Date: 2022-03-04T17:38:19+00:00

Actual source code: hierarchical.c

      2: #include <../src/mat/impls/adj/mpi/mpiadj.h>
      3: #include <petscsf.h>
      4: #include <petsc/private/matimpl.h>

      6: /*
      7:   It is a hierarchical partitioning. The partitioner has two goals:
      8:   (1) Most of current partitioners fail at a large scale. The hierarchical partitioning
      9:   strategy is trying to produce large number of subdomains when number of processor cores is large.
     10:   (2) PCGASM needs one 'big' subdomain across multi-cores. The partitioner provides two
     11:   consistent partitions, coarse parts and fine parts. A coarse part is a 'big' subdomain consisting
     12:   of several small subdomains.
     13: */

     15: PetscErrorCode MatPartitioningHierarchical_DetermineDestination(MatPartitioning,IS,PetscInt,PetscInt,IS*);
     16: PetscErrorCode MatPartitioningHierarchical_AssembleSubdomain(Mat,IS,IS,IS*,Mat*,ISLocalToGlobalMapping*);
     17: PetscErrorCode MatPartitioningHierarchical_ReassembleFineparts(Mat,IS,ISLocalToGlobalMapping,IS*);

     19: typedef struct {
     20:   char*                fineparttype; /* partitioner on fine level */
     21:   char*                coarseparttype; /* partitioner on coarse level */
     22:   PetscInt             nfineparts; /* number of fine parts on each coarse subdomain */
     23:   PetscInt             ncoarseparts; /* number of coarse parts */
     24:   IS                   coarseparts; /* partitioning on coarse level */
     25:   IS                   fineparts; /* partitioning on fine level */
     26:   MatPartitioning      coarseMatPart; /* MatPartititioning on coarse level (first level) */
     27:   MatPartitioning      fineMatPart; /* MatPartitioning on fine level (second level) */
     28:   MatPartitioning      improver; /* Improve the quality of a partition */
     29: } MatPartitioning_Hierarchical;

     31: /*
     32:    Uses a hierarchical partitioning strategy to partition the matrix in parallel.
     33:    Use this interface to make the partitioner consistent with others
     34: */
     35: static PetscErrorCode MatPartitioningApply_Hierarchical(MatPartitioning part,IS *partitioning)
     36: {
     37:   MatPartitioning_Hierarchical *hpart  = (MatPartitioning_Hierarchical*)part->data;
     38:   const PetscInt               *fineparts_indices, *coarseparts_indices;
     39:   PetscInt                     *fineparts_indices_tmp;
     40:   PetscInt                     *parts_indices,i,j,mat_localsize, *offsets;
     41:   Mat                           mat    = part->adj,adj,sadj;
     42:   PetscReal                    *part_weights;
     43:   PetscBool                     flg;
     44:   PetscInt                      bs     = 1;
     45:   PetscInt                     *coarse_vertex_weights = NULL;
     46:   PetscMPIInt                   size,rank;
     47:   MPI_Comm                      comm,scomm;
     48:   IS                            destination,fineparts_temp, vweights, svweights;
     49:   PetscInt                      nsvwegihts,*fp_vweights;
     50:   const PetscInt                *svweights_indices;
     51:   ISLocalToGlobalMapping        mapping;
     52:   const char                    *prefix;
     53:   PetscBool                     use_edge_weights;
     54:   PetscErrorCode                ierr;

     57:   PetscObjectGetComm((PetscObject)part,&comm);
     58:   MPI_Comm_size(comm,&size);
     59:   MPI_Comm_rank(comm,&rank);
     60:   PetscObjectTypeCompare((PetscObject)mat,MATMPIADJ,&flg);
     61:   if (flg) {
     62:     adj = mat;
     63:     PetscObjectReference((PetscObject)adj);
     64:   }else {
     65:     /* bs indicates if the converted matrix is "reduced" from the original and hence the
     66:        resulting partition results need to be stretched to match the original matrix */
     67:    MatConvert(mat,MATMPIADJ,MAT_INITIAL_MATRIX,&adj);
     68:    if (adj->rmap->n > 0) bs = mat->rmap->n/adj->rmap->n;
     69:   }
     70:   /* local size of mat */
     71:   mat_localsize = adj->rmap->n;
     72:   /* check parameters */
     73:   /* how many small subdomains we want from a given 'big' suddomain */
     74:   if (!hpart->nfineparts) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG," must set number of small subdomains for each big subdomain \n");
     75:   if (!hpart->ncoarseparts && !part->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE," did not either set number of coarse parts or total number of parts \n");

