
174  *
175  * Revision 1.56 2004/06/11 14:29:56 j_novak
176  * Scalar::multipole_spectrum() is now a const method.
177  *
178  * Revision 1.55 2004/05/24 14:07:31 e_gourgoulhon
179  * Method set_domain now includes a call to del_deriv() for safety.
180  *
181  * Revision 1.54 2004/05/07 11:26:10 f_limousin
182  * New method filtre_r(int*)
183  *
184  * Revision 1.53 2004/03/22 13:12:43 j_novak
185  * Modification of comments to use doxygen instead of doc++
186  *
187  * Revision 1.52 2004/03/17 15:58:47 p_grandclement
188  * Slight modification of sol_elliptic_no_zec
189  *
190  * Revision 1.51 2004/03/11 12:07:30 e_gourgoulhon
191  * Added method visu_section_anim.
192  *
193  * Revision 1.50 2004/03/08 15:45:38 j_novak
194  * Modif. comment
195  *
196  * Revision 1.49 2004/03/05 15:09:40 e_gourgoulhon
197  * Added method smooth_decay.
198  *
199  * Revision 1.48 2004/03/01 09:57:02 j_novak
200  * the wave equation is solved with Scalars. It now accepts a grid with a
201  * compactified external domain, which the solver ignores and where it copies
202  * the values of the field from one time-step to the next.
203  *
204  * Revision 1.47 2004/02/27 09:43:58 f_limousin
205  * New methods filtre_phi(int) and filtre_theta(int).
206  *
207  * Revision 1.46 2004/02/26 22:46:26 e_gourgoulhon
208  * Added methods derive_cov, derive_con and derive_lie.
209  *
210  * Revision 1.45 2004/02/21 17:03:49 e_gourgoulhon
211  * -- Method "point" renamed "val_grid_point".
212  * -- Method "set_point" renamed "set_grid_point".
213  *
214  * Revision 1.44 2004/02/19 22:07:35 e_gourgoulhon
215  * Added argument "comment" in method spectral_display.
216  *
217  * Revision 1.43 2004/02/11 09:47:44 p_grandclement
218  * Addition of a new elliptic solver, matching with the homogeneous solution
219  * at the outer shell and not solving in the external domain (more details
220  * coming soon ; check your local Lorene dealer...)
221  *
222  * Revision 1.42 2004/01/28 16:46:22 p_grandclement
223  * Addition of the sol_elliptic_fixe_der_zero stuff
224  *
225  * Revision 1.41 2004/01/28 13:25:40 j_novak
226  * The ced_mult_r arguments have been suppressed from the Scalar::*dsd* methods.
227  * In the div/mult _r_dzpuis, there is no more default value.
228  *
229  * Revision 1.40 2004/01/28 10:39:17 j_novak
230  * Comments modified.
231  *
232  * Revision 1.39 2004/01/27 15:10:01 j_novak
233  * New methods Scalar::div_r_dzpuis(int) and Scalar_mult_r_dzpuis(int)
234  * which replace div_r_inc*. Tried to clean the dzpuis handling.
235  * WARNING: no testing at this point!!
236  *
237  * Revision 1.38 2004/01/23 13:25:44 e_gourgoulhon
238  * Added methods set_inner_boundary and set_outer_boundary.
239  * Methods set_val_inf and set_val_hor, which are particular cases of
240  * the above, have been suppressed.
241  *
242  * Revision 1.37 2004/01/22 16:10:09 e_gourgoulhon
243  * Added (provisory) method div_r_inc().
244  *
245  * Revision 1.36 2003/12/16 06:32:20 e_gourgoulhon
246  * Added method visu_box.
247  *
248  * Revision 1.35 2003/12/14 21:46:35 e_gourgoulhon
249  * Added argument start_dx in visu_section.
250  *
251  * Revision 1.34 2003/12/11 16:19:38 e_gourgoulhon
252  * Added method visu_section for visualization with OpenDX.
253  *
254  * Revision 1.33 2003/12/11 14:48:47 p_grandclement
255  * Addition of ALL (and that is a lot !) the files needed for the general elliptic solver ... UNDER DEVELOPEMENT...
256  *
257  * Revision 1.32 2003/11/13 13:43:53 p_grandclement
258  * Addition of things needed for Bhole::update_metric (const Etoile_bin&, double, double)
259  *
260  * Revision 1.31 2003/11/06 14:43:37 e_gourgoulhon
261  * Gave a name to const arguments in certain method prototypes (e.g.
262  * constructors) to correct a bug of DOC++.
263  *
264  * Revision 1.30 2003/11/04 22:55:50 e_gourgoulhon
265  * Added new methods mult_cost(), mult_sint() and div_sint().
266  *
267  * Revision 1.29 2003/10/29 13:09:11 e_gourgoulhon
268  * -- Added integer argument to derivative functions dsdr, etc...
269  * so that one can choose the dzpuis of the result (default=2).
270  * -- Change of method name: laplacien --> laplacian.
271  *
272  * Revision 1.28 2003/10/29 11:00:42 e_gourgoulhon
273  * Virtual functions dec_dzpuis and inc_dzpuis have now an integer argument to
274  * specify by which amount dzpuis is to be increased.
275  * Accordingly virtual methods dec2_dzpuis and inc2_dzpuis have been suppressed.
276  *
277  * Revision 1.27 2003/10/20 14:26:02 j_novak
278  * New assignement operators.
279  *
280  * Revision 1.26 2003/10/19 19:46:33 e_gourgoulhon
281  * -- Method spectral_display now virtual (from Tensor), list of argument
282  * changed.
283  *
284  * Revision 1.25 2003/10/17 13:46:14 j_novak
285  * The argument is now between 1 and 3 (instead of 0->2)
286  *
287  * Revision 1.24 2003/10/16 15:23:41 e_gourgoulhon
288  * Name of method div_r_ced() changed to div_r_inc2().
289  * Name of method div_rsint_ced() changed to div_rsint_inc2().
290  *
291  * Revision 1.23 2003/10/15 21:10:11 e_gourgoulhon
292  * Added method poisson_angu().
293  *
294  * Revision 1.22 2003/10/15 16:03:35 j_novak
295  * Added the angular Laplace operator for Scalar.
296  *
297  * Revision 1.21 2003/10/15 10:29:05 e_gourgoulhon
298  * Added new members p_dsdt and p_stdsdp.
299  * Added new methods dsdt(), stdsdp() and div_tant().
300  *
301  * Revision 1.20 2003/10/13 13:52:39 j_novak
302  * Better managment of derived quantities.
303  *
304  * Revision 1.19 2003/10/10 15:57:27 j_novak
305  * Added the state one (ETATUN) to the class Scalar
306  *
307  * Revision 1.18 2003/10/08 14:24:08 j_novak
308  * replaced mult_r_zec with mult_r_ced
309  *
310  * Revision 1.17 2003/10/06 16:16:02 j_novak
311  * New constructor from a Tensor.
