LORENE
et_bin_nsbh_equilibrium.C
1/*
2 * Method of class Etoile to compute a static spherical configuration
3 * of a neutron star in a NS-BH binary system.
4 *
5 * (see file etoile.h for documentation).
6 *
7 */
8
9/*
10 * Copyright (c) 2003 Keisuke Taniguchi
11 *
12 * This file is part of LORENE.
13 *
14 * LORENE is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU General Public License version 2
16 * as published by the Free Software Foundation.
17 *
18 * LORENE is distributed in the hope that it will be useful,
19 * but WITHOUT ANY WARRANTY; without even the implied warranty of
20 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21 * GNU General Public License for more details.
22 *
23 * You should have received a copy of the GNU General Public License
24 * along with LORENE; if not, write to the Free Software
25 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26 *
27 */
28
29char et_bin_nsbh_equilibrium_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_nsbh_equilibrium.C,v 1.13 2014/10/13 08:52:56 j_novak Exp $" ;
30
31/*
32 * $Id: et_bin_nsbh_equilibrium.C,v 1.13 2014/10/13 08:52:56 j_novak Exp $
33 * $Log: et_bin_nsbh_equilibrium.C,v $
34 * Revision 1.13 2014/10/13 08:52:56 j_novak
35 * Lorene classes and functions now belong to the namespace Lorene.
36 *
37 * Revision 1.12 2014/10/06 15:13:08 j_novak
38 * Modified #include directives to use c++ syntax.
39 *
40 * Revision 1.11 2008/09/26 08:38:45 p_grandclement
41 * get rid of desaliasing
42 *
43 * Revision 1.10 2006/09/05 13:39:45 p_grandclement
44 * update of the bin_ns_bh project
45 *
46 * Revision 1.9 2006/06/01 12:47:53 p_grandclement
47 * update of the Bin_ns_bh project
48 *
49 * Revision 1.8 2006/04/25 07:21:58 p_grandclement
50 * Various changes for the NS_BH project
51 *
52 * Revision 1.7 2006/03/30 07:33:47 p_grandclement
53 * *** empty log message ***
54 *
55 * Revision 1.6 2005/10/18 13:12:33 p_grandclement
56 * update of the mixted binary codes
57 *
58 * Revision 1.5 2005/08/29 15:10:17 p_grandclement
59 * Addition of things needed :
60 * 1) For BBH with different masses
61 * 2) Provisory files for the mixted binaries (Bh and NS) : THIS IS NOT
62 * WORKING YET !!!
63 *
64 * Revision 1.4 2004/03/25 10:29:04 j_novak
65 * All LORENE's units are now defined in the namespace Unites (in file unites.h).
66 *
67 * Revision 1.3 2003/10/24 12:34:06 k_taniguchi
68 * Change the notation as it should be
69 *
70 * Revision 1.2 2003/10/21 11:49:33 k_taniguchi
71 * Change the class from Etoile_bin to sub-class Et_bin_nsbh.
72 *
73 * Revision 1.1 2003/10/20 15:01:55 k_taniguchi
74 * Computation of an equilibrium configuration of a neutron star
75 * in a NS-BH binary system.