     77:   /* Partitioning the domain into one single subdomain is a trivial case, and we should just return  */
     78:   if (part->n==1) {
     79:     PetscCalloc1(bs*adj->rmap->n,&parts_indices);
     80:     ISCreateGeneral(comm,bs*adj->rmap->n,parts_indices,PETSC_OWN_POINTER,partitioning);
     81:     hpart->ncoarseparts = 1;
     82:     hpart->nfineparts = 1;
     83:     PetscStrallocpy("NONE",&hpart->coarseparttype);
     84:     PetscStrallocpy("NONE",&hpart->fineparttype);
     85:     MatDestroy(&adj);
     86:     return(0);
     87:   }

     89:   if (part->n) {
     90:     hpart->ncoarseparts = part->n/hpart->nfineparts;

     92:     if (part->n%hpart->nfineparts != 0) hpart->ncoarseparts++;
     93:   }else{
     94:     part->n = hpart->ncoarseparts*hpart->nfineparts;
     95:   }

     97:   PetscMalloc1(hpart->ncoarseparts+1, &offsets);
     98:   PetscMalloc1(hpart->ncoarseparts, &part_weights);

    100:   offsets[0] = 0;
    101:   if (part->n%hpart->nfineparts != 0) offsets[1] = part->n%hpart->nfineparts;
    102:   else offsets[1] = hpart->nfineparts;

    104:   part_weights[0] = ((PetscReal)offsets[1])/part->n;

    106:   for (i=2; i<=hpart->ncoarseparts; i++) {
    107:     offsets[i] = hpart->nfineparts;
    108:     part_weights[i-1] = ((PetscReal)offsets[i])/part->n;
    109:   }

    111:   offsets[0] = 0;
    112:   for (i=1;i<=hpart->ncoarseparts; i++)
    113:     offsets[i] += offsets[i-1];

    115:   /* If these exists a mat partitioner, we should delete it */
    116:   MatPartitioningDestroy(&hpart->coarseMatPart);
    117:   MatPartitioningCreate(comm,&hpart->coarseMatPart);
    118:   PetscObjectGetOptionsPrefix((PetscObject)part,&prefix);
    119:   PetscObjectSetOptionsPrefix((PetscObject)hpart->coarseMatPart,prefix);
    120:   PetscObjectAppendOptionsPrefix((PetscObject)hpart->coarseMatPart,"hierarch_coarse_");
    121:     /* if did not set partitioning type yet, use parmetis by default */
    122:   if (!hpart->coarseparttype) {
    123: #if defined(PETSC_HAVE_PARMETIS)
    124:     MatPartitioningSetType(hpart->coarseMatPart,MATPARTITIONINGPARMETIS);
    125:     PetscStrallocpy(MATPARTITIONINGPARMETIS,&hpart->coarseparttype);
    126: #elif defined(PETSC_HAVE_PTSCOTCH)
    127:     MatPartitioningSetType(hpart->coarseMatPart,MATPARTITIONINGPTSCOTCH);
    128:     PetscStrallocpy(MATPARTITIONINGPTSCOTCH,&hpart->coarseparttype);
    129: #else
    130:     SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Requires PETSc be installed with ParMetis or run with -mat_partitioning_hierarchical_coarseparttype partitiontype");
    131: #endif
    132:   } else {
    133:     MatPartitioningSetType(hpart->coarseMatPart,hpart->coarseparttype);
    134:   }
    135:   MatPartitioningSetAdjacency(hpart->coarseMatPart,adj);
    136:   MatPartitioningSetNParts(hpart->coarseMatPart, hpart->ncoarseparts);
    137:   /* copy over vertex weights */
    138:   if (part->vertex_weights) {
    139:     PetscMalloc1(mat_localsize,&coarse_vertex_weights);
    140:     PetscArraycpy(coarse_vertex_weights,part->vertex_weights,mat_localsize);
    141:     MatPartitioningSetVertexWeights(hpart->coarseMatPart,coarse_vertex_weights);
    142:   }
    143:   /* Copy use_edge_weights flag from part to coarse part */
    144:   MatPartitioningGetUseEdgeWeights(part,&use_edge_weights);
    145:   MatPartitioningSetUseEdgeWeights(hpart->coarseMatPart,use_edge_weights);