312  *
313  * Revision 1.16 2003/10/06 13:58:45 j_novak
314  * The memory management has been improved.
315  * Implementation of the covariant derivative with respect to the exact Tensor
316  * type.
317  *
318  * Revision 1.15 2003/10/05 21:06:31 e_gourgoulhon
319  * - Added new methods div_r_ced() and div_rsint_ced().
320  * - Added new virtual method std_spectral_base()
321  * - Removed method std_spectral_base_scal()
322  *
323  * Revision 1.14 2003/10/01 13:02:58 e_gourgoulhon
324  * Suppressed the constructor from Map* .
325  *
326  * Revision 1.13 2003/09/29 12:52:56 j_novak
327  * Methods for changing the triad are implemented.
328  *
329  * Revision 1.12 2003/09/25 09:33:36 j_novak
330  * Added methods for integral calculation and various manipulations
331  *
332  * Revision 1.11 2003/09/25 09:11:21 e_gourgoulhon
333  * Added functions for radial operations (divr, etc...)
334  *
335  * Revision 1.10 2003/09/25 08:55:23 e_gourgoulhon
336  * Added members raccord*.
337  *
338  * Revision 1.9 2003/09/25 08:50:11 j_novak
339  * Added the members import
340  *
341  * Revision 1.8 2003/09/25 08:13:51 j_novak
342  * Added method for calculating derivatives
343  *
344  * Revision 1.7 2003/09/25 07:59:26 e_gourgoulhon
345  * Added prototypes for PDE resolutions.
346  *
347  * Revision 1.6 2003/09/25 07:17:58 j_novak
348  * Method asymptot implemented.
349  *
350  * Revision 1.5 2003/09/24 20:53:38 e_gourgoulhon
351  * Added -- constructor by conversion from a Cmp
352  * -- assignment from Cmp
353  *
354  * Revision 1.4 2003/09/24 15:10:54 j_novak
355  * Suppression of the etat flag in class Tensor (still present in Scalar)
356  *
357  * Revision 1.3 2003/09/24 12:01:44 j_novak
358  * Added friend functions for math.
359  *
360  * Revision 1.2 2003/09/24 10:22:01 e_gourgoulhon
361  * still in progress...
362  *
363  * Revision 1.1 2003/09/22 12:50:47 e_gourgoulhon
364  * First version: not ready yet!
365  *
366  *
367  * $Header: /cvsroot/Lorene/C++/Include/scalar.h,v 1.94 2015/12/18 15:52:51 j_novak Exp $
368  *
369  */
370 
371 // Headers Lorene
372 #include "valeur.h"
373 #include "tensor.h"
374 
375 namespace Lorene {
376 class Param ;
377 class Cmp ;
378 class Param_elliptic ;
379 
387 class Scalar : public Tensor {
388 
389  // Data :
390  // -----
391  protected:
392 
396  int etat ;
397 
403  int dzpuis ;
404 
406 
407  // Derived data :
408  // ------------
409  protected:
411  mutable Scalar* p_dsdr ;
412 
416  mutable Scalar* p_srdsdt ;
417 
421  mutable Scalar* p_srstdsdp ;
422 
424  mutable Scalar* p_dsdt ;
425 
429  mutable Scalar* p_stdsdp ;
430 
434  mutable Scalar* p_dsdx ;
435 
439  mutable Scalar* p_dsdy ;
440 
444  mutable Scalar* p_dsdz ;
445 
448  mutable Scalar* p_lap ;
449 
452  mutable Scalar* p_lapang ;
453 
455  mutable Scalar* p_dsdradial ;
456 
458  mutable Scalar* p_dsdrho ;
459 
463  mutable int ind_lap ;
464 
468  mutable Tbl* p_integ ;
469 
470  // Constructors - Destructor
471  // -------------------------
472 
473  public:
474 
475  explicit Scalar(const Map& mpi) ;
476 
478  Scalar(const Tensor& a) ;
479 
480  Scalar(const Scalar& a) ;
481 
482  Scalar(const Cmp& a) ;
483 
485  Scalar(const Map&, const Mg3d&, FILE* ) ;
486 
487  virtual ~Scalar() ;
488 
489 
490  // Memory management
491  // -----------------
492  protected:
493  void del_t() ;
494  virtual void del_deriv() const;
495  void set_der_0x0() const;
496 
497  public:
498 
504  virtual void set_etat_nondef() ;
505 
511  virtual void set_etat_zero() ;
512 
519  virtual void set_etat_qcq() ;
520 
526  void set_etat_one() ;
527 
536  virtual void allocate_all() ;
537 
546  void annule_hard() ;
547 
548  // Extraction of information
549  // -------------------------
550  public:
554  int get_etat() const {return etat;} ;
555 
557  int get_dzpuis() const {return dzpuis;} ;
558 
562  bool dz_nonzero() const ;
563 
568  bool check_dzpuis(int dzi) const ;
569 
575  bool is_nan(bool verbose=false) const ;
576 
577  // Assignment
578  // -----------
579  public:
581  void operator=(const Scalar& a) ;
582 
584  virtual void operator=(const Tensor& a) ;
585 
586  void operator=(const Cmp& a) ;
587  void operator=(const Valeur& a) ;
588  void operator=(const Mtbl& a) ;
589  void operator=(double ) ;
590  void operator=(int ) ;
591 
592  // Conversion oprators
593  //---------------------
594  operator Cmp() const ;
595 
596  // Access to individual elements
597  // -----------------------------
598  public:
599 
601  const Valeur& get_spectral_va() const {return va;} ;
602 
604  Valeur& set_spectral_va() {return va;} ;
605 
615  Tbl& set_domain(int l) {
616  assert(etat == ETATQCQ) ;
617  del_deriv() ;
618  return va.set(l) ;
619  };
620 
625  const Tbl& domain(int l) const {
626  assert( (etat == ETATQCQ) || (etat == ETATUN) ) ;
627  return va(l) ;
628  };
629 
630 
637  double val_grid_point(int l, int k, int j, int i) const {
638  assert(etat != ETATNONDEF) ;
639  if (etat == ETATZERO) {
640  double zero = 0. ;
641  return zero ;
642  }
643  else {
644  if (etat == ETATUN) {
645  double one = 1. ;
646  return one ;
647  }
648  else{
649  return va(l, k, j, i) ;
650  }
651  }
652  };
653 
668  double val_point(double r, double theta, double phi) const ;
669 
670 
684  double& set_grid_point(int l, int k, int j, int i) {
685  assert(etat == ETATQCQ) ;
686  return va.set(l, k, j, i) ;
687  };
688 
689 
700  virtual void annule(int l_min, int l_max) ;
701 
707  void set_inner_boundary(int l, double x) ;
708 
714  void set_outer_boundary(int l, double x) ;
715 
724  Tbl multipole_spectrum () const ;
725 