76 *
77 *
78 * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_nsbh_equilibrium.C,v 1.13 2014/10/13 08:52:56 j_novak Exp $
79 *
80 */
81
82// Headers C
83#include <cmath>
84
85// Headers Lorene
86#include "etoile.h"
87#include "map.h"
88#include "nbr_spx.h"
89#include "et_bin_nsbh.h"
90#include "param.h"
91
92#include "graphique.h"
93#include "utilitaires.h"
94#include "unites.h"
95
96namespace Lorene {
97void Et_bin_nsbh::equilibrium_nsbh(bool adapt, double ent_c, int& niter, int mermax,
98 int mermax_poisson, double relax_poisson,
99 int mermax_potvit, double relax_potvit,
100 Tbl& diff) {
101
102 // Fundamental constants and units
103 // -------------------------------
104 using namespace Unites ;
105
106 // Initializations
107 // --------------
108
109 const Mg3d* mg = mp.get_mg() ;
110 int nz = mg->get_nzone() ; // total number of domains
111
112 // The following is required to initialize mp_prev as a Map_et:
113 Map_et& mp_et = dynamic_cast<Map_et&>(mp) ;
114
115 // Error indicators
116 // ----------------
117 double& diff_ent = diff.set(0) ;
118 double& diff_vel_pot = diff.set(1) ;
119 double& diff_lapse = diff.set(2) ;
120 double& diff_confpsi = diff.set(3) ;
121 double& diff_shift_x = diff.set(4) ;
122 double& diff_shift_y = diff.set(5) ;
123 double& diff_shift_z = diff.set(6) ;
124
125
126 // Parameters for the function Map_et::poisson for n_auto
127 // ------------------------------------------------------
128 double precis_poisson = 1.e-16 ;
129
130 Param par_poisson1 ;
131 par_poisson1.add_int(mermax_poisson, 0) ; // maximum number of iterations
132 par_poisson1.add_double(relax_poisson, 0) ; // relaxation parameter
133 par_poisson1.add_double(precis_poisson, 1) ; // required precision
134 par_poisson1.add_int_mod(niter, 0) ; // number of iterations actually used
135 par_poisson1.add_cmp_mod( ssjm1_lapse ) ;
136
137 // Parameters for the function Map_et::poisson for confpsi_auto
138 // ------------------------------------------------------------
139
140 Param par_poisson2 ;
141 par_poisson2.add_int(mermax_poisson, 0) ; // maximum number of iterations
142 par_poisson2.add_double(relax_poisson, 0) ; // relaxation parameter
143 par_poisson2.add_double(precis_poisson, 1) ; // required precision
144 par_poisson2.add_int_mod(niter, 0) ; // number of iterations actually used
145 par_poisson2.add_cmp_mod( ssjm1_confpsi ) ;
146
147 // Parameters for the function Tenseur::poisson_vect
148 // -------------------------------------------------
149
150 Param par_poisson_vect ;
151 par_poisson_vect.add_int(mermax_poisson, 0) ;
152 // maximum number of iterations
153 par_poisson_vect.add_double(relax_poisson, 0) ; // relaxation parameter
154 par_poisson_vect.add_double(precis_poisson, 1) ; // required precision
155 par_poisson_vect.add_cmp_mod( ssjm1_khi ) ;
156 par_poisson_vect.add_tenseur_mod( ssjm1_wshift ) ;
157 par_poisson_vect.add_int_mod(niter, 0) ;
158
159 // Parameters for the adaptation
160 Param par_adapt ;
161 int nitermax = 100 ;
162 int niter_adapt ;
163 int adapt_flag = (adapt) ? 1 : 0 ;
164 int nz_search = nzet + 1 ;
165 double precis_secant = 1.e-14 ;
166 double alpha_r ;
167 double reg_map = 1. ;
168 int k_b ;
169 int j_b ;
170 Tbl ent_limit(nzet) ;
171
172 par_adapt.add_int(nitermax, 0) ;
173 par_adapt.add_int(nzet, 1) ;
174 par_adapt.add_int(nz_search, 2) ;
175 par_adapt.add_int(adapt_flag, 3) ;
176 par_adapt.add_int(j_b, 4) ;
177 par_adapt.add_int(k_b, 5) ;
178 par_adapt.add_int_mod(niter_adapt, 0) ;
179 par_adapt.add_double(precis_secant, 0) ;
180 par_adapt.add_double(reg_map, 1) ;
181 par_adapt.add_double(alpha_r, 2) ;
182 par_adapt.add_tbl(ent_limit, 0) ;
183
184 // External potential
185 // See Eq (99) from Gourgoulhon et al. (2001)
186 // -----------------------------------------
187
188
189 Tenseur ent_jm1 = ent ; // Enthalpy at previous step
190 Tenseur source(mp) ; // source term in the equation for logn_auto
191 // and beta_auto
192 Tenseur source_shift(mp, 1, CON, ref_triad) ; // source term in the
193 // equation for shift_auto
194
195 //=========================================================================
196 // Start of iteration
197 //=========================================================================
198
199 for(int mer=0 ; mer<mermax ; mer++ ) {
200
201 cout << "-----------------------------------------------" << endl ;
202 cout << "step: " << mer << endl ;
203 cout << "diff_ent = " << diff_ent << endl ;
204 //-----------------------------------------------------
205 // Resolution of the elliptic equation for the velocity
206 // scalar potential
207 //-----------------------------------------------------
208
209 if (irrotational) {
210 diff_vel_pot = velocity_potential(mermax_potvit, precis_poisson,
211 relax_potvit) ;
212 }
213
214 // Equation de la surface
215 //if (adapt) {
216
217 // Rescaling of the radius : (Be carefull !)
