Date: 2025-03-29T05:58:52+00:00

Actual source code: iscoloring.c

      1: #include <petsc/private/isimpl.h>
      2: #include <petscviewer.h>
      3: #include <petscsf.h>

      5: const char *const ISColoringTypes[] = {"global", "ghosted", "ISColoringType", "IS_COLORING_", NULL};

      7: PetscErrorCode ISColoringReference(ISColoring coloring)
      8: {
      9:   PetscFunctionBegin;
     10:   coloring->refct++;
     11:   PetscFunctionReturn(PETSC_SUCCESS);
     12: }

     14: /*@
     15:   ISColoringSetType - indicates if the coloring is for the local representation (including ghost points) or the global representation of a `Mat`

     17:   Collective

     19:   Input Parameters:
     20: + coloring - the coloring object
     21: - type     - either `IS_COLORING_LOCAL` or `IS_COLORING_GLOBAL`

     23:   Level: intermediate

     25:   Notes:
     26:   `IS_COLORING_LOCAL` can lead to faster computations since parallel ghost point updates are not needed for each color

     28:   With `IS_COLORING_LOCAL` the coloring is in the numbering of the local vector, for `IS_COLORING_GLOBAL` it is in the numbering of the global vector

     30: .seealso: `MatFDColoringCreate()`, `ISColoring`, `ISColoringType`, `ISColoringCreate()`, `IS_COLORING_LOCAL`, `IS_COLORING_GLOBAL`, `ISColoringGetType()`
     31: @*/
     32: PetscErrorCode ISColoringSetType(ISColoring coloring, ISColoringType type)
     33: {
     34:   PetscFunctionBegin;
     35:   coloring->ctype = type;
     36:   PetscFunctionReturn(PETSC_SUCCESS);
     37: }

     39: /*@
     40:   ISColoringGetType - gets if the coloring is for the local representation (including ghost points) or the global representation

     42:   Collective

     44:   Input Parameter:
     45: . coloring - the coloring object

     47:   Output Parameter:
     48: . type - either `IS_COLORING_LOCAL` or `IS_COLORING_GLOBAL`

     50:   Level: intermediate

     52: .seealso: `MatFDColoringCreate()`, `ISColoring`, `ISColoringType`, `ISColoringCreate()`, `IS_COLORING_LOCAL`, `IS_COLORING_GLOBAL`, `ISColoringSetType()`
     53: @*/
     54: PetscErrorCode ISColoringGetType(ISColoring coloring, ISColoringType *type)
     55: {
     56:   PetscFunctionBegin;
     57:   *type = coloring->ctype;
     58:   PetscFunctionReturn(PETSC_SUCCESS);
     59: }

     61: /*@
     62:   ISColoringDestroy - Destroys an `ISColoring` coloring context.

     64:   Collective

     66:   Input Parameter:
     67: . iscoloring - the coloring context

     69:   Level: advanced

     71: .seealso: `ISColoring`, `ISColoringView()`, `MatColoring`
     72: @*/
     73: PetscErrorCode ISColoringDestroy(ISColoring *iscoloring)
     74: {
     75:   PetscInt i;

     77:   PetscFunctionBegin;
     78:   if (!*iscoloring) PetscFunctionReturn(PETSC_SUCCESS);
     79:   PetscAssertPointer(*iscoloring, 1);
     80:   if (--(*iscoloring)->refct > 0) {
     81:     *iscoloring = NULL;
     82:     PetscFunctionReturn(PETSC_SUCCESS);
     83:   }

     85:   if ((*iscoloring)->is) {
     86:     for (i = 0; i < (*iscoloring)->n; i++) PetscCall(ISDestroy(&(*iscoloring)->is[i]));
     87:     PetscCall(PetscFree((*iscoloring)->is));
     88:   }
     89:   if ((*iscoloring)->allocated) PetscCall(PetscFree((*iscoloring)->colors));
     90:   PetscCall(PetscCommDestroy(&(*iscoloring)->comm));
     91:   PetscCall(PetscFree(*iscoloring));
     92:   PetscFunctionReturn(PETSC_SUCCESS);
     93: }

     95: /*@
     96:   ISColoringViewFromOptions - Processes command line options to determine if/how an `ISColoring` object is to be viewed.

     98:   Collective

    100:   Input Parameters:
    101: + obj        - the `ISColoring` object
    102: . bobj       - prefix to use for viewing, or `NULL` to use prefix of `mat`
    103: - optionname - option to activate viewing

    105:   Level: intermediate

    107:   Developer Notes:
    108:   This cannot use `PetscObjectViewFromOptions()` because `ISColoring` is not a `PetscObject`

    110: .seealso: `ISColoring`, `ISColoringView()`
    111: @*/
    112: PetscErrorCode ISColoringViewFromOptions(ISColoring obj, PetscObject bobj, const char optionname[])
    113: {
    114:   PetscViewer       viewer;
    115:   PetscBool         flg;
    116:   PetscViewerFormat format;
    117:   char             *prefix;

    119:   PetscFunctionBegin;
    120:   prefix = bobj ? bobj->prefix : NULL;
    121:   PetscCall(PetscOptionsCreateViewer(obj->comm, NULL, prefix, optionname, &viewer, &format, &flg));
    122:   if (flg) {
    123:     PetscCall(PetscViewerPushFormat(viewer, format));
    124:     PetscCall(ISColoringView(obj, viewer));
    125:     PetscCall(PetscViewerPopFormat(viewer));
    126:     PetscCall(PetscViewerDestroy(&viewer));
    127:   }
    128:   PetscFunctionReturn(PETSC_SUCCESS);
    129: }

    131: /*@
    132:   ISColoringView - Views an `ISColoring` coloring context.