732  Tbl tbl_out_bound(int l_dom, bool leave_ylm = false) ;
733 
740  Tbl tbl_in_bound(int n, bool leave_ylm = false) ;
741 
748  Scalar scalar_out_bound(int n, bool leave_ylm = false) ;
749 
750  // Differential operators and others
751  // ---------------------------------
752  public:
757  const Scalar& dsdr() const ;
758 
763  const Scalar& srdsdt() const ;
764 
769  const Scalar& srstdsdp() const ;
770 
773  const Scalar& dsdt() const ;
774 
782  const Scalar& dsdradial() const ;
783 
788  const Scalar& dsdrho() const ;
789 
792  const Scalar& stdsdp() const ;
793 
799  const Scalar& dsdx() const ;
800 
806  const Scalar& dsdy() const ;
807 
813  const Scalar& dsdz() const ;
814 
821  const Scalar& deriv(int i) const ;
822 
827  const Vector& derive_cov(const Metric& gam) const ;
828 
829 
835  const Vector& derive_con(const Metric& gam) const ;
836 
838  Scalar derive_lie(const Vector& v) const ;
839 
840 
849  const Scalar& laplacian(int ced_mult_r = 4) const ;
850 
858  const Scalar& lapang() const ;
859 
861  void div_r() ;
862 
867  void div_r_dzpuis(int ced_mult_r) ;
868 
872  void div_r_ced() ;
873 
875  void mult_r() ;
876 
881  void mult_r_dzpuis(int ced_mult_r) ;
882 
886  void mult_r_ced() ;
887 
889  void mult_rsint() ;
890 
895  void mult_rsint_dzpuis(int ced_mult_r) ;
896 
898  void div_rsint() ;
899 
904  void div_rsint_dzpuis(int ced_mult_r) ;
905 
906  void mult_cost() ;
907 
908  void div_cost() ;
909 
910  void mult_sint() ;
911 
912  void div_sint() ;
913 
914  void div_tant() ;
915 
926  Scalar primr(bool null_infty = true) const ;
927 
935  double integrale() const ;
936 
946  const Tbl& integrale_domains() const ;
947 
952  virtual void dec_dzpuis(int dec = 1) ;
953 
958  virtual void inc_dzpuis(int inc = 1) ;
959 
963  virtual void change_triad(const Base_vect& new_triad) ;
964 
969  void filtre (int n) ;
970 
975  void filtre_r (int* nn) ;
976 
980  void filtre_r (int n, int nzone) ;
981 
992 // virtual void exponential_filter_r(int lzmin, int lzmax, int p,
993 // double alpha= -16.) ;
994  virtual void exponential_filter_r(int lzmin, int lzmax, int p,
995  double alpha= -16.) ;
996 
1007  void sarra_filter_r(int lzmin, int lzmax, double p,
1008  double alpha= -1E-16) ;
1009 
1015  void exp_filter_r_all_domains(Scalar &ss, int p, double alpha=-16.) ;
1016 
1023  void sarra_filter_r_all_domains(double p, double alpha=1E-16) ;
1024 
1032  virtual void exponential_filter_ylm(int lzmin, int lzmax, int p,
1033  double alpha= -16.) ;
1034 
1042  void annule_l (int l_min, int l_max, bool ylm_output= false ) ;
1043 
1048  void filtre_phi (int n, int zone) ;
1049 
1054  void filtre_tp(int nn, int nz1, int nz2) ;
1055 
1056 
1062  void fixe_decroissance (int puis) ;
1063 
1069  void smooth_decay(int k, int n) ;
1070 
1075  void raccord(int n) ;
1076 
1083  void raccord_c1_zec(int puis, int nbre, int lmax) ;
1084 
1088  void raccord_externe(int puis, int nbre, int lmax) ;
1089 
1106  void match_tau(Param& par_bc, Param* par_mat=0x0) ;
1107 
1116  void match_tau_shell(Param& par_bc, Param* par_mat=0x0) ;
1117 
1126  void match_collocation(Param& par_bc, Param* par_mat=0x0) ;
1127 
1128  // Outputs
1129  // -------
1130  public:
1131  virtual void sauve(FILE *) const ;
1132 
1143  virtual void spectral_display(const char* comment = 0x0,
1144  double threshold = 1.e-7, int precision = 4,
1145  ostream& ostr = cout) const ;
1146 
1148  friend ostream& operator<<(ostream& , const Scalar & ) ;
1149 
1173  void visu_section(const char section_type, double aa, double umin, double umax, double vmin,
1174  double vmax, const char* title = 0x0, const char* filename = 0x0,
1175  bool start_dx = true, int nu = 200, int nv = 200) const ;
1176 
1205  void visu_section(const Tbl& plane, double umin, double umax, double vmin,
1206  double vmax, const char* title = 0x0, const char* filename = 0x0,
1207  bool start_dx = true, int nu = 200, int nv = 200) const ;
1208 
1237  void visu_section_anim(const char section_type, double aa, double umin,
1238  double umax, double vmin, double vmax, int jtime, double ttime,
1239  int jgraph = 1, const char* title = 0x0, const char* filename_root = 0x0,
1240  bool start_dx = false, int nu = 200, int nv = 200) const ;
1241 
1263  void visu_box(double xmin, double xmax, double ymin, double ymax,
1264  double zmin, double zmax, const char* title0 = 0x0,
1265  const char* filename0 = 0x0, bool start_dx = true, int nx = 40, int ny = 40,
1266  int nz = 40) const ;
1267 
1268 
1269 
1270  // Member arithmetics
1271  // ------------------
1272  public:
1273  void operator+=(const Scalar &) ;
1274  void operator-=(const Scalar &) ;
1275  void operator*=(const Scalar &) ;
1276 
1277  // Manipulation of spectral bases
1278  // ------------------------------
1282  virtual void std_spectral_base() ;
1283 
1287  virtual void std_spectral_base_odd() ;
1288 
1291  void set_spectral_base(const Base_val& ) ;
1292 
1294  const Base_val& get_spectral_base( ) const {return va.base ;} ;
1295 
1301  void set_dzpuis(int ) ;
1302 
1318  Valeur** asymptot(int n, const int flag = 0) const ;
1319 
1320 
1321  // PDE resolution
1322  // --------------
1323  public:
1333  Scalar poisson() const ;
1334 
1346  void poisson(Param& par, Scalar& uu) const ;
1347 
1357  Scalar poisson_tau() const ;
1358 
1369  void poisson_tau(Param& par, Scalar& uu) const ;
1370 
1385  Scalar poisson_dirichlet (const Valeur& limite, int num) const ;
1386 
1391  Scalar poisson_neumann (const Valeur&, int) const ;
1392 
1393 
1412  Scalar poisson_dir_neu (const Valeur& limite , int num,
1413  double fact_dir, double fact_neu) const ;
