Actual source code: isdiff.c


  2: #include <petsc/private/isimpl.h>
  3: #include <petsc/private/sectionimpl.h>
  4: #include <petscbt.h>

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

  9:    Collective on IS

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

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

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

 23:    If is2 is NULL, the result is the same as for an empty IS, i.e., a duplicate of is1.

 25:    Level: intermediate

 27: .seealso: ISDestroy(), ISView(), ISSum(), ISExpand()
 28: @*/
 29: PetscErrorCode  ISDifference(IS is1,IS is2,IS *isout)
 30: {
 32:   PetscInt       i,n1,n2,imin,imax,nout,*iout;
 33:   const PetscInt *i1,*i2;
 34:   PetscBT        mask;
 35:   MPI_Comm       comm;

 40:   if (!is2) {
 41:     ISDuplicate(is1, isout);
 42:     return(0);
 43:   }

 46:   ISGetIndices(is1,&i1);
 47:   ISGetLocalSize(is1,&n1);

 49:   /* Create a bit mask array to contain required values */
 50:   if (n1) {
 51:     imin = PETSC_MAX_INT;
 52:     imax = 0;
 53:     for (i=0; i<n1; i++) {
 54:       if (i1[i] < 0) continue;
 55:       imin = PetscMin(imin,i1[i]);
 56:       imax = PetscMax(imax,i1[i]);
 57:     }
 58:   } else imin = imax = 0;

 60:   PetscBTCreate(imax-imin,&mask);
 61:   /* Put the values from is1 */
 62:   for (i=0; i<n1; i++) {
 63:     if (i1[i] < 0) continue;
 64:     PetscBTSet(mask,i1[i] - imin);
 65:   }
 66:   ISRestoreIndices(is1,&i1);
 67:   /* Remove the values from is2 */
 68:   ISGetIndices(is2,&i2);
 69:   ISGetLocalSize(is2,&n2);
 70:   for (i=0; i<n2; i++) {
 71:     if (i2[i] < imin || i2[i] > imax) continue;
 72:     PetscBTClear(mask,i2[i] - imin);
 73:   }
 74:   ISRestoreIndices(is2,&i2);

 76:   /* Count the number in the difference */
 77:   nout = 0;
 78:   for (i=0; i<imax-imin+1; i++) {
 79:     if (PetscBTLookup(mask,i)) nout++;
 80:   }

 82:   /* create the new IS containing the difference */
 83:   PetscMalloc1(nout,&iout);
 84:   nout = 0;
 85:   for (i=0; i<imax-imin+1; i++) {
 86:     if (PetscBTLookup(mask,i)) iout[nout++] = i + imin;
 87:   }
 88:   PetscObjectGetComm((PetscObject)is1,&comm);
 89:   ISCreateGeneral(comm,nout,iout,PETSC_OWN_POINTER,isout);

 91:   PetscBTDestroy(&mask);
 92:   return(0);
 93: }

 95: /*@
 96:    ISSum - Computes the sum (union) of two index sets.

 98:    Only sequential version (at the moment)

100:    Input Parameters:
101: +  is1 - index set to be extended
102: -  is2 - index values to be added

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

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

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

112:    Level: intermediate

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

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) {
141:     ISDuplicate(is1,is3);
142:     return(0);
143:   }
144:   ISGetIndices(is1,&i1);
145:   ISGetIndices(is2,&i2);

147:   p1 = 0; p2 = 0; n3 = 0;
148:   do {
149:     if (p1==n1) { /* cleanup for is2 */ n3 += n2-p2; break;
150:     } else {
151:       while (p2<n2 && i2[p2]<i1[p1]) {
152:         n3++; p2++;
153:       }
154:       if (p2==n2) {
155:         /* cleanup for is1 */
156:         n3 += n1-p1; break;
157:       } else {
158:         if (i2[p2]==i1[p1]) { n3++; p1++; p2++; }
159:       }
160:     }
161:     if (p2==n2) {
162:       /* cleanup for is1 */
163:       n3 += n1-p1; break;
164:     } else {
165:       while (p1<n1 && i1[p1]<i2[p2]) {
166:         n3++; p1++;
167:       }
168:       if (p1==n1) {
169:         /* clean up for is2 */
170:         n3 += n2-p2; break;
171:       } else {
172:         if (i1[p1]==i2[p2]) { n3++; p1++; p2++; }
173:       }
174:     }
175:   } while (p1<n1 || p2<n2);

177:   if (n3==n1) { /* no new elements to be added */
178:     ISRestoreIndices(is1,&i1);
179:     ISRestoreIndices(is2,&i2);
180:     ISDuplicate(is1,is3);
181:     return(0);
182:   }
183:   PetscMalloc1(n3,&iout);