    134:   Collective

    136:   Input Parameters:
    137: + iscoloring - the coloring context
    138: - viewer     - the viewer

    140:   Level: advanced

    142: .seealso: `ISColoring()`, `ISColoringViewFromOptions()`, `ISColoringDestroy()`, `ISColoringGetIS()`, `MatColoring`
    143: @*/
    144: PetscErrorCode ISColoringView(ISColoring iscoloring, PetscViewer viewer)
    145: {
    146:   PetscInt  i;
    147:   PetscBool iascii;
    148:   IS       *is;

    150:   PetscFunctionBegin;
    151:   PetscAssertPointer(iscoloring, 1);
    152:   if (!viewer) PetscCall(PetscViewerASCIIGetStdout(iscoloring->comm, &viewer));

    155:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
    156:   if (iascii) {
    157:     MPI_Comm    comm;
    158:     PetscMPIInt size, rank;

    160:     PetscCall(PetscObjectGetComm((PetscObject)viewer, &comm));
    161:     PetscCallMPI(MPI_Comm_size(comm, &size));
    162:     PetscCallMPI(MPI_Comm_rank(comm, &rank));
    163:     PetscCall(PetscViewerASCIIPrintf(viewer, "ISColoring Object: %d MPI processes\n", size));
    164:     PetscCall(PetscViewerASCIIPrintf(viewer, "ISColoringType: %s\n", ISColoringTypes[iscoloring->ctype]));
    165:     PetscCall(PetscViewerASCIIPushSynchronized(viewer));
    166:     PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] Number of colors %" PetscInt_FMT "\n", rank, iscoloring->n));
    167:     PetscCall(PetscViewerFlush(viewer));
    168:     PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    169:   }

    171:   PetscCall(ISColoringGetIS(iscoloring, PETSC_USE_POINTER, PETSC_IGNORE, &is));
    172:   for (i = 0; i < iscoloring->n; i++) PetscCall(ISView(iscoloring->is[i], viewer));
    173:   PetscCall(ISColoringRestoreIS(iscoloring, PETSC_USE_POINTER, &is));
    174:   PetscFunctionReturn(PETSC_SUCCESS);
    175: }

    177: /*@C
    178:   ISColoringGetColors - Returns an array with the color for each local node

    180:   Not Collective

    182:   Input Parameter:
    183: . iscoloring - the coloring context

    185:   Output Parameters:
    186: + n      - number of nodes
    187: . nc     - number of colors
    188: - colors - color for each node

    190:   Level: advanced

    192:   Notes:
    193:   Do not free the `colors` array.

    195:   The `colors` array will only be valid for the lifetime of the `ISColoring`

    197: .seealso: `ISColoring`, `ISColoringValue`, `ISColoringRestoreIS()`, `ISColoringView()`, `ISColoringGetIS()`
    198: @*/
    199: PetscErrorCode ISColoringGetColors(ISColoring iscoloring, PetscInt *n, PetscInt *nc, const ISColoringValue **colors)
    200: {
    201:   PetscFunctionBegin;
    202:   PetscAssertPointer(iscoloring, 1);

    204:   if (n) *n = iscoloring->N;
    205:   if (nc) *nc = iscoloring->n;
    206:   if (colors) *colors = iscoloring->colors;
    207:   PetscFunctionReturn(PETSC_SUCCESS);
    208: }

    210: /*@C
    211:   ISColoringGetIS - Extracts index sets from the coloring context. Each is contains the nodes of one color

    213:   Collective

    215:   Input Parameters:
    216: + iscoloring - the coloring context
    217: - mode       - if this value is `PETSC_OWN_POINTER` then the caller owns the pointer and must free the array of `IS` and each `IS` in the array

    219:   Output Parameters:
    220: + nn   - number of index sets in the coloring context
    221: - isis - array of index sets

    223:   Level: advanced

    225:   Note:
    226:   If mode is `PETSC_USE_POINTER` then `ISColoringRestoreIS()` must be called when the `IS` are no longer needed

    228: .seealso: `ISColoring`, `IS`, `ISColoringRestoreIS()`, `ISColoringView()`, `ISColoringGetColoring()`, `ISColoringGetColors()`
    229: @*/
    230: PetscErrorCode ISColoringGetIS(ISColoring iscoloring, PetscCopyMode mode, PetscInt *nn, IS *isis[])
    231: {
    232:   PetscFunctionBegin;
    233:   PetscAssertPointer(iscoloring, 1);

    235:   if (nn) *nn = iscoloring->n;
    236:   if (isis) {
    237:     if (!iscoloring->is) {
    238:       PetscInt        *mcolors, **ii, nc = iscoloring->n, i, base, n = iscoloring->N;
    239:       ISColoringValue *colors = iscoloring->colors;
    240:       IS              *is;