    147:   MatPartitioningSetPartitionWeights(hpart->coarseMatPart, part_weights);
    148:   MatPartitioningApply(hpart->coarseMatPart,&hpart->coarseparts);

    150:   /* Wrap the original vertex weights into an index set so that we can extract the corresponding
    151:    * vertex weights for each big subdomain using ISCreateSubIS().
    152:    * */
    153:   if (part->vertex_weights) {
    154:     ISCreateGeneral(comm,mat_localsize,part->vertex_weights,PETSC_COPY_VALUES,&vweights);
    155:   }

    157:   PetscCalloc1(mat_localsize, &fineparts_indices_tmp);
    158:   for (i=0; i<hpart->ncoarseparts; i+=size) {
    159:     /* Determine where we want to send big subdomains */
    160:     MatPartitioningHierarchical_DetermineDestination(part,hpart->coarseparts,i,i+size,&destination);
    161:     /* Assemble a submatrix and its vertex weights for partitioning subdomains  */
    162:     MatPartitioningHierarchical_AssembleSubdomain(adj,part->vertex_weights? vweights:NULL,destination,part->vertex_weights? &svweights:NULL,&sadj,&mapping);
    163:     /* We have to create a new array to hold vertex weights since coarse partitioner needs to own the vertex-weights array */
    164:     if (part->vertex_weights) {
    165:       ISGetLocalSize(svweights,&nsvwegihts);
    166:       PetscMalloc1(nsvwegihts,&fp_vweights);
    167:       ISGetIndices(svweights,&svweights_indices);
    168:       PetscArraycpy(fp_vweights,svweights_indices,nsvwegihts);
    169:       ISRestoreIndices(svweights,&svweights_indices);
    170:       ISDestroy(&svweights);
    171:     }

    173:     ISDestroy(&destination);
    174:     PetscObjectGetComm((PetscObject)sadj,&scomm);

    176:     /*
    177:      * If the number of big subdomains is smaller than the number of processor cores, the higher ranks do not
    178:      * need to do partitioning
    179:      * */
    180:     if ((i+rank)<hpart->ncoarseparts) {
    181:       MatPartitioningDestroy(&hpart->fineMatPart);
    182:       /* create a fine partitioner */
    183:       MatPartitioningCreate(scomm,&hpart->fineMatPart);
    184:       PetscObjectSetOptionsPrefix((PetscObject)hpart->fineMatPart,prefix);
    185:       PetscObjectAppendOptionsPrefix((PetscObject)hpart->fineMatPart,"hierarch_fine_");
    186:       /* if do not set partitioning type, use parmetis by default */
    187:       if (!hpart->fineparttype) {
    188: #if defined(PETSC_HAVE_PARMETIS)
    189:         MatPartitioningSetType(hpart->fineMatPart,MATPARTITIONINGPARMETIS);
    190:         PetscStrallocpy(MATPARTITIONINGPARMETIS,&hpart->fineparttype);
    191: #elif defined(PETSC_HAVE_PTSCOTCH)
    192:         MatPartitioningSetType(hpart->fineMatPart,MATPARTITIONINGPTSCOTCH);
    193:         PetscStrallocpy(MATPARTITIONINGPTSCOTCH,&hpart->fineparttype);
    194: #elif defined(PETSC_HAVE_CHACO)
    195:         MatPartitioningSetType(hpart->fineMatPart,MATPARTITIONINGCHACO);
    196:         PetscStrallocpy(MATPARTITIONINGCHACO,&hpart->fineparttype);
    197: #elif defined(PETSC_HAVE_PARTY)
    198:         MatPartitioningSetType(hpart->fineMatPart,MATPARTITIONINGPARTY);
    199:         PetscStrallocpy(PETSC_HAVE_PARTY,&hpart->fineparttype);
    200: #else
    201:         SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Requires PETSc be installed with ParMetis or run with -mat_partitioning_hierarchical_coarseparttype partitiontype");
    202: #endif
    203:       } else {
    204:         MatPartitioningSetType(hpart->fineMatPart,hpart->fineparttype);
    205:       }
    206:       MatPartitioningSetUseEdgeWeights(hpart->fineMatPart,use_edge_weights);
    207:       MatPartitioningSetAdjacency(hpart->fineMatPart,sadj);
    208:       MatPartitioningSetNParts(hpart->fineMatPart, offsets[rank+1+i]-offsets[rank+i]);
    209:       if (part->vertex_weights) {
    210:         MatPartitioningSetVertexWeights(hpart->fineMatPart,fp_vweights);
    211:       }
    212:       MatPartitioningApply(hpart->fineMatPart,&fineparts_temp);
    213:     } else {
    214:       ISCreateGeneral(scomm,0,NULL,PETSC_OWN_POINTER,&fineparts_temp);
    215:     }

