LORENE
star_QI_global.C
1/*
2 * Methods of the class Star_QI to compute global quantities
3 *
4 * (see file compobj.h for documentation).
5 *
6 */
7
8/*
9 * Copyright (c) 2012 Claire Some, Eric Gourgoulhon
10 *
11 * This file is part of LORENE.
12 *
13 * LORENE is free software; you can redistribute it and/or modify
14 * it under the terms of the GNU General Public License version 2
15 * as published by the Free Software Foundation.
16 *
17 * LORENE is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU General Public License for more details.
21 *
22 * You should have received a copy of the GNU General Public License
23 * along with LORENE; if not, write to the Free Software
24 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25 *
26 */
27
28char star_QI_global_C[] = "$Header: /cvsroot/Lorene/C++/Source/Compobj/star_QI_global.C,v 1.3 2014/10/13 08:52:49 j_novak Exp $" ;
29
30/*
31 * $Id: star_QI_global.C,v 1.3 2014/10/13 08:52:49 j_novak Exp $
32 * $Log: star_QI_global.C,v $
33 * Revision 1.3 2014/10/13 08:52:49 j_novak
34 * Lorene classes and functions now belong to the namespace Lorene.
35 *
36 * Revision 1.2 2013/06/05 15:10:41 j_novak
37 * Suppression of FINJAC sampling in r. This Jacobi(0,2) base is now
38 * available by setting colloc_r to BASE_JAC02 in the Mg3d constructor.
39 *
40 * Revision 1.1 2012/11/21 14:54:13 c_some
41 * First version
42 *
43 *
44 *
45 * $Header: /cvsroot/Lorene/C++/Source/Compobj/star_QI_global.C,v 1.3 2014/10/13 08:52:49 j_novak Exp $
46 *
47 */
48
49
50// C headers
51#include <cassert>
52#include <cstdlib>
53
54// Lorene headers
55#include "compobj.h"
56#include "unites.h"
57#include "proto_f77.h"
58
59 //------------------------//
60 // Gravitational mass //
61 //------------------------//
62
63namespace Lorene {
64double Star_QI::mass_g() const {
65
66 if (p_mass_g == 0x0) { // a new computation is required
67
68 Scalar s_euler = stress_euler.trace(gamma) ;
69
70 //## alternative:
71 // assert(*(stress_euler.get_triad()) == mp.get_bvect_spher()) ;
72 // Scalar s_euler = ( stress_euler(1,1) + stress_euler(2,2) ) / a_car
73 // + stress_euler(3,3) / b_car ;
74
75 // Cf. Eq. (4.18) of arXiv:1003.5015v2 with (E+p) U = B * mom_euler(3)
76
77 Scalar source = nn * (ener_euler + s_euler)
78 + 2 * b_car * mom_euler(3)
79 * tnphi ;
80 source = a_car * bbb * source ;
81 source.std_spectral_base() ;
82
83 p_mass_g = new double( source.integrale() ) ;
84
85 }
86
87 return *p_mass_g ;
88
89}
90
91
92 //------------------------//
93 // Angular momentum //
94 //------------------------//
95
96double Star_QI::angu_mom() const {
97
98 if (p_angu_mom == 0x0) { // a new computation is required
99
100 // Cf. Eq. (4.39) of arXiv:1003.5015v2 with (E+p) U = B * mom_euler(3)
101
102 assert(*(mom_euler.get_triad()) == mp.get_bvect_spher()) ;
103
104 Scalar dens = mom_euler(3) ;
105
106 dens.mult_r() ; // Multiplication by
107 dens.set_spectral_va() = (dens.get_spectral_va()).mult_st() ; // r sin(theta)
108
109 dens = a_car * b_car * bbb * dens ;
110
111 p_angu_mom = new double( dens.integrale() ) ;
112
113 }
114
115 return *p_angu_mom ;
116
117}
118
119 //--------------------//
120 // GRV2 //
121 //--------------------//
122
123double Star_QI::grv2() const {
124
125 using namespace Unites ;
126 if (p_grv2 == 0x0) { // a new computation is required
127
128 assert( *(stress_euler.get_triad()) == mp.get_bvect_spher() ) ;
