LORENE
connection.C
1 /*
2  * Methods of class Connection.
3  *
4  * (see file connection.h for documentation)
5  *
6  */
7 
8 /*
9  * Copyright (c) 2003-2004 Eric Gourgoulhon & Jerome Novak
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 
28 
29 
30 /*
31  * $Id: connection.C,v 1.20 2016/12/05 16:17:50 j_novak Exp $
32  * $Log: connection.C,v $
33  * Revision 1.20 2016/12/05 16:17:50 j_novak
34  * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
35  *
36  * Revision 1.19 2014/10/13 08:52:49 j_novak
37  * Lorene classes and functions now belong to the namespace Lorene.
38  *
39  * Revision 1.18 2014/10/06 15:13:04 j_novak
40  * Modified #include directives to use c++ syntax.
41  *
42  * Revision 1.17 2004/02/18 18:44:22 e_gourgoulhon
43  * Method Tensor::scontract renammed Tensor::trace.
44  *
45  * Revision 1.16 2004/01/29 15:21:51 e_gourgoulhon
46  * First implementation of method p_divergence.
47  *
48  * Revision 1.15 2004/01/23 07:58:38 e_gourgoulhon
49  * Method p_derive_cov: treatment of dzpuis: entry with dzpuis = 2 is now
50  * allowed (output: dzpuis=3).
51  *
52  * Revision 1.14 2004/01/22 16:15:53 e_gourgoulhon
53  * First operational version of ricci().
54  *
55  * Revision 1.13 2004/01/19 16:57:44 e_gourgoulhon
56  * First implementation of method ricci().
57  * Not tested yet.
58  *
59  * Revision 1.12 2004/01/13 21:33:33 e_gourgoulhon
60  * Corrected a bug in method p_derive_cov: inverted case CON and case COV.
61  *
62  * Revision 1.11 2004/01/04 20:57:51 e_gourgoulhon
63  * -- Data member delta is now of type Tensor_sym (and no longer
64  * Tensor_delta).
65  * -- Better handling of tensor symmetries in method p_derive_cov().
66  *
67  * Revision 1.10 2004/01/01 11:24:04 e_gourgoulhon
68  * Full reorganization of method p_derive_cov: the main loop is now
69  * on the indices of the *output* tensor (to take into account
70  * symmetries in the input and output tensors).
71  *
72  * Revision 1.9 2003/12/30 22:58:27 e_gourgoulhon
73  * -- Replaced member flat_conn (flat connection) by flat_met (flat metric)
74  * -- Added argument flat_met to the constructors of Connection.
75  * -- Suppressed method fait_ricci() (the computation of the Ricci is
76  * now devoted to the virtual method ricci()).
77  * -- Implementation of methods fait_delta() and derive_cov().
78  *
79  * Revision 1.8 2003/12/27 14:59:05 e_gourgoulhon
80  * Method derive_cov() suppressed.
81  *
82  * Revision 1.7 2003/10/16 14:21:36 j_novak
83  * The calculation of the divergence of a Tensor is now possible.
84  *
85  * Revision 1.6 2003/10/11 14:39:49 e_gourgoulhon
86  * Suppressed declaration of unusued arguments in some methods.
87  *
88  * Revision 1.5 2003/10/06 13:58:46 j_novak
89  * The memory management has been improved.
90  * Implementation of the covariant derivative with respect to the exact Tensor
91  * type.
92  *
93  * Revision 1.4 2003/10/03 14:16:04 e_gourgoulhon
94  * Added set_der_0x0 in some constructors.
95  *
96  * Revision 1.3 2003/10/02 21:32:06 e_gourgoulhon
97  * Added constructor from Metric.
98  * Added functions fait_delta and update.
99  *
100  * Revision 1.2 2003/10/01 15:42:49 e_gourgoulhon
101  * still ongoing...
102  *
103  * Revision 1.1 2003/09/29 21:13:08 e_gourgoulhon
104  * First version --- not ready yet.
