Date: 2022-03-04T17:38:56+00:00

Actual source code: util.c

      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>

      7: /*
      8:    Produces a set of block column indices of the matrix row, one for each block represented in the original row

     10:    n - the number of block indices in cc[]
     11:    cc - the block indices (must be large enough to contain the indices)
     12: */
     13: PETSC_STATIC_INLINE PetscErrorCode MatCollapseRow(Mat Amat,PetscInt row,PetscInt bs,PetscInt *n,PetscInt *cc)
     14: {
     15:   PetscInt       cnt = -1,nidx,j;
     16:   const PetscInt *idx;

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

     33: /*
     34:     Produces a set of block column indices of the matrix block row, one for each block represented in the original set of rows

     36:     ncollapsed - the number of block indices
     37:     collapsed - the block indices (must be large enough to contain the indices)
     38: */
     39: PETSC_STATIC_INLINE PetscErrorCode MatCollapseRows(Mat Amat,PetscInt start,PetscInt bs,PetscInt *w0,PetscInt *w1,PetscInt *w2,PetscInt *ncollapsed,PetscInt **collapsed)
     40: {
     41:   PetscInt       i,nprev,*cprev = w0,ncur = 0,*ccur = w1,*merged = w2,*cprevtmp;

     45:   MatCollapseRow(Amat,start,bs,&nprev,cprev);
     46:   for (i=start+1; i<start+bs; i++) {
     47:     MatCollapseRow(Amat,i,bs,&ncur,ccur);
     48:     PetscMergeIntArray(nprev,cprev,ncur,ccur,&nprev,&merged);
     49:     cprevtmp = cprev; cprev = merged; merged = cprevtmp;
     50:   }
     51:   *ncollapsed = nprev;
     52:   if (collapsed) *collapsed  = cprev;
     53:   return(0);
     54: }

     56: /* -------------------------------------------------------------------------- */
     57: /*
     58:    PCGAMGCreateGraph - create simple scaled scalar graph from matrix

     60:  Input Parameter:
     61:  . Amat - matrix
     62:  Output Parameter:
     63:  . a_Gmaat - eoutput scalar graph (symmetric?)
     64:  */
     65: PetscErrorCode PCGAMGCreateGraph(Mat Amat, Mat *a_Gmat)
     66: {
     68:   PetscInt       Istart,Iend,Ii,jj,kk,ncols,nloc,NN,MM,bs;
     69:   MPI_Comm       comm;
     70:   Mat            Gmat;

     73:   PetscObjectGetComm((PetscObject)Amat,&comm);
     74:   MatGetOwnershipRange(Amat, &Istart, &Iend);
     75:   MatGetSize(Amat, &MM, &NN);
     76:   MatGetBlockSize(Amat, &bs);
     77:   nloc = (Iend-Istart)/bs;

     79:   PetscLogEventBegin(petsc_gamg_setup_events[GRAPH],0,0,0,0);

     81:   /* TODO GPU: these calls are potentially expensive if matrices are large and we want to use the GPU */
     82:   /* A solution consists in providing a new API, MatAIJGetCollapsedAIJ, and each class can provide a fast
     83:      implementation */
     84:   if (bs > 1) {
     85:     const PetscScalar *vals;
     86:     const PetscInt    *idx;
     87:     PetscInt          *d_nnz, *o_nnz,*w0,*w1,*w2;
     88:     PetscBool         ismpiaij,isseqaij;

     90:     /*
     91:        Determine the preallocation needed for the scalar matrix derived from the vector matrix.
     92:     */

     94:     PetscObjectBaseTypeCompare((PetscObject)Amat,MATSEQAIJ,&isseqaij);
     95:     PetscObjectBaseTypeCompare((PetscObject)Amat,MATMPIAIJ,&ismpiaij);
     96:     PetscMalloc2(nloc, &d_nnz,isseqaij ? 0 : nloc, &o_nnz);

     98:     if (isseqaij) {
     99:       PetscInt max_d_nnz;