    217:     MatDestroy(&sadj);

    219:     /* Send partition back to the original owners */
    220:     MatPartitioningHierarchical_ReassembleFineparts(adj,fineparts_temp,mapping,&hpart->fineparts);
    221:     ISGetIndices(hpart->fineparts,&fineparts_indices);
    222:     for (j=0;j<mat_localsize;j++)
    223:       if (fineparts_indices[j] >=0) fineparts_indices_tmp[j] = fineparts_indices[j];

    225:     ISRestoreIndices(hpart->fineparts,&fineparts_indices);
    226:     ISDestroy(&hpart->fineparts);
    227:     ISDestroy(&fineparts_temp);
    228:     ISLocalToGlobalMappingDestroy(&mapping);
    229:   }

    231:   if (part->vertex_weights) {
    232:     ISDestroy(&vweights);
    233:   }

    235:   ISCreateGeneral(comm,mat_localsize,fineparts_indices_tmp,PETSC_OWN_POINTER,&hpart->fineparts);
    236:   ISGetIndices(hpart->fineparts,&fineparts_indices);
    237:   ISGetIndices(hpart->coarseparts,&coarseparts_indices);
    238:   PetscMalloc1(bs*adj->rmap->n,&parts_indices);
    239:   /* Modify the local indices to the global indices by combing the coarse partition and the fine partitions */
    240:   for (i=0; i<adj->rmap->n; i++) {
    241:     for (j=0; j<bs; j++) {
    242:       parts_indices[bs*i+j] = fineparts_indices[i]+offsets[coarseparts_indices[i]];
    243:     }
    244:   }
    245:   ISRestoreIndices(hpart->fineparts,&fineparts_indices);
    246:   ISRestoreIndices(hpart->coarseparts,&coarseparts_indices);
    247:   PetscFree(offsets);
    248:   ISCreateGeneral(comm,bs*adj->rmap->n,parts_indices,PETSC_OWN_POINTER,partitioning);
    249:   MatDestroy(&adj);
    250:   return(0);
    251: }

    253: PetscErrorCode MatPartitioningHierarchical_ReassembleFineparts(Mat adj, IS fineparts, ISLocalToGlobalMapping mapping, IS *sfineparts)
    254: {
    255:   PetscInt            *local_indices, *global_indices,*sfineparts_indices,localsize,i;
    256:   const PetscInt      *ranges,*fineparts_indices;
    257:   PetscMPIInt         rank,*owners;
    258:   MPI_Comm            comm;
    259:   PetscLayout         rmap;
    260:   PetscSFNode        *remote;
    261:   PetscSF             sf;
    262:   PetscErrorCode      ierr;

    266:   PetscObjectGetComm((PetscObject)adj,&comm);
    267:   MPI_Comm_rank(comm,&rank);
    268:   MatGetLayouts(adj,&rmap,NULL);
    269:   ISGetLocalSize(fineparts,&localsize);
    270:   PetscMalloc2(localsize,&global_indices,localsize,&local_indices);
    271:   for (i=0; i<localsize; i++) {
    272:     local_indices[i] = i;
    273:   }
    274:   /* map local indices back to global so that we can permulate data globally */
    275:   ISLocalToGlobalMappingApply(mapping,localsize,local_indices,global_indices);
    276:   PetscCalloc1(localsize,&owners);
    277:   /* find owners for global indices */
    278:   for (i=0; i<localsize; i++) {
    279:     PetscLayoutFindOwner(rmap,global_indices[i],&owners[i]);
    280:   }
    281:   PetscLayoutGetRanges(rmap,&ranges);
    282:   PetscMalloc1(ranges[rank+1]-ranges[rank],&sfineparts_indices);