185:   p1 = 0; p2 = 0; n3 = 0;
186:   do {
187:     if (p1==n1) { /* cleanup for is2 */
188:       while (p2<n2) iout[n3++] = i2[p2++];
189:       break;
190:     } else {
191:       while (p2<n2 && i2[p2]<i1[p1]) iout[n3++] = i2[p2++];
192:       if (p2==n2) { /* cleanup for is1 */
193:         while (p1<n1) iout[n3++] = i1[p1++];
194:         break;
195:       } else {
196:         if (i2[p2]==i1[p1]) { iout[n3++] = i1[p1++]; p2++; }
197:       }
198:     }
199:     if (p2==n2) { /* cleanup for is1 */
200:       while (p1<n1) iout[n3++] = i1[p1++];
201:       break;
202:     } else {
203:       while (p1<n1 && i1[p1]<i2[p2]) iout[n3++] = i1[p1++];
204:       if (p1==n1) { /* clean up for is2 */
205:         while (p2<n2) iout[n3++] = i2[p2++];
206:         break;
207:       } else {
208:         if (i1[p1]==i2[p2]) { iout[n3++] = i1[p1++]; p2++; }
209:       }
210:     }
211:   } while (p1<n1 || p2<n2);

213:   ISRestoreIndices(is1,&i1);
214:   ISRestoreIndices(is2,&i2);
215:   ISCreateGeneral(comm,n3,iout,PETSC_OWN_POINTER,is3);
216:   return(0);
217: }

219: /*@
220:    ISExpand - Computes the union of two index sets, by concatenating 2 lists and
221:    removing duplicates.

223:    Collective on IS

225:    Input Parameters:
226: +  is1 - first index set
227: -  is2 - index values to be added

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

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

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

239:    Level: intermediate

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

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 intersection of two index sets, by sorting and comparing.

308:    Collective on IS

310:    Input Parameters:
311: +  is1 - first index set
312: -  is2 - second index set

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

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

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

323:    Level: intermediate

325: .seealso: ISDestroy(), ISView(), ISDifference(), ISSum(), ISExpand()
326: @*/
327: PetscErrorCode ISIntersect(IS is1,IS is2,IS *isout)
328: {
330:   PetscInt       i,n1,n2,nout,*iout;
331:   const PetscInt *i1,*i2;
332:   IS             is1sorted = NULL, is2sorted = NULL;
333:   PetscBool      sorted, lsorted;
334:   MPI_Comm       comm;

341:   PetscObjectGetComm((PetscObject)is1,&comm);

343:   ISGetLocalSize(is1,&n1);
344:   ISGetLocalSize(is2,&n2);
345:   if (n1 < n2) {
346:     IS       tempis = is1;
347:     PetscInt ntemp = n1;

349:     is1 = is2;
350:     is2 = tempis;
351:     n1  = n2;
352:     n2  = ntemp;
353:   }
354:   ISSorted(is1,&lsorted);
355:   MPIU_Allreduce(&lsorted,&sorted,1,MPIU_BOOL,MPI_LAND,comm);
356:   if (!sorted) {
357:     ISDuplicate(is1,&is1sorted);
358:     ISSort(is1sorted);
359:     ISGetIndices(is1sorted,&i1);
360:   } else {
361:     is1sorted = is1;
362:     PetscObjectReference((PetscObject)is1);
363:     ISGetIndices(is1,&i1);
364:   }
365:   ISSorted(is2,&lsorted);
366:   MPIU_Allreduce(&lsorted,&sorted,1,MPIU_BOOL,MPI_LAND,comm);
367:   if (!sorted) {
368:     ISDuplicate(is2,&is2sorted);
369:     ISSort(is2sorted);
370:     ISGetIndices(is2sorted,&i2);
371:   } else {
372:     is2sorted = is2;
373:     PetscObjectReference((PetscObject)is2);
374:     ISGetIndices(is2,&i2);
375:   }

377:   PetscMalloc1(n2,&iout);

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

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

392:   /* create the new IS containing the sum */
393:   ISCreateGeneral(comm,nout,iout,PETSC_OWN_POINTER,isout);

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

402: PetscErrorCode ISIntersect_Caching_Internal(IS is1, IS is2, IS *isect)
403: {

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

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

425: /*@
426:    ISConcatenate - Forms a new IS by locally concatenating the indices from an IS list without reordering.

428:    Collective.