218 int nt = mg->get_nt(nzet-1) ;
219 int np = mg->get_np(nzet-1) ;
220 int nr = mg->get_nr(nzet-1) ;
221
222 // valeurs au centre
223 double hc = exp(ent_c) ;
224 double gamma_c = exp(loggam())(0,0,0,0) ;
225 double gamma_0_c = exp(-pot_centri())(0,0,0,0) ;
226 double n_auto_c = n_auto()(0,0,0,0) ;
227 double n_comp_c = n_comp()(0,0,0,0) ;
228
229 double alpha_square = 0 ;
230 double constante = 0;
231 for (int k=0; k<np; k++) {
232 for (int j=0; j<nt; j++) {
233
234 // valeurs au bord
235 double gamma_b = exp(loggam())(nzet-1,k,j,nr-1) ;
236 double gamma_0_b = exp(-pot_centri())(nzet-1,k,j,nr-1) ;
237 double n_auto_b = n_auto()(nzet-1,k,j,nr-1) ;
238 double n_comp_b = n_comp()(nzet-1,k,j,nr-1) ;
239
240 // Les solutions :
241 double alpha_square_courant = (gamma_0_c*gamma_b*n_comp_b - hc*gamma_c*gamma_0_b*n_comp_c) /
242 (hc*gamma_c*gamma_0_b*n_auto_c-gamma_0_c*gamma_b*n_auto_b) ;
243 double constante_courant = gamma_b*(n_comp_b+alpha_square_courant*n_auto_b)/gamma_0_b ;
244
245 if (alpha_square_courant > alpha_square) {
246 alpha_square = alpha_square_courant ;
247 k_b = k ;
248 j_b = j ;
249 constante = constante_courant ;
250 }
251 }
252 }
253
254 alpha_r = sqrt(alpha_square) ;
255 cout << "Adaptation : " << k_b << " " << j_b << " " << alpha_r << endl ;
256
257 // Le potentiel :
258 Tenseur potentiel (constante*exp(-loggam-pot_centri)/(n_auto*alpha_square+n_comp)) ;
259 potentiel.set_std_base() ;
260 for (int l=nzet+1 ; l<nz ; l++)
261 potentiel.set().va.set(l) = 1 ;
262
263 Map_et mp_prev = mp_et ;
264 ent = log(potentiel) ;
265 ent.set_std_base() ;
266 ent().va.smooth(nzet, (ent.set().va)) ;
267
268 ent_limit.set_etat_qcq() ;
269 for (int l=0; l<nzet; l++) { // loop on domains inside the star
270 ent_limit.set(l) = ent()(l, k_b, j_b, nr-1) ;
271 }
272
273 // On adapte :
274 mp.adapt(ent(), par_adapt, 4) ;
275 mp_prev.homothetie(alpha_r) ;
276
277 for (int l=nzet ; l<nz-1 ; l++)
278 mp.resize(l, 1./alpha_r) ;
279 mp.reevaluate_symy (&mp_prev, nzet, ent.set()) ;
280
281
282
283 // Equation of state
284 //----------------------------------------------------
285 equation_of_state() ; // computes new values for nbar (n), ener (e)
286 // and press (p) from the new ent (H)
287
288 //---------------------------------------------------------
289 // Matter source terms in the gravitational field equations
290 //---------------------------------------------------------
291 hydro_euler() ; // computes new values for ener_euler (E),
292 // s_euler (S) and u_euler (U^i)
293
294
295 //-------------------------------------------------
296 // Relative change in enthalpy
297 //-------------------------------------------------
