Actual source code: isdiff.c

petsc-3.10.5 2019-03-28
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  2:  #include <petsc/private/isimpl.h>
  3:  #include <petscbt.h>

  5: /*@
  6:    ISDifference - Computes the difference between two index sets.

  8:    Collective on IS

 10:    Input Parameter:
 11: +  is1 - first index, to have items removed from it
 12: -  is2 - index values to be removed

 14:    Output Parameters:
 15: .  isout - is1 - is2

 17:    Notes:
 18:    Negative values are removed from the lists. is2 may have values
 19:    that are not in is1. This requires O(imax-imin) memory and O(imax-imin)
 20:    work, where imin and imax are the bounds on the indices in is1.

 22:    Level: intermediate

 24:    Concepts: index sets^difference
 25:    Concepts: IS^difference

 27: .seealso: ISDestroy(), ISView(), ISSum(), ISExpand()

 29: @*/
 30: PetscErrorCode  ISDifference(IS is1,IS is2,IS *isout)
 31: {
 33:   PetscInt       i,n1,n2,imin,imax,nout,*iout;
 34:   const PetscInt *i1,*i2;
 35:   PetscBT        mask;
 36:   MPI_Comm       comm;


 43:   ISGetIndices(is1,&i1);
 44:   ISGetLocalSize(is1,&n1);

 46:   /* Create a bit mask array to contain required values */
 47:   if (n1) {
 48:     imin = PETSC_MAX_INT;
 49:     imax = 0;
 50:     for (i=0; i<n1; i++) {
 51:       if (i1[i] < 0) continue;
 52:       imin = PetscMin(imin,i1[i]);
 53:       imax = PetscMax(imax,i1[i]);
 54:     }
 55:   } else imin = imax = 0;

 57:   PetscBTCreate(imax-imin,&mask);
 58:   /* Put the values from is1 */
 59:   for (i=0; i<n1; i++) {
 60:     if (i1[i] < 0) continue;
 61:     PetscBTSet(mask,i1[i] - imin);
 62:   }
 63:   ISRestoreIndices(is1,&i1);
 64:   /* Remove the values from is2 */
 65:   ISGetIndices(is2,&i2);
 66:   ISGetLocalSize(is2,&n2);
 67:   for (i=0; i<n2; i++) {
 68:     if (i2[i] < imin || i2[i] > imax) continue;
 69:     PetscBTClear(mask,i2[i] - imin);
 70:   }
 71:   ISRestoreIndices(is2,&i2);

 73:   /* Count the number in the difference */
 74:   nout = 0;
 75:   for (i=0; i<imax-imin+1; i++) {
 76:     if (PetscBTLookup(mask,i)) nout++;
 77:   }

 79:   /* create the new IS containing the difference */
 80:   PetscMalloc1(nout,&iout);
 81:   nout = 0;
 82:   for (i=0; i<imax-imin+1; i++) {
 83:     if (PetscBTLookup(mask,i)) iout[nout++] = i + imin;
 84:   }
 85:   PetscObjectGetComm((PetscObject)is1,&comm);
 86:   ISCreateGeneral(comm,nout,iout,PETSC_OWN_POINTER,isout);

 88:   PetscBTDestroy(&mask);
 89:   return(0);
 90: }

 92: /*@
 93:    ISSum - Computes the sum (union) of two index sets.

 95:    Only sequential version (at the moment)

 97:    Input Parameter:
 98: +  is1 - index set to be extended
 99: -  is2 - index values to be added

101:    Output Parameter:
102: .   is3 - the sum; this can not be is1 or is2

104:    Notes:
105:    If n1 and n2 are the sizes of the sets, this takes O(n1+n2) time;

107:    Both index sets need to be sorted on input.