129 Scalar sou_m = 2 * qpig * a_car * b_car * stress_euler(3,3) ;
130
131 Vector dlogn = logn.derive_cov( mp.flat_met_spher() ) ;
132 Scalar sou_q = 1.5 * ak_car
133 - dlogn(1)*dlogn(1) - dlogn(2)*dlogn(2) - dlogn(3)*dlogn(3) ;
134
135 p_grv2 = new double( double(1) - lambda_grv2(sou_m, sou_q) ) ;
136
137 }
138
139 return *p_grv2 ;
140
141}
142
143
144 //--------------------//
145 // GRV3 //
146 //--------------------//
147
148double Star_QI::grv3(ostream* ost) const {
149
150 using namespace Unites ;
151
152 if (p_grv3 == 0x0) { // a new computation is required
153
154 Scalar source(mp) ;
155
156 // Gravitational term [cf. Eq. (43) of Gourgoulhon & Bonazzola
157 // ------------------ Class. Quantum Grav. 11, 443 (1994)]
158
159 Vector dlogn = logn.derive_cov( mp.flat_met_spher() ) ;
160
161 Scalar alpha = dzeta - logn ;
162 Scalar bet = log( bbb ) ;
163 bet.std_spectral_base() ;
164
165 Vector dalpha = alpha.derive_cov( mp.flat_met_spher() ) ;
166 Vector dbet = bet.derive_cov( mp.flat_met_spher() ) ;
167
168 source = 0.75 * ak_car
169 - dlogn(1)*dlogn(1) - dlogn(2)*dlogn(2) - dlogn(3)*dlogn(3)
170 + 0.5 * ( dalpha(1)*dbet(1) + dalpha(2)*dbet(2) + dalpha(3)*dbet(3) ) ;
171
172 Scalar aa = alpha - 0.5 * bet ;
173 Scalar daadt = aa.srdsdt() ; // 1/r d/dth
174
175 // What follows is valid only for a mapping of class Map_radial :
176 const Map_radial* mpr = dynamic_cast<const Map_radial*>(&mp) ;
177 if (mpr == 0x0) {
178 cout << "Star_rot::grv3: the mapping does not belong"
179 << " to the class Map_radial !" << endl ;
180 abort() ;
181 }
182
183 // Computation of 1/tan(theta) * 1/r daa/dtheta
184 if (daadt.get_etat() == ETATQCQ) {
185 Valeur& vdaadt = daadt.set_spectral_va() ;
186 vdaadt = vdaadt.ssint() ; // division by sin(theta)
187 vdaadt = vdaadt.mult_ct() ; // multiplication by cos(theta)
188 }
189
190 Scalar temp = aa.dsdr() + daadt ;
191 temp = ( bbb - a_car/bbb ) * temp ;
192 temp.std_spectral_base() ;
193
194 // Division by r
195 Valeur& vtemp = temp.set_spectral_va() ;
196 vtemp = vtemp.sx() ; // division by xi in the nucleus
197 // Id in the shells
198 // division by xi-1 in the ZEC
199 vtemp = (mpr->xsr) * vtemp ; // multiplication by xi/r in the nucleus
200 // by 1/r in the shells
201 // by r(xi-1) in the ZEC
202
203 // In the ZEC, a multiplication by r has been performed instead
204 // of the division:
205 temp.set_dzpuis( temp.get_dzpuis() + 2 ) ;
206
207 source = bbb * source + 0.5 * temp ;
208
209 source.std_spectral_base() ;
210
211 double int_grav = source.integrale() ;
212
213 // Matter term
214 // -----------
215
216 Scalar s_euler = stress_euler.trace(gamma) ;
217
218 //## alternative:
219 // assert(*(stress_euler.get_triad()) == mp.get_bvect_spher()) ;
220 // Scalar s_euler = ( stress_euler(1,1) + stress_euler(2,2) ) / a_car
221 // + stress_euler(3,3) / b_car ;
222
223 source = qpig * a_car * bbb * s_euler ;
224
225 source.std_spectral_base() ;
226
227 double int_mat = source.integrale() ;
228
229 // Virial error
230 // ------------
231 if (ost != 0x0) {
232 *ost << "Star_rot::grv3 : gravitational term : " << int_grav
233 << endl ;
234 *ost << "Star_rot::grv3 : matter term : " << int_mat
235 << endl ;
236 }
237
238 p_grv3 = new double( (int_grav + int_mat) / int_mat ) ;
239
240 }
241
242 return *p_grv3 ;
243
244}
245
246 //----------------------------//
247 // Quadrupole moment //