430:    Input Parameters:
431: +  comm    - communicator of the concatenated IS.
432: .  len     - size of islist array (nonnegative)
433: -  islist  - array of index sets

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

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

441:    Level: intermediate

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

445: @*/
446: PetscErrorCode ISConcatenate(MPI_Comm comm, PetscInt len, const IS islist[], IS *isout)
447: {
449:   PetscInt i,n,N;
450:   const PetscInt *iidx;
451:   PetscInt *idx;

455:   if (PetscDefined(USE_DEBUG)) {
457:   }
459:   if (!len) {
460:     ISCreateStride(comm, 0,0,0, isout);
461:     return(0);
462:   }
463:   if (len < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Negative array length: %D", len);
464:   N = 0;
465:   for (i = 0; i < len; ++i) {
466:     if (islist[i]) {
467:       ISGetLocalSize(islist[i], &n);
468:       N   += n;
469:     }
470:   }
471:   PetscMalloc1(N, &idx);
472:   N = 0;
473:   for (i = 0; i < len; ++i) {
474:     if (islist[i]) {
475:       ISGetLocalSize(islist[i], &n);
476:       ISGetIndices(islist[i], &iidx);
477:       PetscArraycpy(idx+N,iidx, n);
478:       ISRestoreIndices(islist[i], &iidx);
479:       N   += n;
480:     }
481:   }
482:   ISCreateGeneral(comm, N, idx, PETSC_OWN_POINTER, isout);
483:   return(0);
484: }

486: /*@
487:    ISListToPair     -    convert an IS list to a pair of ISs of equal length defining an equivalent integer multimap.
488:                         Each IS on the input list is assigned an integer j so that all of the indices of that IS are
489:                         mapped to j.

491:   Collective.

493:   Input arguments:
494: + comm    -  MPI_Comm
495: . listlen -  IS list length
496: - islist  -  IS list

498:   Output arguments:
499: + xis -  domain IS
500: - yis -  range  IS

502:   Level: advanced

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

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

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

517: .seealso ISPairToList()
518: @*/
519: PetscErrorCode ISListToPair(MPI_Comm comm, PetscInt listlen, IS islist[], IS *xis, IS *yis)
520: {
522:   PetscInt       ncolors, *colors,i, leni,len,*xinds, *yinds,k,j;
523:   const PetscInt *indsi;

526:   PetscMalloc1(listlen, &colors);
527:   PetscObjectsListGetGlobalNumbering(comm, listlen, (PetscObject*)islist,&ncolors, colors);
528:   len  = 0;
529:   for (i = 0; i < listlen; ++i) {
530:     ISGetLocalSize(islist[i], &leni);
531:     len += leni;
532:   }
533:   PetscMalloc1(len, &xinds);
534:   PetscMalloc1(len, &yinds);
535:   k    = 0;
536:   for (i = 0; i < listlen; ++i) {
537:     ISGetLocalSize(islist[i], &leni);
538:     ISGetIndices(islist[i],&indsi);
539:     for (j = 0; j < leni; ++j) {
540:       xinds[k] = indsi[j];
541:       yinds[k] = colors[i];
542:       ++k;
543:     }
544:   }
545:   PetscFree(colors);
546:   ISCreateGeneral(comm,len,xinds,PETSC_OWN_POINTER,xis);
547:   ISCreateGeneral(comm,len,yinds,PETSC_OWN_POINTER,yis);
548:   return(0);
549: }

551: /*@
552:    ISPairToList   -   convert an IS pair encoding an integer map to a list of ISs.
553:                      Each IS on the output list contains the preimage for each index on the second input IS.
554:                      The ISs on the output list are constructed on the subcommunicators of the input IS pair.
555:                      Each subcommunicator corresponds to the preimage of some index j -- this subcomm contains
556:                      exactly the ranks that assign some indices i to j.  This is essentially the inverse of
557:                      ISListToPair().

559:   Collective on indis.

561:   Input arguments:
562: + xis -  domain IS
563: - yis -  range IS

565:   Output arguments:
566: + listlen -  length of islist
567: - islist  -  list of ISs breaking up indis by color

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

573:   Level: advanced

575: .seealso ISListToPair()
576:  @*/
577: PetscErrorCode ISPairToList(IS xis, IS yis, PetscInt *listlen, IS **islist)
578: {
580:   IS             indis = xis, coloris = yis;
581:   PetscInt       *inds, *colors, llen, ilen, lstart, lend, lcount,l;
582:   PetscMPIInt    rank, size, llow, lhigh, low, high,color,subsize;
583:   const PetscInt *ccolors, *cinds;
584:   MPI_Comm       comm, subcomm;