109:    Level: intermediate

111: .seealso: ISDestroy(), ISView(), ISDifference(), ISExpand()

113:    Concepts: index sets^union
114:    Concepts: IS^union

116: @*/
117: PetscErrorCode  ISSum(IS is1,IS is2,IS *is3)
118: {
119:   MPI_Comm       comm;
120:   PetscBool      f;
121:   PetscMPIInt    size;
122:   const PetscInt *i1,*i2;
123:   PetscInt       n1,n2,n3, p1,p2, *iout;

129:   PetscObjectGetComm((PetscObject)(is1),&comm);
130:   MPI_Comm_size(comm,&size);
131:   if (size>1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Currently only for uni-processor IS");

133:   ISSorted(is1,&f);
134:   if (!f) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Arg 1 is not sorted");
135:   ISSorted(is2,&f);
136:   if (!f) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Arg 2 is not sorted");

138:   ISGetLocalSize(is1,&n1);
139:   ISGetLocalSize(is2,&n2);
140:   if (!n2) return(0);
141:   ISGetIndices(is1,&i1);
142:   ISGetIndices(is2,&i2);

144:   p1 = 0; p2 = 0; n3 = 0;
145:   do {
146:     if (p1==n1) { /* cleanup for is2 */ n3 += n2-p2; break;
147:     } else {
148:       while (p2<n2 && i2[p2]<i1[p1]) {
149:         n3++; p2++;
150:       }
151:       if (p2==n2) {
152:         /* cleanup for is1 */
153:         n3 += n1-p1; break;
154:       } else {
155:         if (i2[p2]==i1[p1]) { n3++; p1++; p2++; }
156:       }
157:     }
158:     if (p2==n2) {
159:       /* cleanup for is1 */
160:       n3 += n1-p1; break;
161:     } else {
162:       while (p1<n1 && i1[p1]<i2[p2]) {
163:         n3++; p1++;
164:       }
165:       if (p1==n1) {
166:         /* clean up for is2 */
167:         n3 += n2-p2; break;
168:       } else {
169:         if (i1[p1]==i2[p2]) { n3++; p1++; p2++; }
170:       }
171:     }
172:   } while (p1<n1 || p2<n2);

174:   if (n3==n1) { /* no new elements to be added */
175:     ISRestoreIndices(is1,&i1);
176:     ISRestoreIndices(is2,&i2);
177:     ISDuplicate(is1,is3);
178:     return(0);
179:   }
180:   PetscMalloc1(n3,&iout);

182:   p1 = 0; p2 = 0; n3 = 0;
183:   do {
184:     if (p1==n1) { /* cleanup for is2 */
185:       while (p2<n2) iout[n3++] = i2[p2++];
186:       break;
187:     } else {
188:       while (p2<n2 && i2[p2]<i1[p1]) iout[n3++] = i2[p2++];
189:       if (p2==n2) { /* cleanup for is1 */
190:         while (p1<n1) iout[n3++] = i1[p1++];
191:         break;
192:       } else {
193:         if (i2[p2]==i1[p1]) { iout[n3++] = i1[p1++]; p2++; }
194:       }
195:     }
196:     if (p2==n2) { /* cleanup for is1 */
197:       while (p1<n1) iout[n3++] = i1[p1++];
198:       break;
199:     } else {
200:       while (p1<n1 && i1[p1]<i2[p2]) iout[n3++] = i1[p1++];
201:       if (p1==n1) { /* clean up for is2 */
202:         while (p2<n2) iout[n3++] = i2[p2++];
203:         break;
204:       } else {
205:         if (i1[p1]==i2[p2]) { iout[n3++] = i1[p1++]; p2++; }
206:       }
207:     }
208:   } while (p1<n1 || p2<n2);

210:   ISRestoreIndices(is1,&i1);
211:   ISRestoreIndices(is2,&i2);
212:   ISCreateGeneral(comm,n3,iout,PETSC_OWN_POINTER,is3);
213:   return(0);
214: }

216: /*@
217:    ISExpand - Computes the union of two index sets, by concatenating 2 lists and
218:    removing duplicates.

220:    Collective on IS

222:    Input Parameter:
223: +  is1 - first index set
224: -  is2 - index values to be added

226:    Output Parameters:
227: .  isout - is1 + is2 The index set is2 is appended to is1 removing duplicates

229:    Notes:
230:    Negative values are removed from the lists. This requires O(imax-imin)
231:    memory and O(imax-imin) work, where imin and imax are the bounds on the
232:    indices in is1 and is2.

234:    The IS's do not need to be sorted.