    101:       /*
    102:           Determine exact preallocation count for (sequential) scalar matrix
    103:       */
    104:       MatSeqAIJGetMaxRowNonzeros(Amat,&max_d_nnz);
    105:       max_d_nnz = PetscMin(nloc,bs*max_d_nnz);
    106:       PetscMalloc3(max_d_nnz, &w0,max_d_nnz, &w1,max_d_nnz, &w2);
    107:       for (Ii = 0, jj = 0; Ii < Iend; Ii += bs, jj++) {
    108:         MatCollapseRows(Amat,Ii,bs,w0,w1,w2,&d_nnz[jj],NULL);
    109:       }
    110:       PetscFree3(w0,w1,w2);

    112:     } else if (ismpiaij) {
    113:       Mat            Daij,Oaij;
    114:       const PetscInt *garray;
    115:       PetscInt       max_d_nnz;

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

    119:       /*
    120:           Determine exact preallocation count for diagonal block portion of scalar matrix
    121:       */
    122:       MatSeqAIJGetMaxRowNonzeros(Daij,&max_d_nnz);
    123:       max_d_nnz = PetscMin(nloc,bs*max_d_nnz);
    124:       PetscMalloc3(max_d_nnz, &w0,max_d_nnz, &w1,max_d_nnz, &w2);
    125:       for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) {
    126:         MatCollapseRows(Daij,Ii,bs,w0,w1,w2,&d_nnz[jj],NULL);
    127:       }
    128:       PetscFree3(w0,w1,w2);

    130:       /*
    131:          Over estimate (usually grossly over), preallocation count for off-diagonal portion of scalar matrix
    132:       */
    133:       for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) {
    134:         o_nnz[jj] = 0;
    135:         for (kk=0; kk<bs; kk++) { /* rows that get collapsed to a single row */
    136:           MatGetRow(Oaij,Ii+kk,&ncols,NULL,NULL);
    137:           o_nnz[jj] += ncols;
    138:           MatRestoreRow(Oaij,Ii+kk,&ncols,NULL,NULL);
    139:         }
    140:         if (o_nnz[jj] > (NN/bs-nloc)) o_nnz[jj] = NN/bs-nloc;
    141:       }

    143:     } else SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"Require AIJ matrix type");

    145:     /* get scalar copy (norms) of matrix */
    146:     MatCreate(comm, &Gmat);
    147:     MatSetSizes(Gmat,nloc,nloc,PETSC_DETERMINE,PETSC_DETERMINE);
    148:     MatSetBlockSizes(Gmat, 1, 1);
    149:     MatSetType(Gmat, MATAIJ);
    150:     MatSeqAIJSetPreallocation(Gmat,0,d_nnz);
    151:     MatMPIAIJSetPreallocation(Gmat,0,d_nnz,0,o_nnz);
    152:     PetscFree2(d_nnz,o_nnz);

    154:     for (Ii = Istart; Ii < Iend; Ii++) {
    155:       PetscInt dest_row = Ii/bs;
    156:       MatGetRow(Amat,Ii,&ncols,&idx,&vals);
    157:       for (jj=0; jj<ncols; jj++) {
    158:         PetscInt    dest_col = idx[jj]/bs;
    159:         PetscScalar sv       = PetscAbs(PetscRealPart(vals[jj]));
    160:         MatSetValues(Gmat,1,&dest_row,1,&dest_col,&sv,ADD_VALUES);
    161:       }
    162:       MatRestoreRow(Amat,Ii,&ncols,&idx,&vals);
    163:     }
    164:     MatAssemblyBegin(Gmat,MAT_FINAL_ASSEMBLY);
    165:     MatAssemblyEnd(Gmat,MAT_FINAL_ASSEMBLY);
    166:   } else {
    167:     /* just copy scalar matrix - abs() not taken here but scaled later */
    168:     MatDuplicate(Amat, MAT_COPY_VALUES, &Gmat);
    169:   }
    170:   MatPropagateSymmetryOptions(Amat, Gmat);

    172:   PetscLogEventEnd(petsc_gamg_setup_events[GRAPH],0,0,0,0);

    174:   *a_Gmat = Gmat;
    175:   return(0);
    176: }

    178: /* -------------------------------------------------------------------------- */
    179: /*@C
    180:    PCGAMGFilterGraph - filter (remove zero and possibly small values from the) graph and make it symmetric if requested

    182:    Collective on Mat

    184:    Input Parameters:
    185: +   a_Gmat - the graph
    186: .   vfilter - threshold parameter [0,1)
    187: -   symm - make the result symmetric

    189:    Level: developer

    191:    Notes:
    192:     This is called before graph coarsers are called.