1414 
1421  Scalar poisson_frontiere_double (const Valeur&, const Valeur&, int) const ;
1422 
1447  void poisson_regular(int k_div, int nzet, double unsgam1, Param& par,
1448  Scalar& uu, Scalar& uu_regu, Scalar& uu_div,
1449  Tensor& duu_div,
1450  Scalar& source_regu, Scalar& source_div) const ;
1451 
1486  Tbl test_poisson(const Scalar& uu, ostream& ostr,
1487  bool detail = false) const ;
1488 
1502  Scalar poisson_angu(double lambda =0) const ;
1503 
1536  Scalar avance_dalembert(Param& par, const Scalar& fJm1, const Scalar& source)
1537  const ;
1538 
1543  Scalar sol_elliptic(Param_elliptic& params) const ;
1544 
1554  Scalar sol_elliptic_boundary(Param_elliptic& params, const Mtbl_cf& bound,
1555  double fact_dir, double fact_neu) const ;
1556 
1561  Scalar sol_elliptic_boundary(Param_elliptic& params, const Scalar& bound,
1562  double fact_dir, double fact_neu) const ;
1563 
1564 
1572 
1578 
1586  Scalar sol_elliptic_no_zec(Param_elliptic& params, double val = 0) const ;
1587 
1594  Scalar sol_elliptic_only_zec(Param_elliptic& params, double val) const ;
1595 
1605  Scalar sol_elliptic_sin_zec(Param_elliptic& params, double* coefs, double* phases) const ;
1606 
1607 
1615  Scalar sol_elliptic_fixe_der_zero(double val,
1616  Param_elliptic& params) const ;
1617 
1618 
1629  Scalar sol_divergence(int n) const ;
1630 
1631  // Import from other mapping
1632  // -------------------------
1633 
1639  void import(const Scalar& ci) ;
1640 
1647  void import_symy(const Scalar& ci) ;
1648 
1656  void import_asymy(const Scalar& ci) ;
1657 
1669  void import(int nzet, const Scalar& ci) ;
1670 
1683  void import_symy(int nzet, const Scalar& ci) ;
1684 
1698  void import_asymy(int nzet, const Scalar& ci) ;
1699 
1700  protected:
1714  void import_gal(int nzet, const Scalar& ci) ;
1715 
1729  void import_align(int nzet, const Scalar& ci) ;
1730 
1745  void import_anti(int nzet, const Scalar& ci) ;
1746 
1761  void import_align_symy(int nzet, const Scalar& ci) ;
1762 
1778  void import_anti_symy(int nzet, const Scalar& ci) ;
1779 
1795  void import_align_asymy(int nzet, const Scalar& ci) ;
1796 
1813  void import_anti_asymy(int nzet, const Scalar& ci) ;
1814 
1815 
1816  friend Scalar operator-(const Scalar& ) ;
1817  friend Scalar operator+(const Scalar&, const Scalar &) ;
1818  friend Scalar operator+(const Scalar&, const Mtbl&) ;
1819  friend Scalar operator+(const Scalar&, double ) ;
1820  friend Scalar operator-(const Scalar &, const Scalar &) ;
1821  friend Scalar operator-(const Scalar&, const Mtbl&) ;
1822  friend Scalar operator-(const Scalar&, double ) ;
1823  friend Scalar operator*(const Scalar &, const Scalar &) ;
1824  friend Scalar operator%(const Scalar &, const Scalar &) ;
1825  friend Scalar operator|(const Scalar &, const Scalar &) ;
1826  friend Scalar operator*(const Mtbl&, const Scalar &) ;
1827  friend Scalar operator*(double, const Scalar &) ;
1828  friend Scalar operator/(const Scalar &, const Scalar &) ;
1829  friend Scalar operator/(const Scalar &, const Mtbl &) ;
1830  friend Scalar operator/(const Mtbl &, const Scalar &) ;
1831  friend Scalar operator/(const Scalar&, double ) ;
1832  friend Scalar operator/(double, const Scalar &) ;
1833 
1834  friend Scalar sin(const Scalar& ) ;
1835  friend Scalar cos(const Scalar& ) ;
1836  friend Scalar tan(const Scalar& ) ;
1837  friend Scalar asin(const Scalar& ) ;
1838  friend Scalar acos(const Scalar& ) ;
1839  friend Scalar atan(const Scalar& ) ;
1840  friend Scalar exp(const Scalar& ) ;
1841  friend Scalar Heaviside(const Scalar& ) ;
1842  friend Scalar log(const Scalar& ) ;
1843  friend Scalar log10(const Scalar& ) ;
1844  friend Scalar sqrt(const Scalar& ) ;
1845  friend Scalar racine_cubique (const Scalar& ) ;
1846  friend Scalar pow(const Scalar& , int ) ;
1847  friend Scalar pow(const Scalar& , double ) ;
1848  friend Scalar abs(const Scalar& ) ;
1849 
1850  friend double totalmax(const Scalar& ) ;
1851  friend double totalmin(const Scalar& ) ;
1852  friend Tbl max(const Scalar& ) ;
1853  friend Tbl min(const Scalar& ) ;
1854  friend Tbl norme(const Scalar& ) ;
1855  friend Tbl diffrel(const Scalar& a, const Scalar& b) ;
1856  friend Tbl diffrelmax(const Scalar& a, const Scalar& b) ;
1857 
1858 };
1859 
1860 ostream& operator<<(ostream& , const Scalar & ) ;
1861 
1862 // Prototypage de l'arithmetique
1869 Scalar operator+(const Scalar& ) ;
1870 Scalar operator-(const Scalar& ) ;
1871 Scalar operator+(const Scalar&, const Scalar &) ;
1872 Scalar operator+(const Scalar&, const Mtbl&) ;
1873 Scalar operator+(const Mtbl&, const Scalar&) ;
1874 Scalar operator+(const Scalar&, double ) ;
1875 Scalar operator+(double, const Scalar& ) ;
1876 Scalar operator+(const Scalar&, int ) ;
1877 Scalar operator+(int, const Scalar& ) ;
1878 Scalar operator-(const Scalar &, const Scalar &) ;
1879 Scalar operator-(const Scalar&, const Mtbl&) ;
1880 Scalar operator-(const Mtbl&, const Scalar&) ;
1881 Scalar operator-(const Scalar&, double ) ;
1882 Scalar operator-(double, const Scalar& ) ;
1883 Scalar operator-(const Scalar&, int ) ;
1884 Scalar operator-(int, const Scalar& ) ;
1885 Scalar operator*(const Scalar &, const Scalar &) ;
1886 
1888 Scalar operator%(const Scalar &, const Scalar &) ;
1889 
1891 Scalar operator|(const Scalar &, const Scalar &) ;
1892 
1893 Scalar operator*(const Mtbl&, const Scalar&) ;
1894 Scalar operator*(const Scalar&, const Mtbl&) ;
1895 
1896 Scalar operator*(const Scalar&, double ) ;
1897 Scalar operator*(double, const Scalar &) ;
1898 Scalar operator*(const Scalar&, int ) ;
1899 Scalar operator*(int, const Scalar& ) ;