105  *
106  *
107  *
108  *
109  * $Header: /cvsroot/Lorene/C++/Source/Connection/connection.C,v 1.20 2016/12/05 16:17:50 j_novak Exp $
110  *
111  */
112 
113 // C++ headers
114 #include "headcpp.h"
115 
116 // C headers
117 #include <cstdlib>
118 
119 // Lorene headers
120 #include "connection.h"
121 #include "metric.h"
122 
123 
124  //-----------------------//
125  // Constructors //
126  //-----------------------//
127 
128 
129 // Constructor ab initio
130 
131 namespace Lorene {
133  const Metric_flat& flat_met_i)
134  : mp(&(delta_i.get_mp())),
135  triad(delta_i.get_triad()),
136  delta(delta_i),
137  assoc_metric(false),
138  flat_met(&flat_met_i) {
139 
140  assert( delta_i.get_valence() == 3 ) ;
141  assert( delta_i.sym_index1() == 1 ) ;
142  assert( delta_i.sym_index2() == 2 ) ;
143  assert( delta_i.get_index_type(0) == CON ) ;
144  assert( delta_i.get_index_type(1) == COV ) ;
145  assert( delta_i.get_index_type(2) == COV ) ;
146 
147  set_der_0x0() ;
148 }
149 
150 
151 // Standard constructor from a metric.
152 
154  const Metric_flat& flat_met_i)
155  : mp(&(met.get_mp())),
156  triad(met.cov().get_triad()),
157  delta(*mp, CON, COV, COV, *triad, 1, 2),
158  assoc_metric(true),
159  flat_met(&flat_met_i) {
160 
161  fait_delta(met) ; // Computes delta
162 
163  set_der_0x0() ;
164 }
165 
166 
167 // Copy constructor
168 
169 Connection::Connection(const Connection& conn_i) : mp(conn_i.mp),
170  triad(conn_i.triad),
171  delta(conn_i.delta),
172  assoc_metric(conn_i.assoc_metric),
173  flat_met(conn_i.flat_met) {
174 
175  set_der_0x0() ;
176 
177 }
178 
179 
180 // Constructor for derived classes
181 
182 Connection::Connection(const Map& mpi, const Base_vect& bi) : mp(&mpi),
183  triad(&bi),
184  delta(mpi, CON, COV, COV, bi, 1, 2),
185  assoc_metric(false),
186  flat_met(0x0){
187 
188  set_der_0x0() ;
189 
190 }
191 
192 
193 
194  //-----------------------//
195  // Destructor //
196  //-----------------------//
197 
199 
200  del_deriv() ;
201 
202 }
203 
204  //-----------------------------//
205  // Memory management //
206  //-----------------------------//
207 
208 void Connection::del_deriv() const {
209 
210  if (p_ricci != 0x0) delete p_ricci ;
211 
212  set_der_0x0() ;
213 
214 }
215 
217 
218  p_ricci = 0x0 ;
219 
220 }
221 
222 
223  //-----------------------------//
224  // Mutators / assignment //
225  //-----------------------------//
226 
227 
229 
230  assert( triad == ci.triad ) ;
231  delta = ci.delta ;
232  flat_met = ci.flat_met ;
233 
234  del_deriv() ;
235 
236 }
237 
238 void Connection::update(const Tensor_sym& delta_i) {
239 
240  assert(assoc_metric == false) ;
241 
242  assert(flat_met != 0x0) ; // to guarantee we are not in a derived class
243 
244  assert( delta_i.get_valence() == 3 ) ;
245  assert( delta_i.sym_index1() == 1 ) ;
246  assert( delta_i.sym_index2() == 2 ) ;
247  assert( delta_i.get_index_type(0) == CON ) ;
248  assert( delta_i.get_index_type(1) == COV ) ;
249  assert( delta_i.get_index_type(2) == COV ) ;
250 
251  delta = delta_i ;
252 
253  del_deriv() ;
254 
255 }
256 
257 
258 void Connection::update(const Metric& met) {
259 
260  assert(assoc_metric == true) ;