298
299 Tbl diff_ent_tbl = diffrel( ent(), ent_jm1() ) ;
300 diff_ent = diff_ent_tbl(0) ;
301 for (int l=1; l<nzet; l++) {
302 diff_ent += diff_ent_tbl(l) ;
303 }
304 diff_ent /= nzet ;
305
306 ent_jm1 = ent ;
307
308
309 //--------------------------------------------------------
310 // Poisson equation for n_auto
311 //--------------------------------------------------------
312
313 // Source
314 // See Eq (50) from Gourgoulhon et al. (2001)
315 // ------------------------------------------
316
317 Tenseur confpsi_q = pow(confpsi, 4.) ;
318 Tenseur confpsi_c = pow(confpsi, 5.) ;
319
320 if (relativistic) {
321 Tenseur tmp = flat_scalar_prod(tkij_tot, tkij_auto) ;
322 Tenseur kk (mp) ;
323 kk = 0 ;
324 Tenseur tmp2(mp) ;
325 tmp2.set_etat_qcq() ;
326 for (int i=0 ; i<3 ; i++) {
327 tmp2.set() = tmp(i, i) ;
328 kk = kk + tmp2 ;
329 }
330
331 source = qpig * nnn * confpsi_q * (ener_euler + s_euler)
332 + nnn * confpsi_q * kk
334 confpsi ;
335 }
336 else {
337 cout <<
338 "WARNING : Et_bin_nsbh is for the relativistic calculation"
339 << endl ;
340 abort() ;
341 }
342
343 source.set_std_base() ;
344
345 // Resolution of the Poisson equation
346 // ----------------------------------
347 Cmp n_auto_old (n_auto()) ;
348 source().poisson(par_poisson1, n_auto.set()) ;
349 n_auto.set() = n_auto() + 0.5 ;
350
351 // Difference pas précédent
352 // -----------------------------------------------------
353
354 Tbl tdiff_lapse = diffrel(n_auto(), n_auto_old) ;
355 cout <<
356 "Relative difference on n_auto : "
357 << endl ;
358 for (int l=0; l<nz; l++) {
359 cout << tdiff_lapse(l) << " " ;
360 }
361 cout << endl ;
362 diff_lapse = max(abs(tdiff_lapse)) ;
363
364 if (relativistic) {
365
366
367 //--------------------------------------------------------
368 // Poisson equation for confpsi_auto
369 //--------------------------------------------------------
370
371 // Source
372 // See Eq (51) from Gourgoulhon et al. (2001)
373 // ------------------------------------------
374
375 Tenseur tmp = flat_scalar_prod(tkij_tot, tkij_auto) ;
376 Tenseur kk (mp) ;
377 kk = 0 ;
378 Tenseur tmp2(mp) ;
379 tmp2.set_etat_qcq() ;
380 for (int i=0 ; i<3 ; i++) {
381 tmp2.set() = tmp(i, i) ;
382 kk = kk + tmp2 ;
383 }
384
385 source = -0.5 * qpig * confpsi_c * ener_euler
386 - 0.125 * confpsi_c * kk ;
387
388 source.set_std_base() ;
389
390 // Resolution of the Poisson equation
391 // ----------------------------------
392 Cmp psi_old (confpsi_auto()) ;
393 source().poisson(par_poisson2, confpsi_auto.set()) ;
394 confpsi_auto.set() = confpsi_auto() + 0.5 ;
395
396
397 // Check: has the Poisson equation been correctly solved ?