1900 Scalar operator/(const Scalar &, const Scalar &) ;
1901 Scalar operator/(const Scalar&, double ) ;
1902 Scalar operator/(double, const Scalar &) ;
1903 Scalar operator/(const Scalar&, int ) ;
1904 Scalar operator/(int, const Scalar &) ;
1905 Scalar operator/(const Scalar &, const Mtbl&) ;
1906 Scalar operator/(const Mtbl&, const Scalar &) ;
1907 
1908 
1909 Scalar sin(const Scalar& ) ;
1910 Scalar cos(const Scalar& ) ;
1911 Scalar tan(const Scalar& ) ;
1912 Scalar asin(const Scalar& ) ;
1913 Scalar acos(const Scalar& ) ;
1914 Scalar atan(const Scalar& ) ;
1915 Scalar exp(const Scalar& ) ;
1916 Scalar Heaviside(const Scalar& ) ;
1917 Scalar log(const Scalar& ) ;
1918 Scalar log10(const Scalar& ) ;
1919 Scalar sqrt(const Scalar& ) ;
1920 Scalar racine_cubique (const Scalar& ) ;
1921 Scalar pow(const Scalar& , int ) ;
1922 Scalar pow(const Scalar& , double ) ;
1923 Scalar abs(const Scalar& ) ;
1924 
1930 double totalmax(const Scalar& ) ;
1931 
1937 double totalmin(const Scalar& ) ;
1938 
1944 Tbl max(const Scalar& ) ;
1945 
1951 Tbl min(const Scalar& ) ;
1952 
1959 Tbl norme(const Scalar& ) ;
1960 
1969 Tbl diffrel(const Scalar& a, const Scalar& b) ;
1970 
1979 Tbl diffrelmax(const Scalar& a, const Scalar& b) ;
1980 
1985 void exp_filter_ylm_all_domains(Scalar& ss, int p, double alpha=-16.) ;
1986 
1988 }
1989 #endif
Bases of the spectral expansions.
Definition: base_val.h:322
Vectorial bases (triads) with respect to which the tensorial components are defined.
Definition: base_vect.h:105
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition: cmp.h:446
Base class for coordinate mappings.
Definition: map.h:670
Metric for tensor calculation.
Definition: metric.h:90
Multi-domain grid.
Definition: grilles.h:273
Coefficients storage for the multi-domain spectral method.
Definition: mtbl_cf.h:186
Multi-domain array.
Definition: mtbl.h:118
This class contains the parameters needed to call the general elliptic solver.
Parameter storage.
Definition: param.h:125
Tensor field of valence 0 (or component of a tensorial field).
Definition: scalar.h:387
Scalar poisson_neumann(const Valeur &, int) const
Idem as Scalar::poisson_dirichlet , the boundary condition being on the radial derivative of the solu...
virtual void sauve(FILE *) const
Save in a file.
Definition: scalar.C:686
void annule_l(int l_min, int l_max, bool ylm_output=false)
Sets all the multipolar components between l_min and l_max to zero.
Definition: scalar_manip.C:111
friend Scalar exp(const Scalar &)
Exponential.
Definition: scalar_math.C:323
void div_cost()
Division by .
Scalar sol_divergence(int n) const
Resolution of a divergence-like equation.
const Scalar & lapang() const
Returns the angular Laplacian of *this , where .
Definition: scalar_deriv.C:461
void set_etat_one()
Sets the logical state to ETATUN (one).
Definition: scalar.C:334
const Base_val & get_spectral_base() const
Returns the spectral bases of the Valeur va
Definition: scalar.h:1294
const Scalar & srdsdt() const
Returns of *this .
Definition: scalar_deriv.C:145
void raccord(int n)
Performs the matching of the nucleus with respect to the first shell.
virtual void del_deriv() const
Logical destructor of the derivatives.
Definition: scalar.C:287
friend Scalar log(const Scalar &)
Neperian logarithm.
Definition: scalar_math.C:385
Scalar * p_lap
Pointer on the Laplacian of *this (0x0 if not up to date)
Definition: scalar.h:448
friend Scalar cos(const Scalar &)
Cosine.
Definition: scalar_math.C:104
const Vector & derive_cov(const Metric &gam) const
Returns the gradient (1-form = covariant vector) of *this
Definition: scalar_deriv.C:390
void import_align(int nzet, const Scalar &ci)
Assignment to another Scalar defined on a different mapping, when the two mappings have aligned Carte...
Scalar * p_dsdy
Pointer on of *this , where (0x0 if not up to date)
Definition: scalar.h:439
void sarra_filter_r(int lzmin, int lzmax, double p, double alpha=-1E-16)
Applies an exponential filter to the spectral coefficients in the radial direction.
Scalar sol_elliptic_pseudo_1d(Param_elliptic &) const
Solves a pseudo-1d elliptic equation with *this as a source.
Definition: scalar_pde.C:430
void div_rsint_dzpuis(int ced_mult_r)
Division by but with the output flag dzpuis set to ced_mult_r .
const Scalar & deriv(int i) const
Returns of *this , where .
Definition: scalar_deriv.C:359
void div_r_dzpuis(int ced_mult_r)
Division by r everywhere but with the output flag dzpuis set to ced_mult_r .
const Scalar & dsdz() const
Returns of *this , where .
Definition: scalar_deriv.C:328
void import_asymy(const Scalar &ci)
Assignment to another Scalar defined on a different mapping.
Scalar scalar_out_bound(int n, bool leave_ylm=false)
Returns the Scalar containing the values of angular coefficients at the outer boundary.
Definition: scalar_manip.C:467
void filtre(int n)
Sets the n lasts coefficients in r to 0 in the external domain.
Definition: scalar_manip.C:151
const Scalar & dsdt() const
Returns of *this .
Definition: scalar_deriv.C:208
void div_sint()
Division by .
virtual ~Scalar()
Destructor.
Definition: scalar.C:267
Scalar poisson() const
Solves the scalar Poisson equation with *this as a source.
Definition: scalar_pde.C:136
friend Tbl norme(const Scalar &)
Sums of the absolute values of all the values of the Scalar in each domain.
Definition: scalar_math.C:667
int get_dzpuis() const
Returns dzpuis.
Definition: scalar.h:557
const Scalar & laplacian(int ced_mult_r=4) const
Returns the Laplacian of *this.
Definition: scalar_deriv.C:436
const Scalar & dsdy() const
Returns of *this , where .