261 
262  assert(flat_met != 0x0) ; // to guarantee we are not in a derived class
263 
264  fait_delta(met) ;
265 
266  del_deriv() ;
267 
268 }
269 
270 
271 
272  //-----------------------------//
273  // Computational methods //
274  //-----------------------------//
275 
276 
277 //--------------------------------------
278 // Computation of the Delta coefficients
279 //--------------------------------------
280 
281 void Connection::fait_delta(const Metric& gam) {
282 
283  assert(flat_met != 0x0) ;
284 
285  const Tensor& dgam = gam.cov().derive_cov(*flat_met) ;
286 
287  for (int k=1; k<=3; k++) {
288  for (int i=1; i<=3; i++) {
289  for (int j=1; j<=i; j++) {
290  Scalar& cc = delta.set(k,i,j) ;
291  cc = 0 ;
292  for (int l=1; l<=3; l++) {
293  cc += gam.con()(k,l) * (
294  dgam(l,j,i) + dgam(i,l,j) - dgam(i,j,l) ) ;
295 
296  }
297  cc = 0.5 * cc ;
298  }
299  }
300  }
301 
302 
303 }
304 
305 
306 //---------------------
307 // Covariant derivative
308 //---------------------
309 
311 
312  // Notations: suffix 0 in name <=> input tensor
313  // suffix 1 in name <=> output tensor
314 
315  int valence0 = uu.get_valence() ;
316  int valence1 = valence0 + 1 ;
317  int valence1m1 = valence1 - 1 ; // same as valence0, but introduced for
318  // the sake of clarity
319  int ncomp0 = uu.get_n_comp() ;
320 
321  // Protections
322  // -----------
323  if (valence0 >= 1) {
324  assert(uu.get_triad() == triad) ;
325  }
326  assert(flat_met != 0x0) ;
327 
328  // Creation of the result (pointer)
329  // --------------------------------
330  Tensor* resu ;
331 
332  // If uu is a Scalar, the result is a Vector
333  if (valence0 == 0)
334  resu = new Vector(*mp, COV, triad) ;
335  else {
336 
337  // Type of indices of the result :
338  Itbl tipe(valence1) ;
339  const Itbl& tipeuu = uu.get_index_type() ;
340  for (int id = 0; id<valence0; id++) {
341  tipe.set(id) = tipeuu(id) ; // First indices = same as uu
342  }
343  tipe.set(valence1m1) = COV ; // last index is the derivation index
344 
345  // if uu is a Tensor_sym, the result is also a Tensor_sym:
346  const Tensor* puu = &uu ;
347  const Tensor_sym* puus = dynamic_cast<const Tensor_sym*>(puu) ;
348  if ( puus != 0x0 ) { // the input tensor is symmetric
349  resu = new Tensor_sym(*mp, valence1, tipe, *triad,
350  puus->sym_index1(), puus->sym_index2()) ;
351  }
352  else {
353  resu = new Tensor(*mp, valence1, tipe, *triad) ; // no symmetry
354  }
355  }
356 
357  int ncomp1 = resu->get_n_comp() ;
358 
359  Itbl ind1(valence1) ; // working Itbl to store the indices of resu
360  Itbl ind0(valence0) ; // working Itbl to store the indices of uu
361  Itbl ind(valence0) ; // working Itbl to store the indices of uu
362 
363  Scalar tmp(*mp) ; // working scalar
364 
365  // Determination of the dzpuis parameter of the input --> dz_in
366  // ---------------------------------------------------
367  int dz_in = 0 ;
368  for (int ic=0; ic<ncomp0; ic++) {
369  int dzp = uu(uu.indices(ic)).get_dzpuis() ;
370  assert(dzp >= 0) ;
371  if (dzp > dz_in) dz_in = dzp ;
372  }
373 
374 #ifndef NDEBUG
375  // Check : do all components have the same dzpuis ?
