Date: 2015-10-02T22:19:32+00:00

Actual source code: tools.c
petsc-3.6.2 2015-10-02
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      1: /*
      2:  GAMG geometric-algebric multigrid PC - Mark Adams 2011
      3:  */
      4: #include <petsc/private/matimpl.h>
      5: #include <../src/ksp/pc/impls/gamg/gamg.h>           /*I "petscpc.h" I*/
      6: #include <petsc/private/kspimpl.h>

     10: /*
     11:    Produces a set of block column indices of the matrix row, one for each block represented in the original row

     13:    n - the number of block indices in cc[]
     14:    cc - the block indices (must be large enough to contain the indices)
     15: */
     16: PETSC_STATIC_INLINE PetscErrorCode MatCollapseRow(Mat Amat,PetscInt row,PetscInt bs,PetscInt *n,PetscInt *cc)
     17: {
     18:   PetscInt       cnt = -1,nidx,j;
     19:   const PetscInt *idx;

     23:   MatGetRow(Amat,row,&nidx,&idx,NULL);
     24:   if (nidx) {
     25:     cnt = 0;
     26:     cc[cnt] = idx[0]/bs;
     27:     for (j=1; j<nidx; j++) {
     28:       if (cc[cnt] < idx[j]/bs) cc[++cnt] = idx[j]/bs;
     29:     }
     30:   }
     31:   MatRestoreRow(Amat,row,&nidx,&idx,NULL);
     32:   *n = cnt+1;
     33:   return(0);
     34: }

     38: /*
     39:     Produces a set of block column indices of the matrix block row, one for each block represented in the original set of rows

     41:     ncollapsed - the number of block indices
     42:     collapsed - the block indices (must be large enough to contain the indices)
     43: */
     44: PETSC_STATIC_INLINE PetscErrorCode MatCollapseRows(Mat Amat,PetscInt start,PetscInt bs,PetscInt *w0,PetscInt *w1,PetscInt *w2,PetscInt *ncollapsed,PetscInt **collapsed)
     45: {
     46:   PetscInt       i,nprev,*cprev = w0,ncur = 0,*ccur = w1,*merged = w2,*cprevtmp;

     50:   MatCollapseRow(Amat,start,bs,&nprev,cprev);
     51:   for (i=start+1; i<start+bs; i++) {
     52:     MatCollapseRow(Amat,i,bs,&ncur,ccur);
     53:     PetscMergeIntArray(nprev,cprev,ncur,ccur,&nprev,&merged);
     54:     cprevtmp = cprev; cprev = merged; merged = cprevtmp;
     55:   }
     56:   *ncollapsed = nprev;
     57:   if (collapsed) *collapsed  = cprev;
     58:   return(0);
     59: }

     62: /* -------------------------------------------------------------------------- */
     63: /*
     64:    PCGAMGCreateGraph - create simple scaled scalar graph from matrix

     66:  Input Parameter:
     67:  . Amat - matrix
     68:  Output Parameter:
     69:  . a_Gmaat - eoutput scalar graph (symmetric?)
     70:  */
     73: PetscErrorCode PCGAMGCreateGraph(Mat Amat, Mat *a_Gmat)
     74: {
     76:   PetscInt       Istart,Iend,Ii,i,jj,kk,ncols,nloc,NN,MM,bs;
     77:   MPI_Comm       comm;
     78:   Mat            Gmat;
     79:   MatType        mtype;

     82:   PetscObjectGetComm((PetscObject)Amat,&comm);
     83:   MatGetOwnershipRange(Amat, &Istart, &Iend);
     84:   MatGetSize(Amat, &MM, &NN);
     85:   MatGetBlockSize(Amat, &bs);
     86:   nloc = (Iend-Istart)/bs;

     88: #if defined PETSC_GAMG_USE_LOG
     89:   PetscLogEventBegin(petsc_gamg_setup_events[GRAPH],0,0,0,0);
     90: #endif