    242:       if (PetscDefined(USE_DEBUG)) {
    243:         for (i = 0; i < n; i++) PetscCheck(((PetscInt)colors[i]) < nc, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Coloring is our of range index %" PetscInt_FMT "value %d number colors %" PetscInt_FMT, i, (int)colors[i], nc);
    244:       }

    246:       /* generate the lists of nodes for each color */
    247:       PetscCall(PetscCalloc1(nc, &mcolors));
    248:       for (i = 0; i < n; i++) mcolors[colors[i]]++;

    250:       PetscCall(PetscMalloc1(nc, &ii));
    251:       PetscCall(PetscMalloc1(n, &ii[0]));
    252:       for (i = 1; i < nc; i++) ii[i] = ii[i - 1] + mcolors[i - 1];
    253:       PetscCall(PetscArrayzero(mcolors, nc));

    255:       if (iscoloring->ctype == IS_COLORING_GLOBAL) {
    256:         PetscCallMPI(MPI_Scan(&iscoloring->N, &base, 1, MPIU_INT, MPI_SUM, iscoloring->comm));
    257:         base -= iscoloring->N;
    258:         for (i = 0; i < n; i++) ii[colors[i]][mcolors[colors[i]]++] = i + base; /* global idx */
    259:       } else if (iscoloring->ctype == IS_COLORING_LOCAL) {
    260:         for (i = 0; i < n; i++) ii[colors[i]][mcolors[colors[i]]++] = i; /* local idx */
    261:       } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not provided for this ISColoringType type");

    263:       PetscCall(PetscMalloc1(nc, &is));
    264:       for (i = 0; i < nc; i++) PetscCall(ISCreateGeneral(iscoloring->comm, mcolors[i], ii[i], PETSC_COPY_VALUES, is + i));

    266:       if (mode != PETSC_OWN_POINTER) iscoloring->is = is;
    267:       *isis = is;
    268:       PetscCall(PetscFree(ii[0]));
    269:       PetscCall(PetscFree(ii));
    270:       PetscCall(PetscFree(mcolors));
    271:     } else {
    272:       *isis = iscoloring->is;
    273:       if (mode == PETSC_OWN_POINTER) iscoloring->is = NULL;
    274:     }
    275:   }
    276:   PetscFunctionReturn(PETSC_SUCCESS);
    277: }

    279: /*@C
    280:   ISColoringRestoreIS - Restores the index sets extracted from the coloring context with `ISColoringGetIS()` using `PETSC_USE_POINTER`

    282:   Collective

    284:   Input Parameters:
    285: + iscoloring - the coloring context
    286: . mode       - who retains ownership of the is
    287: - is         - array of index sets

    289:   Level: advanced

    291: .seealso: `ISColoring()`, `IS`, `ISColoringGetIS()`, `ISColoringView()`, `PetscCopyMode`
    292: @*/
    293: PetscErrorCode ISColoringRestoreIS(ISColoring iscoloring, PetscCopyMode mode, IS *is[])
    294: {
    295:   PetscFunctionBegin;
    296:   PetscAssertPointer(iscoloring, 1);

    298:   /* currently nothing is done here */
    299:   PetscFunctionReturn(PETSC_SUCCESS);
    300: }

    302: /*@
    303:   ISColoringCreate - Generates an `ISColoring` context from lists (provided by each MPI process) of colors for each node.

    305:   Collective

    307:   Input Parameters:
    308: + comm    - communicator for the processors creating the coloring
    309: . ncolors - max color value
    310: . n       - number of nodes on this processor
    311: . colors  - array containing the colors for this MPI rank, color numbers begin at 0, for each local node
    312: - mode    - see `PetscCopyMode` for meaning of this flag.

    314:   Output Parameter:
    315: . iscoloring - the resulting coloring data structure

    317:   Options Database Key:
    318: . -is_coloring_view - Activates `ISColoringView()`

    320:   Level: advanced

    322:   Notes:
    323:   By default sets coloring type to  `IS_COLORING_GLOBAL`

    325: .seealso: `ISColoring`, `ISColoringValue`, `MatColoringCreate()`, `ISColoringView()`, `ISColoringDestroy()`, `ISColoringSetType()`
    326: @*/
    327: PetscErrorCode ISColoringCreate(MPI_Comm comm, PetscInt ncolors, PetscInt n, const ISColoringValue colors[], PetscCopyMode mode, ISColoring *iscoloring)
    328: {
    329:   PetscMPIInt size, rank, tag;
    330:   PetscInt    base, top, i;
    331:   PetscInt    nc, ncwork;
    332:   MPI_Status  status;

    334:   PetscFunctionBegin;
    335:   if (ncolors != PETSC_DECIDE && ncolors > IS_COLORING_MAX) {
    336:     PetscCheck(ncolors <= PETSC_UINT16_MAX, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Max color value exceeds %d limit. This number is unrealistic. Perhaps a bug in code? Current max: %d user requested: %" PetscInt_FMT, PETSC_UINT16_MAX, PETSC_IS_COLORING_MAX, ncolors);
    337:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Max color value exceeds limit. Perhaps reconfigure PETSc with --with-is-color-value-type=short? Current max: %d user requested: %" PetscInt_FMT, PETSC_IS_COLORING_MAX, ncolors);
    338:   }
    339:   PetscCall(PetscNew(iscoloring));
    340:   PetscCall(PetscCommDuplicate(comm, &(*iscoloring)->comm, &tag));
    341:   comm = (*iscoloring)->comm;