376  for (int ic=0; ic<ncomp0; ic++) {
377  if ( !(uu(uu.indices(ic)).check_dzpuis(dz_in)) ) {
378  cout << "######## WARNING #######\n" ;
379  cout << " Connection::p_derive_cov : the tensor components \n"
380  << " do not have all the same dzpuis ! : \n"
381  << " ic, dzpuis(ic), dz_in : " << ic << " "
382  << uu(uu.indices(ic)).get_dzpuis() << " " << dz_in << endl ;
383  }
384  }
385 #endif
386 
387 
388  // Initialisation to the flat derivative
389  // -------------------------------------
390 
391  *resu = uu.derive_cov(*flat_met) ;
392 
393  // Addition of the Delta terms
394  // ----------------------------
395  // loop on all the components of the output tensor
396  for (int ic=0; ic<ncomp1; ic++) {
397 
398  // indices corresponding to the component no. ic in the output tensor
399  ind1 = resu->indices(ic) ;
400 
401  // Indices of the input tensor
402  for (int id = 0; id < valence0; id++) {
403  ind0.set(id) = ind1(id) ;
404  }
405 
406  // Value of last index (derivation index)
407  int k = ind1(valence1m1) ;
408 
409  tmp = 0 ;
410 
411  // Loop on the number of indices of uu
412  for (int id=0; id<valence0; id++) {
413 
414  ind = ind0 ;
415 
416  switch( uu.get_index_type(id) ) {
417 
418  case CON : {
419  for (int l=1; l<=3; l++) {
420  ind.set(id) = l ;
421  tmp += delta(ind0(id), k, l) * uu(ind) ;
422  }
423  break ;
424  }
425 
426  case COV : {
427  for (int l=1; l<=3; l++) {
428  ind.set(id) = l ;
429  tmp -= delta(l, k, ind0(id)) * uu(ind) ;
430  }
431  break ;
432  }
433 
434  default : {
435  cerr <<
436  "Connection::p_derive_cov : unexpected type of index !\n" ;
437  abort() ;
438  break ;
439  }
440 
441  } // end of switch on index type
442 
443  } // end of loop on the number of indices of uu
444 
445 
446  if (dz_in > 0) tmp.dec_dzpuis() ; // to get the same dzpuis as
447  // the flat covariant derivative
448 
449  resu->set(ind1) += tmp ; // addition to the flat derivative part
450 
451  } // end of loop on all the components of the output tensor
452 
453  // C'est fini !
454  // ------------
455 
456  return resu ;
457 
458 }
459 
460 
461 
462 //---------------------------------
463 // Divergence, returning a pointer.
464 //---------------------------------
465 
467 
468 
469  // Notations: suffix 0 in name <=> input tensor
470  // suffix 1 in name <=> output tensor
471 
472  int valence0 = uu.get_valence() ;
473  int valence1 = valence0 - 1 ;
474  int valence0m1 = valence0 - 1 ; // same as valence1 but introduced for
475  // the sake of clarity
476  int ncomp0 = uu.get_n_comp() ;
477 
478  // Protections
479  // -----------
480  assert (valence0 >= 1) ;
481  assert (uu.get_triad() == triad) ;
482 
483  // Last index must be contravariant:
484  assert (uu.get_index_type(valence0m1) == CON) ;
485 
486 
487  // Creation of the pointer on the result tensor
488  // --------------------------------------------
489  Tensor* resu ;
490 
491  if (valence0 == 1) // if u is a Vector, the result is a Scalar
492  resu = new Scalar(*mp) ;
493  else {
494 
495  // Type of indices of the result :
496  Itbl tipe(valence1) ;
497  const Itbl& tipeuu = uu.get_index_type() ;
498  for (int id = 0; id<valence1; id++) {
499  tipe.set(id) = tipeuu(id) ; // type of remaining indices =
500  } // same as uu indices
501 
502  if (valence0 == 2) { // if u is a rank 2 tensor, the result is a Vector
503  resu = new Vector(*mp, tipe(0), *triad) ;
504  }
505  else {
506  // if uu is a Tensor_sym, the result might be also a Tensor_sym:
507  const Tensor* puu = &uu ;
508  const Tensor_sym* puus = dynamic_cast<const Tensor_sym*>(puu) ;
509  if ( puus != 0x0 ) { // the input tensor is symmetric
510 
511  if (puus->sym_index2() != valence0 - 1) {
512 
513  // the symmetry is preserved:
514 
515  if (valence1 == 2) {