236:    Level: intermediate

238: .seealso: ISDestroy(), ISView(), ISDifference(), ISSum()

240:    Concepts: index sets^difference
241:    Concepts: IS^difference

243: @*/
244: PetscErrorCode ISExpand(IS is1,IS is2,IS *isout)
245: {
247:   PetscInt       i,n1,n2,imin,imax,nout,*iout;
248:   const PetscInt *i1,*i2;
249:   PetscBT        mask;
250:   MPI_Comm       comm;


257:   if (!is1 && !is2) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Both arguments cannot be NULL");
258:   if (!is1) {ISDuplicate(is2, isout);return(0);}
259:   if (!is2) {ISDuplicate(is1, isout);return(0);}
260:   ISGetIndices(is1,&i1);
261:   ISGetLocalSize(is1,&n1);
262:   ISGetIndices(is2,&i2);
263:   ISGetLocalSize(is2,&n2);

265:   /* Create a bit mask array to contain required values */
266:   if (n1 || n2) {
267:     imin = PETSC_MAX_INT;
268:     imax = 0;
269:     for (i=0; i<n1; i++) {
270:       if (i1[i] < 0) continue;
271:       imin = PetscMin(imin,i1[i]);
272:       imax = PetscMax(imax,i1[i]);
273:     }
274:     for (i=0; i<n2; i++) {
275:       if (i2[i] < 0) continue;
276:       imin = PetscMin(imin,i2[i]);
277:       imax = PetscMax(imax,i2[i]);
278:     }
279:   } else imin = imax = 0;

281:   PetscMalloc1(n1+n2,&iout);
282:   nout = 0;
283:   PetscBTCreate(imax-imin,&mask);
284:   /* Put the values from is1 */
285:   for (i=0; i<n1; i++) {
286:     if (i1[i] < 0) continue;
287:     if (!PetscBTLookupSet(mask,i1[i] - imin)) iout[nout++] = i1[i];
288:   }
289:   ISRestoreIndices(is1,&i1);
290:   /* Put the values from is2 */
291:   for (i=0; i<n2; i++) {
292:     if (i2[i] < 0) continue;
293:     if (!PetscBTLookupSet(mask,i2[i] - imin)) iout[nout++] = i2[i];
294:   }
295:   ISRestoreIndices(is2,&i2);

297:   /* create the new IS containing the sum */
298:   PetscObjectGetComm((PetscObject)is1,&comm);
299:   ISCreateGeneral(comm,nout,iout,PETSC_OWN_POINTER,isout);

301:   PetscBTDestroy(&mask);
302:   return(0);
303: }

305: /*@
306:    ISIntersect - Computes the union of two index sets, by concatenating 2 lists, sorting,
307:    and finding duplicates.

309:    Collective on IS

311:    Input Parameter:
312: +  is1 - first index set
313: -  is2 - second index set

315:    Output Parameters:
316: .  isout - the sorted intersection of is1 and is2

318:    Notes:
319:    Negative values are removed from the lists. This requires O(min(is1,is2))
320:    memory and O(max(is1,is2)log(max(is1,is2))) work

322:    The IS's do not need to be sorted.

324:    Level: intermediate

326: .seealso: ISDestroy(), ISView(), ISDifference(), ISSum(), ISExpand()

328:    Concepts: index sets^intersection
329:    Concepts: IS^intersection

331: @*/
332: PetscErrorCode ISIntersect(IS is1,IS is2,IS *isout)
333: {
335:   PetscInt       i,n1,n2,nout,*iout;
336:   const PetscInt *i1,*i2;
337:   IS             is1sorted = NULL, is2sorted = NULL;
338:   PetscBool      sorted;
339:   MPI_Comm       comm;


346:   ISGetLocalSize(is1,&n1);
347:   ISGetLocalSize(is2,&n2);
348:   if (n1 < n2) {
349:     IS tempis = is1;
350:     int ntemp = n1;