    284:   for (i=0; i<ranges[rank+1]-ranges[rank]; i++) {
    285:     sfineparts_indices[i] = -1;
    286:   }

    288:   ISGetIndices(fineparts,&fineparts_indices);
    289:   PetscSFCreate(comm,&sf);
    290:   PetscMalloc1(localsize,&remote);
    291:   for (i=0; i<localsize; i++) {
    292:     remote[i].rank  = owners[i];
    293:     remote[i].index = global_indices[i]-ranges[owners[i]];
    294:   }
    295:   PetscSFSetType(sf,PETSCSFBASIC);
    296:   /* not sure how to add prefix to sf */
    297:   PetscSFSetFromOptions(sf);
    298:   PetscSFSetGraph(sf,localsize,localsize,NULL,PETSC_OWN_POINTER,remote,PETSC_OWN_POINTER);
    299:   PetscSFReduceBegin(sf,MPIU_INT,fineparts_indices,sfineparts_indices,MPI_REPLACE);
    300:   PetscSFReduceEnd(sf,MPIU_INT,fineparts_indices,sfineparts_indices,MPI_REPLACE);
    301:   PetscSFDestroy(&sf);
    302:   ISRestoreIndices(fineparts,&fineparts_indices);
    303:   ISCreateGeneral(comm,ranges[rank+1]-ranges[rank],sfineparts_indices,PETSC_OWN_POINTER,sfineparts);
    304:   PetscFree2(global_indices,local_indices);
    305:   PetscFree(owners);
    306:   return(0);
    307: }

    309: PetscErrorCode MatPartitioningHierarchical_AssembleSubdomain(Mat adj,IS vweights, IS destination,IS *svweights,Mat *sadj,ISLocalToGlobalMapping *mapping)
    310: {
    311:   IS              irows,icols;
    312:   PetscInt        irows_ln;
    313:   PetscMPIInt     rank;
    314:   const PetscInt *irows_indices;
    315:   MPI_Comm        comm;
    316:   PetscErrorCode  ierr;

    319:   PetscObjectGetComm((PetscObject)adj,&comm);
    320:   MPI_Comm_rank(comm,&rank);
    321:   /* figure out where data comes from  */
    322:   ISBuildTwoSided(destination,NULL,&irows);
    323:   ISDuplicate(irows,&icols);
    324:   ISGetLocalSize(irows,&irows_ln);
    325:   ISGetIndices(irows,&irows_indices);
    326:   ISLocalToGlobalMappingCreate(comm,1,irows_ln,irows_indices,PETSC_COPY_VALUES,mapping);
    327:   ISRestoreIndices(irows,&irows_indices);
    328:   MatCreateSubMatrices(adj,1,&irows,&icols,MAT_INITIAL_MATRIX,&sadj);
    329:   if (vweights && svweights) {
    330:     ISCreateSubIS(vweights,irows,svweights);
    331:   }
    332:   ISDestroy(&irows);
    333:   ISDestroy(&icols);
    334:   return(0);
    335: }

    337: PetscErrorCode MatPartitioningHierarchical_DetermineDestination(MatPartitioning part, IS partitioning, PetscInt pstart, PetscInt pend, IS *destination)
    338: {
    339:   MPI_Comm            comm;
    340:   PetscMPIInt         rank,size,target;
    341:   PetscInt            plocalsize,*dest_indices,i;
    342:   const PetscInt     *part_indices;
    343:   PetscErrorCode      ierr;