516  resu = new Sym_tensor(*mp, tipe, *triad) ;
517  }
518  else {
519  resu = new Tensor_sym(*mp, valence1, tipe, *triad,
520  puus->sym_index1(), puus->sym_index2()) ;
521  }
522  }
523  else { // the symmetry is lost:
524 
525  resu = new Tensor(*mp, valence1, tipe, *triad) ;
526  }
527  }
528  else { // no symmetry in the input tensor:
529  resu = new Tensor(*mp, valence1, tipe, *triad) ;
530  }
531  }
532 
533  }
534 
535  int ncomp1 = resu->get_n_comp() ;
536 
537  Itbl ind0(valence0) ; // working Itbl to store the indices of uu
538  Itbl ind1(valence1) ; // working Itbl to store the indices of resu
539  Itbl ind(valence0) ; // working Itbl to store the indices of uu
540 
541  Scalar tmp(*mp) ; // working scalar
542 
543 
544  // Determination of the dzpuis parameter of the input --> dz_in
545  // ---------------------------------------------------
546  int dz_in = 0 ;
547  for (int ic=0; ic<ncomp0; ic++) {
548  int dzp = uu(uu.indices(ic)).get_dzpuis() ;
549  assert(dzp >= 0) ;
550  if (dzp > dz_in) dz_in = dzp ;
551  }
552 
553 #ifndef NDEBUG
554  // Check : do all components have the same dzpuis ?
555  for (int ic=0; ic<ncomp0; ic++) {
556  if ( !(uu(uu.indices(ic)).check_dzpuis(dz_in)) ) {
557  cout << "######## WARNING #######\n" ;
558  cout << " Connection::p_divergence : the tensor components \n"
559  << " do not have all the same dzpuis ! : \n"
560  << " ic, dzpuis(ic), dz_in : " << ic << " "
561  << uu(uu.indices(ic)).get_dzpuis() << " " << dz_in << endl ;
562  }
563  }
564 #endif
565 
566  // The 1-form Delta^k_{lk} is required
567  // -----------------------------------
568 
569  Vector delta_trace = delta.trace(0,2) ; // Delta^k_{lk}
570 
571  // Initialisation to the flat divergence
572  // -------------------------------------
573 
574  *resu = uu.divergence(*flat_met) ;
575 
576 
577  // Addition of the Delta terms
578  // ----------------------------
579  // loop on all the components of the output tensor
580  for (int ic=0; ic<ncomp1; ic++) {
581 
582  // indices corresponding to the component no. ic in the output tensor
583  ind1 = resu->indices(ic) ;
584 
585  // Indices of the input tensor (but the last one)
586  for (int id = 0; id < valence1; id++) {
587  ind0.set(id) = ind1(id) ;
588  }
589 
590  // Addition of the Delta^k_{lk} term
591  tmp = 0 ;
592 
593  for (int l=1; l<=3; l++) {
594  ind0.set(valence0m1) = l ; // summation on the last index of uu
595  tmp += delta_trace(l) * uu(ind0) ;
596  }
597 
598  ind0.set(valence0m1) = -1 ; // unvalid value for the last index
599  // because it should no longer be used
600 
601 
602  // Addition of the other Delta terms
603 
604  for (int id=0; id<valence1; id++) { // Loop on the number of indices
605  // the result
606 
607  ind = ind0 ;
608 
609  switch( uu.get_index_type(id) ) {
610 
611  case CON : {
612  for (int l=1; l<=3; l++) {
613  ind.set(id) = l ;
614  for (int k=1; k<=3; k++) {
615  ind.set(valence0m1) = k ;
616  tmp += delta(ind0(id), l, k) * uu(ind) ;
617  }
618  }
619  break ;
620  }
621 
622  case COV : {
623  for (int l=1; l<=3; l++) {
624  ind.set(id) = l ;
625  for (int k=1; k<=3; k++) {
626  ind.set(valence0m1) = k ;
627  tmp -= delta(l, ind0(id), k) * uu(ind) ;
628  }
629  }
630  break ;
631  }
632 
633  default : {
634  cerr <<
635  "Connection::p_divergence : unexpected type of index !\n" ;
636  abort() ;
637  break ;
638  }
639 
640  } // end of switch on index type
641 
642  } // end of loop on the number of indices of the result
643 
644 
645  if (dz_in > 0) tmp.dec_dzpuis() ; // to get the same dzpuis as
646  // the flat divergence
647 
648  resu->set(ind1) += tmp ; // addition to the flat divergence part
649 
650 
651  } // end of loop on all the components of the output tensor
652 
653  // C'est fini !