352:     is1 = is2;
353:     is2 = tempis;
354:     n1  = n2;
355:     n2  = ntemp;
356:   }
357:   ISSorted(is1,&sorted);
358:   if (!sorted) {
359:     ISDuplicate(is1,&is1sorted);
360:     ISSort(is1sorted);
361:     ISGetIndices(is1sorted,&i1);
362:   } else {
363:     is1sorted = is1;
364:     PetscObjectReference((PetscObject)is1);
365:     ISGetIndices(is1,&i1);
366:   }
367:   ISSorted(is2,&sorted);
368:   if (!sorted) {
369:     ISDuplicate(is2,&is2sorted);
370:     ISSort(is2sorted);
371:     ISGetIndices(is2sorted,&i2);
372:   } else {
373:     is2sorted = is2;
374:     PetscObjectReference((PetscObject)is2);
375:     ISGetIndices(is2,&i2);
376:   }

378:   PetscMalloc1(n2,&iout);

380:   for (i = 0, nout = 0; i < n2; i++) {
381:     PetscInt key = i2[i];
382:     PetscInt loc;

384:     ISLocate(is1sorted,key,&loc);
385:     if (loc >= 0) {
386:       if (!nout || iout[nout-1] < key) {
387:         iout[nout++] = key;
388:       }
389:     }
390:   }
391:   PetscRealloc(sizeof (PetscInt) * (size_t) nout,&iout);

393:   /* create the new IS containing the sum */
394:   PetscObjectGetComm((PetscObject)is1,&comm);
395:   ISCreateGeneral(comm,nout,iout,PETSC_OWN_POINTER,isout);

397:   ISRestoreIndices(is2sorted,&i2);
398:   ISDestroy(&is2sorted);
399:   ISRestoreIndices(is1sorted,&i1);
400:   ISDestroy(&is1sorted);
401:   return(0);
402: }

404: PetscErrorCode ISIntersect_Caching_Internal(IS is1, IS is2, IS *isect)
405: {

409:   *isect = NULL;
410:   if (is2 && is1) {
411:     char           composeStr[33] = {0};
412:     PetscObjectId  is2id;

414:     PetscObjectGetId((PetscObject)is2,&is2id);
415:     PetscSNPrintf(composeStr,32,"ISIntersect_Caching_%x",is2id);
416:     PetscObjectQuery((PetscObject) is1, composeStr, (PetscObject *) isect);
417:     if (*isect == NULL) {
418:       ISIntersect(is1, is2, isect);
419:       PetscObjectCompose((PetscObject) is1, composeStr, (PetscObject) *isect);
420:     } else {
421:       PetscObjectReference((PetscObject) *isect);
422:     }
423:   }
424:   return(0);
425: }

427: /*@
428:    ISConcatenate - Forms a new IS by locally concatenating the indices from an IS list without reordering.


431:    Collective on comm.

433:    Input Parameter:
434: +  comm    - communicator of the concatenated IS.
435: .  len     - size of islist array (nonnegative)
436: -  islist  - array of index sets

438:    Output Parameters:
439: .  isout   - The concatenated index set; empty, if len == 0.

441:    Notes:
442:     The semantics of calling this on comm imply that the comms of the members if islist also contain this rank.

444:    Level: intermediate

446: .seealso: ISDifference(), ISSum(), ISExpand()

448:    Concepts: index sets^concatenation
449:    Concepts: IS^concatenation

451: @*/
452: PetscErrorCode ISConcatenate(MPI_Comm comm, PetscInt len, const IS islist[], IS *isout)
453: {
455:   PetscInt i,n,N;
456:   const PetscInt *iidx;
457:   PetscInt *idx;

461: #if defined(PETSC_USE_DEBUG)
463: #endif
465:   if (!len) {
466:     ISCreateStride(comm, 0,0,0, isout);
467:     return(0);
468:   }
469:   if (len < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Negative array length: %D", len);
470:   N = 0;
471:   for (i = 0; i < len; ++i) {
472:     if (islist[i]) {
473:       ISGetLocalSize(islist[i], &n);
474:       N   += n;
475:     }
476:   }
477:   PetscMalloc1(N, &idx);
478:   N = 0;
479:   for (i = 0; i < len; ++i) {
480:     if (islist[i]) {
481:       ISGetLocalSize(islist[i], &n);
482:       ISGetIndices(islist[i], &iidx);
483:       PetscMemcpy(idx+N,iidx, sizeof(PetscInt)*n);
484:       ISRestoreIndices(islist[i], &iidx);
485:       N   += n;
486:     }
487:   }
488:   ISCreateGeneral(comm, N, idx, PETSC_OWN_POINTER, isout);
489:   return(0);
490: }

492: /*@
493:    ISListToPair     -    convert an IS list to a pair of ISs of equal length defining an equivalent integer multimap.
494:                         Each IS on the input list is assigned an integer j so that all of the indices of that IS are
495:                         mapped to j.