     92:   if (bs > 1) {
     93:     const PetscScalar *vals;
     94:     const PetscInt    *idx;
     95:     PetscInt          *d_nnz, *o_nnz,*blockmask = NULL,maskcnt,*w0,*w1,*w2;
     96:     PetscBool         ismpiaij,isseqaij;

     98:     /*
     99:        Determine the preallocation needed for the scalar matrix derived from the vector matrix.
    100:     */

    102:     PetscObjectTypeCompare((PetscObject)Amat,MATSEQAIJ,&isseqaij);
    103:     PetscObjectTypeCompare((PetscObject)Amat,MATMPIAIJ,&ismpiaij);

    105:     PetscMalloc2(nloc, &d_nnz,isseqaij ? 0 : nloc, &o_nnz);

    107:     if (isseqaij) {
    108:       PetscInt       max_d_nnz;

    110:       /*
    111:           Determine exact preallocation count for (sequential) scalar matrix
    112:       */
    113:       MatSeqAIJGetMaxRowNonzeros(Amat,&max_d_nnz);
    114:       max_d_nnz = PetscMin(nloc,bs*max_d_nnz);
    115:       PetscMalloc3(max_d_nnz, &w0,max_d_nnz, &w1,max_d_nnz, &w2);
    116:       for (Ii = 0, jj = 0; Ii < Iend; Ii += bs, jj++) {
    117:         MatCollapseRows(Amat,Ii,bs,w0,w1,w2,&d_nnz[jj],NULL);
    118:       }
    119:       PetscFree3(w0,w1,w2);

    121:     } else if (ismpiaij) {
    122:       Mat            Daij,Oaij;
    123:       const PetscInt *garray;
    124:       PetscInt       max_d_nnz;

    126:       MatMPIAIJGetSeqAIJ(Amat,&Daij,&Oaij,&garray);

    128:       /*
    129:           Determine exact preallocation count for diagonal block portion of scalar matrix
    130:       */
    131:       MatSeqAIJGetMaxRowNonzeros(Daij,&max_d_nnz);
    132:       max_d_nnz = PetscMin(nloc,bs*max_d_nnz);
    133:       PetscMalloc3(max_d_nnz, &w0,max_d_nnz, &w1,max_d_nnz, &w2);
    134:       for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) {
    135:         MatCollapseRows(Daij,Ii,bs,w0,w1,w2,&d_nnz[jj],NULL);
    136:       }
    137:       PetscFree3(w0,w1,w2);

    139:       /*
    140:          Over estimate (usually grossly over), preallocation count for off-diagonal portion of scalar matrix
    141:       */
    142:       for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) {
    143:         o_nnz[jj] = 0;
    144:         for (kk=0; kk<bs; kk++) { /* rows that get collapsed to a single row */
    145:           MatGetRow(Oaij,Ii+kk,&ncols,0,0);
    146:           o_nnz[jj] += ncols;
    147:           MatRestoreRow(Oaij,Ii+kk,&ncols,0,0);
    148:         }
    149:         if (o_nnz[jj] > (NN/bs-nloc)) o_nnz[jj] = NN/bs-nloc;
    150:       }

    152:     } else {
    153:       /*

    155:        This is O(nloc*nloc/bs) work!

    157:        This is accurate for the "diagonal" block of the matrix but will be grossly high for the
    158:        off diagonal block most of the time but could be too low for the off-diagonal.

    160:        This should be fixed to be accurate for the off-diagonal portion. Cannot just use a mask
    161:        for the off-diagonal portion since for huge matrices that would require too much memory per
    162:        MPI process.
    163:       */
    164:       PetscMalloc1(nloc, &blockmask);
    165:       for (Ii = Istart, jj = 0; Ii < Iend; Ii += bs, jj++) {
    166:         o_nnz[jj] = 0;
    167:         PetscMemzero(blockmask,nloc*sizeof(PetscInt));
    168:         for (kk=0; kk<bs; kk++) { /* rows that get collapsed to a single row */
    169:           MatGetRow(Amat,Ii+kk,&ncols,&idx,0);
    170:           for (i=0; i<ncols; i++) {
    171:             if (idx[i] >= Istart && idx[i] < Iend) {
    172:               blockmask[(idx[i] - Istart)/bs] = 1;
    173:             }
    174:           }
    175:           if (ncols > o_nnz[jj]) {
    176:             o_nnz[jj] = ncols;
    177:             if (o_nnz[jj] > (NN/bs-nloc)) o_nnz[jj] = NN/bs-nloc;
    178:           }
    179:           MatRestoreRow(Amat,Ii+kk,&ncols,&idx,0);
    180:         }
    181:         maskcnt = 0;
    182:         for (i=0; i<nloc; i++) {
    183:           if (blockmask[i]) maskcnt++;
    184:         }
    185:         d_nnz[jj] = maskcnt;
    186:       }
    187:       PetscFree(blockmask);
    188:     }