654  // ------------
655 
656  return resu ;
657 
658 }
659 
660 
661 //--------------
662 // Ricci tensor
663 //--------------
664 
665 const Tensor& Connection::ricci() const {
666 
667  if (p_ricci == 0x0) { // a new computation is necessary
668 
669  if (assoc_metric) { // The Ricci tensor is symmetric if the
670  // connection is associated with some metric
671  p_ricci = new Sym_tensor(*mp, COV, *triad) ;
672  }
673  else {
674  p_ricci = new Tensor(*mp, 2, COV, *triad) ;
675  }
676 
677  const Tensor& d_delta = delta.derive_cov(*flat_met) ;
678 
679  for (int i=1; i<=3; i++) {
680 
681  int jmax = assoc_metric ? i : 3 ;
682 
683  for (int j=1; j<=jmax; j++) {
684 
685  Scalar tmp1(*mp) ;
686  tmp1.set_etat_zero() ;
687  for (int k=1; k<=3; k++) {
688  tmp1 += d_delta(k,i,j,k) ;
689  }
690 
691  Scalar tmp2(*mp) ;
692  tmp2.set_etat_zero() ;
693  for (int k=1; k<=3; k++) {
694  tmp2 += d_delta(k,i,k,j) ;
695  }
696 
697  Scalar tmp3(*mp) ;
698  tmp3.set_etat_zero() ;
699  for (int k=1; k<=3; k++) {
700  for (int m=1; m<=3; m++) {
701  tmp3 += delta(k,k,m) * delta(m,i,j) ;
702  }
703  }
704  tmp3.dec_dzpuis() ; // dzpuis 4 -> 3
705 
706  Scalar tmp4(*mp) ;
707  tmp4.set_etat_zero() ;
708  for (int k=1; k<=3; k++) {
709  for (int m=1; m<=3; m++) {
710  tmp4 += delta(k,j,m) * delta(m,i,k) ;
711  }
712  }
713  tmp4.dec_dzpuis() ; // dzpuis 4 -> 3
714 
715  p_ricci->set(i,j) = tmp1 - tmp2 + tmp3 - tmp4 ;
716 
717  }
718  }
719 
720  }
721 
722  return *p_ricci ;
723 
724 }
725 
726 
727 
728 
729 
730 
731 
732 
733 
734 
735 
736 
737 
738 }
Metric for tensor calculation.
Definition: metric.h:90
virtual const Sym_tensor & con() const
Read-only access to the contravariant representation.
Definition: metric.C:293
int & set(int i)
Read/write of a particular element (index i ) (1D case)
Definition: itbl.h:247
virtual const Tensor & ricci() const
Computes (if not up to date) and returns the Ricci tensor associated with the current connection...
Definition: connection.C:665
void set_der_0x0() const
Sets to 0x0 all the pointers on derived quantities.