    343:   /* compute the number of the first node on my processor */
    344:   PetscCallMPI(MPI_Comm_size(comm, &size));

    346:   /* should use MPI_Scan() */
    347:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    348:   if (rank == 0) {
    349:     base = 0;
    350:     top  = n;
    351:   } else {
    352:     PetscCallMPI(MPI_Recv(&base, 1, MPIU_INT, rank - 1, tag, comm, &status));
    353:     top = base + n;
    354:   }
    355:   if (rank < size - 1) PetscCallMPI(MPI_Send(&top, 1, MPIU_INT, rank + 1, tag, comm));

    357:   /* compute the total number of colors */
    358:   ncwork = 0;
    359:   for (i = 0; i < n; i++) {
    360:     if (ncwork < colors[i]) ncwork = colors[i];
    361:   }
    362:   ncwork++;
    363:   PetscCallMPI(MPIU_Allreduce(&ncwork, &nc, 1, MPIU_INT, MPI_MAX, comm));
    364:   PetscCheck(nc <= ncolors, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Number of colors passed in %" PetscInt_FMT " is less than the actual number of colors in array %" PetscInt_FMT, ncolors, nc);
    365:   (*iscoloring)->n     = nc;
    366:   (*iscoloring)->is    = NULL;
    367:   (*iscoloring)->N     = n;
    368:   (*iscoloring)->refct = 1;
    369:   (*iscoloring)->ctype = IS_COLORING_GLOBAL;
    370:   if (mode == PETSC_COPY_VALUES) {
    371:     PetscCall(PetscMalloc1(n, &(*iscoloring)->colors));
    372:     PetscCall(PetscArraycpy((*iscoloring)->colors, colors, n));
    373:     (*iscoloring)->allocated = PETSC_TRUE;
    374:   } else if (mode == PETSC_OWN_POINTER) {
    375:     (*iscoloring)->colors    = (ISColoringValue *)colors;
    376:     (*iscoloring)->allocated = PETSC_TRUE;
    377:   } else {
    378:     (*iscoloring)->colors    = (ISColoringValue *)colors;
    379:     (*iscoloring)->allocated = PETSC_FALSE;
    380:   }
    381:   PetscCall(ISColoringViewFromOptions(*iscoloring, NULL, "-is_coloring_view"));
    382:   PetscCall(PetscInfo(0, "Number of colors %" PetscInt_FMT "\n", nc));
    383:   PetscFunctionReturn(PETSC_SUCCESS);
    384: }

    386: /*@
    387:   ISBuildTwoSided - Takes an `IS` that describes where each element will be mapped globally over all ranks.
    388:   Generates an `IS` that contains new numbers from remote or local on the `IS`.

    390:   Collective

    392:   Input Parameters:
    393: + ito    - an `IS` describes to which rank each entry will be mapped. Negative target rank will be ignored
    394: - toindx - an `IS` describes what indices should send. `NULL` means sending natural numbering

    396:   Output Parameter:
    397: . rows - contains new numbers from remote or local

    399:   Level: advanced

    401:   Developer Notes:
    402:   This manual page is incomprehensible and still needs to be fixed

    404: .seealso: [](sec_scatter), `IS`, `MatPartitioningCreate()`, `ISPartitioningToNumbering()`, `ISPartitioningCount()`
    405: @*/
    406: PetscErrorCode ISBuildTwoSided(IS ito, IS toindx, IS *rows)
    407: {
    408:   const PetscInt *ito_indices, *toindx_indices;
    409:   PetscInt       *send_indices, rstart, *recv_indices, nrecvs, nsends;
    410:   PetscInt       *tosizes, *fromsizes, j, *tosizes_tmp, *tooffsets_tmp, ito_ln;
    411:   PetscMPIInt    *toranks, *fromranks, size, target_rank, *fromperm_newtoold, nto, nfrom;
    412:   PetscLayout     isrmap;
    413:   MPI_Comm        comm;
    414:   PetscSF         sf;
    415:   PetscSFNode    *iremote;