498:   Collective on comm.

500:   Input arguments:
501: + comm    -  MPI_Comm
502: . listlen -  IS list length
503: - islist  -  IS list

505:   Output arguments:
506: + xis -  domain IS
507: - yis -  range  IS

509:   Level: advanced

511:   Notes:
512:   The global integers assigned to the ISs of the local input list might not correspond to the
513:   local numbers of the ISs on that list, but the two *orderings* are the same: the global
514:   integers assigned to the ISs on the local list form a strictly increasing sequence.

516:   The ISs on the input list can belong to subcommunicators of comm, and the subcommunicators
517:   on the input IS list are assumed to be in a "deadlock-free" order.

519:   Local lists of PetscObjects (or their subcommes) on a comm are "deadlock-free" if subcomm1
520:   preceeds subcomm2 on any local list, then it preceeds subcomm2 on all ranks.
521:   Equivalently, the local numbers of the subcomms on each local list are drawn from some global
522:   numbering. This is ensured, for example, by ISPairToList().

524: .seealso ISPairToList()
525: @*/
526: PetscErrorCode ISListToPair(MPI_Comm comm, PetscInt listlen, IS islist[], IS *xis, IS *yis)
527: {
529:   PetscInt       ncolors, *colors,i, leni,len,*xinds, *yinds,k,j;
530:   const PetscInt *indsi;

533:   PetscMalloc1(listlen, &colors);
534:   PetscObjectsListGetGlobalNumbering(comm, listlen, (PetscObject*)islist,&ncolors, colors);
535:   len  = 0;
536:   for (i = 0; i < listlen; ++i) {
537:     ISGetLocalSize(islist[i], &leni);
538:     len += leni;
539:   }
540:   PetscMalloc1(len, &xinds);
541:   PetscMalloc1(len, &yinds);
542:   k    = 0;
543:   for (i = 0; i < listlen; ++i) {
544:     ISGetLocalSize(islist[i], &leni);
545:     ISGetIndices(islist[i],&indsi);
546:     for (j = 0; j < leni; ++j) {
547:       xinds[k] = indsi[j];
548:       yinds[k] = colors[i];
549:       ++k;
550:     }
551:   }
552:   PetscFree(colors);
553:   ISCreateGeneral(comm,len,xinds,PETSC_OWN_POINTER,xis);
554:   ISCreateGeneral(comm,len,yinds,PETSC_OWN_POINTER,yis);
555:   return(0);
556: }


559: /*@
560:    ISPairToList   -   convert an IS pair encoding an integer map to a list of ISs.
561:                      Each IS on the output list contains the preimage for each index on the second input IS.
562:                      The ISs on the output list are constructed on the subcommunicators of the input IS pair.
563:                      Each subcommunicator corresponds to the preimage of some index j -- this subcomm contains
564:                      exactly the ranks that assign some indices i to j.  This is essentially the inverse of
565:                      ISListToPair().

567:   Collective on indis.

569:   Input arguments:
570: + xis -  domain IS
571: - yis -  range IS

573:   Output arguments:
574: + listlen -  length of islist
575: - islist  -  list of ISs breaking up indis by color

577:   Note:
578: + xis and yis must be of the same length and have congruent communicators.
579: - The resulting ISs have subcommunicators in a "deadlock-free" order (see ISListToPair()).