    346:   PetscObjectGetComm((PetscObject)part,&comm);
    347:   MPI_Comm_rank(comm,&rank);
    348:   MPI_Comm_size(comm,&size);
    349:   if ((pend-pstart)>size) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"range [%D, %D] should be smaller than or equal to size %D",pstart,pend,size);
    350:   if (pstart>pend) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP," pstart %D should be smaller than pend %D",pstart,pend);
    351:   ISGetLocalSize(partitioning,&plocalsize);
    352:   PetscMalloc1(plocalsize,&dest_indices);
    353:   ISGetIndices(partitioning,&part_indices);
    354:   for (i=0; i<plocalsize; i++) {
    355:     /* compute target */
    356:     target = part_indices[i]-pstart;
    357:     /* mark out of range entity as -1 */
    358:     if (part_indices[i]<pstart || part_indices[i]>=pend) target = -1;
    359:     dest_indices[i] = target;
    360:   }
    361:   ISCreateGeneral(comm,plocalsize,dest_indices,PETSC_OWN_POINTER,destination);
    362:   return(0);
    363: }

    365: PetscErrorCode MatPartitioningView_Hierarchical(MatPartitioning part,PetscViewer viewer)
    366: {
    367:   MatPartitioning_Hierarchical *hpart = (MatPartitioning_Hierarchical*)part->data;
    368:   PetscErrorCode           ierr;
    369:   PetscMPIInt              rank;
    370:   PetscBool                iascii;
    371:   PetscViewer              sviewer;

    374:   MPI_Comm_rank(PetscObjectComm((PetscObject)part),&rank);
    375:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    376:   if (iascii) {
    377:     PetscViewerASCIIPrintf(viewer," Number of coarse parts: %D\n",hpart->ncoarseparts);
    378:     PetscViewerASCIIPrintf(viewer," Coarse partitioner: %s\n",hpart->coarseparttype);
    379:     if (hpart->coarseMatPart) {
    380:       PetscViewerASCIIPushTab(viewer);
    381:       MatPartitioningView(hpart->coarseMatPart,viewer);
    382:       PetscViewerASCIIPopTab(viewer);
    383:     }
    384:     PetscViewerASCIIPrintf(viewer," Number of fine parts: %D\n",hpart->nfineparts);
    385:     PetscViewerASCIIPrintf(viewer," Fine partitioner: %s\n",hpart->fineparttype);
    386:     PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
    387:     if (rank == 0 && hpart->fineMatPart) {
    388:       PetscViewerASCIIPushTab(viewer);
    389:       MatPartitioningView(hpart->fineMatPart,sviewer);
    390:       PetscViewerASCIIPopTab(viewer);
    391:     }
    392:     PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
    393:   }
    394:   return(0);
    395: }

    397: PetscErrorCode MatPartitioningHierarchicalGetFineparts(MatPartitioning part,IS *fineparts)
    398: {
    399:   MatPartitioning_Hierarchical *hpart = (MatPartitioning_Hierarchical*)part->data;
    400:   PetscErrorCode                ierr;

    403:   *fineparts = hpart->fineparts;
    404:   PetscObjectReference((PetscObject)hpart->fineparts);
    405:   return(0);
    406: }

    408: PetscErrorCode MatPartitioningHierarchicalGetCoarseparts(MatPartitioning part,IS *coarseparts)
    409: {
    410:   MatPartitioning_Hierarchical *hpart = (MatPartitioning_Hierarchical*)part->data;
    411:   PetscErrorCode                ierr;

    414:   *coarseparts = hpart->coarseparts;
    415:   PetscObjectReference((PetscObject)hpart->coarseparts);
    416:   return(0);
    417: }

    419: PetscErrorCode MatPartitioningHierarchicalSetNcoarseparts(MatPartitioning part, PetscInt ncoarseparts)
    420: {
    421:   MatPartitioning_Hierarchical *hpart = (MatPartitioning_Hierarchical*)part->data;

    424:   hpart->ncoarseparts = ncoarseparts;
    425:   return(0);
    426: }

    428: PetscErrorCode MatPartitioningHierarchicalSetNfineparts(MatPartitioning part, PetscInt nfineparts)
    429: {
    430:   MatPartitioning_Hierarchical *hpart = (MatPartitioning_Hierarchical*)part->data;