Definition: connection.C:216
const Map *const mp
Reference mapping.
Definition: connection.h:119
virtual void set_etat_zero()
Sets the logical state to ETATZERO (zero).
Definition: scalar.C:330
int sym_index1() const
Number of the first symmetric index (0<= id_sym1 < valence )
Definition: tensor.h:1162
bool assoc_metric
Indicates whether the connection is associated with a metric (in which case the Ricci tensor is symme...
Definition: connection.h:147
Lorene prototypes.
Definition: app_hor.h:67
void operator=(const Connection &)
Assignment to another Connection.
Definition: connection.C:228
Flat metric for tensor calculation.
Definition: metric.h:261
Tensor field of valence 0 (or component of a tensorial field).
Definition: scalar.h:393
Base class for coordinate mappings.
Definition: map.h:688
virtual Tensor * p_derive_cov(const Tensor &tens) const
Computes the covariant derivative of a tensor (with respect to the current connection).
Definition: connection.C:310
int get_n_comp() const
Returns the number of stored components.
Definition: tensor.h:885
int sym_index2() const
Number of the second symmetric index (id_sym1 < id_sym2 < valence )
Definition: tensor.h:1167
Basic integer array class.
Definition: itbl.h:122
Tensor_sym delta
Tensor which defines the connection with respect to the flat one: is the difference between the con...
Definition: connection.h:141
Tensor field of valence 1.
Definition: vector.h:188
const Tensor_sym & derive_cov(const Metric &gam) const
Returns the covariant derivative of this with respect to some metric .
Vectorial bases (triads) with respect to which the tensorial components are defined.
Definition: base_vect.h:105
const Metric_flat * flat_met
Flat metric with respect to which (member delta ) is defined.
Definition: connection.h:156
const Base_vect * get_triad() const
Returns the vectorial basis (triad) on which the components are defined.
Definition: tensor.h:879
void del_deriv() const
Deletes all the derived quantities.
Definition: connection.C:208
Class Connection.
Definition: connection.h:113
int get_index_type(int i) const
Gives the type (covariant or contravariant) of the index number i .
Definition: tensor.h:899
void update(const Tensor_sym &delta_i)
Update the connection when it is defined ab initio.
Definition: connection.C:238
Connection(const Tensor_sym &delta_i, const Metric_flat &flat_met_i)
Standard constructor ab initio.
Definition: connection.C:132
virtual ~Connection()
Destructor.
Definition: connection.C:198
Tensor handling.
Definition: tensor.h:294
const Tensor & derive_cov(const Metric &gam) const
Returns the covariant derivative of this with respect to some metric .
Definition: tensor.C:1011
int get_valence() const
Returns the valence.
Definition: tensor.h:882
const Tensor & divergence(const Metric &gam) const
Computes the divergence of this with respect to some metric .
Definition: tensor.C:1064
virtual const Sym_tensor & cov() const
Read-only access to the covariant representation.
Definition: metric.C:283
Scalar & set(const Itbl &ind)
Returns the value of a component (read/write version).
Definition: tensor.C:663
void fait_delta(const Metric &)
Computes the difference between the connection coefficients and that a the flat connection in the ca...
Definition: connection.C:281
Symmetric tensors (with respect to two of their arguments).
Definition: tensor.h:1050
Tensor * p_ricci
Pointer of the Ricci tensor associated with the connection.
Definition: connection.h:164
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...
const Base_vect *const triad
Triad with respect to which the connection coefficients are defined.
Definition: connection.h:124
Class intended to describe valence-2 symmetric tensors.
Definition: sym_tensor.h:226
virtual Itbl indices(int pos) const
Returns the indices of a component given by its position in the array cmp .
Definition: tensor.C:548
Tensor trace(int ind1, int ind2) const
Trace on two different type indices.
virtual Tensor * p_divergence(const Tensor &tens) const
Computes the divergence of a tensor (with respect to the current connection).
Definition: connection.C:466