    194: .seealso: PCGAMGSetThreshold()
    195: @*/
    196: PetscErrorCode PCGAMGFilterGraph(Mat *a_Gmat,PetscReal vfilter,PetscBool symm)
    197: {
    198:   PetscErrorCode    ierr;
    199:   PetscInt          Istart,Iend,Ii,jj,ncols,nnz0,nnz1, NN, MM, nloc;
    200:   PetscMPIInt       rank;
    201:   Mat               Gmat  = *a_Gmat, tGmat;
    202:   MPI_Comm          comm;
    203:   const PetscScalar *vals;
    204:   const PetscInt    *idx;
    205:   PetscInt          *d_nnz, *o_nnz;
    206:   Vec               diag;

    209:   PetscLogEventBegin(petsc_gamg_setup_events[GRAPH],0,0,0,0);

    211:   /* TODO GPU: optimization proposal, each class provides fast implementation of this
    212:      procedure via MatAbs API */
    213:   if (vfilter < 0.0 && !symm) {
    214:     /* Just use the provided matrix as the graph but make all values positive */
    215:     MatInfo     info;
    216:     PetscScalar *avals;
    217:     PetscBool isaij,ismpiaij;
    218:     PetscObjectBaseTypeCompare((PetscObject)Gmat,MATSEQAIJ,&isaij);
    219:     PetscObjectBaseTypeCompare((PetscObject)Gmat,MATMPIAIJ,&ismpiaij);
    220:     if (!isaij && !ismpiaij) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"Require (MPI)AIJ matrix type");
    221:     if (isaij) {
    222:       MatGetInfo(Gmat,MAT_LOCAL,&info);
    223:       MatSeqAIJGetArray(Gmat,&avals);
    224:       for (jj = 0; jj<info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
    225:       MatSeqAIJRestoreArray(Gmat,&avals);
    226:     } else {
    227:       Mat_MPIAIJ  *aij = (Mat_MPIAIJ*)Gmat->data;
    228:       MatGetInfo(aij->A,MAT_LOCAL,&info);
    229:       MatSeqAIJGetArray(aij->A,&avals);
    230:       for (jj = 0; jj<info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
    231:       MatSeqAIJRestoreArray(aij->A,&avals);
    232:       MatGetInfo(aij->B,MAT_LOCAL,&info);
    233:       MatSeqAIJGetArray(aij->B,&avals);
    234:       for (jj = 0; jj<info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
    235:       MatSeqAIJRestoreArray(aij->B,&avals);
    236:     }
    237:     PetscLogEventEnd(petsc_gamg_setup_events[GRAPH],0,0,0,0);
    238:     return(0);
    239:   }

    241:   /* TODO GPU: this can be called when filter = 0 -> Probably provide MatAIJThresholdCompress that compresses the entries below a threshold?
    242:                Also, if the matrix is symmetric, can we skip this
    243:                operation? It can be very expensive on large matrices. */
    244:   PetscObjectGetComm((PetscObject)Gmat,&comm);
    245:   MPI_Comm_rank(comm,&rank);
    246:   MatGetOwnershipRange(Gmat, &Istart, &Iend);
    247:   nloc = Iend - Istart;
    248:   MatGetSize(Gmat, &MM, &NN);

    250:   if (symm) {
    251:     Mat matTrans;
    252:     MatTranspose(Gmat, MAT_INITIAL_MATRIX, &matTrans);
    253:     MatAXPY(Gmat, 1.0, matTrans, Gmat->structurally_symmetric ? SAME_NONZERO_PATTERN : DIFFERENT_NONZERO_PATTERN);
    254:     MatDestroy(&matTrans);
    255:   }

    257:   /* scale Gmat for all values between -1 and 1 */
    258:   MatCreateVecs(Gmat, &diag, NULL);
    259:   MatGetDiagonal(Gmat, diag);
    260:   VecReciprocal(diag);
    261:   VecSqrtAbs(diag);
    262:   MatDiagonalScale(Gmat, diag, diag);
    263:   VecDestroy(&diag);