398 // -----------------------------------------------------
399
400 Tbl tdiff_confpsi = diffrel(confpsi_auto(), psi_old) ;
401 cout <<
402 "Relative difference on confpsi_auto : "
403 << endl ;
404 for (int l=0; l<nz; l++) {
405 cout << tdiff_confpsi(l) << " " ;
406 }
407 cout << endl ;
408 diff_confpsi = max(abs(tdiff_confpsi)) ;
409
410 //--------------------------------------------------------
411 // Vector Poisson equation for shift_auto
412 //--------------------------------------------------------
413
414 // Source
415 // See Eq (52) from Gourgoulhon et al. (2001)
416 // ------
417 Tenseur vtmp = d_n_auto -6. * nnn * d_confpsi_auto / confpsi ;
418 source_shift = 4.*qpig * nnn *confpsi_q *(ener_euler + press)
419 * u_euler ;
420 if (tkij_tot.get_etat() != ETATZERO)
421 source_shift = source_shift + 2.* flat_scalar_prod(tkij_tot, vtmp) ;
422 source_shift.set_std_base() ;
423 // Resolution of the Poisson equation
424 // ----------------------------------
425 // Filter for the source of shift vector
426 for (int i=0 ; i<3 ; i++)
427 if (source_shift(i).get_etat() != ETATZERO)
428 source_shift.set(i).va.coef_i() ;
429
430for (int i=0; i<3; i++)
431 if ((source_shift(i).get_etat() != ETATZERO) && (source_shift(i).va.c->t[nz-1]->get_etat() != ETATZERO))
432 source_shift.set(i).filtre(4) ;
433 for (int i=0; i<3; i++) {
434 if(source_shift(i).dz_nonzero()) {
435 assert( source_shift(i).get_dzpuis() == 4 ) ;
436 }
437 else{
438 (source_shift.set(i)).set_dzpuis(4) ;
439 }
440 }
441 //##
442 // source_shift.dec2_dzpuis() ; // dzpuis 4 -> 2
443
444 double lambda_shift = double(1) / double(3) ;
445 // ON DOIT CHANGER DE TRIADE
446 source_shift.change_triad(mp.get_bvect_cart()) ;
447 Tenseur shift_old (shift_auto) ;
448 source_shift.poisson_vect_oohara(lambda_shift, par_poisson_vect,
451
452 // Check: has the equation for shift_auto been correctly solved ?
453 // --------------------------------------------------------------
454
455
456
457 Tbl tdiff_shift_x = diffrel(shift_auto(0), shift_old(0)) ;
458 Tbl tdiff_shift_y = diffrel(shift_auto(1), shift_old(1)) ;
459 Tbl tdiff_shift_z = diffrel(shift_auto(2), shift_old(2)) ;
460
461 cout <<
462 "Relative difference on shift_auto : "
463 << endl ;
464 cout << "x component : " ;
465 for (int l=0; l<nz; l++) {
466 cout << tdiff_shift_x(l) << " " ;
467 }
468 cout << endl ;
469 cout << "y component : " ;
470 for (int l=0; l<nz; l++) {
471 cout << tdiff_shift_y(l) << " " ;
472 }
473 cout << endl ;
474 cout << "z component : " ;
475 for (int l=0; l<nz; l++) {
476 cout << tdiff_shift_z(l) << " " ;
477 }
478 cout << endl ;
479
480 diff_shift_x = max(abs(tdiff_shift_x)) ;
481 diff_shift_y = max(abs(tdiff_shift_y)) ;
482 diff_shift_z = max(abs(tdiff_shift_z)) ;
483 } // End of relativistic equations
484
485
486 } // End of main loop
487
488 //=========================================================================
489 // End of iteration
490 //=========================================================================
491}
492
493// Truc pourri
494void Et_bin_nsbh::equilibrium_nsbh (double, int, int, double,
495 int, double, double, const Tbl&, Tbl&) {
496
497 cout << "Not implemented !" << endl ;
498 abort() ;
499}
500}
Valeur va
The numerical value of the Cmp
Definition cmp.h:464
Tenseur confpsi_auto
Part of the conformal factor $\Psi$ generated principaly by the star.
Tenseur d_confpsi_comp
Gradient of {\tt confpsi_comp} (Cartesian components with respect to {\tt ref_triad})
Cmp ssjm1_confpsi
Effective source at the previous step for the resolution of the Poisson equation for {\tt confpsi_aut...
Tenseur_sym tkij_tot
Total extrinsic curvature tensor $K^{ij}$ generated by {\tt shift_auto} and {\tt shift_comp}.
virtual void equilibrium_nsbh(double ent_c, int mermax, int mermax_poisson, double relax_poisson, int mermax_potvit, double relax_potvit, double thres_adapt, const Tbl &fact, Tbl &diff)
Computes an equilibrium configuration in a NS-BH binary system.