Definition: scalar_deriv.C:297
void smooth_decay(int k, int n)
Performs a matching of the last non-compactified shell with a decaying function where is the spher...
void import_anti_asymy(int nzet, const Scalar &ci)
Assignment to another Scalar defined on a different mapping, when the two mappings have anti-aligned ...
Scalar * p_dsdrho
Pointer on of *this
Definition: scalar.h:458
void fixe_decroissance(int puis)
Substracts all the components behaving like in the external domain, with n strictly lower than puis ...
Definition: scalar_manip.C:346
void operator=(const Scalar &a)
Assignment to another Scalar defined on the same mapping.
Definition: scalar.C:446
Tbl tbl_in_bound(int n, bool leave_ylm=false)
Returns the Tbl containing the values of angular coefficients at the inner boundary.
Definition: scalar_manip.C:448
virtual void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: scalar.C:353
double integrale() const
Computes the integral over all space of *this .
Definition: scalar_integ.C:61
bool dz_nonzero() const
Returns true if the last domain is compactified and *this is not zero in this domain.
Definition: scalar.C:814
void mult_cost()
Multiplication by .
Tbl & set_domain(int l)
Read/write of the value in a given domain.
Definition: scalar.h:615
friend Scalar operator%(const Scalar &, const Scalar &)
Scalar * Scalar with desaliasing.
Scalar poisson_angu(double lambda=0) const
Solves the (generalized) angular Poisson equation with *this as source.
Definition: scalar_pde.C:200
friend Scalar asin(const Scalar &)
Arcsine.
Definition: scalar_math.C:167
const Scalar & srstdsdp() const
Returns of *this .
Definition: scalar_deriv.C:177
friend Scalar tan(const Scalar &)
Tangent.
Definition: scalar_math.C:136
friend double totalmax(const Scalar &)
Maximum values of a Scalar in each domain.
Definition: scalar_math.C:553
friend double totalmin(const Scalar &)
Minimum values of a Scalar in each domain.
Definition: scalar_math.C:582
void raccord_externe(int puis, int nbre, int lmax)
Matching of the external domain with the outermost shell.
Scalar * p_dsdr
Pointer on of *this (0x0 if not up to date)
Definition: scalar.h:411
Scalar * p_stdsdp
Pointer on of *this (0x0 if not up to date)
Definition: scalar.h:429
Scalar * p_dsdx
Pointer on of *this , where (0x0 if not up to date)
Definition: scalar.h:434
virtual void std_spectral_base()
Sets the spectral bases of the Valeur va to the standard ones for a scalar field.
Definition: scalar.C:784
double val_grid_point(int l, int k, int j, int i) const
Returns the value of the field at a specified grid point.
Definition: scalar.h:637
const Scalar & dsdrho() const
Returns of *this .
Definition: scalar_deriv.C:522
Tbl tbl_out_bound(int l_dom, bool leave_ylm=false)
Returns the Tbl containing the values of angular coefficients at the outer boundary.
Definition: scalar_manip.C:430
void import_gal(int nzet, const Scalar &ci)
Assignment to another Scalar defined on a different mapping, when the two mappings do not have a part...
friend Tbl min(const Scalar &)
Minimum values of a Scalar in each domain.
Definition: scalar_math.C:639
friend Scalar operator+(const Scalar &, const Scalar &)
Scalar + Scalar.
virtual void inc_dzpuis(int inc=1)
Increases by inc units the value of dzpuis and changes accordingly the values of the Scalar in the co...
friend Scalar Heaviside(const Scalar &)
Heaviside function.
Definition: scalar_math.C:355
Tbl test_poisson(const Scalar &uu, ostream &ostr, bool detail=false) const
Checks if a Poisson equation with *this as a source has been correctly solved.
bool is_nan(bool verbose=false) const
Looks for NaNs (not a number) in the scalar field.
Definition: scalar.C:1008
void visu_box(double xmin, double xmax, double ymin, double ymax, double zmin, double zmax, const char *title0=0x0, const char *filename0=0x0, bool start_dx=true, int nx=40, int ny=40, int nz=40) const
3D visualization (volume rendering) via OpenDX.
Definition: scalar_visu.C:342
const Scalar & stdsdp() const
Returns of *this .
Definition: scalar_deriv.C:238
friend Scalar operator*(const Scalar &, const Scalar &)
Scalar * Scalar.
void operator-=(const Scalar &)
-= Scalar
void match_tau_shell(Param &par_bc, Param *par_mat=0x0)
Method for matching accross domains and imposing boundary condition.
Scalar * p_dsdz
Pointer on of *this , where (0x0 if not up to date)
Definition: scalar.h:444
bool check_dzpuis(int dzi) const
Returns false if the last domain is compactified and *this is not zero in this domain and dzpuis is n...
Definition: scalar.C:873
Scalar avance_dalembert(Param &par, const Scalar &fJm1, const Scalar &source) const
Performs one time-step integration (from ) of the scalar d'Alembert equation with *this being the val...
Definition: scalar_pde.C:217
void div_r()
Division by r everywhere; dzpuis is not changed.
void exp_filter_r_all_domains(Scalar &ss, int p, double alpha=-16.)
Applies an exponential filter in radial direction in all domains.
void operator+=(const Scalar &)
+= Scalar
const Scalar & dsdx() const
Returns of *this , where .
Definition: scalar_deriv.C:266
double & set_grid_point(int l, int k, int j, int i)
Setting the value of the field at a given grid point.
Definition: scalar.h:684
virtual void set_etat_zero()
Sets the logical state to ETATZERO (zero).
Definition: scalar.C:324
void div_tant()
Division by .
const Scalar & dsdr() const
Returns of *this .
Definition: scalar_deriv.C:113
virtual void change_triad(const Base_vect &new_triad)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Definition: scalar.C:997
const Scalar & dsdradial() const
Returns of *this if the mapping is affine (class Map_af) and of *this if the mapping is logarithmic...
Definition: scalar_deriv.C:491
int ind_lap
Power of r by which the last computed Laplacian has been multiplied in the compactified external doma...
Definition: scalar.h:463
virtual void exponential_filter_ylm(int lzmin, int lzmax, int p, double alpha=-16.)
Applies an exponential filter to the spectral coefficients in the angular directions.
friend Scalar sin(const Scalar &)
Sine.
Definition: scalar_math.C:72
virtual void annule(int l_min, int l_max)
Sets the Scalar to zero in several domains.
Definition: scalar.C:391
Scalar * p_srstdsdp
Pointer on of *this (0x0 if not up to date)
Definition: scalar.h:421
void visu_section_anim(const char section_type, double aa, double umin, double umax, double vmin, double vmax, int jtime, double ttime, int jgraph=1, const char *title=0x0, const char *filename_root=0x0, bool start_dx=false, int nu=200, int nv=200) const
3D visualization via time evolving plane section (animation).