248 //----------------------------//
249
250double Star_QI::mom_quad() const {
251
252 using namespace Unites ;
253 if (p_mom_quad == 0x0) { // a new computation is required
254
255 // Source for of the Poisson equation for nu
256 // -----------------------------------------
257
258 Scalar source(mp) ;
259
260 Scalar s_euler = stress_euler.trace(gamma) ;
261
262 //## alternative:
263 // assert(*(stress_euler.get_triad()) == mp.get_bvect_spher()) ;
264 // Scalar s_euler = ( stress_euler(1,1) + stress_euler(2,2) ) / a_car
265 // + stress_euler(3,3) / b_car ;
266
267 Scalar bet = log(bbb) ;
268 bet.std_spectral_base() ;
269
270 Vector dlogn = logn.derive_cov( mp.flat_met_spher() ) ;
271 Vector dlogn_bet = dlogn + bet.derive_cov( mp.flat_met_spher() ) ;
272
273 source = qpig * a_car *( ener_euler + s_euler ) + ak_car
274 - dlogn(1)*dlogn_bet(1) - dlogn(2)*dlogn_bet(2) - dlogn(3)*dlogn_bet(3) ;
275
276 source.std_spectral_base() ;
277
278 // Multiplication by -r^2 P_2(cos(theta))
279 // [cf Eq.(7) of Salgado et al. Astron. Astrophys. 291, 155 (1994) ]
280 // ------------------------------------------------------------------
281
282 // Multiplication by r^2 :
283 // ----------------------
284 source.mult_r() ;
285 source.mult_r() ;
286 if (source.check_dzpuis(2)) {
287 source.inc_dzpuis(2) ;
288 }
289
290 // Muliplication by cos^2(theta) :
291 // -----------------------------
292 Scalar temp = source ;
293
294 // What follows is valid only for a mapping of class Map_radial :
295 assert( dynamic_cast<const Map_radial*>(&mp) != 0x0 ) ;
296
297 if (temp.get_etat() == ETATQCQ) {
298 Valeur& vtemp = temp.set_spectral_va() ;
299 vtemp = vtemp.mult_ct() ; // multiplication by cos(theta)
300 vtemp = vtemp.mult_ct() ; // multiplication by cos(theta)
301 }
302
303 // Muliplication by -P_2(cos(theta)) :
304 // ----------------------------------
305 source = 0.5 * source - 1.5 * temp ;
306
307 // Final result
308 // ------------
309
310 p_mom_quad = new double( source.integrale() / qpig ) ;
311
312 }
313
314 return *p_mom_quad ;
315
316}
317
318
319// Function Star_QI::lambda_grv2
320
321double Star_QI::lambda_grv2(const Scalar& sou_m, const Scalar& sou_q) {
322
323 const Map_radial* mprad = dynamic_cast<const Map_radial*>( &sou_m.get_mp() ) ;
324
325 if (mprad == 0x0) {
326 cout << "Star_rot::lambda_grv2: the mapping of sou_m does not"
327 << endl << " belong to the class Map_radial !" << endl ;
328 abort() ;
329 }
330
331 assert( &sou_q.get_mp() == mprad ) ;
332
333 sou_q.check_dzpuis(4) ;
334
335 const Mg3d* mg = mprad->get_mg() ;
336 int nz = mg->get_nzone() ;
337
338 // Construction of a Map_af which coincides with *mp on the equator
339 // ----------------------------------------------------------------
340
341 double theta0 = M_PI / 2 ; // Equator
342 double phi0 = 0 ;
343
344 Map_af mpaff(*mprad) ;
345
346 for (int l=0 ; l<nz ; l++) {
347 double rmax = mprad->val_r(l, double(1), theta0, phi0) ;
348 switch ( mg->get_type_r(l) ) {
349 case RARE: {
350 double rmin = mprad->val_r(l, double(0), theta0, phi0) ;
351 mpaff.set_alpha(rmax - rmin, l) ;
352 mpaff.set_beta(rmin, l) ;
353 break ;
354 }
355
356 case FIN: {
357 double rmin = mprad->val_r(l, double(-1), theta0, phi0) ;
358 mpaff.set_alpha( double(.5) * (rmax - rmin), l ) ;
359 mpaff.set_beta( double(.5) * (rmax + rmin), l) ;
360 break ;
361 }
362
363 case UNSURR: {