581:   Level: advanced

583: .seealso ISListToPair()
584:  @*/
585: PetscErrorCode ISPairToList(IS xis, IS yis, PetscInt *listlen, IS **islist)
586: {
588:   IS             indis = xis, coloris = yis;
589:   PetscInt       *inds, *colors, llen, ilen, lstart, lend, lcount,l;
590:   PetscMPIInt    rank, size, llow, lhigh, low, high,color,subsize;
591:   const PetscInt *ccolors, *cinds;
592:   MPI_Comm       comm, subcomm;

600:   PetscObjectGetComm((PetscObject)xis,&comm);
601:   MPI_Comm_rank(comm, &rank);
602:   MPI_Comm_rank(comm, &size);
603:   /* Extract, copy and sort the local indices and colors on the color. */
604:   ISGetLocalSize(coloris, &llen);
605:   ISGetLocalSize(indis,   &ilen);
606:   if (llen != ilen) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Incompatible IS sizes: %D and %D", ilen, llen);
607:   ISGetIndices(coloris, &ccolors);
608:   ISGetIndices(indis, &cinds);
609:   PetscMalloc2(ilen,&inds,llen,&colors);
610:   PetscMemcpy(inds,cinds,ilen*sizeof(PetscInt));
611:   PetscMemcpy(colors,ccolors,llen*sizeof(PetscInt));
612:   PetscSortIntWithArray(llen, colors, inds);
613:   /* Determine the global extent of colors. */
614:   llow   = 0; lhigh  = -1;
615:   lstart = 0; lcount = 0;
616:   while (lstart < llen) {
617:     lend = lstart+1;
618:     while (lend < llen && colors[lend] == colors[lstart]) ++lend;
619:     llow  = PetscMin(llow,colors[lstart]);
620:     lhigh = PetscMax(lhigh,colors[lstart]);
621:     ++lcount;
622:   }
623:   MPIU_Allreduce(&llow,&low,1,MPI_INT,MPI_MIN,comm);
624:   MPIU_Allreduce(&lhigh,&high,1,MPI_INT,MPI_MAX,comm);
625:   *listlen = 0;
626:   if (low <= high) {
627:     if (lcount > 0) {
628:       *listlen = lcount;
629:       if (!*islist) {
630:         PetscMalloc1(lcount, islist);
631:       }
632:     }
633:     /*
634:      Traverse all possible global colors, and participate in the subcommunicators
635:      for the locally-supported colors.
636:      */
637:     lcount = 0;
638:     lstart = 0; lend = 0;
639:     for (l = low; l <= high; ++l) {
640:       /*
641:        Find the range of indices with the same color, which is not smaller than l.
642:        Observe that, since colors is sorted, and is a subsequence of [low,high],
643:        as soon as we find a new color, it is >= l.
644:        */
645:       if (lstart < llen) {
646:         /* The start of the next locally-owned color is identified.  Now look for the end. */
647:         if (lstart == lend) {
648:           lend = lstart+1;
649:           while (lend < llen && colors[lend] == colors[lstart]) ++lend;
650:         }
651:         /* Now check whether the identified color segment matches l. */
652:         if (colors[lstart] < l) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Locally owned color %D at location %D is < than the next global color %D", colors[lstart], lcount, l);
653:       }
654:       color = (PetscMPIInt)(colors[lstart] == l);
655:       /* Check whether a proper subcommunicator exists. */
656:       MPIU_Allreduce(&color,&subsize,1,MPI_INT,MPI_SUM,comm);

658:       if (subsize == 1) subcomm = PETSC_COMM_SELF;
659:       else if (subsize == size) subcomm = comm;
660:       else {
661:         /* a proper communicator is necessary, so we create it. */
662:         MPI_Comm_split(comm, color, rank, &subcomm);
663:       }
664:       if (colors[lstart] == l) {
665:         /* If we have l among the local colors, we create an IS to hold the corresponding indices. */
666:         ISCreateGeneral(subcomm, lend-lstart,inds+lstart,PETSC_COPY_VALUES,*islist+lcount);
667:         /* Position lstart at the beginning of the next local color. */
668:         lstart = lend;
669:         /* Increment the counter of the local colors split off into an IS. */
670:         ++lcount;
671:       }
672:       if (subsize > 0 && subsize < size) {
673:         /*
674:          Irrespective of color, destroy the split off subcomm:
675:          a subcomm used in the IS creation above is duplicated
676:          into a proper PETSc comm.
677:          */
678:         MPI_Comm_free(&subcomm);
679:       }
680:     } /* for (l = low; l < high; ++l) */
681:   } /* if (low <= high) */
682:   PetscFree2(inds,colors);
683:   return(0);
684: }


687: /*@
688:    ISEmbed   -   embed IS a into IS b by finding the locations in b that have the same indices as in a.
689:                  If c is the IS of these locations, we have a = b*c, regarded as a composition of the
690:                  corresponding ISLocalToGlobalMaps.