    265:   /* Determine upper bound on nonzeros needed in new filtered matrix */
    266:   PetscMalloc2(nloc, &d_nnz,nloc, &o_nnz);
    267:   for (Ii = Istart, jj = 0; Ii < Iend; Ii++, jj++) {
    268:     MatGetRow(Gmat,Ii,&ncols,NULL,NULL);
    269:     d_nnz[jj] = ncols;
    270:     o_nnz[jj] = ncols;
    271:     MatRestoreRow(Gmat,Ii,&ncols,NULL,NULL);
    272:     if (d_nnz[jj] > nloc) d_nnz[jj] = nloc;
    273:     if (o_nnz[jj] > (MM-nloc)) o_nnz[jj] = MM - nloc;
    274:   }
    275:   MatCreate(comm, &tGmat);
    276:   MatSetSizes(tGmat,nloc,nloc,MM,MM);
    277:   MatSetBlockSizes(tGmat, 1, 1);
    278:   MatSetType(tGmat, MATAIJ);
    279:   MatSeqAIJSetPreallocation(tGmat,0,d_nnz);
    280:   MatMPIAIJSetPreallocation(tGmat,0,d_nnz,0,o_nnz);
    281:   MatSetOption(tGmat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    282:   PetscFree2(d_nnz,o_nnz);

    284:   for (Ii = Istart, nnz0 = nnz1 = 0; Ii < Iend; Ii++) {
    285:     MatGetRow(Gmat,Ii,&ncols,&idx,&vals);
    286:     for (jj=0; jj<ncols; jj++,nnz0++) {
    287:       PetscScalar sv = PetscAbs(PetscRealPart(vals[jj]));
    288:       if (PetscRealPart(sv) > vfilter) {
    289:         nnz1++;
    290:         MatSetValues(tGmat,1,&Ii,1,&idx[jj],&sv,INSERT_VALUES);
    291:       }
    292:     }
    293:     MatRestoreRow(Gmat,Ii,&ncols,&idx,&vals);
    294:   }
    295:   MatAssemblyBegin(tGmat,MAT_FINAL_ASSEMBLY);
    296:   MatAssemblyEnd(tGmat,MAT_FINAL_ASSEMBLY);
    297:   if (symm) {
    298:     MatSetOption(tGmat,MAT_SYMMETRIC,PETSC_TRUE);
    299:   } else {
    300:     MatPropagateSymmetryOptions(Gmat,tGmat);
    301:   }
    302:   PetscLogEventEnd(petsc_gamg_setup_events[GRAPH],0,0,0,0);

    304: #if defined(PETSC_USE_INFO)
    305:   {
    306:     double t1 = (!nnz0) ? 1. : 100.*(double)nnz1/(double)nnz0, t2 = (!nloc) ? 1. : (double)nnz0/(double)nloc;
    307:     PetscInfo4(*a_Gmat,"\t %g%% nnz after filtering, with threshold %g, %g nnz ave. (N=%D)\n",t1,vfilter,t2,MM);
    308:   }
    309: #endif
    310:   MatDestroy(&Gmat);
    311:   *a_Gmat = tGmat;
    312:   return(0);
    313: }

    315: /* -------------------------------------------------------------------------- */
    316: /*
    317:    PCGAMGGetDataWithGhosts - hacks into Mat MPIAIJ so this must have size > 1

    319:    Input Parameter:
    320:    . Gmat - MPIAIJ matrix for scattters
    321:    . data_sz - number of data terms per node (# cols in output)
    322:    . data_in[nloc*data_sz] - column oriented data
    323:    Output Parameter:
    324:    . a_stride - numbrt of rows of output
    325:    . a_data_out[stride*data_sz] - output data with ghosts
    326: */
    327: PetscErrorCode PCGAMGGetDataWithGhosts(Mat Gmat,PetscInt data_sz,PetscReal data_in[],PetscInt *a_stride,PetscReal **a_data_out)
    328: {
    330:   Vec            tmp_crds;
    331:   Mat_MPIAIJ     *mpimat = (Mat_MPIAIJ*)Gmat->data;
    332:   PetscInt       nnodes,num_ghosts,dir,kk,jj,my0,Iend,nloc;
    333:   PetscScalar    *data_arr;
    334:   PetscReal      *datas;
    335:   PetscBool      isMPIAIJ;