    417:   PetscFunctionBegin;
    418:   PetscCall(PetscObjectGetComm((PetscObject)ito, &comm));
    419:   PetscCallMPI(MPI_Comm_size(comm, &size));
    420:   PetscCall(ISGetLocalSize(ito, &ito_ln));
    421:   PetscCall(ISGetLayout(ito, &isrmap));
    422:   PetscCall(PetscLayoutGetRange(isrmap, &rstart, NULL));
    423:   PetscCall(ISGetIndices(ito, &ito_indices));
    424:   PetscCall(PetscCalloc2(size, &tosizes_tmp, size + 1, &tooffsets_tmp));
    425:   for (PetscInt i = 0; i < ito_ln; i++) {
    426:     if (ito_indices[i] < 0) continue;
    427:     else PetscCheck(ito_indices[i] < size, comm, PETSC_ERR_ARG_OUTOFRANGE, "target rank %" PetscInt_FMT " is larger than communicator size %d ", ito_indices[i], size);
    428:     tosizes_tmp[ito_indices[i]]++;
    429:   }
    430:   nto = 0;
    431:   for (PetscMPIInt i = 0; i < size; i++) {
    432:     tooffsets_tmp[i + 1] = tooffsets_tmp[i] + tosizes_tmp[i];
    433:     if (tosizes_tmp[i] > 0) nto++;
    434:   }
    435:   PetscCall(PetscCalloc2(nto, &toranks, 2 * nto, &tosizes));
    436:   nto = 0;
    437:   for (PetscMPIInt i = 0; i < size; i++) {
    438:     if (tosizes_tmp[i] > 0) {
    439:       toranks[nto]         = i;
    440:       tosizes[2 * nto]     = tosizes_tmp[i];   /* size */
    441:       tosizes[2 * nto + 1] = tooffsets_tmp[i]; /* offset */
    442:       nto++;
    443:     }
    444:   }
    445:   nsends = tooffsets_tmp[size];
    446:   PetscCall(PetscCalloc1(nsends, &send_indices));
    447:   if (toindx) PetscCall(ISGetIndices(toindx, &toindx_indices));
    448:   for (PetscInt i = 0; i < ito_ln; i++) {
    449:     if (ito_indices[i] < 0) continue;
    450:     PetscCall(PetscMPIIntCast(ito_indices[i], &target_rank));
    451:     send_indices[tooffsets_tmp[target_rank]] = toindx ? toindx_indices[i] : (i + rstart);
    452:     tooffsets_tmp[target_rank]++;
    453:   }
    454:   if (toindx) PetscCall(ISRestoreIndices(toindx, &toindx_indices));
    455:   PetscCall(ISRestoreIndices(ito, &ito_indices));
    456:   PetscCall(PetscFree2(tosizes_tmp, tooffsets_tmp));
    457:   PetscCall(PetscCommBuildTwoSided(comm, 2, MPIU_INT, nto, toranks, tosizes, &nfrom, &fromranks, &fromsizes));
    458:   PetscCall(PetscFree2(toranks, tosizes));
    459:   PetscCall(PetscMalloc1(nfrom, &fromperm_newtoold));
    460:   for (PetscMPIInt i = 0; i < nfrom; i++) fromperm_newtoold[i] = i;
    461:   PetscCall(PetscSortMPIIntWithArray(nfrom, fromranks, fromperm_newtoold));
    462:   nrecvs = 0;
    463:   for (PetscMPIInt i = 0; i < nfrom; i++) nrecvs += fromsizes[i * 2];
    464:   PetscCall(PetscCalloc1(nrecvs, &recv_indices));
    465:   PetscCall(PetscMalloc1(nrecvs, &iremote));
    466:   nrecvs = 0;
    467:   for (PetscMPIInt i = 0; i < nfrom; i++) {
    468:     for (j = 0; j < fromsizes[2 * fromperm_newtoold[i]]; j++) {
    469:       iremote[nrecvs].rank    = fromranks[i];
    470:       iremote[nrecvs++].index = fromsizes[2 * fromperm_newtoold[i] + 1] + j;
    471:     }
    472:   }
    473:   PetscCall(PetscSFCreate(comm, &sf));
    474:   PetscCall(PetscSFSetGraph(sf, nsends, nrecvs, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    475:   PetscCall(PetscSFSetType(sf, PETSCSFBASIC));
    476:   /* how to put a prefix ? */
    477:   PetscCall(PetscSFSetFromOptions(sf));
    478:   PetscCall(PetscSFBcastBegin(sf, MPIU_INT, send_indices, recv_indices, MPI_REPLACE));
    479:   PetscCall(PetscSFBcastEnd(sf, MPIU_INT, send_indices, recv_indices, MPI_REPLACE));
    480:   PetscCall(PetscSFDestroy(&sf));
    481:   PetscCall(PetscFree(fromranks));
    482:   PetscCall(PetscFree(fromsizes));
    483:   PetscCall(PetscFree(fromperm_newtoold));
    484:   PetscCall(PetscFree(send_indices));
    485:   if (rows) {
    486:     PetscCall(PetscSortInt(nrecvs, recv_indices));
    487:     PetscCall(ISCreateGeneral(comm, nrecvs, recv_indices, PETSC_OWN_POINTER, rows));
    488:   } else {
    489:     PetscCall(PetscFree(recv_indices));
    490:   }
    491:   PetscFunctionReturn(PETSC_SUCCESS);
    492: }

    494: /*@
    495:   ISPartitioningToNumbering - Takes an `IS' that represents a partitioning (the MPI rank that each local entry belongs to) and on each MPI process
    496:   generates an `IS` that contains a new global node number in the new ordering for each entry

    498:   Collective

    500:   Input Parameter:
    501: . part - a partitioning as generated by `MatPartitioningApply()` or `MatPartitioningApplyND()`

    503:   Output Parameter:
    504: . is - on each processor the index set that defines the global numbers
    505:          (in the new numbering) for all the nodes currently (before the partitioning)
    506:          on that processor

    508:   Level: advanced

    510:   Note:
    511:   The resulting `IS` tells where each local entry is mapped to in a new global ordering