Tenseur d_n_auto
Gradient of {\tt n_auto} (Cartesian components with respect to {\tt ref_triad})
Definition et_bin_nsbh.h:93
Cmp ssjm1_lapse
Effective source at the previous step for the resolution of the Poisson equation for {\tt n_auto} by ...
Tenseur_sym tkij_auto
Part of the extrinsic curvature tensor $K^{ij}$ generated by {\tt shift_auto}.
Tenseur n_auto
Part of the lapse {\it N} generated principaly by the star.
Definition et_bin_nsbh.h:85
Tenseur n_comp
Part of the lapse {\it N} generated principaly by the companion star.
Definition et_bin_nsbh.h:88
Tenseur confpsi
Total conformal factor $\Psi$.
Tenseur d_confpsi_auto
Gradient of {\tt confpsi_auto} (Cartesian components with respect to {\tt ref_triad})
Cmp ssjm1_khi
Effective source at the previous step for the resolution of the Poisson equation for the scalar by m...
Definition etoile.h:973
double velocity_potential(int mermax, double precis, double relax)
Computes the non-translational part of the velocity scalar potential by solving the continuity equat...
const Base_vect & ref_triad
Reference triad ("absolute frame"), with respect to which the components of all the member Tenseur 's...
Definition etoile.h:828
bool irrotational
true for an irrotational star, false for a corotating one
Definition etoile.h:822
virtual void hydro_euler()
Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid fram...
Tenseur ssjm1_wshift
Effective source at the previous step for the resolution of the vector Poisson equation for by means...
Definition etoile.h:983
Tenseur pot_centri
Centrifugal potential.
Definition etoile.h:953
Tenseur loggam
Logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
Definition etoile.h:849
Tenseur shift_auto
Part of the shift vector generated principaly by the star.
Definition etoile.h:889
Tenseur khi_shift
Scalar used in the decomposition of shift_auto , following Shibata's prescription [Prog.
Definition etoile.h:918
int nzet
Number of domains of *mp occupied by the star.
Definition etoile.h:432
Tenseur nnn
Total lapse function.
Definition etoile.h:509
virtual void equation_of_state()
Computes the proper baryon and energy density, as well as pressure from the enthalpy.
Definition etoile.C:566
Tenseur u_euler
Fluid 3-velocity with respect to the Eulerian observer.
Definition etoile.h:474
Map & mp
Mapping associated with the star.
Definition etoile.h:429
Tenseur press
Fluid pressure.
Definition etoile.h:461
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one.
Definition etoile.h:437
Tenseur ener_euler
Total energy density in the Eulerian frame.
Definition etoile.h:465
Tenseur s_euler
Trace of the stress tensor in the Eulerian frame.
Definition etoile.h:468
Tenseur ent
Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case)
Definition etoile.h:457
const Base_vect_cart & get_bvect_cart() const
Returns the Cartesian basis associated with the coordinates (x,y,z) of the mapping,...
Definition map.h:791
virtual void resize(int l, double lambda)=0
Rescales the outer boundary of one domain.
virtual void reevaluate_symy(const Map *mp_prev, int nzet, Cmp &uu) const =0
Recomputes the values of a Cmp at the collocation points after a change in the mapping.
virtual void adapt(const Cmp &ent, const Param &par, int nbr=0)=0
Adaptation of the mapping to a given scalar field.
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition map.h:765
int get_nzone() const
Returns the number of domains.
Definition grilles.h:448
Basic array class.
Definition tbl.h:161
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition tenseur.C:824
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tenseur.C:636
void set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition tenseur.C:1170
void change_triad(const Base_vect &new_triad)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Definition tenseur.C:668
int get_etat() const
Returns the logical state.
Definition tenseur.h:707
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Cmp exp(const Cmp &)
Exponential.
Definition cmp_math.C:270
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition cmp_math.C:504
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 abs(const Cmp &)
Absolute value.
Definition cmp_math.C:410
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
Tenseur flat_scalar_prod(const Tenseur &t1, const Tenseur &t2)
Scalar product of two Tenseur when the metric is : performs the contraction of the last index of t1 w...
Lorene prototypes.
Definition app_hor.h:64
Standard units of space, time and mass.