    338:   PetscObjectBaseTypeCompare((PetscObject)Gmat, MATMPIAIJ, &isMPIAIJ);
    339:   MatGetOwnershipRange(Gmat, &my0, &Iend);
    340:   nloc      = Iend - my0;
    341:   VecGetLocalSize(mpimat->lvec, &num_ghosts);
    342:   nnodes    = num_ghosts + nloc;
    343:   *a_stride = nnodes;
    344:   MatCreateVecs(Gmat, &tmp_crds, NULL);

    346:   PetscMalloc1(data_sz*nnodes, &datas);
    347:   for (dir=0; dir<data_sz; dir++) {
    348:     /* set local, and global */
    349:     for (kk=0; kk<nloc; kk++) {
    350:       PetscInt    gid = my0 + kk;
    351:       PetscScalar crd = (PetscScalar)data_in[dir*nloc + kk]; /* col oriented */
    352:       datas[dir*nnodes + kk] = PetscRealPart(crd);

    354:       VecSetValues(tmp_crds, 1, &gid, &crd, INSERT_VALUES);
    355:     }
    356:     VecAssemblyBegin(tmp_crds);
    357:     VecAssemblyEnd(tmp_crds);
    358:     /* get ghost datas */
    359:     VecScatterBegin(mpimat->Mvctx,tmp_crds,mpimat->lvec,INSERT_VALUES,SCATTER_FORWARD);
    360:     VecScatterEnd(mpimat->Mvctx,tmp_crds,mpimat->lvec,INSERT_VALUES,SCATTER_FORWARD);
    361:     VecGetArray(mpimat->lvec, &data_arr);
    362:     for (kk=nloc,jj=0;jj<num_ghosts;kk++,jj++) datas[dir*nnodes + kk] = PetscRealPart(data_arr[jj]);
    363:     VecRestoreArray(mpimat->lvec, &data_arr);
    364:   }
    365:   VecDestroy(&tmp_crds);
    366:   *a_data_out = datas;
    367:   return(0);
    368: }

    370: PetscErrorCode PCGAMGHashTableCreate(PetscInt a_size, PCGAMGHashTable *a_tab)
    371: {
    373:   PetscInt       kk;

    376:   a_tab->size = a_size;
    377:   PetscMalloc2(a_size, &a_tab->table,a_size, &a_tab->data);
    378:   for (kk=0; kk<a_size; kk++) a_tab->table[kk] = -1;
    379:   return(0);
    380: }

    382: PetscErrorCode PCGAMGHashTableDestroy(PCGAMGHashTable *a_tab)
    383: {

    387:   PetscFree2(a_tab->table,a_tab->data);
    388:   return(0);
    389: }

    391: PetscErrorCode PCGAMGHashTableAdd(PCGAMGHashTable *a_tab, PetscInt a_key, PetscInt a_data)
    392: {
    393:   PetscInt kk,idx;

    396:   if (a_key<0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_USER,"Negative key %D.",a_key);
    397:   for (kk = 0, idx = GAMG_HASH(a_key); kk < a_tab->size; kk++, idx = (idx==(a_tab->size-1)) ? 0 : idx + 1) {
    398:     if (a_tab->table[idx] == a_key) {
    399:       /* exists */
    400:       a_tab->data[idx] = a_data;
    401:       break;
    402:     } else if (a_tab->table[idx] == -1) {
    403:       /* add */
    404:       a_tab->table[idx] = a_key;
    405:       a_tab->data[idx]  = a_data;
    406:       break;
    407:     }
    408:   }
    409:   if (kk==a_tab->size) {
    410:     /* this is not to efficient, waiting until completely full */
    411:     PetscInt       oldsize = a_tab->size, new_size = 2*a_tab->size + 5, *oldtable = a_tab->table, *olddata = a_tab->data;

    414:     a_tab->size = new_size;
    415:     PetscMalloc2(a_tab->size, &a_tab->table,a_tab->size, &a_tab->data);
    416:     for (kk=0;kk<a_tab->size;kk++) a_tab->table[kk] = -1;
    417:     for (kk=0;kk<oldsize;kk++) {
    418:       if (oldtable[kk] != -1) {
    419:         PCGAMGHashTableAdd(a_tab, oldtable[kk], olddata[kk]);
    420:        }
    421:     }
    422:     PetscFree2(oldtable,olddata);
    423:     PCGAMGHashTableAdd(a_tab, a_key, a_data);
    424:   }
    425:   return(0);
    426: }