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

650:       if (subsize == 1) subcomm = PETSC_COMM_SELF;
651:       else if (subsize == size) subcomm = comm;
652:       else {
653:         /* a proper communicator is necessary, so we create it. */
654:         MPI_Comm_split(comm, color, rank, &subcomm);
655:       }
656:       if (colors[lstart] == l) {
657:         /* If we have l among the local colors, we create an IS to hold the corresponding indices. */
658:         ISCreateGeneral(subcomm, lend-lstart,inds+lstart,PETSC_COPY_VALUES,*islist+lcount);
659:         /* Position lstart at the beginning of the next local color. */
660:         lstart = lend;
661:         /* Increment the counter of the local colors split off into an IS. */
662:         ++lcount;
663:       }
664:       if (subsize > 0 && subsize < size) {
665:         /*
666:          Irrespective of color, destroy the split off subcomm:
667:          a subcomm used in the IS creation above is duplicated
668:          into a proper PETSc comm.
669:          */
670:         MPI_Comm_free(&subcomm);
671:       }
672:     } /* for (l = low; l < high; ++l) */
673:   } /* if (low <= high) */
674:   PetscFree2(inds,colors);
675:   return(0);
676: }

678: /*@
679:    ISEmbed   -   embed IS a into IS b by finding the locations in b that have the same indices as in a.
680:                  If c is the IS of these locations, we have a = b*c, regarded as a composition of the
681:                  corresponding ISLocalToGlobalMaps.

683:   Not collective.

685:   Input arguments:
686: + a    -  IS to embed
687: . b    -  IS to embed into
688: - drop -  flag indicating whether to drop a's indices that are not in b.

690:   Output arguments:
691: . c    -  local embedding indices

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

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

700:   Level: advanced

702: .seealso ISLocalToGlobalMapping
703:  @*/
704: PetscErrorCode ISEmbed(IS a, IS b, PetscBool drop, IS *c)
705: {
706:   PetscErrorCode             ierr;
707:   ISLocalToGlobalMapping     ltog;
708:   ISGlobalToLocalMappingMode gtoltype = IS_GTOLM_DROP;
709:   PetscInt                   alen, clen, *cindices, *cindices2;
710:   const PetscInt             *aindices;

716:   ISLocalToGlobalMappingCreateIS(b, &ltog);
717:   ISGetLocalSize(a, &alen);
718:   ISGetIndices(a, &aindices);
719:   PetscMalloc1(alen, &cindices);
720:   if (!drop) gtoltype = IS_GTOLM_MASK;
721:   ISGlobalToLocalMappingApply(ltog,gtoltype,alen,aindices,&clen,cindices);
722:   ISLocalToGlobalMappingDestroy(&ltog);
723:   if (clen != alen) {
724:     cindices2 = cindices;
725:     PetscMalloc1(clen, &cindices);
726:     PetscArraycpy(cindices,cindices2,clen);
727:     PetscFree(cindices2);
728:   }
729:   ISCreateGeneral(PETSC_COMM_SELF,clen,cindices,PETSC_OWN_POINTER,c);
730:   return(0);
731: }

733: /*@
734:   ISSortPermutation  -  calculate the permutation of the indices into a nondecreasing order.

736:   Not collective.

738:   Input arguments:
739: + f      -  IS to sort
740: - always -  build the permutation even when f's indices are nondecreasing.

742:   Output argument:
743: . h    -  permutation or NULL, if f is nondecreasing and always == PETSC_FALSE.

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

750:   Level: advanced

752: .seealso ISLocalToGlobalMapping, ISSort()
753:  @*/
754: PetscErrorCode ISSortPermutation(IS f,PetscBool always,IS *h)
755: {
756:   PetscErrorCode  ierr;
757:   const PetscInt  *findices;
758:   PetscInt        fsize,*hindices,i;
759:   PetscBool       isincreasing;

764:   ISGetLocalSize(f,&fsize);
765:   ISGetIndices(f,&findices);
766:   *h = NULL;
767:   if (!always) {
768:     isincreasing = PETSC_TRUE;
769:     for (i = 1; i < fsize; ++i) {
770:       if (findices[i] <= findices[i-1]) {
771:         isincreasing = PETSC_FALSE;
772:         break;
773:       }
774:     }
775:     if (isincreasing) {
776:       ISRestoreIndices(f,&findices);
777:       return(0);
778:     }
779:   }
780:   PetscMalloc1(fsize,&hindices);
781:   for (i = 0; i < fsize; ++i) hindices[i] = i;
782:   PetscSortIntWithPermutation(fsize,findices,hindices);
783:   ISRestoreIndices(f,&findices);
784:   ISCreateGeneral(PETSC_COMM_SELF,fsize,hindices,PETSC_OWN_POINTER,h);
785:   ISSetInfo(*h,IS_PERMUTATION,IS_LOCAL,PETSC_FALSE,PETSC_TRUE);
786:   return(0);
787: }