692:   Not collective.

694:   Input arguments:
695: + a    -  IS to embed
696: . b    -  IS to embed into
697: - drop -  flag indicating whether to drop a's indices that are not in b.

699:   Output arguments:
700: . c    -  local embedding indices

702:   Note:
703:   If some of a's global indices are not among b's indices the embedding is impossible.  The local indices of a
704:   corresponding to these global indices are either mapped to -1 (if !drop) or are omitted (if drop).  In the former
705:   case the size of c is that same as that of a, in the latter case c's size may be smaller.

707:   The resulting IS is sequential, since the index substition it encodes is purely local.

709:   Level: advanced

711: .seealso ISLocalToGlobalMapping
712:  @*/
713: PetscErrorCode ISEmbed(IS a, IS b, PetscBool drop, IS *c)
714: {
715:   PetscErrorCode             ierr;
716:   ISLocalToGlobalMapping     ltog;
717:   ISGlobalToLocalMappingMode gtoltype = IS_GTOLM_DROP;
718:   PetscInt                   alen, clen, *cindices, *cindices2;
719:   const PetscInt             *aindices;

725:   ISLocalToGlobalMappingCreateIS(b, &ltog);
726:   ISGetLocalSize(a, &alen);
727:   ISGetIndices(a, &aindices);
728:   PetscMalloc1(alen, &cindices);
729:   if (!drop) gtoltype = IS_GTOLM_MASK;
730:   ISGlobalToLocalMappingApply(ltog,gtoltype,alen,aindices,&clen,cindices);
731:   ISLocalToGlobalMappingDestroy(&ltog);
732:   if (clen != alen) {
733:     cindices2 = cindices;
734:     PetscMalloc1(clen, &cindices);
735:     PetscMemcpy(cindices,cindices2,clen*sizeof(PetscInt));
736:     PetscFree(cindices2);
737:   }
738:   ISCreateGeneral(PETSC_COMM_SELF,clen,cindices,PETSC_OWN_POINTER,c);
739:   return(0);
740: }


743: /*@
744:   ISSortPermutation  -  calculate the permutation of the indices into a nondecreasing order.

746:   Not collective.

748:   Input arguments:
749: + f      -  IS to sort
750: - always -  build the permutation even when f's indices are nondecreasin.

752:   Output argument:
753: . h    -  permutation or NULL, if f is nondecreasing and always == PETSC_TRUE.


756:   Note: Indices in f are unchanged. f[h[i]] is the i-th smallest f index.
757:         If always == PETSC_FALSE, an extra check is peformed to see whether
758:         the f indices are nondecreasing. h is built on PETSC_COMM_SELF, since
759:         the permutation has a local meaning only.

761:   Level: advanced

763: .seealso ISLocalToGlobalMapping, ISSort(), PetscIntSortWithPermutation()
764:  @*/
765: PetscErrorCode ISSortPermutation(IS f,PetscBool always,IS *h)
766: {
767:   PetscErrorCode  ierr;
768:   const PetscInt  *findices;
769:   PetscInt        fsize,*hindices,i;
770:   PetscBool       isincreasing;

775:   ISGetLocalSize(f,&fsize);
776:   ISGetIndices(f,&findices);
777:   *h = NULL;
778:   if (!always) {
779:     isincreasing = PETSC_TRUE;
780:     for (i = 1; i < fsize; ++i) {
781:       if (findices[i] <= findices[i-1]) {
782:         isincreasing = PETSC_FALSE;
783:         break;
784:       }
785:     }
786:     if (isincreasing) {
787:       ISRestoreIndices(f,&findices);
788:       return(0);
789:     }
790:   }
791:   PetscMalloc1(fsize,&hindices);
792:   for (i = 0; i < fsize; ++i) hindices[i] = i;
793:   PetscSortIntWithPermutation(fsize,findices,hindices);
794:   ISRestoreIndices(f,&findices);
795:   ISCreateGeneral(PETSC_COMM_SELF,fsize,hindices,PETSC_OWN_POINTER,h);
796:   return(0);
797: }