    513: .seealso: [](sec_scatter), `IS`, `MatPartitioningCreate()`, `AOCreateBasic()`, `ISPartitioningCount()`
    514: @*/
    515: PetscErrorCode ISPartitioningToNumbering(IS part, IS *is)
    516: {
    517:   MPI_Comm        comm;
    518:   IS              ndorder;
    519:   PetscInt        n, *starts = NULL, *sums = NULL, *lsizes = NULL, *newi = NULL;
    520:   const PetscInt *indices = NULL;
    521:   PetscMPIInt     np, npt;

    523:   PetscFunctionBegin;
    525:   PetscAssertPointer(is, 2);
    526:   /* see if the partitioning comes from nested dissection */
    527:   PetscCall(PetscObjectQuery((PetscObject)part, "_petsc_matpartitioning_ndorder", (PetscObject *)&ndorder));
    528:   if (ndorder) {
    529:     PetscCall(PetscObjectReference((PetscObject)ndorder));
    530:     *is = ndorder;
    531:     PetscFunctionReturn(PETSC_SUCCESS);
    532:   }

    534:   PetscCall(PetscObjectGetComm((PetscObject)part, &comm));
    535:   /* count the number of partitions, i.e., virtual processors */
    536:   PetscCall(ISGetLocalSize(part, &n));
    537:   PetscCall(ISGetIndices(part, &indices));
    538:   np = 0;
    539:   for (PetscInt i = 0; i < n; i++) PetscCall(PetscMPIIntCast(PetscMax(np, indices[i]), &np));
    540:   PetscCallMPI(MPIU_Allreduce(&np, &npt, 1, MPI_INT, MPI_MAX, comm));
    541:   np = npt + 1; /* so that it looks like a MPI_Comm_size output */

    543:   /*
    544:      lsizes - number of elements of each partition on this particular processor
    545:      sums - total number of "previous" nodes for any particular partition
    546:      starts - global number of first element in each partition on this processor
    547:   */
    548:   PetscCall(PetscMalloc3(np, &lsizes, np, &starts, np, &sums));
    549:   PetscCall(PetscArrayzero(lsizes, np));
    550:   for (PetscInt i = 0; i < n; i++) lsizes[indices[i]]++;
    551:   PetscCallMPI(MPIU_Allreduce(lsizes, sums, np, MPIU_INT, MPI_SUM, comm));
    552:   PetscCallMPI(MPI_Scan(lsizes, starts, np, MPIU_INT, MPI_SUM, comm));
    553:   for (PetscMPIInt i = 0; i < np; i++) starts[i] -= lsizes[i];
    554:   for (PetscMPIInt i = 1; i < np; i++) {
    555:     sums[i] += sums[i - 1];
    556:     starts[i] += sums[i - 1];
    557:   }

    559:   /*
    560:       For each local index give it the new global number
    561:   */
    562:   PetscCall(PetscMalloc1(n, &newi));
    563:   for (PetscInt i = 0; i < n; i++) newi[i] = starts[indices[i]]++;
    564:   PetscCall(PetscFree3(lsizes, starts, sums));

    566:   PetscCall(ISRestoreIndices(part, &indices));
    567:   PetscCall(ISCreateGeneral(comm, n, newi, PETSC_OWN_POINTER, is));
    568:   PetscCall(ISSetPermutation(*is));
    569:   PetscFunctionReturn(PETSC_SUCCESS);
    570: }

    572: /*@
    573:   ISPartitioningCount - Takes a `IS` that represents a partitioning (the MPI rank that each local entry belongs to) and determines the number of
    574:   resulting elements on each (partition) rank

    576:   Collective

    578:   Input Parameters:
    579: + part - a partitioning as generated by `MatPartitioningApply()` or `MatPartitioningApplyND()`
    580: - len  - length of the array count, this is the total number of partitions

    582:   Output Parameter:
    583: . count - array of length size, to contain the number of elements assigned
    584:         to each partition, where size is the number of partitions generated
    585:          (see notes below).

    587:   Level: advanced

    589:   Notes:
    590:   By default the number of partitions generated (and thus the length
    591:   of count) is the size of the communicator associated with `IS`,
    592:   but it can be set by `MatPartitioningSetNParts()`.

    594:   The resulting array of lengths can for instance serve as input of `PCBJacobiSetTotalBlocks()`.

    596:   If the partitioning has been obtained by `MatPartitioningApplyND()`, the returned count does not include the separators.

    598: .seealso: [](sec_scatter), `IS`, `MatPartitioningCreate()`, `AOCreateBasic()`, `ISPartitioningToNumbering()`,
    599:           `MatPartitioningSetNParts()`, `MatPartitioningApply()`, `MatPartitioningApplyND()`
    600: @*/
    601: PetscErrorCode ISPartitioningCount(IS part, PetscInt len, PetscInt count[])
    602: {
    603:   MPI_Comm        comm;
    604:   PetscInt        i, n, *lsizes;
    605:   const PetscInt *indices;

    607:   PetscFunctionBegin;
    608:   PetscCall(PetscObjectGetComm((PetscObject)part, &comm));
    609:   if (len == PETSC_DEFAULT) {
    610:     PetscMPIInt size;

    612:     PetscCallMPI(MPI_Comm_size(comm, &size));
    613:     len = size;
    614:   }