    190:     /* get scalar copy (norms) of matrix -- AIJ specific!!! */
    191:     MatGetType(Amat,&mtype);
    192:     MatCreate(comm, &Gmat);
    193:     MatSetSizes(Gmat,nloc,nloc,PETSC_DETERMINE,PETSC_DETERMINE);
    194:     MatSetBlockSizes(Gmat, 1, 1);
    195:     MatSetType(Gmat, mtype);
    196:     MatSeqAIJSetPreallocation(Gmat,0,d_nnz);
    197:     MatMPIAIJSetPreallocation(Gmat,0,d_nnz,0,o_nnz);
    198:     PetscFree2(d_nnz,o_nnz);

    200:     for (Ii = Istart; Ii < Iend; Ii++) {
    201:       PetscInt dest_row = Ii/bs;
    202:       MatGetRow(Amat,Ii,&ncols,&idx,&vals);
    203:       for (jj=0; jj<ncols; jj++) {
    204:         PetscInt    dest_col = idx[jj]/bs;
    205:         PetscScalar sv       = PetscAbs(PetscRealPart(vals[jj]));
    206:         MatSetValues(Gmat,1,&dest_row,1,&dest_col,&sv,ADD_VALUES);
    207:       }
    208:       MatRestoreRow(Amat,Ii,&ncols,&idx,&vals);
    209:     }
    210:     MatAssemblyBegin(Gmat,MAT_FINAL_ASSEMBLY);
    211:     MatAssemblyEnd(Gmat,MAT_FINAL_ASSEMBLY);
    212:   } else {
    213:     /* just copy scalar matrix - abs() not taken here but scaled later */
    214:     MatDuplicate(Amat, MAT_COPY_VALUES, &Gmat);
    215:   }

    217: #if defined PETSC_GAMG_USE_LOG
    218:   PetscLogEventEnd(petsc_gamg_setup_events[GRAPH],0,0,0,0);
    219: #endif

    221:   *a_Gmat = Gmat;
    222:   return(0);
    223: }

    225: /* -------------------------------------------------------------------------- */
    226: /*
    227:    PCGAMGFilterGraph - filter (remove zero and possibly small values from the) graph and symetrize if needed

    229:  Input Parameter:
    230:  . vfilter - threshold paramter [0,1)
    231:  . symm - symetrize?
    232:  In/Output Parameter:
    233:  . a_Gmat - original graph
    234:  */
    237: PetscErrorCode PCGAMGFilterGraph(Mat *a_Gmat,PetscReal vfilter,PetscBool symm)
    238: {
    239:   PetscErrorCode    ierr;
    240:   PetscInt          Istart,Iend,Ii,jj,ncols,nnz0,nnz1, NN, MM, nloc;
    241:   PetscMPIInt       rank;
    242:   Mat               Gmat  = *a_Gmat, tGmat, matTrans;
    243:   MPI_Comm          comm;
    244:   const PetscScalar *vals;
    245:   const PetscInt    *idx;
    246:   PetscInt          *d_nnz, *o_nnz;
    247:   Vec               diag;
    248:   MatType           mtype;