    433:   hpart->nfineparts = nfineparts;
    434:   return(0);
    435: }

    437: PetscErrorCode MatPartitioningSetFromOptions_Hierarchical(PetscOptionItems *PetscOptionsObject,MatPartitioning part)
    438: {
    439:   MatPartitioning_Hierarchical *hpart = (MatPartitioning_Hierarchical*)part->data;
    441:   char           value[1024];
    442:   PetscBool      flag = PETSC_FALSE;

    445:   PetscOptionsHead(PetscOptionsObject,"Set hierarchical partitioning options");
    446:   PetscOptionsString("-mat_partitioning_hierarchical_coarseparttype","coarse part type",NULL,NULL,value,sizeof(value),&flag);
    447:   if (flag) {
    448:    PetscStrallocpy(value,&hpart->coarseparttype);
    449:   }
    450:   PetscOptionsString("-mat_partitioning_hierarchical_fineparttype","fine part type",NULL,NULL,value,sizeof(value),&flag);
    451:   if (flag) {
    452:     PetscStrallocpy(value,&hpart->fineparttype);
    453:   }
    454:   PetscOptionsInt("-mat_partitioning_hierarchical_ncoarseparts","number of coarse parts",NULL,hpart->ncoarseparts,&hpart->ncoarseparts,&flag);
    455:   PetscOptionsInt("-mat_partitioning_hierarchical_nfineparts","number of fine parts",NULL,hpart->nfineparts,&hpart->nfineparts,&flag);
    456:   PetscOptionsTail();
    457:   return(0);
    458: }

    460: PetscErrorCode MatPartitioningDestroy_Hierarchical(MatPartitioning part)
    461: {
    462:   MatPartitioning_Hierarchical *hpart = (MatPartitioning_Hierarchical*)part->data;
    463:   PetscErrorCode           ierr;

    466:   if (hpart->coarseparttype) {PetscFree(hpart->coarseparttype);}
    467:   if (hpart->fineparttype) {PetscFree(hpart->fineparttype);}
    468:   ISDestroy(&hpart->fineparts);
    469:   ISDestroy(&hpart->coarseparts);
    470:   MatPartitioningDestroy(&hpart->coarseMatPart);
    471:   MatPartitioningDestroy(&hpart->fineMatPart);
    472:   MatPartitioningDestroy(&hpart->improver);
    473:   PetscFree(hpart);
    474:   return(0);
    475: }

    477: /*
    478:    Improves the quality  of a partition
    479: */
    480: static PetscErrorCode MatPartitioningImprove_Hierarchical(MatPartitioning part, IS *partitioning)
    481: {
    482:   PetscErrorCode               ierr;
    483:   MatPartitioning_Hierarchical *hpart = (MatPartitioning_Hierarchical*)part->data;
    484:   Mat                           mat = part->adj, adj;
    485:   PetscBool                    flg;
    486:   const char                   *prefix;
    487: #if defined(PETSC_HAVE_PARMETIS)
    488:   PetscInt                     *vertex_weights;
    489: #endif

    492:   PetscObjectTypeCompare((PetscObject)mat,MATMPIADJ,&flg);
    493:   if (flg) {
    494:     adj = mat;
    495:     PetscObjectReference((PetscObject)adj);
    496:   }else {
    497:     /* bs indicates if the converted matrix is "reduced" from the original and hence the
    498:        resulting partition results need to be stretched to match the original matrix */
    499:    MatConvert(mat,MATMPIADJ,MAT_INITIAL_MATRIX,&adj);
    500:   }

    502:   /* If there exists a mat partitioner, we should delete it */
    503:   MatPartitioningDestroy(&hpart->improver);
    504:   MatPartitioningCreate(PetscObjectComm((PetscObject)part),&hpart->improver);
    505:   PetscObjectGetOptionsPrefix((PetscObject)part,&prefix);
    506:   PetscObjectSetOptionsPrefix((PetscObject)hpart->improver,prefix);
    507:   PetscObjectAppendOptionsPrefix((PetscObject)hpart->improver,"hierarch_improver_");
    508:   /* Only parmetis supports to refine a partition */
    509: #if defined(PETSC_HAVE_PARMETIS)
    510:   MatPartitioningSetType(hpart->improver,MATPARTITIONINGPARMETIS);
    511:   MatPartitioningSetAdjacency(hpart->improver,adj);
    512:   MatPartitioningSetNParts(hpart->improver, part->n);
    513:   /* copy over vertex weights */
    514:   if (part->vertex_weights) {
    515:     PetscMalloc1(adj->rmap->n,&vertex_weights);
    516:     PetscArraycpy(vertex_weights,part->vertex_weights,adj->rmap->n);
    517:     MatPartitioningSetVertexWeights(hpart->improver,vertex_weights);
    518:   }
    519:   MatPartitioningImprove(hpart->improver,partitioning);
    520:   MatDestroy(&adj);
    521:   return(0);
    522: #else
    523:   SETERRQ(PetscObjectComm((PetscObject)adj),PETSC_ERR_SUP,"Requires PETSc be installed with ParMetis\n");
    524: #endif
    525: }