    616:   /* count the number of partitions */
    617:   PetscCall(ISGetLocalSize(part, &n));
    618:   PetscCall(ISGetIndices(part, &indices));
    619:   if (PetscDefined(USE_DEBUG)) {
    620:     PetscInt np = 0, npt;
    621:     for (i = 0; i < n; i++) np = PetscMax(np, indices[i]);
    622:     PetscCallMPI(MPIU_Allreduce(&np, &npt, 1, MPIU_INT, MPI_MAX, comm));
    623:     np = npt + 1; /* so that it looks like a MPI_Comm_size output */
    624:     PetscCheck(np <= len, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Length of count array %" PetscInt_FMT " is less than number of partitions %" PetscInt_FMT, len, np);
    625:   }

    627:   /*
    628:         lsizes - number of elements of each partition on this particular processor
    629:         sums - total number of "previous" nodes for any particular partition
    630:         starts - global number of first element in each partition on this processor
    631:   */
    632:   PetscCall(PetscCalloc1(len, &lsizes));
    633:   for (i = 0; i < n; i++) {
    634:     if (indices[i] > -1) lsizes[indices[i]]++;
    635:   }
    636:   PetscCall(ISRestoreIndices(part, &indices));
    637:   PetscCallMPI(MPIU_Allreduce(lsizes, count, len, MPIU_INT, MPI_SUM, comm));
    638:   PetscCall(PetscFree(lsizes));
    639:   PetscFunctionReturn(PETSC_SUCCESS);
    640: }

    642: /*@
    643:   ISAllGather - Given an index set `IS` on each processor, generates a large
    644:   index set (same on each processor) by concatenating together each
    645:   processors index set.

    647:   Collective

    649:   Input Parameter:
    650: . is - the distributed index set

    652:   Output Parameter:
    653: . isout - the concatenated index set (same on all processors)

    655:   Level: intermediate

    657:   Notes:
    658:   `ISAllGather()` is clearly not scalable for large index sets.

    660:   The `IS` created on each processor must be created with a common
    661:   communicator (e.g., `PETSC_COMM_WORLD`). If the index sets were created
    662:   with `PETSC_COMM_SELF`, this routine will not work as expected, since
    663:   each process will generate its own new `IS` that consists only of
    664:   itself.

    666:   The communicator for this new `IS` is `PETSC_COMM_SELF`

    668: .seealso: [](sec_scatter), `IS`, `ISCreateGeneral()`, `ISCreateStride()`, `ISCreateBlock()`
    669: @*/
    670: PetscErrorCode ISAllGather(IS is, IS *isout)
    671: {
    672:   PetscInt       *indices, n, i, N, step, first;
    673:   const PetscInt *lindices;
    674:   MPI_Comm        comm;
    675:   PetscMPIInt     size, *sizes = NULL, *offsets = NULL, nn;
    676:   PetscBool       stride;

    678:   PetscFunctionBegin;
    680:   PetscAssertPointer(isout, 2);

    682:   PetscCall(PetscObjectGetComm((PetscObject)is, &comm));
    683:   PetscCallMPI(MPI_Comm_size(comm, &size));
    684:   PetscCall(ISGetLocalSize(is, &n));
    685:   PetscCall(PetscObjectTypeCompare((PetscObject)is, ISSTRIDE, &stride));
    686:   if (size == 1 && stride) { /* should handle parallel ISStride also */
    687:     PetscCall(ISStrideGetInfo(is, &first, &step));
    688:     PetscCall(ISCreateStride(PETSC_COMM_SELF, n, first, step, isout));
    689:   } else {
    690:     PetscCall(PetscMalloc2(size, &sizes, size, &offsets));

    692:     PetscCall(PetscMPIIntCast(n, &nn));
    693:     PetscCallMPI(MPI_Allgather(&nn, 1, MPI_INT, sizes, 1, MPI_INT, comm));
    694:     offsets[0] = 0;
    695:     for (i = 1; i < size; i++) {
    696:       PetscInt s = offsets[i - 1] + sizes[i - 1];
    697:       PetscCall(PetscMPIIntCast(s, &offsets[i]));
    698:     }
    699:     N = offsets[size - 1] + sizes[size - 1];

    701:     PetscCall(PetscMalloc1(N, &indices));
    702:     PetscCall(ISGetIndices(is, &lindices));
    703:     PetscCallMPI(MPI_Allgatherv((void *)lindices, nn, MPIU_INT, indices, sizes, offsets, MPIU_INT, comm));
    704:     PetscCall(ISRestoreIndices(is, &lindices));
    705:     PetscCall(PetscFree2(sizes, offsets));

    707:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, N, indices, PETSC_OWN_POINTER, isout));
    708:   }
    709:   PetscFunctionReturn(PETSC_SUCCESS);
    710: }

    712: /*@C
    713:   ISAllGatherColors - Given a set of colors on each processor, generates a large
    714:   set (same on each processor) by concatenating together each processors colors

    716:   Collective

    718:   Input Parameters:
    719: + comm     - communicator to share the indices
    720: . n        - local size of set
    721: - lindices - local colors

    723:   Output Parameters:
    724: + outN       - total number of indices
    725: - outindices - all of the colors

    727:   Level: intermediate

    729:   Note:
    730:   `ISAllGatherColors()` is clearly not scalable for large index sets.