    251: #if defined PETSC_GAMG_USE_LOG
    252:   PetscLogEventBegin(petsc_gamg_setup_events[GRAPH],0,0,0,0);
    253: #endif
    254:   /* scale Gmat for all values between -1 and 1 */
    255:   MatCreateVecs(Gmat, &diag, 0);
    256:   MatGetDiagonal(Gmat, diag);
    257:   VecReciprocal(diag);
    258:   VecSqrtAbs(diag);
    259:   MatDiagonalScale(Gmat, diag, diag);
    260:   VecDestroy(&diag);

    262:   if (vfilter < 0.0 && !symm) {
    263:     /* Just use the provided matrix as the graph but make all values positive */
    264:     Mat_MPIAIJ  *aij = (Mat_MPIAIJ*)Gmat->data;
    265:     MatInfo     info;
    266:     PetscScalar *avals;
    267:     PetscMPIInt size;

    269:     MPI_Comm_size(PetscObjectComm((PetscObject)Gmat),&size);
    270:     if (size == 1) {
    271:       MatGetInfo(Gmat,MAT_LOCAL,&info);
    272:       MatSeqAIJGetArray(Gmat,&avals);
    273:       for (jj = 0; jj<info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
    274:       MatSeqAIJRestoreArray(Gmat,&avals);
    275:     } else {
    276:       MatGetInfo(aij->A,MAT_LOCAL,&info);
    277:       MatSeqAIJGetArray(aij->A,&avals);
    278:       for (jj = 0; jj<info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
    279:       MatSeqAIJRestoreArray(aij->A,&avals);
    280:       MatGetInfo(aij->B,MAT_LOCAL,&info);
    281:       MatSeqAIJGetArray(aij->B,&avals);
    282:       for (jj = 0; jj<info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
    283:       MatSeqAIJRestoreArray(aij->B,&avals);
    284:     }
    285: #if defined PETSC_GAMG_USE_LOG
    286:     PetscLogEventEnd(petsc_gamg_setup_events[GRAPH],0,0,0,0);
    287: #endif
    288:     return(0);
    289:   }

    291:   PetscObjectGetComm((PetscObject)Gmat,&comm);
    292:   MPI_Comm_rank(comm,&rank);
    293:   MatGetOwnershipRange(Gmat, &Istart, &Iend);
    294:   nloc = Iend - Istart;
    295:   MatGetSize(Gmat, &MM, &NN);

    297:   if (symm) {
    298:     MatTranspose(Gmat, MAT_INITIAL_MATRIX, &matTrans);
    299:   }

    301:   /* Determine upper bound on nonzeros needed in new filtered matrix */
    302:   PetscMalloc2(nloc, &d_nnz,nloc, &o_nnz);
    303:   for (Ii = Istart, jj = 0; Ii < Iend; Ii++, jj++) {
    304:     MatGetRow(Gmat,Ii,&ncols,NULL,NULL);
    305:     d_nnz[jj] = ncols;
    306:     o_nnz[jj] = ncols;
    307:     MatRestoreRow(Gmat,Ii,&ncols,NULL,NULL);
    308:     if (symm) {
    309:       MatGetRow(matTrans,Ii,&ncols,NULL,NULL);
    310:       d_nnz[jj] += ncols;
    311:       o_nnz[jj] += ncols;
    312:       MatRestoreRow(matTrans,Ii,&ncols,NULL,NULL);
    313:     }
    314:     if (d_nnz[jj] > nloc) d_nnz[jj] = nloc;
    315:     if (o_nnz[jj] > (MM-nloc)) o_nnz[jj] = MM - nloc;
    316:   }
    317:   MatGetType(Gmat,&mtype);
    318:   MatCreate(comm, &tGmat);
    319:   MatSetSizes(tGmat,nloc,nloc,MM,MM);
    320:   MatSetBlockSizes(tGmat, 1, 1);
    321:   MatSetType(tGmat, mtype);
    322:   MatSeqAIJSetPreallocation(tGmat,0,d_nnz);
    323:   MatMPIAIJSetPreallocation(tGmat,0,d_nnz,0,o_nnz);
    324:   PetscFree2(d_nnz,o_nnz);
    325:   if (symm) {
    326:     MatDestroy(&matTrans);
    327:   } else {
    328:     /* all entries are generated locally so MatAssembly will be slightly faster for large process counts */
    329:     MatSetOption(tGmat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    330:   }