364 double rmin = mprad->val_r(l, double(-1), theta0, phi0) ;
365 double umax = double(1) / rmin ;
366 double umin = double(1) / rmax ;
367 mpaff.set_alpha( double(.5) * (umin - umax), l) ;
368 mpaff.set_beta( double(.5) * (umin + umax), l) ;
369 break ;
370 }
371
372 default: {
373 cout << "Star_rot::lambda_grv2: unknown type_r ! " << endl ;
374 abort () ;
375 break ;
376 }
377
378 }
379 }
380
381
382 // Reduced Jacobian of
383 // the transformation (r,theta,phi) <-> (dzeta,theta',phi')
384 // ------------------------------------------------------------
385
386 Mtbl jac = 1 / ( (mprad->xsr) * (mprad->dxdr) ) ;
387 // R/x dR/dx in the nucleus
388 // R dR/dx in the shells
389 // - U/(x-1) dU/dx in the ZEC
390 for (int l=0; l<nz; l++) {
391 switch ( mg->get_type_r(l) ) {
392 case RARE: {
393 double a1 = mpaff.get_alpha()[l] ;
394 *(jac.t[l]) = *(jac.t[l]) / (a1*a1) ;
395 break ;
396 }
397
398 case FIN: {
399 double a1 = mpaff.get_alpha()[l] ;
400 double b1 = mpaff.get_beta()[l] ;
401 assert( jac.t[l]->get_etat() == ETATQCQ ) ;
402 double* tjac = jac.t[l]->t ;
403 double* const xi = mg->get_grille3d(l)->x ;
404 for (int k=0; k<mg->get_np(l); k++) {
405 for (int j=0; j<mg->get_nt(l); j++) {
406 for (int i=0; i<mg->get_nr(l); i++) {
407 *tjac = *tjac /
408 (a1 * (a1 * xi[i] + b1) ) ;
409 tjac++ ;
410 }
411 }
412 }
413
414 break ;
415 }
416
417 case UNSURR: {
418 double a1 = mpaff.get_alpha()[l] ;
419 *(jac.t[l]) = - *(jac.t[l]) / (a1*a1) ;
420 break ;
421 }
422
423 default: {
424 cout << "Star_rot::lambda_grv2: unknown type_r ! " << endl ;
425 abort () ;
426 break ;
427 }
428
429 }
430
431 }
432
433
434 // Multiplication of the sources by the reduced Jacobian:
435 // -----------------------------------------------------
436
437 Mtbl s_m(mg) ;
438 if ( sou_m.get_etat() == ETATZERO ) {
439 s_m = 0 ;
440 }
441 else{
442 assert(sou_m.get_spectral_va().get_etat() == ETATQCQ) ;
443 sou_m.get_spectral_va().coef_i() ;
444 s_m = *(sou_m.get_spectral_va().c) ;
445 }
446
447 Mtbl s_q(mg) ;
448 if ( sou_q.get_etat() == ETATZERO ) {
449 s_q = 0 ;
450 }
451 else{
452 assert(sou_q.get_spectral_va().get_etat() == ETATQCQ) ;
453 sou_q.get_spectral_va().coef_i() ;
454 s_q = *(sou_q.get_spectral_va().c) ;
455 }
456
457 s_m *= jac ;
458 s_q *= jac ;
459
460
461 // Preparations for the call to the Fortran subroutine
462 // ---------------------------------------------------
463
464 int np1 = 1 ; // Axisymmetry enforced
465 int nt = mg->get_nt(0) ;
466 int nt2 = 2*nt - 1 ; // Number of points for the theta sampling
467 // in [0,Pi], instead of [0,Pi/2]
468
469 // Array NDL
470 // ---------
471 int* ndl = new int[nz+4] ;
472 ndl[0] = nz ;
473 for (int l=0; l<nz; l++) {
474 ndl[1+l] = mg->get_nr(l) ;
475 }
476 ndl[1+nz] = nt2 ;
477 ndl[2+nz] = np1 ;
478 ndl[3+nz] = nz ;
479
480 // Parameters NDR, NDT, NDP
481 // ------------------------
482 int nrmax = 0 ;
483 for (int l=0; l<nz ; l++) {
484 nrmax = ( ndl[1+l] > nrmax ) ? ndl[1+l] : nrmax ;
485 }
486 int ndr = nrmax + 5 ;
487 int ndt = nt2 + 2 ;
488 int ndp = np1 + 2 ;
489
490 // Array ERRE
491 // ----------
492
493 double* erre = new double [nz*ndr] ;
494
495 for (int l=0; l<nz; l++) {
496 double a1 = mpaff.get_alpha()[l] ;
497 double b1 = mpaff.get_beta()[l] ;
498 for (int i=0; i<ndl[1+l]; i++) {
499 double xi = mg->get_grille3d(l)->x[i] ;
500 erre[ ndr*l + i ] = a1 * xi + b1 ;
501 }
502 }
503