    732: .seealso: `ISColoringValue`, `ISColoring()`, `ISCreateGeneral()`, `ISCreateStride()`, `ISCreateBlock()`, `ISAllGather()`
    733: @*/
    734: PetscErrorCode ISAllGatherColors(MPI_Comm comm, PetscInt n, ISColoringValue lindices[], PetscInt *outN, ISColoringValue *outindices[])
    735: {
    736:   ISColoringValue *indices;
    737:   PetscInt         N;
    738:   PetscMPIInt      size, *offsets = NULL, *sizes = NULL, nn;

    740:   PetscFunctionBegin;
    741:   PetscCall(PetscMPIIntCast(n, &nn));
    742:   PetscCallMPI(MPI_Comm_size(comm, &size));
    743:   PetscCall(PetscMalloc2(size, &sizes, size, &offsets));

    745:   PetscCallMPI(MPI_Allgather(&nn, 1, MPI_INT, sizes, 1, MPI_INT, comm));
    746:   offsets[0] = 0;
    747:   for (PetscMPIInt i = 1; i < size; i++) offsets[i] = offsets[i - 1] + sizes[i - 1];
    748:   N = offsets[size - 1] + sizes[size - 1];
    749:   PetscCall(PetscFree2(sizes, offsets));

    751:   PetscCall(PetscMalloc1(N + 1, &indices));
    752:   PetscCallMPI(MPI_Allgatherv(lindices, nn, MPIU_COLORING_VALUE, indices, sizes, offsets, MPIU_COLORING_VALUE, comm));

    754:   *outindices = indices;
    755:   if (outN) *outN = N;
    756:   PetscFunctionReturn(PETSC_SUCCESS);
    757: }

    759: /*@
    760:   ISComplement - Given an index set `IS` generates the complement index set. That is
    761:   all indices that are NOT in the given set.

    763:   Collective

    765:   Input Parameters:
    766: + is   - the index set
    767: . nmin - the first index desired in the local part of the complement
    768: - nmax - the largest index desired in the local part of the complement (note that all indices in `is` must be greater or equal to `nmin` and less than `nmax`)

    770:   Output Parameter:
    771: . isout - the complement

    773:   Level: intermediate

    775:   Notes:
    776:   The communicator for `isout` is the same as for the input `is`

    778:   For a parallel `is`, this will generate the local part of the complement on each process

    780:   To generate the entire complement (on each process) of a parallel `is`, first call `ISAllGather()` and then
    781:   call this routine.

    783: .seealso: [](sec_scatter), `IS`, `ISCreateGeneral()`, `ISCreateStride()`, `ISCreateBlock()`, `ISAllGather()`
    784: @*/
    785: PetscErrorCode ISComplement(IS is, PetscInt nmin, PetscInt nmax, IS *isout)
    786: {
    787:   const PetscInt *indices;
    788:   PetscInt        n, i, j, unique, cnt, *nindices;
    789:   PetscBool       sorted;

    791:   PetscFunctionBegin;
    793:   PetscAssertPointer(isout, 4);
    794:   PetscCheck(nmin >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "nmin %" PetscInt_FMT " cannot be negative", nmin);
    795:   PetscCheck(nmin <= nmax, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "nmin %" PetscInt_FMT " cannot be greater than nmax %" PetscInt_FMT, nmin, nmax);
    796:   PetscCall(ISSorted(is, &sorted));
    797:   PetscCheck(sorted, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Index set must be sorted");

    799:   PetscCall(ISGetLocalSize(is, &n));
    800:   PetscCall(ISGetIndices(is, &indices));
    801:   if (PetscDefined(USE_DEBUG)) {
    802:     for (i = 0; i < n; i++) {
    803:       PetscCheck(indices[i] >= nmin, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Index %" PetscInt_FMT "'s value %" PetscInt_FMT " is smaller than minimum given %" PetscInt_FMT, i, indices[i], nmin);
    804:       PetscCheck(indices[i] < nmax, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Index %" PetscInt_FMT "'s value %" PetscInt_FMT " is larger than maximum given %" PetscInt_FMT, i, indices[i], nmax);
    805:     }
    806:   }
    807:   /* Count number of unique entries */
    808:   unique = (n > 0);
    809:   for (i = 0; i < n - 1; i++) {
    810:     if (indices[i + 1] != indices[i]) unique++;
    811:   }
    812:   PetscCall(PetscMalloc1(nmax - nmin - unique, &nindices));
    813:   cnt = 0;
    814:   for (i = nmin, j = 0; i < nmax; i++) {
    815:     if (j < n && i == indices[j]) do {
    816:         j++;
    817:       } while (j < n && i == indices[j]);
    818:     else nindices[cnt++] = i;
    819:   }
    820:   PetscCheck(cnt == nmax - nmin - unique, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of entries found in complement %" PetscInt_FMT " does not match expected %" PetscInt_FMT, cnt, nmax - nmin - unique);
    821:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)is), cnt, nindices, PETSC_OWN_POINTER, isout));
    822:   PetscCall(ISSetInfo(*isout, IS_SORTED, IS_GLOBAL, PETSC_FALSE, PETSC_TRUE));
    823:   PetscCall(ISRestoreIndices(is, &indices));
    824:   PetscFunctionReturn(PETSC_SUCCESS);
    825: }