    332:   for (Ii = Istart, nnz0 = nnz1 = 0; Ii < Iend; Ii++) {
    333:     MatGetRow(Gmat,Ii,&ncols,&idx,&vals);
    334:     for (jj=0; jj<ncols; jj++,nnz0++) {
    335:       PetscScalar sv = PetscAbs(PetscRealPart(vals[jj]));
    336:       if (PetscRealPart(sv) > vfilter) {
    337:         nnz1++;
    338:         if (symm) {
    339:           sv  *= 0.5;
    340:           MatSetValues(tGmat,1,&Ii,1,&idx[jj],&sv,ADD_VALUES);
    341:           MatSetValues(tGmat,1,&idx[jj],1,&Ii,&sv,ADD_VALUES);
    342:         } else {
    343:           MatSetValues(tGmat,1,&Ii,1,&idx[jj],&sv,ADD_VALUES);
    344:         }
    345:       }
    346:     }
    347:     MatRestoreRow(Gmat,Ii,&ncols,&idx,&vals);
    348:   }
    349:   MatAssemblyBegin(tGmat,MAT_FINAL_ASSEMBLY);
    350:   MatAssemblyEnd(tGmat,MAT_FINAL_ASSEMBLY);

    352: #if defined PETSC_GAMG_USE_LOG
    353:   PetscLogEventEnd(petsc_gamg_setup_events[GRAPH],0,0,0,0);
    354: #endif

    356: #if defined(PETSC_USE_INFO)
    357:   {
    358:     double t1 = (!nnz0) ? 1. : 100.*(double)nnz1/(double)nnz0, t2 = (!nloc) ? 1. : (double)nnz0/(double)nloc;
    359:     PetscInfo4(*a_Gmat,"\t %g%% nnz after filtering, with threshold %g, %g nnz ave. (N=%D)\n",t1,vfilter,t2,MM);
    360:   }
    361: #endif
    362:   MatDestroy(&Gmat);
    363:   *a_Gmat = tGmat;
    364:   return(0);
    365: }

    367: /* -------------------------------------------------------------------------- */
    368: /*
    369:    PCGAMGGetDataWithGhosts - hacks into Mat MPIAIJ so this must have > 1 pe

    371:    Input Parameter:
    372:    . Gmat - MPIAIJ matrix for scattters
    373:    . data_sz - number of data terms per node (# cols in output)
    374:    . data_in[nloc*data_sz] - column oriented data
    375:    Output Parameter:
    376:    . a_stride - numbrt of rows of output
    377:    . a_data_out[stride*data_sz] - output data with ghosts
    378: */
    381: PetscErrorCode PCGAMGGetDataWithGhosts(Mat Gmat,PetscInt data_sz,PetscReal data_in[],PetscInt *a_stride,PetscReal **a_data_out)
    382: {
    384:   MPI_Comm       comm;
    385:   Vec            tmp_crds;
    386:   Mat_MPIAIJ     *mpimat = (Mat_MPIAIJ*)Gmat->data;
    387:   PetscInt       nnodes,num_ghosts,dir,kk,jj,my0,Iend,nloc;
    388:   PetscScalar    *data_arr;
    389:   PetscReal      *datas;
    390:   PetscBool      isMPIAIJ;

    393:   PetscObjectGetComm((PetscObject)Gmat,&comm);
    394:   PetscObjectTypeCompare((PetscObject)Gmat, MATMPIAIJ, &isMPIAIJ);
    395:   MatGetOwnershipRange(Gmat, &my0, &Iend);
    396:   nloc      = Iend - my0;
    397:   VecGetLocalSize(mpimat->lvec, &num_ghosts);
    398:   nnodes    = num_ghosts + nloc;
    399:   *a_stride = nnodes;
    400:   MatCreateVecs(Gmat, &tmp_crds, 0);