504 // Arrays containing the data
505 // --------------------------
506
507 int ndrt = ndr*ndt ;
508 int ndrtp = ndr*ndt*ndp ;
509 int taille = ndrtp*nz ;
510
511 double* tsou_m = new double[ taille ] ;
512 double* tsou_q = new double[ taille ] ;
513
514 // Initialisation to zero :
515 for (int i=0; i<taille; i++) {
516 tsou_m[i] = 0 ;
517 tsou_q[i] = 0 ;
518 }
519
520 // Copy of s_m into tsou_m
521 // -----------------------
522
523 for (int l=0; l<nz; l++) {
524 for (int k=0; k<np1; k++) {
525 for (int j=0; j<nt; j++) {
526 for (int i=0; i<mg->get_nr(l); i++) {
527 double xx = s_m(l, k, j, i) ;
528 tsou_m[ndrtp*l + ndrt*k + ndr*j + i] = xx ;
529 // point symetrique par rapport au plan theta = pi/2 :
530 tsou_m[ndrtp*l + ndrt*k + ndr*(nt2-1-j) + i] = xx ;
531 }
532 }
533 }
534 }
535
536 // Copy of s_q into tsou_q
537 // -----------------------
538
539 for (int l=0; l<nz; l++) {
540 for (int k=0; k<np1; k++) {
541 for (int j=0; j<nt; j++) {
542 for (int i=0; i<mg->get_nr(l); i++) {
543 double xx = s_q(l, k, j, i) ;
544 tsou_q[ndrtp*l + ndrt*k + ndr*j + i] = xx ;
545 // point symetrique par rapport au plan theta = pi/2 :
546 tsou_q[ndrtp*l + ndrt*k + ndr*(nt2-1-j) + i] = xx ;
547 }
548 }
549 }
550 }
551
552
553 // Computation of the integrals
554 // ----------------------------
555
556 double int_m, int_q ;
557 F77_integrale2d(ndl, &ndr, &ndt, &ndp, erre, tsou_m, &int_m) ;
558 F77_integrale2d(ndl, &ndr, &ndt, &ndp, erre, tsou_q, &int_q) ;
559
560 // Cleaning
561 // --------
562
563 delete [] ndl ;
564 delete [] erre ;
565 delete [] tsou_m ;
566 delete [] tsou_q ;
567
568 // Computation of lambda
569 // ---------------------
570
571 double lambda ;
572 if ( int_q != double(0) ) {
573 lambda = - int_m / int_q ;
574 }
575 else{
576 lambda = 0 ;
577 }
578
579 return lambda ;
580
581}
582
583}
Scalar ak_car
Scalar .
Definition compobj.h:315
Scalar b_car
Square of the metric factor B.
Definition compobj.h:293
Scalar bbb
Metric factor B.
Definition compobj.h:290
Scalar a_car
Square of the metric factor A.
Definition compobj.h:287
double * p_angu_mom
Angular momentum.
Definition compobj.h:321
Vector mom_euler
Total 3-momentum density in the Eulerian frame.
Definition compobj.h:147
Sym_tensor stress_euler
Stress tensor with respect to the Eulerian observer.
Definition compobj.h:150
Scalar ener_euler
Total energy density E in the Eulerian frame.
Definition compobj.h:144
Metric gamma
3-metric
Definition compobj.h:141
Scalar nn
Lapse function N .
Definition compobj.h:135
Map & mp
Mapping describing the coordinate system (r,theta,phi)
Definition compobj.h:132
double * x
Array of values of at the nr collocation points.
Definition grilles.h:209
Affine radial mapping.
Definition map.h:2027
const double * get_beta() const
Returns the pointer on the array beta.
Definition map_af.C:481
const double * get_alpha() const
Returns the pointer on the array alpha.
Definition map_af.C:477
void set_beta(double beta0, int l)
Modifies the value of in domain no. l.
Definition map_af.C:641
void set_alpha(double alpha0, int l)
Modifies the value of in domain no. l.
Definition map_af.C:630
Base class for pure radial mappings.
Definition map.h:1536
Coord xsr
in the nucleus; \ 1/R in the non-compactified shells; \ in the compactified outer domain.
Definition map.h:1549
Coord dxdr
in the nucleus and in the non-compactified shells; \ in the compactified outer domain.