    527: /*MC
    528:    MATPARTITIONINGHIERARCH - Creates a partitioning context via hierarchical partitioning strategy.
    529:    The graph is partitioned into a number of subgraphs, and each subgraph is further split into a few smaller
    530:    subgraphs. The idea can be applied in a recursive manner. It is useful when you want to partition the graph
    531:    into a large number of subgraphs (often more than 10K) since partitions obtained with existing partitioners
    532:    such as ParMETIS and PTScotch are far from ideal. The hierarchical partitioning also tries to avoid off-node
    533:    communication as much as possible for multi-core processor. Another user case for the hierarchical partitioning
    534:    is to improve PCGASM convergence by generating multi-rank connected subdomain.

    536:    Collective

    538:    Input Parameter:
    539: .  part - the partitioning context

    541:    Options Database Keys:
    542: +     -mat_partitioning_hierarchical_coarseparttype - partitioner type at the first level and parmetis is used by default
    543: .     -mat_partitioning_hierarchical_fineparttype - partitioner type at the second level and parmetis is used by default
    544: .     -mat_partitioning_hierarchical_ncoarseparts - number of subgraphs is required at the first level, which is often the number of compute nodes
    545: -     -mat_partitioning_hierarchical_nfineparts - number of smaller subgraphs for each subgraph, which is often the number of cores per compute node

    547:    Level: beginner

    549:    References:
    550:   1.  Fande Kong, Xiao-Chuan Cai, A highly scalable multilevel Schwarz method with boundary geometry preserving coarse spaces for 3D elasticity
    551:       problems on domains with complex geometry,   SIAM Journal on Scientific Computing 38 (2), C73-C95, 2016
    552:   2.  Fande Kong, Roy H. Stogner, Derek Gaston, John W. Peterson, Cody J. Permann, Andrew E. Slaughter, and Richard C. Martineau,
    553:       A general-purpose hierarchical mesh partitioning method with node balancing strategies for large-scale numerical simulations,
    554:       arXiv preprint arXiv:1809.02666CoRR, 2018.

    556: .seealso: MatPartitioningSetType(), MatPartitioningType

    558: M*/

    560: PETSC_EXTERN PetscErrorCode MatPartitioningCreate_Hierarchical(MatPartitioning part)
    561: {
    562:   PetscErrorCode                ierr;
    563:   MatPartitioning_Hierarchical *hpart;

    566:   PetscNewLog(part,&hpart);
    567:   part->data = (void*)hpart;

    569:   hpart->fineparttype       = NULL; /* fine level (second) partitioner */
    570:   hpart->coarseparttype     = NULL; /* coarse level (first) partitioner */
    571:   hpart->nfineparts         = 1;    /* we do not further partition coarse partition any more by default */
    572:   hpart->ncoarseparts       = 0;    /* number of coarse parts (first level) */
    573:   hpart->coarseparts        = NULL;
    574:   hpart->fineparts          = NULL;
    575:   hpart->coarseMatPart      = NULL;
    576:   hpart->fineMatPart        = NULL;

    578:   part->ops->apply          = MatPartitioningApply_Hierarchical;
    579:   part->ops->view           = MatPartitioningView_Hierarchical;
    580:   part->ops->destroy        = MatPartitioningDestroy_Hierarchical;
    581:   part->ops->setfromoptions = MatPartitioningSetFromOptions_Hierarchical;
    582:   part->ops->improve        = MatPartitioningImprove_Hierarchical;
    583:   return(0);
    584: }