Definition: scalar_visu.C:535
void annule_hard()
Sets the Scalar to zero in a hard way.
Definition: scalar.C:380
friend ostream & operator<<(ostream &, const Scalar &)
Display.
Definition: scalar.C:702
void mult_sint()
Multiplication by .
void del_t()
Logical destructor.
Definition: scalar.C:279
Scalar poisson_dir_neu(const Valeur &limite, int num, double fact_dir, double fact_neu) const
Is identicall to Scalar::poisson() .
void mult_r_ced()
Multiplication by r in the compactified external domain (CED), the dzpuis flag is not changed.
friend Scalar operator/(const Scalar &, const Scalar &)
Scalar / Scalar.
void filtre_tp(int nn, int nz1, int nz2)
Sets the n lasts coefficients in to 0 in the domain nz1 to nz2 when expressed in spherical harmonics...
Definition: scalar_manip.C:270
int etat
The logical state ETATNONDEF (undefined), ETATZERO (null), ETATUN (one), or ETATQCQ (ordinary).
Definition: scalar.h:396
int get_etat() const
Returns the logical state ETATNONDEF (undefined), ETATZERO (null) or ETATQCQ (ordinary).
Definition: scalar.h:554
virtual void allocate_all()
Sets the logical state to ETATQCQ (ordinary state) and performs the memory allocation of all the elem...
Definition: scalar.C:365
virtual void set_etat_nondef()
Sets the logical state to ETATNONDEF (undefined).
Definition: scalar.C:344
void visu_section(const char section_type, double aa, double umin, double umax, double vmin, double vmax, const char *title=0x0, const char *filename=0x0, bool start_dx=true, int nu=200, int nv=200) const
3D visualization via a plane section.
Definition: scalar_visu.C:78
void mult_rsint()
Multiplication by everywhere; dzpuis is not changed.
void set_dzpuis(int)
Modifies the dzpuis flag.
Definition: scalar.C:808
Scalar sol_elliptic_boundary(Param_elliptic &params, const Mtbl_cf &bound, double fact_dir, double fact_neu) const
Resolution of a general elliptic equation, putting zero at infinity and with inner boundary condition...
Definition: scalar_pde.C:256
friend Tbl diffrelmax(const Scalar &a, const Scalar &b)
Relative difference between two Scalar (max version).
Definition: scalar_math.C:730
Scalar poisson_frontiere_double(const Valeur &, const Valeur &, int) const
Idem as Scalar::poisson_dirichlet , the boundary condition being on both the function and its radial ...
void set_inner_boundary(int l, double x)
Sets the value of the Scalar at the inner boundary of a given domain.
Definition: scalar_manip.C:283
void raccord_c1_zec(int puis, int nbre, int lmax)
Performs the matching of the external domain with respect to the last shell using function like wit...
void filtre_r(int *nn)
Sets the n lasts coefficients in r to 0 in all domains.
Definition: scalar_manip.C:180
friend Scalar racine_cubique(const Scalar &)
Cube root.
Definition: scalar_math.C:293
void match_tau(Param &par_bc, Param *par_mat=0x0)
Method for matching accross domains and imposing boundary condition.
void import_align_symy(int nzet, const Scalar &ci)
Assignment to another Scalar defined on a different mapping, when the two mappings have aligned Carte...
friend Scalar abs(const Scalar &)
Absolute value.
Definition: scalar_math.C:523
const Valeur & get_spectral_va() const
Returns va (read only version)
Definition: scalar.h:601
Scalar * p_lapang
Pointer on the Laplacian of *this (0x0 if not up to date)
Definition: scalar.h:452
Valeur & set_spectral_va()
Returns va (read/write version)
Definition: scalar.h:604
void div_rsint()
Division by everywhere; dzpuis is not changed.
Scalar sol_elliptic(Param_elliptic &params) const
Resolution of a general elliptic equation, putting zero at infinity.
Definition: scalar_pde.C:234
friend Scalar sqrt(const Scalar &)
Square root.
Definition: scalar_math.C:263
void mult_rsint_dzpuis(int ced_mult_r)
Multiplication by but with the output flag dzpuis set to ced_mult_r .
friend Scalar log10(const Scalar &)
Basis 10 logarithm.
Definition: scalar_math.C:418
double val_point(double r, double theta, double phi) const
Computes the value of the field at an arbitrary point , by means of the spectral expansion.
Definition: scalar.C:890
void mult_r_dzpuis(int ced_mult_r)
Multiplication by r everywhere but with the output flag dzpuis set to ced_mult_r .
Scalar sol_elliptic_only_zec(Param_elliptic &params, double val) const
Resolution of a general elliptic equation solving in the compactified domain and putting a given valu...
Definition: scalar_pde.C:341
friend Scalar pow(const Scalar &, int)
Power .
Definition: scalar_math.C:451
void match_collocation(Param &par_bc, Param *par_mat=0x0)
Method for matching accross domains and imposing boundary condition.
void operator*=(const Scalar &)
*= Scalar
void filtre_phi(int n, int zone)
Sets the n lasts coefficients in to 0 in the domain zone .
Definition: scalar_manip.C:249
const Tbl & domain(int l) const
Read-only of the value in a given domain.
Definition: scalar.h:625
Tbl multipole_spectrum() const
Gives the spectrum in terms of multipolar modes l .
Definition: scalar.C:956
void sarra_filter_r_all_domains(double p, double alpha=1E-16)
Applies an exponential filter in radial direction in all domains for the case where p is a double (se...
virtual void std_spectral_base_odd()
Sets the spectral bases of the Valeur va to the standard odd ones for a scalar field.
Definition: scalar.C:791
void set_outer_boundary(int l, double x)
Sets the value of the Scalar at the outer boundary of a given domain.
Definition: scalar_manip.C:315
const Vector & derive_con(const Metric &gam) const
Returns the "contravariant" derivative of *this with respect to some metric , by raising the index of...
Definition: scalar_deriv.C:402
Scalar sol_elliptic_no_zec(Param_elliptic &params, double val=0) const
Resolution of a general elliptic equation, putting a given value at the outermost shell and not solvi...
Definition: scalar_pde.C:314
Valeur va
The numerical value of the Scalar
Definition: scalar.h:405
virtual void spectral_display(const char *comment=0x0, double threshold=1.e-7, int precision=4, ostream &ostr=cout) const
Displays the spectral coefficients and the associated basis functions.
Definition: scalar.C:741
void poisson_regular(int k_div, int nzet, double unsgam1, Param &par, Scalar &uu, Scalar &uu_regu, Scalar &uu_div, Tensor &duu_div, Scalar &source_regu, Scalar &source_div) const
Solves the scalar Poisson equation with *this as a source (version with parameters to control the res...
void import_anti(int nzet, const Scalar &ci)
Assignment to another Scalar defined on a different mapping, when the two mappings have anti-aligned ...