    402:   PetscMalloc1(data_sz*nnodes, &datas);
    403:   for (dir=0; dir<data_sz; dir++) {
    404:     /* set local, and global */
    405:     for (kk=0; kk<nloc; kk++) {
    406:       PetscInt    gid = my0 + kk;
    407:       PetscScalar crd = (PetscScalar)data_in[dir*nloc + kk]; /* col oriented */
    408:       datas[dir*nnodes + kk] = PetscRealPart(crd);

    410:       VecSetValues(tmp_crds, 1, &gid, &crd, INSERT_VALUES);
    411:     }
    412:     VecAssemblyBegin(tmp_crds);
    413:     VecAssemblyEnd(tmp_crds);
    414:     /* get ghost datas */
    415:     VecScatterBegin(mpimat->Mvctx,tmp_crds,mpimat->lvec,INSERT_VALUES,SCATTER_FORWARD);
    416:     VecScatterEnd(mpimat->Mvctx,tmp_crds,mpimat->lvec,INSERT_VALUES,SCATTER_FORWARD);
    417:     VecGetArray(mpimat->lvec, &data_arr);
    418:     for (kk=nloc,jj=0;jj<num_ghosts;kk++,jj++) datas[dir*nnodes + kk] = PetscRealPart(data_arr[jj]);
    419:     VecRestoreArray(mpimat->lvec, &data_arr);
    420:   }
    421:   VecDestroy(&tmp_crds);
    422:   *a_data_out = datas;
    423:   return(0);
    424: }

    427: /*
    428:  *
    429:  *  GAMGTableCreate
    430:  */

    434: PetscErrorCode GAMGTableCreate(PetscInt a_size, GAMGHashTable *a_tab)
    435: {
    437:   PetscInt       kk;

    440:   a_tab->size = a_size;
    441:   PetscMalloc1(a_size, &a_tab->table);
    442:   PetscMalloc1(a_size, &a_tab->data);
    443:   for (kk=0; kk<a_size; kk++) a_tab->table[kk] = -1;
    444:   return(0);
    445: }

    449: PetscErrorCode GAMGTableDestroy(GAMGHashTable *a_tab)
    450: {

    454:   PetscFree(a_tab->table);
    455:   PetscFree(a_tab->data);
    456:   return(0);
    457: }

    461: PetscErrorCode GAMGTableAdd(GAMGHashTable *a_tab, PetscInt a_key, PetscInt a_data)
    462: {
    463:   PetscInt kk,idx;

    466:   if (a_key<0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_USER,"Negative key %d.",a_key);
    467:   for (kk = 0, idx = GAMG_HASH(a_key);
    468:        kk < a_tab->size;
    469:        kk++, idx = (idx==(a_tab->size-1)) ? 0 : idx + 1) {

    471:     if (a_tab->table[idx] == a_key) {
    472:       /* exists */
    473:       a_tab->data[idx] = a_data;
    474:       break;
    475:     } else if (a_tab->table[idx] == -1) {
    476:       /* add */
    477:       a_tab->table[idx] = a_key;
    478:       a_tab->data[idx]  = a_data;
    479:       break;
    480:     }
    481:   }
    482:   if (kk==a_tab->size) {
    483:     /* this is not to efficient, waiting until completely full */
    484:     PetscInt       oldsize = a_tab->size, new_size = 2*a_tab->size + 5, *oldtable = a_tab->table, *olddata = a_tab->data;

    487:     a_tab->size = new_size;

    489:     PetscMalloc1(a_tab->size, &a_tab->table);
    490:     PetscMalloc1(a_tab->size, &a_tab->data);

    492:     for (kk=0;kk<a_tab->size;kk++) a_tab->table[kk] = -1;
    493:     for (kk=0;kk<oldsize;kk++) {
    494:       if (oldtable[kk] != -1) {
    495:         GAMGTableAdd(a_tab, oldtable[kk], olddata[kk]);
    496:        }
    497:     }
    498:     PetscFree(oldtable);
    499:     PetscFree(olddata);
    500:     GAMGTableAdd(a_tab, a_key, a_data);
    501:   }
    502:   return(0);
    503: }