Definition map.h:1560
const Base_vect_spher & get_bvect_spher() const
Returns the orthonormal vectorial basis associated with the coordinates of the mapping.
Definition map.h:783
virtual double val_r(int l, double xi, double theta, double pphi) const =0
Returns the value of the radial coordinate r for a given in a given domain.
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition map.h:765
const Metric_flat & flat_met_spher() const
Returns the flat metric associated with the spherical coordinates and with components expressed in th...
Definition map.C:321
Multi-domain grid.
Definition grilles.h:273
const Grille3d * get_grille3d(int l) const
Returns a pointer on the 3D mono-grid for domain no. l.
Definition grilles.h:500
int get_np(int l) const
Returns the number of points in the azimuthal direction ( ) in domain no. l.
Definition grilles.h:462
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition grilles.h:457
int get_nzone() const
Returns the number of domains.
Definition grilles.h:448
int get_nr(int l) const
Returns the number of points in the radial direction ( ) in domain no. l.
Definition grilles.h:452
int get_type_r(int l) const
Returns the type of sampling in the radial direction in domain no.
Definition grilles.h:474
Multi-domain array.
Definition mtbl.h:118
Tbl ** t
Array (size nzone ) of pointers on the Tbl 's.
Definition mtbl.h:132
Tensor field of valence 0 (or component of a tensorial field).
Definition scalar.h:387
const Scalar & srdsdt() const
Returns of *this .
const Vector & derive_cov(const Metric &gam) const
Returns the gradient (1-form = covariant vector) of *this
int get_dzpuis() const
Returns dzpuis.
Definition scalar.h:557
double integrale() const
Computes the integral over all space of *this .
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
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...
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
const Scalar & dsdr() const
Returns of *this .
Valeur & set_spectral_va()
Returns va (read/write version)
Definition scalar.h:604
const Valeur & get_spectral_va() const
Returns va (read only version)
Definition scalar.h:601
int get_etat() const
Returns the logical state ETATNONDEF (undefined), ETATZERO (null) or ETATQCQ (ordinary).
Definition scalar.h:554
void set_dzpuis(int)
Modifies the dzpuis flag.
Definition scalar.C:808
void mult_r()
Multiplication by r everywhere; dzpuis is not changed.
virtual double grv2() const
Error on the virial identity GRV2.
double * p_grv2
Error on the virial identity GRV2.
Definition compobj.h:585
Scalar logn
Logarithm of the lapse N .
Definition compobj.h:495
double * p_mass_g
Gravitational mass (ADM mass as a volume integral)
Definition compobj.h:588
virtual double grv3(ostream *ost=0x0) const
Error on the virial identity GRV3.
virtual double mom_quad() const
Quadrupole moment.
double * p_grv3
Error on the virial identity GRV3.
Definition compobj.h:586
static double lambda_grv2(const Scalar &sou_m, const Scalar &sou_q)
Computes the coefficient which ensures that the GRV2 virial identity is satisfied.
virtual double angu_mom() const
Angular momentum.
virtual double mass_g() const
Gravitational mass.
Scalar tnphi
Component of the shift vector.
Definition compobj.h:500
double * p_mom_quad
Quadrupole moment
Definition compobj.h:587
Scalar dzeta
Metric potential .
Definition compobj.h:513
int get_etat() const
Gives the logical state.
Definition tbl.h:394
double * t
The array of double.
Definition tbl.h:173
Values and coefficients of a (real-value) function.
Definition valeur.h:287
const Valeur & mult_ct() const
Returns applied to *this.
const Valeur & sx() const
Returns (r -sampling = RARE ) \ Id (r sampling = FIN ) \ (r -sampling = UNSURR )
Definition valeur_sx.C:110
int get_etat() const
Returns the logical state.
Definition valeur.h:726
Mtbl * c
Values of the function at the points of the multi-grid
Definition valeur.h:299
const Valeur & ssint() const
Returns of *this.
void coef_i() const
Computes the physical value of *this.
Tensor field of valence 1.
Definition vector.h:188
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
const Map & get_mp() const
Returns the mapping.
Definition tensor.h:861
const Base_vect * get_triad() const
Returns the vectorial basis (triad) on which the components are defined.
Definition tensor.h:866
Tensor trace(int ind1, int ind2) const
Trace on two different type indices.
Lorene prototypes.
Definition app_hor.h:64
Standard units of space, time and mass.