Scalar * p_dsdradial
Pointer on of *this
Definition: scalar.h:455
Tbl * p_integ
Pointer on the space integral of *this (values in each domain) (0x0 if not up to date)
Definition: scalar.h:468
Scalar * p_dsdt
Pointer on of *this (0x0 if not up to date)
Definition: scalar.h:424
Scalar poisson_dirichlet(const Valeur &limite, int num) const
Is identicall to Scalar::poisson() .
friend Tbl diffrel(const Scalar &a, const Scalar &b)
Relative difference between two Scalar (norme version).
Definition: scalar_math.C:695
const Tbl & integrale_domains() const
Computes the integral in each domain of *this .
Definition: scalar_integ.C:79
friend Tbl max(const Scalar &)
Maximum values of a Scalar in each domain.
Definition: scalar_math.C:611
Scalar sol_elliptic_2d(Param_elliptic &) const
Solves the scalar 2-dimensional elliptic equation with *this as a source.
Definition: scalar_pde.C:409
Scalar sol_elliptic_fixe_der_zero(double val, Param_elliptic &params) const
Resolution of a general elliptic equation fixing the dericative at the origin and relaxing one contin...
Definition: scalar_pde.C:386
Scalar poisson_tau() const
Solves the scalar Poisson equation with *this as a source using a real Tau method The source of the ...
Definition: scalar_pde.C:169
void set_der_0x0() const
Sets the pointers for derivatives to 0x0.
Definition: scalar.C:306
virtual void dec_dzpuis(int dec=1)
Decreases by dec units the value of dzpuis and changes accordingly the values of the Scalar in the co...
void import_anti_symy(int nzet, const Scalar &ci)
Assignment to another Scalar defined on a different mapping, when the two mappings have anti-aligned ...
Scalar primr(bool null_infty=true) const
Computes the radial primitive which vanishes for .
Definition: scalar_integ.C:101
Scalar sol_elliptic_sin_zec(Param_elliptic &params, double *coefs, double *phases) const
General elliptic solver.
Definition: scalar_pde.C:363
friend Scalar acos(const Scalar &)
Arccosine.
Definition: scalar_math.C:199
void import_align_asymy(int nzet, const Scalar &ci)
Assignment to another Scalar defined on a different mapping, when the two mappings have aligned Carte...
void mult_r()
Multiplication by r everywhere; dzpuis is not changed.
Valeur ** asymptot(int n, const int flag=0) const
Asymptotic expansion at r = infinity.
Scalar * p_srdsdt
Pointer on of *this (0x0 if not up to date)
Definition: scalar.h:416
friend Scalar operator-(const Scalar &)
- Scalar
Definition: scalar_arithm.C:90
Scalar derive_lie(const Vector &v) const
Computes the derivative of this along a vector field v.
Definition: scalar_deriv.C:419
void div_r_ced()
Division by r in the compactified external domain (CED), the dzpuis flag is not changed.
void import_symy(const Scalar &ci)
Assignment to another Scalar defined on a different mapping.
void set_spectral_base(const Base_val &)
Sets the spectral bases of the Valeur va
Definition: scalar.C:797
int dzpuis
Power of r by which the quantity represented by this must be divided in the compactified external d...
Definition: scalar.h:403
friend Scalar operator|(const Scalar &, const Scalar &)
Scalar * Scalar with desaliasing only in r.
virtual void exponential_filter_r(int lzmin, int lzmax, int p, double alpha=-16.)
Applies an exponential filter to the spectral coefficients in the radial direction.
friend Scalar atan(const Scalar &)
Arctangent.
Definition: scalar_math.C:231
Basic array class.
Definition: tbl.h:161
Tensor handling.
Definition: tensor.h:288
Values and coefficients of a (real-value) function.
Definition: valeur.h:287
Base_val base
Bases on which the spectral expansion is performed.
Definition: valeur.h:305
Tbl & set(int l)
Read/write of the value in a given domain (configuration space).
Definition: valeur.h:363
Tensor field of valence 1.
Definition: vector.h:188
Base_val operator*(const Base_val &, const Base_val &)
This operator is used when calling multiplication or division of Valeur .
Cmp operator-(const Cmp &)
- Cmp
Definition: cmp_arithm.C:108
Cmp atan(const Cmp &)
Arctangent.
Definition: cmp_math.C:195
Cmp sqrt(const Cmp &)
Square root.
Definition: cmp_math.C:220
Cmp log10(const Cmp &)
Basis 10 logarithm.
Definition: cmp_math.C:322
Cmp operator/(const Cmp &, const Cmp &)
Cmp / Cmp.
Definition: cmp_arithm.C:457
Cmp operator%(const Cmp &, const Cmp &)
Cmp * Cmp with desaliasing.
Definition: cmp_arithm.C:364
Cmp exp(const Cmp &)
Exponential.
Definition: cmp_math.C:270
Cmp sin(const Cmp &)
Sine.
Definition: cmp_math.C:69
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition: cmp_math.C:504
Tbl norme(const Cmp &)
Sums of the absolute values of all the values of the Cmp in each domain.
Definition: cmp_math.C:481
Cmp acos(const Cmp &)
Arccosine.
Definition: cmp_math.C:169
Cmp asin(const Cmp &)
Arcsine.
Definition: cmp_math.C:144
Cmp racine_cubique(const Cmp &)
Cube root.
Definition: cmp_math.C:245
Tbl min(const Cmp &)
Minimum values of a Cmp in each domain.
Definition: cmp_math.C:458
Tbl max(const Cmp &)
Maximum values of a Cmp in each domain.
Definition: cmp_math.C:435
Cmp pow(const Cmp &, int)
Power .
Definition: cmp_math.C:348
Cmp cos(const Cmp &)
Cosine.
Definition: cmp_math.C:94
Cmp abs(const Cmp &)
Absolute value.
Definition: cmp_math.C:410
Tbl diffrelmax(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (max version).
Definition: cmp_math.C:539
Cmp operator+(const Cmp &)
Definition: cmp_arithm.C:104
Cmp tan(const Cmp &)
Tangent.
Definition: cmp_math.C:120
Cmp log(const Cmp &)
Neperian logarithm.
Definition: cmp_math.C:296
Mtbl Heaviside(const Mtbl &)
Heaviside function.
Definition: mtbl_math.C:317
double totalmin(const Mtbl &)
Minimum value of the Mtbl elements in all domain.
Definition: mtbl_math.C:522
double totalmax(const Mtbl &)
Maximum value of the Mtbl elements in all domains.
Definition: mtbl_math.C:494
Scalar operator|(const Scalar &, const Scalar &)
Scalar * Scalar with desaliasing only in r.
void exp_filter_ylm_all_domains(Scalar &ss, int p, double alpha=-16.)
Applies an exponential filter in angular directions in all domains.
Lorene prototypes.
Definition: app_hor.h:64